Birkhäuser Mathematics Spring 2008

Birkhäuser Mathematics Spring 2008

New and noteworthy books and journals

NEW

Highlights Spring 2008

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Editorial Matters / Contents

Editorial Matters

Contents

Birkhäuser Boston 675 Massachusetts Avenue Cambridge, MA 02139-3309 USA Phone: 1-617-876-2333 Fax: 1-617-876-1272

Modern Birkhäuser Classics

4

Algebra

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Editors: Ann Kostant Editorial Director, Mathematics [email protected] Tom Grasso Editor, Computational Sciences and Engineering [email protected] Birkhäuser Verlag AG Viaduktstrasse 42 4051 Basel/Switzerland Phone: +41 61 205 0707 Fax: +41 61 205 0799 Editors: Dr. Thomas Hempfling Executive Editor, Mathematics [email protected]

Combinatorics / Number Theory

15

Logic and Foundations

21

Geometry / Topology

24

Group Theory / Representation Theory

36

Analysis / Operator Theory

43

Differential Equations / Dynamical Systems

61

Mathematical Physics / Physics

74

Probability and Statistics

82

Applications / Computational Sciences and Engineering

90

Systems and Control

108

General Interest

115

History of Science

120

Series

128

Journals

132

Order form

147

Marc Herbstritt Editor, Applied Sciences/ Computer Science [email protected] Dr. Karin Neidhart Editor, History of Science [email protected]




Textbooks suitable for undergraduate, advanced undergraduate or graduate students

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Modern Birkhäuser Classics

Many of the original research and survey monographs in pure and applied mathematics published by Birkhäuser in recent decades have been groundbreaking and have come to be regarded as foundational to the subject. Through the MBC Series, a select number of these modern classics, entirely uncorrected, are being re-released in paperback (and as eBooks) to ensure that these treasures remain accessible to new generations of students, scholars, and researchers.

Knot Theory and Its Applications




K. Murasugi, University of Toronto, ON, Canada Reprint of the 1996 ed. 2008. XII, 342 p. 307 illus. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4718-6 $39.95

Algebraic K-Theory




V. Srinivas, Tata Institute, India 2nd ed. 1996. 3rd printing 2008. XX, 342 p. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4736-0 $39.95

Introduction to Quantum Groups




G. Lusztig, Massachusetts Institute of Technology, Cambridge, MA, USA

Discriminants, Resultants, and Multidimensional Determinants I. M. Gelfand, Rutgers University, New Brunswick, NJ, USA; M. Kapranov, Yale, New Haven, CT, USA; A. Zelevinsky, Northeastern University, Boston, MA, USA 1st ed. 1994. 2nd printing 2008. Approx. 535 p. 30 illus. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4770-4 $39.95

Loop Spaces, Characteristic Classes and Geometric Quantization

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Differentiable Manifolds




Second Edition L. Conlon, Washington University, St. Louis, MO, USA 2nd ed. 2001. 2nd printing 2008. Approx. 435 p. 48 illus. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4766-7 $39.95




J. Brylinski, Pennsylvania State University, University Park, PA, USA 1st ed. 1993. 3rd printing 2008. XVIII, 302 p. 6 illus. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4730-8 $39.95

1st ed. 1993. Corr. 2nd printing 1994. 3rd. printing 2008. XII, 342 p. 14 illus. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4716-2 $39.95

Intersection Cohomology A. Borel, deceased 1st ed. 1984. 2nd printing 2008. Approx. 245 p. 15 illus. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4764-3 $39.95

Indiscrete Thoughts G. Rota, deceased F. Palombi, University of Torino, Italy (Ed.) 1st ed. 1996. 2nd printing 2008. Approx. 305 p. 1 illus. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4780-3 $39.95

The Non-Euclidean Revolution




R. Trudeau, Stonehill College, North Easton, MA, USA 1st ed. 2001. 2nd printing 2008. Approx. 285 p. 255 illus. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4782-7 $39.95

Discrete Thoughts Essays on Mathematics, Science, and Philosophy M. Kac; G. Rota, deceased J. Schwartz, Professor Emeritus, New York University, NY 2nd ed. 1993. 2nd printing 2008. Approx. 280 p. 5 illus. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4774-2 $39.95

Perspectives on the History of Mathematical Logic T. Drucker, University of WisconsinWhitewater, WI, USA (Ed.) 1st printing 1991. 2nd printing. 2008. Approx. 220 p. 10 illus. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4768-1 $39.95

Logic for Computer Scientists

Bernhard Riemann 1826-1866 Turning Points in the Conception of Mathematics




U. Schöning, University of Ulm, Germany

D. Laugwitz, Technische Hochschule, Darmstadt, Germany Translated by: A. Shenitzer, York University, Ontario, Canada 1st ed. 1999. 2nd printing 2008. Approx. 380 p. 40 illus. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4776-6 $39.95

Reprint of the 1989 ed. 2008. XII, 166 p. 32 illus. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4762-9 $39.95

Algorithms and Programming




Problems and Solutions

Riemann, Topology, and Physics M. I. Monastyrsky, Institute for Theoretical and Experimental Physics, Moscow, Russia

A. Shen, Institute of Problems of Information Transmission, Moscow, Russia Softcover reprint of the 1996 ed. 2008. XIV, 218 p. 30 illus. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4760-5 $39.95

2nd ed. 1999. 2nd printing 2008. Approx. 235 p. 45 illus. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4778-0 $39.95

Linear Differential Equations and Group Theory from Riemann to Poincare

Mathematics for the Analysis of Algorithms


Second Edition J. J. Gray, The Open University, Milton Keynes, UK 2nd ed. 2000. 2nd printing 2008. Approx. 360 p. 30 illus. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4772-8 $39.95




Third Edition D. H. Greene, Xerox Palo Alto Research Center, Palo Alto, CA, USA; D. E. Knuth, Stanford University, Palo Alto, CA, USA 3rd ed. 1990. 2nd printing 2008. X, 132 p. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4728-5 $39.95

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Modern Birkhäuser Classics

Mathematical Control Theory




An Introduction J. Zabczyk, Polish Academy of Sciences, Warsaw, Poland 1st ed. 1992. 2nd, corr. printing 1995. Reprint 2008. XII, 260 p. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4732-2 $39.95

Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations M. Bardi, Università di Padova, Italy; I. Capuzzo-Dolcetta, Università di Roma “La Sapienza,” Italy Softcover reprint of the 1997 ed. 2008. XX, 570 p. 17 illus. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4754-4 $39.95

H-Infinity Optimal Control and Related Minimax Design Problems A Dynamic Game Approach Second Edition T. Basar, University of Illinois, Urbana, IL, USA; P. Bernhard, Nice Sophia Antipolis University, France Softcover reprint of the 1995 2nd ed. 2008. XIV, 412 p. 7 illus. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4756-8 $39.95

Robust Nonlinear Control Design State-Space and Lyapunov Techniques R. A. Freeman, Northwestern University, Evanston, IL, USA; P. V. Kokotovic, University of California, Santa Barbara, CA, USA Softcover reprint of the 1996 ed. 2008. XIV, 258 p. 28 illus. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4758-2 $39.95

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The Grothendieck Festschrift, Volume I A Collection of Articles Written in Honor of the 60th Birthday of Alexander Grothendieck P. Cartier, Institut des Hautes Études Scientifiques, Bures-sur-Yvette, France; L. Illusie, Université de Paris-Sud, Orsay, France; N. M. Katz, Princeton University, Princeton, NJ, USA; G. Laumon, Université de Paris-Sud, Orsay, France; Y. I. Manin, Max-Planck Institut für Mathematik, Bonn, Germany; K. A. Ribet, University of California, Berkeley, CA, USA (Eds.) 1st ed. 1990. 2nd printing 2007. XX, 498 p. 13 illus. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4566-3 $39.95

The Grothendieck Festschrift, Volume II A Collection of Articles Written in Honor of the 60th Birthday of Alexander Grothendieck P. Cartier, Institut des Hautes Etudes Scientifiques, Bures-sur-Yvette, France; L. Illusie, Université de Paris-Sud, Orsay, France; N. M. Katz, Princeton University, Princeton, NJ, USA; G. Laumon, Université de Paris-Sud, Orsay, France; Y. I. Manin, Max-Planck Institut für Mathematik, Bonn, Germany; K. A. Ribet, University of California, Berkeley, CA, USA (Eds.) Reprint of the 1990 ed. 2007. VIII, 563 p. 7 illus. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4567-0 $39.95

The Grothendieck Festschrift, Volume III A Collection of Articles Written in Honor of the 60th Birthday of Alexander Grothendieck P. Cartier, Institut des Hautes Etudes Scientifiques, Bures-sur-Yvette, France; L. Illusie, Université de Paris-Sud, Orsay, France; N. M. Katz, Princeton University, Princeton, NJ, USA; G. Laumon, Université de Paris-Sud, Orsay, France; Y. I. Manin, Max-Planck Institut für Mathematik, Bonn, Germany; K. A. Ribet, University of California, Berkeley, CA, USA (Eds.) Reprint of the 1990 ed. 2007. VII, 495 p. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4568-7 $39.95

Metric Structures for Riemannian and Non-Riemannian Spaces M. Gromov, Institut des Hautes Etudes Scientifiques, Bures-sur-Yvette, France J. LaFontaine, Université de Montpellier, France; P. Pansu, Université de Paris-Sud, Orsay, France (Eds.) Appendices by M. Katz, P. Pansu, S. Semmes

Tata Lectures on Theta I D. Mumford, Brown University, Providence, RI, USA In collaboration with: C. Musili, M. Nori, E. Previato, M. Stillman Reprint of the 1983 ed. 2007. XIII, 235 p. 7 illus. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4572-4 $39.95

Tata Lectures on Theta II Jacobian theta functions and differential equations D. Mumford, Brown University, Providence, RI, USA In collaboration with: C. Musili, M. Nori, E. Previato, M. Stillman, H. Umemura Reprint of the 1984 ed. 2007. XIV, 272 p. 21 illus. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4569-4 $39.95

Tata Lectures on Theta III D. Mumford, Brown University, Providence, RI, USA In collaboration with: M. Nori, P. Norman 1st ed. 1991. 2nd printing 2007. VIII, 202 p. 2 illus. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4570-0 $39.95

1st ed. 1999. Corr. 2nd printing 2001. 3rd printing 2007. XX, 586 p. 100 illus. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4582-3 $39.95

Number Theory An approach through history from Hammurapi to Legendre A. Weil, deceased 1st ed. 1987., 4th printing 2007. XXII, 376 p. 18 illus. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4565-6 $39.95

Notions of Convexity L. Hörmander, University of Lund, Sweden Reprint of the 1st ed. 1994 2007. VIII, 414 p. (Modern Birkhäuser Classics) Softcover ISBN 978-0-8176-4584-7 $39.95

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Algebra







Basic Algebra

D-Modules, Perverse Sheaves, and Representation Theory

A. W. Knapp, State University of New York, Stony Brook, NY, USA “Finally, the author’s notorious masterly style of writing, which stands out by its high degree of clarity, elegance, refinement, and accuracy, also rules over this newest textbook of his, which is very likely to become one of the great standard texts in algebra for generations.”—Zentralblatt MATH 2006. XXII, 717 p. 42 illus. (Cornerstones) Hardcover ISBN 978-0-8176-3248-9 $69.95

Advanced Algebra




A. W. Knapp, State University of New York, Stony Brook, USA Advanced Algebra includes chapters on modern algebra which treat various topics in commutative and noncommutative algebra and provide introductions to the theory of associative algebras, homological algebras, algebraic number theory, and algebraic geometry. Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems. 2007. XXIV, 736 p. 10 illus. (Cornerstones) Hardcover ISBN 978-0-8176-4522-9 $69.95

Basic Algebra and Advanced Algebra Set 2008. XLVI, 1454 p. (Cornerstones) ISBN 978-0-8176-4533-5 $89.95

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R. Hotta, Okayama University of Science, Okayama, Japan; K. Takeuchi, University of Tsukuba, Japan; T. Tanisaki, Osaka City University, Osaka, Japan Translated by: K. Takeuchi, University of Tsukuba, Japan D-modules continues to be an active area of stimulating research in such mathematical areas as algebra, analysis, differential equations, and representation theory. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors’ essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics. Significant concepts and topics that have emerged over the last few decades are presented, including a treatment of the theory of holonomic D-modules, perverse sheaves, the allimportant Riemann-Hilbert correspondence, Hodge modules, and the solution to the Kazhdan-Lusztig-conjecture using D-module theory. To further aid the reader, and to make the work as self-contained as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, and representation theory. 2008. XII, 412 p. 66 illus. (Progress in Mathematics, Volume 236) Hardcover ISBN 978-0-8176-4363-8 $89.95

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Determinantal Ideals Winner of the Ferran Sunyer i Balaguer Prize 2007 R. M. Miró-Roig, Universitat de Barcelona, Spain Determinantal ideals are ideals generated by minors of a homogeneous polynomial matrix. Some classical ideals that can be generated in this way are the ideal of the Veronese varieties, the Segre varieties, and the rational normal scrolls. Determinantal ideals are a central topic in both commutative algebra and algebraic geometry, and they also have numerous connections with invariant theory, representation theory, and combinatorics. Due to their important role, their study has attracted many researchers and has received considerable attention in the literature. In this book three crucial problems are addressed: CI-liaison class and G-liaison class of standard determinantal ideals; the multiplicity conjecture for standard determinantal ideals; and unobstructedness and dimension of families of standard determinantal ideals.

Representation Theory and Automorphic Forms T. Kobayashi, Kyoto University, Japan; W. Schmid, Harvard University, Cambridge, MA, USA; J. Yang, Inha University, Incheon, Korea (Eds.) This volume uses a unified approach to representation theory and automorphic forms. The invited papers, written by leading mathematicians in related fields, track recent progress in the ever expanding fields of representation theory and automorphic forms, and their association with number theory and differential geometry. Both graduate students and researchers will find inspiration in this volume. Contributors include: T. Ikeda, S. Miller, W. Schmid, D. Ramakrishnan, F. Shahidi, J. Yang, K. Yoshikawa 2008. VIII, 216 p. 10 illus. (Progress in Mathematics, Volume 255) Hardcover ISBN 978-0-8176-4505-2 $69.95

2008. Approx. 155 p. (Progress in Mathematics, Volume 264) Hardcover ISBN 978-3-7643-8534-7 $54.95

9

Algebra

Quadratic Mappings and Clifford Algebras J. Helmstetter, Université de Grenoble, France; A. Micali, Université de Montpellier II, France After general properties of quadratic mappings over rings, the authors more intensely study quadratic forms, and especially their Clifford algebras. To this purpose they review the required part of commutative algebra, and they present a significant part of the theory of graded Azumaya algebras. Interior multiplications and deformations of Clifford algebras are treated with the most efficient methods. The connection between orthogonal transformations and Clifford algebras is established in a new way, by means of Lipschitz monoids. Lipschitz monoids also allow a more efficient study of hyperbolic spaces. 2008. Approx. 400 p. Hardcover ISBN 978-3-7643-8605-4 $109.00

Artinian Modules over Group Rings L. A. Kurdachenko, Dnipropetrovsk National University, Ukraine; J. Otal, University of Zaragoza, Spain; I. Y. Subbotin, National University, Los Angeles, CA, USA This book highlights important developments on artinian modules over group rings of generalized nilpotent groups. Along with traditional topics such as direct decompositions of artinian modules, criteria of complementability for some important modules, and criteria of semisimplicity of artinian modules, it also focuses on recent advanced results on these matters. This book highlights important developments on artinian modules over group rings of generalized nilpotent groups. Along with traditional topics such as direct decompositions of artinian modules, criteria of complementability for some important modules, and criteria of semisimplicity of artinian modules, it also focuses on recent advanced results on these matters. The theory of modules over groups has its own specific character that plays an imperative role here and, for example, allows a significant generalization of the classical Maschke Theorem on some classes of infinite groups. Conversely, it leads to establishing direct decompositions of artinian modules related to important natural formations, which, in turn, find very efficient applications in infinite groups. 2007. XII, 247 p. (Frontiers in Mathematics) Softcover ISBN 978-3-7643-7764-9 $49.95

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Functional Identities




M. Brešar, University of Maribor, Slovenia; M. A. Chebotar, Kent State University, USA; W. S. Martindale III, University of Massachusetts, Amherst, MA, USA A functional identity can be informally described as an identical relation involving arbitrary elements in an associative ring together with arbitrary (unknown) functions. The theory of functional identities is relatively new, and this is the first book on this subject. The book is accessible to a wide audience and touches on a variety of mathematical areas such as ring theory, algebra and operator theory. 2007. 272 p. (Frontiers in Mathematics) Softcover ISBN 978-3-7643-7795-3 $49.95

Graph Theory in Paris Proceedings of a Conference in Memory of Claude Berge A. Bondy, Université Claude Bernard Lyon 1, France; J. Fonlupt, Université Paris VI, France; J. Fouquet, Laboratoire d’Informatique Fondamentale d’Orléans, France; J. Fournier, J. L. Ramírez Alfonsín, Université Paris VI, France (Eds.) In July 2004, a conference on graph theory was held in Paris in memory of Claude Berge, one of the pioneers of the field. The event brought together many prominent specialists on topics such as perfect graphs and matching theory, upon which Claude Berge’s work has had a major impact. This volume includes contributions to these and other topics from many of the participants.

The Congruences of a Finite Lattice A Proof-by-Picture Approach G. Grätzer, University of Manitoba, Winnipeg, MB, Canada “The book is self-contained, with many detailed poofs presented that can be followed step-by-step. [I]n addition to giving the full formal detals of the proofs, the author chooses a somehow more pedagogical way that he calls Proofby-Picture, somehow related to the combinatorial (as opposed to algebraic) nature of many of the presented results. I believe that this book is a much-needed tool for any mathematician wishing a gentle introduction to the field of congruences representations of finite lattices, with emphasisi on the more ‘geometric’ aspects.” —Mathematical Reviews 2006. XXII, 282 p. 110 illus. Hardcover ISBN 978-0-8176-3224-3 $59.95

2007. VI, 389 p. 83 illus. (Trends in Mathematics) Hardcover ISBN 978-3-7643-7228-6 $169.00

For more titles in the series "Trends in Mathematics" please see birkhauser.com

11

Algebra

Lifting Modules Supplements and Projectivity in Module Theory J. Clark, University of Otago, New Zealand; C. Lomp, Universidade di Porto, Portugal; N. Vanaja, Mumbai University, India; R. Wisbauer, Universität Düsseldorf, Germany

Near Polygons B. De Bruyn, Gent University, Belgium This monograph gives an extensive overview of the basic theory of general near polygons. The first part of the book includes a discussion of the classes of dense near polygons, regular near polygons, and glued near polygons. Also valuations, one of the most important tools for classifying dense near polygons, are treated in detail. The second part of the book discusses the classification of dense near polygons with three points per line. The book is self-contained and almost all theorems are accompanied with proofs. Several new results are presented. Many known results occur in a more general form and the proofs are often more streamlined than their original versions. 2006. XI, 263 p. (Frontiers in Mathematics) Softcover ISBN 978-3-7643-7552-2 $54.95

Extending modules are generalizations of injective modules and, dually, lifting modules generalize projective supplemented modules. This duality exhibits a certain asymmetry. While the theory of extending modules is well documented in monographs and text books, the purpose of this monograph is to provide a thorough study of supplements and projectivity conditions needed to investigate classes of modules related to lifting modules. 2006. XII, 394 p. (Frontiers in Mathematics) Softcover ISBN 978-3-7643-7572-0 $59.95

Module Theory Endomorphism rings and direct sum decompositions in some classes of modules A. Facchini 1998. 285 p. (Progress in Mathematics, Volume 167) Hardcover ISBN 978-3-7643-5908-9 $151.00

Introduction to Liaison Theory and Deficiency Modules J. C. Migliore 1998. 230 p. (Progress in Mathematics, Volume 165) Hardcover ISBN 978-0-8176-4027-9 $79.95

12

Linear Algebra







Second Edition J. H. Kwak, S. Hong, Pohang University of Science and Technology, Pohang, Republic of South Korea

Introduction to Plane Algebraic Curves E. Kunz, University of Regensburg, Germany Translator: R. G. Belshoff, Southwest Missouri State University, Springfield, MO, USA “This text stands out by the author’s... writing style characterized by its systematic representations, didactical perfection, comprehensiveness, mathematical rigor, thematic determination, and striving for self-containedness. Like in most of his other textbooks on algebra and algebraic geometry [the author] focuses on the inseparable interplay between those two branches of mathematics, and again he presents hints for further reading. There is no doubt that the international mathematical community, including students and teachers, will welcome the overdue English edition of this masterly textbook as a very special and useful addition to the great standard texts on plane curves.”—Zentralblatt MATH ;,,SLOOXV:LWKRQOLQHßOHVXSGDWH6RIWFRYHU ISBN 978-0-8176-4381-2 $59.95

Introduction to Commutative Algebra and Algebraic Geometry




“As linear algebra is one of the most important subjects in the study of science and engineering because of widespread applications in social or natural science, computer science, physics, or economics this book covers one of the most useful courses in undergraduate mathematics, providing essential tooks for inductrial scientists. . . The primary purpose of the book is to give a careful presentation of the basic concepts of linear algebra as a coherent part of mathematics, and to illustrate its power and utility through applications of other disciplines.”—Educational Book Review 2nd ed. 2004. XIV, 390 p. 40 illus. Softcover ISBN 978-0-8176-4294-5 $59.95

Polynomial Identity Rings V. Drensky, Bulgarian Academy of Sciences, Sofia, Bulgaria; E. Formanek, Pennsylvania State University, Philadelphia, PA, USA “The book under review consists of two excellent monographs on the PI-theory by two leading researchers, V. Drensky and E. Formanek … In summary, both expositions are very well written, and the book is recommended both for graduate students and researchers.”—Mathematical Reviews 2004. VI, 200 p. (Advanced Courses in Mathematics CRM Barcelona) Softcover ISBN 978-3-7643-7126-5 $39.95

E. Kunz, University of Regensburg, Germany 1984. 250 p. Hardcover ISBN 978-0-8176-3065-2 $59.95

13

Algebra

Coxeter Matroids




A. V. Borovik, UMIST, Manchester, UK; I. M. Gelfand, Rutgers University, Piscataway, NJ, USA; N. White, University of Florida, Gainesville, FL, USA “This largely self-contained text provides an intuitive and interdisciplinary treatment of Coxeter matroids, a new and beautiful generalization of matroids which is based on a finite Coxeter group.”—Zentralblatt MATH 2003. XXII, 264 p. 65 illus. (Progress in Mathematics, Volume 216) Hardcover ISBN 978-0-8176-3764-4 $79.95

This book is a type of encyclopedia on discrete integrable systems, unifying the features of a research monograph and a handbook. It is supplied with an extensive bibliography and detailed bibliographic remarks at the end of each chapter. Largely self-contained, it will be accessible to graduate and post-graduate students as well as to researchers in the area of integrable dynamical systems. 2003. XXI, 1070 p. (Progress in Mathematics, Volume 219) Hardcover ISBN 978-3-7643-6995-8 $199.00

2003. XII, 300 p. 100 illus. (Mathematics: Theory & Applications) Hardcover ISBN 978-0-8176-4250-1 $79.95

H. E. Rose, University of Bristol, UK “Rose’s Linear Algebra is a highly sophisticated undergraduate work . . . This book would be excellent for mathematics majors or for non-majors with access to a second course in which applications were presented. Summing Up: Recommended for lower- and upper-division undergraduates.” —Choice

Singular Loci of Schubert Varieties

Y. B. Suris, Technische Universität Berlin, Germany

G. Castellini, University of Puerto Rico, Mayaguez, Puerto Rico, USA




A Pure Mathematical Approach

2002. XIV, 250 p. Softcover ISBN 978-3-7643-6792-3 $34.95

The Problem of Integrable Discretization: Hamiltonian Approach

Categorical Closure Operators

Linear Algebra




S. Billey, Massachusetts Institute of Technology, Cambridge, Ma, USA; V. Lakshmibai, Northeastern University, Boston, MA, USA 2000. CXX, 251 p. (Progress in Mathematics, Volume 182) Hardcover ISBN 978-0-8176-4092-7 $79.95

Linear Algebraic Groups




Second Edition T. Springer, Universiteit Utrecht, Utrecht, NL “[The first] ten chapters...are an efficient, accessible, and self-contained introduction to affine algebraic groups over an algebraically closed field. The author includes exercises and the book is certainly usable by graduate students as a text or for self-study...the author [has a] student-friendly style… [The following] seven chapters... would also be a good introduction to rationality issues for algebraic groups. A number of results from the literature…appear for the first time in a text.”—Mathematical Reviews 2nd ed. 1998. 352 p. (Progress in Mathematics, Volume 9) Hardcover ISBN 978-0-8176-4021-7 $69.95

14

Combinatorics / Number Theory




104 Number Theory Problems From the Training of the USA IMO Team T. Andreescu, The University of Texas at Dallas, Richardson, TX, USA; D. Andrica, “Babes-Bolyai” University, Cluj-Napoca, Romania; Z. Feng, Phillips Exeter Academy, Exeter, NH, USA “In short, this book is a very valuable tool for any student/coach interested in preparing for mathematics competitions, especially the International Mathematical Olympiad. College students participating in the Putnam competition might also find quite a few interesting problems. Moreover, any course in number theory could be supplemented with this book and could use some of the references included. Even research mathematicians working in number theory will find this book of value in their pursuits.” —MAA Online 2007. XII, 204 p. Softcover ISBN 978-0-8176-4527-4 $39.95




Complex Numbers from A to ...Z T. Andreescu, The University of Texas at Dallas, Richardson, TX, USA; D. Andrica, “Babes-Bolyai” University, Cluj-Napoca, Romania “The book is a real treasure trove of nontrivial elementary key concepts and applications of complex numbers developed in a systematic manner with a focus on problem-solving techniques. Much of the book goes to geometric applications, of course, but there are also sections on polynomial equations, trigonometry, combinatorics.... Problems constitute an integral part of the book alongside theorems, lemmas and examples. The problems are embedded in the text throughout the book, partly as illustrations to the discussed concepts, partly as the testing grounds for the techniques just studied, but mostly I believe to emphasize the centrality of problem solving in the authors’ world view.... The book is really about solving problems and developing tools that exploit properties of complex numbers.... The reader will find a good deal of elegant and simple sample problems and even a greater quantity of technically taxing ones. The book supplies many great tools to help solve those problems. As the techniques go, the book is truly From ‘A to Z’.”—MAA 2005. XI, 321 p. Softcover ISBN 978-0-8176-4326-3 $49.95

15

Combinatorics / Number Theory

A Path to Combinatorics for Undergraduates




Counting Strategies T. Andreescu, The University of Texas at Dallas, Richardson, TX, USA; Z. Feng, Phillips Exeter Academy, Exeter, NH, USA “This book is an introduction to counting strategies in combinatorial theory. The main mathematical ideas are carefully worked into organized, challenging, and instructive examples given in the nine chapters of this book. In the last chapter we find 111 problems (without solutions). The greater part of them are from various mathematical contests. The…experience of the authors in preparing students for various mathematical competitions allowed them to present a big collection of beautiful problems. By studying this book, undergraduates will be wellequipped to further their knowledge in more abstract combinatorics and its related fields.” —MAA Online 2004. XVIII, 228 p. 40 illus. Softcover ISBN 978-0-8176-4288-4 $39.95

102 Combinatorial Problems




From the Training of the USA IMO Team T. Andreescu, The University of Texas at Dallas, Richardson, TX, USA; Z. Feng, Phillips Exeter Academy, Exeter, NH, USA “Andreescu’s 51 ‘introductory problems’ and 51 ‘advanced problems,’ all novel, would nicely supplement any university course in combinatorics or discrete mathematics. This volume contains detailed solutions, sometimes multiple solutions, for all the problems, and some solutions offer additional twists for further thought... “ —Choice 2003. XII, 116 p. 40 illus. Softcover ISBN 978-0-8176-4317-1 $29.95

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Eisenstein Series and Applications W. T. Gan, UCSD, La Jolla, CA, USA; S. S. Kudla, University of Maryland, College Park, MD, USA; Y. Tschinkel, Courant Institute of Mathematical Sciences/NYU, New York, USA (Eds.) Eisenstein series are an essential ingredient in the spectral theory of automorphic forms and an important tool in the theory of L-functions. They have also been exploited extensively by number theorists for many arithmetic purposes. Bringing together contributions from areas that are not usually interacting with each other, this volume introduces diverse users of Eisenstein series to a variety of important applications. With this juxtaposition of perspectives, the reader obtains deeper insights into the arithmetic of Eisenstein series. The exposition focuses on the common structural properties of Eisenstein series occurring in many related applications that have arisen in several recent developments in arithmetic: Arakelov intersection theory on Shimura varieties, special values of L-functions and Iwasawa theory, and equidistribution of rational/integer points on homogeneous varieties. Key questions that are considered include: Is it possible to identify a class of Eisenstein series whose Fourier coefficients (resp. special values) encode significant arithmetic information? Do such series fit into p-adic families? Are the Eisenstein series that arise in counting problems of this type? Contributors include: B. Brubaker, D. Bump, J. Franke, S. Friedberg, W.T. Gan, P. Garrett, M. Harris, D. Jiang, S.S. Kudla, E. Lapid, K. Prasanna, A. Raghuram, F. Shahidi, R. Takloo-Bighash 2008. Approx. 330 p. (Progress in Mathematics, Volume 258) Hardcover ISBN 978-0-8176-4496-3 $69.95







Second Edition

Number Theory An Introduction via the Distribution of Primes B. Fine, Fairfield University, Fairfield, CT, USA; G. Rosenberger, University of Dortmund, Germany This book provides an introduction and overview of number theory based on the distribution and properties of primes. This unique approach provides both a firm background in the standard material as well as an overview of the whole discipline. All the essential topics are covered: fundamental theorem of arithmetic, theory of congruences, quadratic reciprocity, arithmetic functions, and the distribution of primes. Analytic number theory and algebraic number theory both receive a solid introductory treatment. The book’s user-friendly style, historical context, and wide range of exercises from simple to quite difficult (with solutions and hints provided for select ones) make it ideal for self-study as well as classroom use. Intended for upper level undergraduates and beginning graduate students, the only prerequisites are a basic knowledge of calculus, multivariable calculus, and some linear algebra. All necessary concepts from abstract algebra and complex analysis are introduced in the book. 2007. XIII, 342 p. 12 illus. Softcover ISBN 978-0-8176-4472-7 $59.95

A Beginner’s Guide to Graph Theory Second Edition W. Wallis, Southern Illinois University, Carbondale, IL, USA This second edition includes new chapters on labeling and communications networks and small-worlds, as well as expanded beginner’s material in the early chapters, including more examples, exercises, hints and solutions to key problems. Many additional changes, improvements, and corrections resulting from classroom use and feedback have been added throughout. “Altogether the book gives a comprehensive introduction to graphs, their theory and their application…The use of the text is optimized when the exercises are solved. The obtained skills improve understanding of graph theory as well… It is very useful that the solutions of these exercises are collected in an appendix.” —Simulation News Europe (review of the first edition) 2nd ed. 2007. XX, 260 p. 160 illus. Softcover ISBN 978-0-8176-4484-0 $39.95

Magic Graphs W. Wallis, Southern Illinois University, Carbondale, IL, USA 2001. XIV, 146 p. 21 illus. Softcover ISBN 978-0-8176-4252-5 $59.95

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Combinatorics / Number Theory

Walks on Ordinals and Their Characteristics

General Lattice Theory

S. Todorcevic, Université Paris VII - CNRS, Paris, France and University of Toronto, Canada

G. Grätzer, University of Manitoba, Winnipeg, MB, Canada

The analysis of the characteristics of walks on ordinals is a powerful new technique for building mathematical structures, developed by the author over the last twenty years. This is the first book-length exposition of this method. Particular emphasis is placed on applications which are presented in a unified and comprehensive manner and which stretch across several areas of mathematics such as set theory, combinatorics, general topology, functional analysis, and general algebra. 2007. VI, 324 p. (Progress in Mathematics, Volume 263) Hardcover ISBN 978-3-7643-8528-6 $79.95

Second Edition

Appendix by: B. Davey, R. Freese, B. Ganter, M. Greferath, P. Jipsen, H. Priestley, H. Rose, E. Schmidt, S. Schmidt, F. Wehrung, R. Wille “…Grätzer’s ‘General Lattice Theory’ has become the lattice theorist’s bible. Now…we have the second edition, in which the old testament is augmented by a new testament…. The new testament gospel is provided by leading and acknowledged experts in their fields…. Each [of these eight contributions] is itself a gold mine. This is an excellent and engaging second edition that will long remain a standard reference.” —Mathematical Reviews “Despite the large number of coauthors the style is uniform and the book is well written. As the first edition of this book had a deep influence on the development of lattice theory, I expect that the new edition will continue to hold its leading position among the books on lattice theory.”—Zentralblatt MATH 2007. XIX, 663 p. Softcover ISBN 978-3-7643-6996-5 $92.00

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Algebraic Geometry and Number Theory

and this book is a wonderfully well-written introduction to the area.”—MAA Reviews

In Honor of Vladimir Drinfeld’s 50th Birthday

2006. XVI, 652 p. 20 illus. (Mathematics: Theory & Applications) Hardcover ISBN 978-0-8176-4480-2 $89.95

V. Ginzburg, University of Chicago, IL, USA (Ed.) One of the most creative mathematicians of our times, Vladimir Drinfeld received the Fields Medal in 1990 for his groundbreaking contributions to the Langlands program and to the theory of quantum groups. These ten original articles by prominent mathematicians, dedicated to Drinfeld on the occasion of his 50th birthday, broadly reflect the range of Drinfeld’s own interests in algebra, algebraic geometry, and number theory. Contributors: A. Eskin, V.V. Fock, E. Frenkel, D. Gaitsgory, V. Ginzburg, A.B. Goncharov, E. Hrushovski, Y. Ihara, D. Kazhdan, M. Kisin, I. Krichever, G. Laumon, Yu.I. Manin, A. Okounkov, V. Schechtman, and M.A. Tsfasman.

P. Hu, Shandong University, China; C. Yang, Hong Kong University of Science and Technology, China The subject of the book is Diophantine approximation and Nevanlinna theory. This book proves not just some new results and directions but challenging open problems in Diophantine approximation and Nevanlinna theory. The authors’ newest research activities on these subjects over the past eight years are collected here. Some of the significant findings are the proof of GreenGriffiths conjecture by using meromorphic connections and Jacobian sections, generalized abc-conjecture, and more. 2006. XI, 543 p. Hardcover ISBN 978-3-7643-7568-3 $125.00

2006. XVIII, 643 p. 19 illus. (Progress in Mathematics, Volume 253) Hardcover ISBN 978-0-8176-4471-0 $129.00

Topics in the Theory of Algebraic Function Fields

Value Distribution Theory Related to Number Theory




G. D. Villa Salvador, CINVESTAV del IPN, Mexico City, Mexico “...In the book, Salvador covers a large amount of material at a wide range of levels of difficulty, and as such his book could be used in a wide variety of settings.... The entire book is very well written and Villa Salvador includes many examples to both illustrate and motivate the theory being presented. There are also a handful of exercises in each chapter.... The study of function fields is a beautiful area of mathematics which seems to be ever-increasing in importance,

Geometric Methods in Algebra and Number Theory




F. Bogomolov, New York University, NY, USA; Y. Tschinkel, Princeton University, NJ, USA (Eds.) 2005. VIII, 362 p. 6 illus. (Progress in Mathematics, Volume 235) Hardcover ISBN 978-0-8176-4349-2 $79.95

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Combinatorics / Number Theory

Arithmetic of Higher-Dimensional Algebraic Varieties

Combinatorics and Commutative Algebra

B. Poonen, University of California, Berkeley, CA, USA; Y. Tschinkel, Princeton University, USA (Eds.)

Second Edition

2004. XVI, 287 p. 10 illus. (Progress in Mathematics, Volume 226) Hardcover ISBN 978-0-8176-3259-5 $84.95

An Introduction to the Langlands Program




J. Bernstein, University of Tel Aviv, Israel; S. Gelbart, The Weizmann Institute of Science, Rehovot, Israel (Eds.) With contrib. by: S. Kudla, E. Kowalski, E. d. Shalit, D. Gaitsgory, J. Cogdell, D. Bump This book presents a broad, user-friendly introduction to the Langlands program, that is, the theory of automorphic forms and its connection with the theory of L-functions and other fields of mathematics, suitable for graduate students and researchers. Each of the 12 chapters focuses on a particular topic devoted to special cases of the program. “... the present volume constitutes the most readable entrée into the subject to date, suitable both for serious reading and for browsing, and should attract a new generation to this exciting subject. ... Recommended.”—Choice 2003. VIII, 281 p. 5 illus. Softcover ISBN 978-0-8176-3211-3 $42.95

Diophantine Equations and Power Integral Bases in Algebraic Number Fields I. Gaal, University of Debrecen, Hungary 2002. 208 p. Softcover ISBN 978-0-8176-4271-6 $69.95

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R. P. Stanley, Massachusetts Institute of Technology, MA, USA “The book is an indispensable tool for a mathematician working on the borderline between combinatorics and commutative algebra.”—Mathematical Reviews (Review of the Second Edition) 2nd ed. 1996. X, 180 p. (Progress in Mathematics, Volume 41) Softcover ISBN 978-0-8176-4369-0 $59.95

Logic and Foundations

Studies in Universal Logic

NEW SERIES

Institution-independent Model Theory

Completeness Theory for Propositional Logics

R. Diaconescu, Simion Stoilow Romanian Academy, Romania

W. A. Pogorzelski, University of Bialystok, Poland; P. Wojtylak, Silesian University Katowice, Poland

This book develops model theory independently of any concrete logical system or structure, within the abstract category-theoretic framework of ‘institution theory’. The concept of institution provides a model theory oriented mathematical formulation for the intuitive concept of logical system and had arisen within computing science as a response to the population explosion of specification logics. The described development includes most of the important methods and concepts of conventional concrete model theory at the abstract institution-independent level. It is easily applicable to a diverse, rather large collection of logics from the mathematical and computing science practice, many of them not having a proper model theory prior to this work. The top-down methodology proposed leads to an understanding of model theoretic phenomena. This facilitates the access to deep results and even the discovery of new ones in well worked areas of conventional concrete model theories. The book contains also some applications to computational science. 2008. Approx. 360 p. (Studies in Universal Logic) Softcover ISBN 978-3-7643-8707-5 $94.95

This book develops the theory of one of the most important notions in the methodology of formal systems. Particularly, completeness plays an important role in propositional logic where many variants of the notion have been defined. This approach allows also for a more profound view upon some essential properties of propositional systems. For these purposes, the theory of logical matrices, and the theory of consequence operations is exploited. The book develops the theory of one of the most important notions in the methodology of formal systems. Particularly, completeness plays an important role in propositional logic where many variants of the notion have been defined. Global variants of the notion mean the possibility of getting all correct and reliable schemata of inference. Its local variants refer to the notion of truth given by some semantics. A uniform theory of completeness in its general and local meaning is carried out and it generalizes and systematizes some variety of the notion of completeness such as Postcompleteness, structural completeness and many others. This approach allows also for a more profound view upon some essential properties (e.g. two-valuedness) of propositional systems. For these purposes, the theory of logical matrices, and the theory of consequence operations is exploited. 2008. Approx. 180 p. (Studies in Universal Logic) Softcover ISBN 978-3-7643-8517-0 $69.95

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Logic and Foundations




Logica Universalis Towards a General Theory of Logic

A Beginner‘s Guide to Discrete Mathematics

J. Beziau, University of Neuchâtel, Switzerland (Ed.)

W. Wallis, Southern Illinois University, Carbondale, IL, USA

Universal Logic is not a new logic, but a general theory of logics, considered as mathematical structures. The name was introduced about ten years ago, but the subject is as old as the beginning of modern logic: Alfred Tarski and other Polish logicians such as Adolf Lindenbaum developed a general theory of logics at the end of the 1920s based on consequence operations and logical matrices. The subject was revived after the flowering of thousands of new logics during the last thirty years: there was a need for a systematic theory of logics to put some order in this chaotic multiplicity. This book contains recent works on universal logic by first-class researchers from all around the world. The book is full of new and challenging ideas that will guide the future of this exciting subject. It will be of interest for people who want to better understand what logic is. Tools and concepts are provided here for those who want to study classes of already existing logics or want to design and build new ones.

This introduction to discrete mathematics is aimed primarily at undergraduates in mathematics and computer science at the freshmen and sophomore levels. The text has a distinctly applied orientation and begins with a survey of number systems and elementary set theory. Additional chapters treat: data structures, counting, probability, relations and functions, graph theory, matrices, number theory and cryptography. Good examples occur throughout and there are problem sets with selected solutions at the end of each section. A college algebra course is the only prerequisite.

2nd ed. 2007. 246 p. Softcover ISBN 978-3-7643-8353-4 $79.95

2003. 388 p. 43 illus. Softcover ISBN 978-0-8176-4269-3 $39.95

“Wallis’s book on discrete mathematics is a resource for an introductory course in a subject fundamental to both mathematics and computer science, a course that is expected not only to cover certain specific topics but also to introduce students to important modes of thought specific to each discipline . . . Lower-division undergraduates through graduate students.”—Choice

A Set Theory Workbook I. Adamson 1997. 162 p. Softcover ISBN 978-0-8176-4028-6 $49.95

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A Beginner‘s Guide to Finite Mathematics







A First Course in Abstract Mathematics

For Business, Management, and the Social Sciences

E. D. Bloch, Bard College, Annandale-onHudson, NY, USA

W. Wallis, Southern Illinois University, Carbondale, IL, USA “Requiring little mathematical background beyond high school algebra, the text will be especially useful for business and liberal arts majors. Its straightforward treatment of the essential concepts in finite mathematics will appeal to a wide audience of students and teachers.”—Zentralblatt MATH 2004. XII, 354 p. 100 illus. Softcover ISBN 978-0-8176-4270-9 $54.95

Ordered Sets

Proofs and Fundamentals

“This is a well-written book, based on very sound pedagogical ideas.”—Zentralblatt MATH 2000. XXI, 424 p. Hardcover ISBN 978-0-8176-4111-5 $49.95

Foundations of Logic and Mathematics




Applications to Computer Science and Cryptography


An Introduction B. Schröder, Louisiana Tech University, Ruston, LA, USA “The author has done the field a service by producing an excellent text strong in the presentation of certain topological aspects of the underlying diagrams, e.g., which should serve the developing community and field well and which can be recommended without reservations as one of the volumes which should grace a poseteer’s library whether she is interested only or mainly in the theory of these objects or has directed her gaze towards applications.”—Zentralblatt MATH 2003. XVII, 391 p. 35 illus. Hardcover ISBN 978-0-8176-4128-3 $59.95

Handbook of Logic and Proof Techniques for Computer Science

Y. Nievergelt, Eastern Washington University, Cheney, WA, USA “While the range of topics is relatively standard, the way they are presented is highly original. The author has chosen a strictly formal and axiomatic approach. All the results are proved in full detail from first principles . . . remarkably, all the arithmetic laws on the rational numbers are proved, step after step, starting from the very definitions! . . . a valuable reference text and a useful companion for anybody wondering how the basic mathematical concepts can be rigorously developed within set theory. The author has managed to combine the foundational approach with a careful treatment of many applications. More than 1000 exercises complete the text. ...” —Mathematical Reviews 2001. XVI, 415 p. 22 illus. Hardcover ISBN 978-0-8176-4249-5 $69.95

S. G. Krantz, Washington University, St. Louis, MO, USA

Set Theory: An Introduction

2002. XIX, 245 p. 16 illus. Hardcover ISBN 978-0-8176-4220-4 $62.95

R. L. Vaught, University of California, Berkeley, CA, USA 2nd ed. 1995. 1st softcover printing 2001. 184 p. 8 illus. Softcover ISBN 978-0-8176-4256-3 $79.95




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Geometry / Topology




Suites de Sturm, indice de Maslov et périodicité de Bott J. Barge, J. Lannes, Ecole Polytechnique, Paris, France

An Invitation to Quantum Cohomology Kontsevich’s Formula for Rational Plane Curves J. Kock, Universitat Autònoma de Barcelona, Spain; I. Vainsencher, Universidade Federal de Minas Gerais, Pampulha – Belo Horizonte, Brazil This book is an elementary introduction to stable maps and quantum cohomology, starting with an introduction to stable pointed curves, and culminating with a proof of the associativity of the quantum product. The viewpoint is mostly that of enumerative geometry, and the red thread of the exposition is the problem of counting rational plane curves. Emphasis is given to examples, heuristic discussions, and simple applications of the basic tools to best convey the intuition behind the subject. The book demystifies these new quantum techniques by showing how they fit into classical algebraic geometry. Some familiarity with basic algebraic geometry and elementary intersection theory is assumed. Each chapter concludes with some historical comments and an outline of key topics and themes as a guide for further study, followed by a collection of exercises that complement the material covered and reinforce computational skills. 2007. XII, 159 p. (Progress in Mathematics, Volume 249) Hardcover ISBN 978-0-8176-4456-7 $49.95

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The classical theory of Sturm sequences provides an algorithm for determining the number of roots of a polynomial with real coefficients contained in an open interval. The main purpose of this monograph is to show that a suitable generalization of the theory of Sturm sequences provides, among others: a notion of the Maslov index for an algebraic loop of lagrangians defined over a commutative ring; a proof of the fundamental theorem of (algebraic) hermitian K-theory (theorem due to M. Karoubi); a proof of the theorems of (topological) Bott periodicity (in the spirit of the work of F. Latour); the computation of the relative K2-group, symplectic-linear, for all commutative ring (in the spirit of the work of R. Sharpe). 2008. Approx. 210 p. (Progress in Mathematics, Volume 267) Hardcover ISBN 978-3-7643-8709-9 $79.95

From Geometry to Quantum Mechanics In Honor of Hideki Omori Y. Maeda, Keio University, Yokohama-shi, Japan; P. Michor, Universität Wien, Austria; T. Ochiai, Nippon Sport Science University, Tokyo, Japan; A. Yoshioka, Tokyo University of Science, Tokyo, Japan (Eds.) This volume is composed of invited expository articles by well-known mathematicians in differential geometry and mathematical physics. They have been arranged in celebration of Hideki Omori’s retirement from Tokyo University of Science and in honor of his fundamental contributions to these areas. These articles will appeal to graduate students in mathematics and quantum mechanics, as

well as researchers, differential geometers, and mathematical physicists. 2007. XVII, 324 p. 7 illus. (Progress in Mathematics, Volume 252) Hardcover ISBN 978-0-8176-4512-0 $99.00

L’isomorphisme entre les tours de Lubin-Tate et de Drinfeld

Second Edition

L. Fargues, A. Genestier, Laboratoire de Mathématiques, Orsay, France; V. Lafforgue, Université Paris 6, France

Classical Geometries in Modern Contexts

This book gives a complete and thorough proof of the existence of an equivariant isomorphism between Lubin-Tate and Drinfeld towers in infinite level. The result is established in equal and inequal characteristics. Moreover, the book contains as an application the proof of the equality between the equivariant cohomology of both towers, a result that has applications to the local Langlands correspondence. Along the proof background and complements are given on the structure of both moduli spaces, p-divisible formal groups and p-adic rigid analytic geometry.

W. Benz, University of Hamburg, Germany

2008. Approx. 430 p. (Progress in Mathematics, Volume 262) Hardcover ISBN 978-3-7643-8455-5 $79.95

Geometry of Real Inner Product Spaces

This book is based on real inner product spaces X of arbitrary (finite or infinite) dimension greater than or equal to 2. Designed as a two term graduate course, the book helps students to understand great ideas of classical geometries in a modern and general context. A real benefit is the dimension-free approach to important geometrical theories. The only prerequisites are basic linear algebra and basic 2- and 3-dimensional real geometry. 2nd ed. 2007. XII, 277 p. Hardcover ISBN 978-3-7643-8540-8 $109.00

The Mathematics of Minkowski Space-Time With an Introduction to Commutative Hypercomplex Numbers D. Boccaletti, Università di Roma “La Sapienza”, Italy; F. Catoni, Roma, Italy; R. Cannata, ENEA, C.R. Casaccia, Italy; V. Catoni, Roma, Italy; E. Nichelatti, P. Zampetti, ENEA, C.R. Casaccia, Italy This book arose out of original research on the extension of well-established applications of complex numbers related to Euclidean geometry and to the spacetime symmetry of two-dimensional Special Relativity. The system of hyperbolic numbers is extensively studied, and a plain exposition

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Geometry / Topology

of space-time geometry and trigonometry is given. Commutative hypercomplex systems with four unities are studied and attention is drawn to their interesting properties.




2008. Approx. 250 p. (Frontiers in Mathematics) Softcover ISBN 978-3-7643-8613-9 $54.95

Discrete Differential Geometry A. I. Bobenko, TU Berlin, Germany; P. Schröder, California Institute of Technology, Pasadena, CA, USA; J. M. Sullivan, G. M. Ziegler, TU Berlin, Germany (Eds.) This is the first book on a newly emerging field of discrete differential geometry providing an excellent way to access this exciting area. It provides discrete equivalents of the geometric notions and methods of differential geometry, such as notions of curvature and integrability for polyhedral surfaces. The carefully edited collection of essays gives a lively, multifacetted introduction to this emerging field. 2008. Approx. 350 p. (Oberwolfach Seminars, Volume 38) Softcover ISBN 978-3-7643-8620-7 $39.95

Algebraic Cycles, Sheaves, Shtukas, and Moduli Impanga Lecture Notes P. Pragacz, Polish Academy of Sciences, Torun, Poland (Ed.) Articles examine the contributions of the great mathematician J. M. Hoene-Wronski. Although much of his work was dismissed during his lifetime, it is now recognized that his work offers valuable insight into the nature of mathematics. The book begins with elementary-level discussions and ends with discussions of current research. Most of the material has never been published before.

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2008. Approx. 245 p. (Trends in Mathematics) Hardcover ISBN 978-3-7643-8536-1 $139.00

Introduction to Classical Geometries A. I. Ramírez Galarza, J. Seade, Universidad Nacional Autónoma de México This book follows Klein’s proposal of studying geometry by looking at the symmetries (or rigid motions) of the space in question. In this way the classical geometries are studied: Euclidean, affine, elliptic, projective, and hyperbolic. For simplicity the focus is on the twodimensional case, which is already rich enough, though some aspects of the 3 or n-dimensional geometries are included. Once plane geometry is well understood, it is much easier to go into higher dimensions. The book appeals to, and develops, the geometric intuition of the reader. Some basic notions of algebra and analysis are also used to get better understandings of various concepts and results. 2007. VIII, 219 p. Softcover ISBN 978-3-7643-7517-1 $39.95




q-Clan Geometries in Characteristic 2

Topological and Bivariant K-Theory

I. Cardinali, Università di Siena, Italy; S. E. Payne, University of Colorado, Denver, CO, USA

J. Cuntz, Westfälische Wilhelms-Universität, Münster, Germany; R. Meyer, Georg-AugustUniversität, Göttingen, Germany; J. M. Rosenberg, University of Maryland, College Park, MD, USA

This book offers a complete proof of the Fundamental Theorem of q-Clan Geometry, followed by a detailed study of the known examples. It completely works out the collineation groups of the associated generalized quadrangles and the stabilizers of their associated ovals. 2007. XIV, 166 p. (Frontiers in Mathematics) Softcover ISBN 978-3-7643-8507-1 $54.95

Diophantine Geometry Proceedings U. Zannier, Scuola Normale Superiore, Pisa, Italy (Ed.) This book contains research articles on Diophantine Geometry, written by participants of a research program held at the Ennio De Giorgi Mathematical Research Center in Pisa, Italy, between April and July 2005. The authors are eminent experts in the field and present several subfields of the main topic. The volume provides a broad overview of recent research developments.

Topological K-theory is one of the most important invariants for noncommutative algebras. Bott periodicity, homotopy invariance, and various long exact sequences distinguish it from algebraic K-theory. This book describes a bivariant K-theory for bornological algebras, which provides a vast generalization of topological K-theory. In addition, it details other approaches to bivariant K-theories for operator algebras. The book studies a number of applications, including K-theory of crossed products, the Baum-Connes assembly map, twisted K-theory with some of its applications, and some variants of the Atiyah-Singer Index Theorem. 2007. XI, 262 p. (Oberwolfach Seminars, Volume 36) Softcover ISBN 978-3-7643-8398-5 $39.95

2007. XVIII, 390 p. (Publications of the Scuola Normale Superiore / CRM Series, Volume 4) Softcover ISBN 978-88-7642-206-5 $34.95

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Geometry / Topology




Geometric Problems on Maxima and Minima T. Andreescu, The University of Texas at Dallas, Richardson, TX, USA; O. Mushkarov, Bulgarian Academy of Sciences, Sofia, Bulgaria; L. Stoyanov, University of Western Australia, Crawley, Western Australia “As an avid problem solver with a strong interest in inequalities…I am delighted to supplement my repertoire with the techniques illustrated in this volume…. The book contains hundreds of problems, classical and modern, all with hints or complete solutions…. Over the years, Titu Andreescu and various collaborators have used their experiences as teachers and as Olympiad coaches to produce a series of excellent problem-solving manuals…. The present volume continues that tradition and should appeal to a wide audience ranging from advanced high school students to professional mathematicians.”—MAA 2006. X, 264 p. 262 illus. Softcover ISBN 978-0-8176-3517-6 $69.95

The Algebra of Secondary Cohomology Operations H. Baues, Max-Planck-Institut für Mathematik, Bonn, Germany The algebra of primary cohomology operations computed by the well-known Steenrod algebra is one of the most powerful tools of algebraic topology. This book computes the algebra of secondary

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cohomology operations which enriches the structure of the Steenrod algebra in a new and unexpected way. The book solves a long-standing problem on the algebra of secondary cohomology operations by developing a new algebraic theory of such operations. The results have strong impact on the Adams spectral sequence and hence on the computation of homotopy groups of spheres. 2006. XXXII, 483 p. (Progress in Mathematics, Volume 247) Hardcover ISBN 978-3-7643-7448-8 $149.00

Differential Geometry and Analysis on CR Manifolds S. Dragomir, Università della Basilicata, Romana, Potenza, Italy; G. Tomassini, Scuola Normale Superiore, Pisa, Italy The study of CR manifolds lies at the intersection of three main mathematical disciplines, partial differential equations: complex analysis in several complex variables, and differential geometry. While the PDE and complex analytic aspects have been intensely studied in the last fifty years, much effort has been recently made to understand the differential geometric side of the subject. This monograph provides a unified presentation of several differential geometric aspects in the theory of CR manifolds and tangential Cauchy–Riemann equations. Motivated by clear exposition, many examples, explicitly worked-out geometric results, and stimulating unproved statements and comments referring to the most recent aspects of the theory, this monograph is suitable for researchers and graduate students in differential geometry, complex analysis, and PDEs. 2006. XIV, 487 p. (Progress in Mathematics, Volume 246) Hardcover ISBN 978-0-8176-4388-1 $109.00

Cycle Spaces of Flag Domains




A Complex Geometric Viewpoint G. Fels, University of Tübingen, Germany; A. Huckleberry, University of Bochum, Germany; J. A. Wolf, University of California, Berkeley, CA, USA “Cycle spaces can be a useful tool in the study of real semisimple Lie groups, and the research monograph which is reviewed here is devoted to describing their features. The exposition … is in principle self-contained for a good graduate reader, who will also find a wealth of concrete examples. … the approach used by the authors throughout this monograph is based on a combination of group-theoretical methods … the result is an intriguing melting pot, opening interesting perspectives of interaction among different research branches.”—Mathematical Reviews 2006. XX, 339 p. (Progress in Mathematics, Volume 245) Hardcover ISBN 978-0-8176-4391-1 $74.95

Selected Topics in Convex Geometry




M. Moszynska, Warsaw University, Warsaw, Poland The field of convex geometry has become a fertile subject of mathematical activity in the past few decades. This exposition, examining in detail those topics in convex geometry that are concerned with Euclidean space, is enriched by numerous examples, illustrations, and exercises, with a good bibliography and index. It requires of the reader only a basic knowledge of geometry, linear algebra, analysis, topology, and measure theory. 2006. XVI, 226 p. 30 illus. Softcover ISBN 978-0-8176-4396-6 $59.95

Differential Geometry of Curves and Surfaces A Concise Guide V. A. Toponogov, Sobolev Institute of Mathematics, Novosibirsk, Russia With the editorial assisstance of V. Y. Rovenski, University of Haifa, Israel Differential Geometry of Curves and Surfaces: A Concise Guide presents traditional material in this field along with important ideas of Riemannian geometry. The reader is introduced to curves, then to surfaces, and finally to more complex topics. Standard theoretical material is combined with more difficult theorems and complex problems, while maintaining a clear distinction between the two levels. This rigorous exposition, with well-motivated topics, is ideal for advanced undergraduate and first-year graduate students seeking to enter the fascinating world of geometry. “This book by the late author covers … the subjects which are normally taught in a course on the differential geometry of curves and surfaces. ... the book is very welcome since it is an original contribution in various aspects and gives a number of geometric insights … . Numerous illustrations make the reading enjoyable.”—Mathematical Reviews 2006. XII, 206 p. 70 illus. Softcover ISBN 978-0-8176-4384-3 $59.95

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Geometry / Topology

String Topology and Cyclic Homology




R. L. Cohen, Stanford University, USA; K. Hess, EPFL Lausanne, Switzerland; A. A. Voronov, University of Minnesota, Minneapolis, MN, USA The subject of this book is string topology, Hochschild and cyclic homology. The first part consists of an excellent exposition of various approaches to string topology and the Chas-Sullivan loop product. The second gives a complete and clear construction of an algebraic model for computing topological cyclic homology. The book provides many references for the reader wishing to learn more about the subject, to which it gives a perfect introduction. It is certainly the best source of much information that was until now available only to specialists and covers material from the elementary bases to the most recent developments. 2006. VI, 163 p. (Advanced Courses in Mathematics CRM Barcelona) Softcover ISBN 978-3-7643-2182-6 $29.95

Geometric Qp Functions

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The Monodromy Group H. Zoladek, University of Warsaw, Poland In singularity theory and algebraic geometry the monodromy group is embodied in the Picard-Lefschetz formula and the PicardFuchs equations. It has applications in the weakened 16th Hilbert problem and in mixed Hodge structures. In the theory of systems of linear differential equations one has the Riemann-Hilbert problem, the Stokes phenomena and the hypergeometric functions with their multidimensional generalizations. In the theory of homomorphic foliations there appear the Ecalle-Voronin-Martinet-Ramis moduli. On the other hand, there is a deep connection of monodromy theory with Galois theory of differential equations and algebraic functions. All this is presented in this book, underlining the unifying role of the monodromy group. ;,S0RQRJUDßH0DWHPDW\F]QH9ROXPH  Hardcover ISBN 978-3-7643-7535-5 $129.00

The Breadth of Symplectic and Poisson Geometry

J. Xiao, Memorial University of Newfoundland, St. John’s, NF, Canada

Festschrift in Honor of Alan Weinstein

This book documents the rich structure of the holomorphic Q functions which are geometric in the sense that they transform naturally under conformal mappings. Particular emphasis is placed on recent developments based on the interaction between geometric function / measure theory and other branches of mathematical analysis, including potential theory, complex variables, harmonic analysis, functional analysis, and operator theory. Largely selfcontained, this book will be an instructional and reference work for advanced courses and research in conformal analysis, geometry, and function spaces.

One of the world’s foremost geometers, Alan Weinstein has made deep contributions to symplectic and differential geometry, Lie theory, mechanics, and related fields. Written in his honor, the invited papers in this volume reflect the active and vibrant research in these areas and are a tribute to Weinstein’s ongoing influence.

2006. X, 240 p. (Frontiers in Mathematics) Softcover ISBN 978-3-7643-7762-5 $49.95

J. E. Marsden, California Institute of Technology, Pasadena, USA; T. S. Ratiu, Ecole Polytechnique Fédérale de Lausanne, Switzerland (Eds.)

Contributors: H. Bursztyn, M. Cahen, M. Crainic, J. J. Duistermaat, K. Ehlers, S. Evens, V. L. Ginzburg, A. B. Givental, S. Gutt, D. D. Holm, J. Huebschmann,

L. Jeffrey, F. Kirwan, M. Kogan, J. Koiller, Y. Kosmann-Schwarzbach, B. Kostant, C. Laurent-Gengoux, J-H. Lu, J. E. Marsden, K. C. H. Mackenzie, Y. Maeda, C-M. Marle, T. E. Milanov, N. Miyazaki, R. Montgomery, Y-G. Oh, J-P. Ortega, H. Omori, T. S. Ratiu, P. M. Rios, L. Schwachhöfer, J. Stasheff, I. Vaisman, A. Yoshioka, P. Xu, and S. Zelditch. 2005. XXIII, 654 p. 30 illus. (Progress in Mathematics, Volume 232) Hardcover ISBN 978-0-8176-3565-7 $99.00

Number Fields and Function Fields – Two Parallel Worlds G. van der Geer, B. Moonen, University of Amsterdam, The Netherlands; R. Schoof, Università di Roma “Tor Vergata”, Roma, Italy (Eds.) Ever since the analogy between number fields and function fields was discovered, it has been a source of inspiration for new ideas, and a long history has not in any way detracted from the appeal of the subject. As a deeper understanding of this analogy could have tremendous consequences, the search for a unified approach has become a sort of Holy Grail. These invited articles by leading researchers in the field explore various aspects of the parallel worlds of function fields and number fields. Topics range from Arakelov geometry, the search for a theory of varieties over the field with one element, via Eisenstein series to Drinfeld modules, and t-motives. 2005. XIV, 318 p. (Progress in Mathematics, Volume 239) Hardcover ISBN 978-0-8176-4397-3 $89.95

Geometric Mechanics on Riemannian Manifolds




Applications to Partial Differential Equations O. Calin, Eastern Michigan University, East Lansing, USA; D. Chang, Georgetown University, Washington, USA “...This book, which contains some very interesting ideas and results, is primarily oriented towards graduate or advanced undergraduate students in mathematics and theoretical physics with interests in differential geometry, the calculus of variations and the study of PDE’s, as well as in classical and quantum mechanics. In addition, for more experienced researchers in these fields, it may be a useful resource, written in a style that makes it easily accessible to a wide audience...” —Mathematical Reviews 2005. XV, 278 p. 26 illus. (Applied and Numerical Harmonic Analysis) Hardcover ISBN 978-0-8176-4354-6 $89.95

The Novikov Conjecture




Geometry and Algebra M. Kreck, Universität Heidelberg, Germany; W. Lück, Universität Münster, Germany “This very readable book provides an excellent introduction to the circle of ideas related to the Novikov conjecture.” —Monatshefte für Mathematik 2005. XV, 266 p. (Oberwolfach Seminars, Volume 33) Softcover ISBN 978-3-7643-7141-8 $54.95

Tubes Second Edition A. Gray “The new book by Alfred Gray will do much to make Weyl’s tube formula more accessible to modern readers. The first five chapters give

31

Geometry / Topology

a careful and thorough discussion of each step in the derivation and its application to the Gauss–Bonnet formula. Gray’s pace is quite leisurely, and a gradualte student who has completed a basic differential geometry course will have little difficulty following the presentation. In the remaining chapters of the book, one can find an extension of Weyl’s tube formula to complex submanifolds of complex projective space, power series expansions for tube volumes, and the ‘halftube formula’ for hypersurfaces. A high point is the presentation of estimates for the volumes of tubes in ambient Riemannian manifolds whose curvature is bounded above or below.”—Bulletin of the AMS (Review of the First Edition) 2nd ed. 2004. XIII, 280 p. (Progress in Mathematics, Volume 221) Hardcover ISBN 978-3-7643-6907-1 $94.95

Torus Actions on Symplectic Manifolds Second Edition M. Audin, Université Louis Pasteur et CNRS, Strasbourg, France “...Th[is] second edition contains more material, and includes several new results and techniques. Topics included in the first edition are now presented more thoroughly, with more results, illustrated by well-chosen examples, and many new exercises. ... By including detailed proofs, illuminating examples and figures, and numerous exercises, the author has made this book a suitable text for a graduate course, especially one centered on Hamiltonian torus actions and their applications.”—Mathematical Reviews 2nd revised ed. 2004. VIII, 325 p. (Progress in Mathematics, Volume 93) Hardcover ISBN 978-3-7643-2176-5 $99.00

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Symplectic Geometry of Integrable Hamiltonian Systems




M. Audin, Université Louis Pasteur et CNRS, Strasbourg, France; A. Cannas da Silva, Lisboa, Portugal; E. Lerman, University of Illinois at Urbana-Champaign, USA 2003. 236 p. (Advanced Courses in Mathematics - CRM Barcelona) Softcover ISBN 978-3-7643-2167-3 $39.95

Lines and Curves




A Practical Geometry Handbook V. Gutenmacher, VISTAGY, Inc., Waltham, MA, U.S.A.; N. Vasilyev, Lomonosov Moscow State University, Moscow, Russia “If only some of the ideas of this book would slip [into the] teaching at school the pupils would not lament for boring mathematics. And if you [are looking] for a fascinating, exciting, but by no means trivial approach to the beginnings of the theory of algebraic curves buy this book!”—Monashefte für Mathematik 2004. XVIII, 158 p. 350 illus. Softcover ISBN 978-0-8176-4161-0 $44.95

Torsions of 3-dimensional Manifolds V. Turaev, CNRS, Strasbourg, France 2003. X, 196 p. (Progress in Mathematics, Volume 208) Hardcover ISBN 978-3-7643-6911-8 $114.00

Rigid Analytic Geometry and Its Applications




J. Fresnel, Université de Bordeaux I, Talence, France; M. van der Put, Rijksuniversiteit Groningen, The Netherlands 2003. XII, 300 p. 10 illus. (Progress in Mathematics, Volume 218) Hardcover ISBN 978-0-8176-4206-8 $79.95

Proper Group Actions and the Baum-Connes Conjecture G. Mislin, ETH Zürich, Switzerland; A. Valette, Université de Neuchâtel, Switzerland

is inevitable in a book of this size (around 100 pages) and not necessarily a bad thing.“ —Mathematical Reviews 2002. X, 104 p. (Lectures in Mathematics. ETH Zürich) Softcover ISBN 978-3-7643-6706-0 $29.95

2003. 131 p. (Advanced Courses in Mathematics CRM Barcelona) Softcover ISBN 978-3-7643-0408-9 $39.95

Elements of Noncommutative Geometry Riemannian Geometry of Contact and Symplectic Manifolds D. E. Blair, Michigan State University, East Lansing, MI, USA “The book . . . supplies a lot of examples, and includes many recent results. It can be used either as an introduction to the subject or as a reference for students and researchers . . . [it] gives a clear and complete account of the main ideas . . . and studies a vast amount of related subjects such as integral submanifolds, symplectic structure of tangent bundles, curvature of contact metric manifolds and curvature functionals on spaces of associated metrics.” —Mathematical Reviews 2002. XII, 276 p. 5 illus. (Progress in Mathematics, Volume 203) Hardcover ISBN 978-0-8176-4261-7 $69.95

Introduction to the Baum-Connes Conjecture A. Valette, Université de Neuchâtel, Switzerland “Overall, the book is a very valuable addition to the literature on the Baum-Connes conjecture. It is highly recommended reading for anyone interested in learning more about the conjecture, or who does research in areas related to it. Of course, the reader who wants to be an expert will eventually have to consult the original literature, but such




J. M. Gracia-Bondia, J. C. Varilly, H. Figueroa, University of Costa Rica, San Jose, Costa Rica “In collecting the material in a coherent form, the authors have performed a valuable service and this book will no doubt open noncommutative geometry to a wider audience.... [A] large number of metaphorical and mathematical remarks embedded in the text...highlight the plethora of connections between the material of the book and other areas of mathematics.”—Mathematical Reviews 2001. XVII, 685 p. (Birkhäuser Advanced Texts / Basler Lehrbücher) Hardcover ISBN 978-0-8176-4124-5 $79.95

Hyperbolic Manifolds and Discrete Groups Notes on Thurston’s Hyperbolization




M. Kapovich, University of Utah, Salt Lake City, UT, USA “The book is very clearly written and fairly self-contained. It will be useful to researchers and advanced graduate students in the field and can serve as an ideal guide to Thurston’s work and its recent developments.”—Mathematical Reviews 2001. XXV, 467 p. 75 illus. (Progress in Mathematics, Volume 183) Hardcover ISBN 978-0-8176-3904-4 $94.95

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Geometry / Topology

Homology of Linear Groups K. P. Knudson, Wayne State University, Detroit, MI, USA “This marks the first time that many of these results have been collected in a single volume…”—Mathematical Reviews 2001. XI, 192 p. (Progress in Mathematics, Volume 193) Hardcover ISBN 978-3-7643-6415-1 $109.00

Cohomological Theory of Dynamical Zeta Functions A. Juhl, Universitet Uppsala, Sweden 2001. X, 709 p. (Progress in Mathematics, Volume 194) Hardcover ISBN 978-3-7643-6405-2 $219.00

Quantization of Singular Symplectic Quotients N. Landsman, Universiteit van Amsterdam, The Netherlands; M. Pflaum, HumboldtUniversität zu Berlin, Germany; M. Schlichenmaier, University of Mannheim, Germany (Eds.) 2001. XII, 355 p. (Progress in Mathematics, Volume 198) Hardcover ISBN 978-3-7643-6608-7 $151.00

Braids and Self-Distributivity P. Dehornoy, Universite Campus 2, Caen, France 2000. XIX, 623 p. (Progress in Mathematics, Volume 192) Hardcover ISBN 978-3-7643-6343-7 $138.00

34

Canonical Metrics in Kähler Geometry G. Tian, Massachusetts Institute of Technology, Cambridge, MA, USA “This little monograph offers an essentially self-contained introduction to the theory of canonical Kähler metrics on complex manifolds. …The author presents some advanced topics which are hard [to] find elsewhere… This graduate course on KählerEinstein metrics can be recommended to all those interested in recent developments within complex differential geometry.” —Publicationes Mathematicae 2000. VII, 101 p. (Lectures in Mathematics. ETH Zürich) Softcover ISBN 978-3-7643-6194-5 $34.95

A First Course in Geometric Topology and Differential Geometry




E. Bloch, Bard College, Annandale-onHudson, NY, USA “[The author] avoids aimless wandering among the topics by explicitly heading towards milestone theorems... [His] directed path through these topics should make an effective course on the mathematics of surfaces. The exercises and hints are well chosen to clarify the central threads rather than diverting into byways.”—Computing Reviews 1996. 440 p. Hardcover ISBN 978-0-8176-3840-5 $69.95

A General Topology Workbook




Riemannian Geometry




I. T. Adamson, University of Dundee, Scotland

M. P. do Carmo, Instituto de Matematica Pura e Aplicada (IMPA), Rio de Janeiro, Brazil

“This well-printed, attractive little volume offers a first introduction to general topology, cast into the form of a problem collection... well-suited both for classroom use and for individual study.”—Publ. Math. Debrecen

“This is one of the best (if even not just the best) book for those who want to get a good, smooth and quick, but yet thorough introduction to modern Riemannian geometry.” Publicationes Mathematicae

1st ed. 1995. 164 p. Softcover ISBN 978-0-8176-3844-3 $49.95

“This is a very nice introduction to global Riemannian geometry, which leads the reader quickly to the heart of the topic. Nevertheless, classical results are also discussed on many occasions, and almost 60 pages are devoted to exercises.” —Newsletter of the EMS

Symplectic Invariants and Hamiltonian Dynamics




H. Hofer, E. Zehnder, ETH Zurich, Switzerland “This book, written by two experienced researchers, will certainly fill in a gap in the theory of symplectic topology. The authors have taken part in the development of such a theory by themselves or by their collaboration with other outstanding people in the area.”—Zentralblatt MATH

1992. XVI, 300 p. 53 illus. (Mathematics: Theory & Applications) Hardcover ISBN 978-0-8176-3490-2 $49.95

1994. 356 p. (Birkhäuser Advanced Texts) Hardcover ISBN 978-3-7643-5066-6 $69.95

Geometry and Spectra of Compact Riemann Surface J. Buser, EPFL, Lausanne, Switzerland “Anyone familiar with the author's handson approach to Riemann surfaces will be gratified by both the breadth and the depth of the topics considered here. The exposition is also extremely clear and thorough. Anyone not familiar with the author's approach is in for a real treat.”—Mathematical Reviews 1992. 468 p. (Progress in Mathematics, Vol. 106) Hardcover ISBN 978-0-8176-3406-3 $109.00

35

Group Theory / Representation Theory




Geometry and Dynamics of Groups and Spaces In Memory of Alexander Reznikov M. Kapranov, Yale University, New Haven, CT, USA; S. Kolyada, Ukraine and MPI for Mathematics, Bonn, Germany; Y. I. Manin, MPI for Mathematics, Bonn, Germany and Northwestern University, USA; P. Moree, MPI for Mathematics, Bonn, Germany; L. Potyagailo, Université de Lille I, France (Eds.) This book presents 18 articles by prominent mathematicians, dedicated to the memory of Alexander Reznikov (1960-2003), a brilliant highly original mathematician with broad mathematical interests. In addition it contains an influential, so far unpublished manuscript of Reznikov of book length. The research articles broadly reflect the range of Reznikov’s own interests in geometry, group and number theory, functional analysis, dynamical systems and topology. Contributions by V. Armitage, J.-M. Bismut, D.V. Borisov, P. Bressler, A. Danilenko, T. Delzant, H. Esnault, A. Fel’shtyn, D. Goncalves, A. Goncharov, A. Gorokhovsky, R. Grigorchuk, B. Guilfoyle, P.H. Hai, J.N. Iyer, M. Kapovich, W. Klingenberg, V. Lyubashenko, Y.I. Manin, O. Manzyuk, V.T. Milman, P. Moree, M. Morishita, R. Nest, J.-P. Otal, J.R. Parker, A. Reznikov, C.T. Simpson, Y. Soibelman, X. Sun, B. Tsygan, M. Zaidenberg. 2008. Approx. 770 p. (Progress in Mathematics, Volume 265) Hardcover ISBN 978-3-7643-8607-8 $109.00

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The Geometry of the Word Problem for Finitely Generated Groups N. Brady, University of Oklahoma, Norman, OK, USA; T. Riley, Cornell University, Ithaca, NY, USA; H. Short, Université de Provence, Marseille, France The origins of the word problem are in group theory, decidability and complexity, but, through the vision of M. Gromov and the language of filling functions, the topic now impacts the world of large-scale geometry, including topics such as soap films, isoperimetry, coarse invariants and curvature. The first part introduces van Kampen diagrams in Cayley graphs of finitely generated, infinite groups; it discusses the van Kampen lemma, the isoperimetric functions or Dehn functions, the theory of small cancellation groups and an introduction to hyperbolic groups. One of the main tools in geometric group theory is the study of spaces, in particular geodesic spaces and manifolds, such that the groups act upon. The second part is thus dedicated to Dehn functions, negatively curved groups, in particular, CAT(0) groups, cubings and cubical complexes. In the last part, filling functions are presented from geometric, algebraic and algorithmic points of view; it is discussed how filling functions interact, and applications to nilpotent groups, hyperbolic groups and asymptotic cones are given. Many examples and open problems are included. 2007. VII, 206 p. 68 illus. (Advanced Courses in Mathematics - CRM Barcelona) Softcover ISBN 978-3-7643-7949-0 $39.95

The Unity of Mathematics In Honor of the Ninetieth Birthday of I.M. Gelfand P. Etingof, Massachusetts Institute of Technology, Cambridge, MA, USA; V. Retakh, Rutgers University, Piscataway, NJ, USA; I. Singer, Massachusetts Institute of Technology, Cambridge, MA, USA (Eds.)

An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem L. Capogna, University of Arkansas, Fayetteville, AR, USA; D. Danielli, Purdue University, West Lafayette, IN, USA; S. D. Pauls, Dartmouth College, Hanover, NH, USA; J. T. Tyson, University of Illinois, Urbana-Champaign, IL, USA This book provides an introduction to the basics of sub-Riemannian differential geometry and geometric analysis in the Heisenberg group, focusing primarily on the current state of knowledge regarding Pierre Pansu’s celebrated 1982 conjecture regarding the sub-Riemannian isoperimetric profile. It presents a detailed description of Heisenberg submanifold geometry and geometric measure theory, which provides an opportunity to collect for the first time in one location the various known partial results and methods of attack on Pansu’s problem. As such it serves simultaneously as an introduction to the area for graduate students and beginning researchers, and as a research monograph focused on the isoperimetric problem suitable for experts in the area. 2007. XVI, 223 p. (Progress in Mathematics, Volume 259) Hardcover ISBN 978-3-7643-8132-5 $59.95

“This book is a unique and wonderful collection of papers presented at a conference honoring one of the most productive, influential and still young mathematicians of the 20th century, I. M. Gelfand. .... The authors of the papers are some of the best mathematicians of present day...[and] most of them emphasize the crucial contribution that Gelfand’s work had in many different ways.... [T]he papers are unique, very deep and very well written.” —MAA 2006. XXII, 632 p. 41 illus. (Progress in Mathematics, Volume 244) Hardcover ISBN 978-0-8176-4076-7 $115.00

Studies in Lie Theory Dedicated to A. Joseph on his Sixtieth Birthday J. Bernstein, University of Tel Aviv, Israel; V. Hinich, A. Melnikov, University of Haifa, Israel (Eds.) Contributors: J. Alev; A. Beilinson; A. Braverman; I. Cherednik; J. Dixmier; F. Dumas; P. Etingof; D. Farkas; D. Gaitsgory; F. Ivorra; A. Joseph; D. Joseph; M. Kashiwara; D. Kazhdan; A.A. Kirillov; B. Kostant; S. Kumar; G. Letzter; T. Levasseur; G. Lusztig; L. Makar-Limanov; W. McGovern; M. Nazarov; K-H. Neeb; L.G. Rybnikov; P. Schapira; V. Schechtman; A. Sergeev; J.T. Stafford; Ya. Varshavsky; N. Wallach; and I. Waschkies. 2006. XXII, 494 p. 2 illus. (Progress in Mathematics, Volume 243) Hardcover ISBN 978-0-8176-4342-3 $99.00

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Group Theory / Representation Theory

The Fourfold Way in Real Analysis An Alternative to the Metaplectic Representation A. Unterberger, Université de Reims, France The fourfold way starts with the consideration of entire functions of one variable satisfying specific estimates at infinity, both on the real line and the pure imaginary line. A major part of classical analysis, mainly that which deals with Fourier analysis and related concepts, can then be given a parameter-dependent analogue. Even though the whole development touches upon notions of representation theory, pseudodifferential operator theory, and algebraic geometry, it remains completely elementary in all these aspects. 2006. X, 220 p. (Progress in Mathematics, Volume 250) Hardcover ISBN 978-3-7643-7544-7 $109.00

Compactifications of Symmetric and Locally Symmetric Spaces A. Borel, L. Ji, University of Michigan, Ann Arbor, MI, USA Noncompact symmetric and locally symmetric spaces naturally appear in many mathematical theories, including analysis (representation theory, nonabelian harmonic analysis), number theory (automorphic forms), algebraic geometry (modulae) and algebraic topology (cohomology of discrete groups). The main purpose of this book is to introduce uniform constructions of most of the known compactifications with emphasis on their geometric and topological structures. “In the book under review the authors pursue three chief goals: to give a comprehensive overview of existing compactifications … to explain the relations among them and to provide a uniform construction. … The

38

style is user-friendly … . It can be highly recommended and will be very useful to anyone, graduate student or research mathematician, interested in the geometry and topology of (locally) symmetric spaces.” —Mathematical Reviews 2006. XIII, 479 p. (Mathematics: Theory & Applications) Hardcover ISBN 978-0-8176-3247-2 $79.95

Dirac Operators in Representation Theory J. Huang, Hong Kong University of Science and Technology, Hong Kong, China; P. Pandzic, University of Zagreb, Croatia The concept of Dirac cohomology, which is defined using Dirac operators, is a farreaching generalization that connects index theory in differential geometry to representation theory. Using Dirac operators as a unifying theme, the authors demonstrate how some of the most important results in representation theory fit together when viewed from this perspective. “This book contains a more detailed explanation of the results from several recent papers of the authors. The book is aimed at a somewhat broader audience. Clifford algebras are presented rather thoroughly. Some basics of Lie groups and their representations are mostly relegated to earlier literature. There is a good introduction to the so-called cohomological induction, which is short but still gives the main ideas of some parts of the proofs.”—MathSciNet 2006. X, 199 p. (Mathematics: Theory & Applications) Hardcover ISBN 978-0-8176-3218-2 $59.95

Symplectic Geometry and Quantum Mechanics M. de Gosson, Universität Potsdam, Germany This book offers a complete discussion of techniques and topics intervening in the mathematical treatment of quantum and semi-classical mechanics. It starts with a very readable introduction to symplectic geometry. Many topics are also of genuine interest for pure mathematicians working in geometry and topology. 2006. XX, 367 p. (Operator Theory: Advances and Applications, Advances in Partial Differential Equations, Volume 166) Hardcover ISBN 978-3-7643-7574-4 $179.00

Lie Theory Harmonic Analysis on Symmetric Spaces – General Plancherel Theorems J. Anker, Université d’Orléans, France; B. Orsted, University of Southern Denmark, Odense, Denmark (Eds.) 2005. VIII, 175 p. 3 illus. (Progress in Mathematics, Volume 230) Hardcover ISBN 978-0-8176-3777-4 $74.95

Lie Theory Unitary Representations and Compactifications of Symmetric Spaces J. Anker, Université d’Orléans, France; B. Orsted, University of Southern Denmark, Odense, Denmark (Eds.) Lie Theory: Unitary Representations and Compactifications of Symmetric Spaces, a self-contained work by A. Borel, L. Ji and T. Kobayashi, focuses on two fundamental questions in the theory of semisimple Lie groups: the geometry of Riemannian symmetric spaces and their compactifications; and branching laws

for unitary representations, i.e. restricting unitary representations to (typically, but not exclusively, symmetric) subgroups and decomposing the ensuing representations into irreducibles. 2005. X, 207 p. 20 illus. (Progress in Mathematics, Volume 229) Hardcover ISBN 978-0-8176-3526-8 $74.95

Lie Theory Lie Algebras and Representations J. Anker, Université d’Orléans, France; B. Orsted, University of Southern Denmark, Odense (Eds.) “Some of Jantzen’s techniques seem to be unmotivated at first, but he rewards the patient reader with background and motivation as he moves through the book, often starting with a simple case in a classical group/algebra and providing motivation by generalizing the situation later. The detailed work is also surprisingly free of logical and typographical errors; Jantzen has been very careful at every turn...Neeb’s article is a good starting point for learning about the analytic side of the unitary representation theory of infinite-dimensional groups.”—SIAM Book Reviews 2004. IX, 328 p. (Progress in Mathematics, Volume 228) Hardcover ISBN 978-0-8176-3373-8 $69.95

Frobenius Splitting Methods in Geometry and Representation Theory




M. Brion, Université Grenoble 1 - CNRS, St.-Martin d’Hères, France; S. Kumar, University of North Carolina, Chapel Hill, USA 2005. VIII, 250 p. (Progress in Mathematics, Volume 231) Hardcover ISBN 978-0-8176-4191-7 $69.95

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Group Theory / Representation Theory

Poisson Structures and Their Normal Forms J. Dufour, Université de Montpellier, France; N. T. Zung, Université Paul Sabatier, Toulouse, France The aim of this book is twofold. On the one hand, it gives a quick, self-contained introduction to Poisson geometry and related subjects. On the other hand, it presents a comprehensive treatment of the normal form problem in Poisson geometry. Even when it comes to classical results, the book gives new insights. It contains results obtained over the past 10 years which are not available in other books. 2005. XV, 321 p. (Progress in Mathematics, Volume 242) Hardcover ISBN 978-3-7643-7334-4 $64.95

Infinite Groups: Geometric, Combinatorial and Dynamical Aspects L. Bartholdi, Ecole Polytechnique Fédérale, Lausanne, Switzerland; T. CeccheriniSilberstein, Università degli Studi del Sannio, Benevento, Italy; T. SmirnovaNagnibeda, University of Geneva, Switzerland; A. Zuk, Université Pierre et Marie Curie, Paris, France (Eds.) Contributions by G. Baumslag, A. Borovik / A. Lubotzky / A. Myasnikov, T. Delzant / M. Gromov, W. Dicks / E. Formanek, R. Grigorchuk, P. de la Harpe / C. Pache, W. Lück, G. Pisier, A. Shalev, S. Sidki, E. Zelmanov. 2005. 413 p. (Progress in Mathematics, Volume 248) Hardcover ISBN 978-3-7643-7446-4 $109.00

Introduction to Vertex Operator Algebras and Their Representations




J. Lepowsky, Rutgers University, Piscataway, NJ, USA; H. Li, Rutgers University, Camden, NJ, USA; and, Harbin Normal University, China 2004. XI, 318 p. (Progress in Mathematics, Volume 227) Hardcover ISBN 978-0-8176-3408-7 $89.95

Momentum Maps and Hamiltonian Reduction




J. Ortega, CNRS, Université de FrancheComté, Besançon, France; T. S. Ratiu, Ecole Polytechnique Fédérale de Lausanne, Switzerland 2004. XXXIV, 497 p. 10 illus. (Progress in Mathematics, Volume 222) Hardcover ISBN 978-0-8176-4307-2 $74.95

Discrete Groups, Expanding Graphs and Invariant Measures A. Lubotzky, Hebrew University, Jerusalem, Israel Winner of the Ferran Sunyer i Balaguer Prize 1993. 1994. 210 p. (Progress in Mathematics, Volume 125) Hardcover ISBN 978-3-7643-5075-8 $69.95

Subgroup Growth A. Lubotzky, Hebrew University, Jerusalem, Israel; D. Segal, All Souls College, Oxford, UK Winner of the Ferran Sunyer i Balaguer Prize 2001 2003. XXII, 454 p. (Progress in Mathematics, Volume 212) Hardcover ISBN 978-3-7643-6989-7 $139.00

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Studies in Memory of Issai Schur A. Joseph, A. Melnikov, R. Rentschler, Universite Pierre et Marie Curie, Paris, France (Eds.) 2003. 560 p. 30 illus. (Progress in Mathematics, Volume 210) Hardcover ISBN 978-0-8176-4208-2 $105.00

Analysis on Lie Groups with Polynomial Growth




N. Dungey, Australian National University, Canberra, NSW, Australia; A. ter Elst, Eindhoven University of Technology, Eindhoven, The Netherlands; D. W. Robinson, Australian National University, Canberra, NSW, Australia 2003. VIII, 312 p. (Progress in Mathematics, Volume 214) Hardcover ISBN 978-0-8176-3225-0 $79.95

Lie Groups Beyond an Introduction Second Edition A. W. Knapp, State University of New York at Stony Brook, NY, USA

Kac-Moody Groups, their Flag Varieties and Representation Theory




S. Kumar, University of North Carolina, Chapel Hill, NC, USA “It is clear that this book is a valuable reference for all those interested in flag varieties and representation theory in the semi-simple or Kac-Moody case.” — Mathematical Reviews “A lot of different topics are treated in this monumental work....many of the topics of the book will be useful for those only interested in the finite-dimensional case. The book is self contained, but is on the level of advanced graduate students....For the motivated reader who is willing to spend considerable time on the material, the book can be a gold mine.”—Zentralblatt MATH 2002. 632 p. 86 illus. (Progress in Mathematics, Volume 204) Hardcover ISBN 978-0-8176-4227-3 $69.95




“Anthony Knapp’s Lie Groups Beyond an Introduction, 2nd edition, is a beautiful introduction to this area of mathematics, appropriate for a variety different audiences.... The book is well-organized with concise, focused introductions to each chapter, a very thorough index of notation, and appendices.... In addition, there are hints to the hundreds of exercises, and a section on historical notes.... Knapp’s writing is clear, and he avoids excessive notation. The first few chapters comprise a standard introductory course in Lie theory, while numerous second courses could be taught out of the later chapters. Its breadth of coverage and extensive tables also make the book a valuable reference for researchers in representation theory.”—MAA Reviews (review of the second edition) 2nd ed. 2002. XVIII, 812 p. 8 illus. (Progress in Mathematics, Volume 140) Hardcover ISBN 978-0-8176-4259-4 $69.95

Lectures on Algebraic Quantum Groups




K. A. Brown, University of Glasgow, UK; K. R. Goodearl, University of California, Santa Barbara, CA, USA “The proofs, sketches of proofs, and quotations from the literature are carefully written. Numerous examples and exercises are included, and bibliographical notes conclude each chapter. The second and third parts end with a discussion of open problems and perspectives for further research.” —Mathematical Reviews 2002. IX, 348 p. (Advanced Courses in Mathematics CRM Barcelona) Softcover ISBN 978-3-7643-6714-5 $49.95

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Group Theory / Representation Theory

Tree Lattices H. Bass, University of Michigan, Ann Arbor, MI, USA; A. Lubotzky, Hebrew University, Jerusalem, Israel Hyman Bass is the recipient of the National Medal of Science 2001. XIII, 233 p. 80 illus. (Progress in Mathematics, Volume 176) Hardcover ISBN 978-0-8176-4120-7 $79.95

Groups with the Haagerup Property Gromov’s a-T-menability P. Cherix, M. Cowling, P. Jolissaint, P. Julg, A. Valette The aim of this book is to cover, for the first time in book form, various aspects of the Haagerup property. New characterizations are brought in, using ergodic theory or operator algebras. Several new examples are given, and new approaches to previously known examples are proposed. Connected Lie groups with the Haagerup property are completely characterized. 2001. 134 p. (Progress in Mathematics, Volume 197) Hardcover ISBN 978-3-7643-6598-1 $74.95

42

Analysis / Operator Theory

Distributions Theory and Applications J. J. Duistermaat, J. A. Kolk, Universiteit Utrecht, The Netherlands

CORNERSTONES SERIES




This text is a concise, application-oriented introduction to the theory of distributions. It presents distributions as a natural method of analysis from both a mathematical and physical point of view. Methods are developed to justify many formal calculations that do not make sense in the classical framework. The discussion emphasizes applications to the general study of linear partial differential equations. The topics include an introduction to distributions, differentiation, convergence, and convolution of distributions, as well as Fourier transformations and spaces of distributions having special properties. The applications relate the theory to solutions of partial differential equations occurring in physics, for instance, in mechanics, optics, quantum mechanics, quantum field theory and signal analysis, which students may encounter throughout their studies. Advanced undergraduate and graduate students in mathematics, theoretical physics and engineering will find this textbook a welcome introduction to the theory of distributions, a subject often requiring a strong mathematical background. Here the subject is motivated by many examples, exercises, hints and solutions that guide the student along a path requiring only a minimal mathematical background.

Geometric Integration Theory S. G. Krantz, Washington University, St. Louis, MO, USA; H. Parks, Oregon State University, Corvallis, OR, USA

CORNERSTONES SERIES




This textbook introduces geometric measure theory through the notion of currents. Currents, continuous linear functionals on spaces of differential forms, are a natural language in which to formulate types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis. The text provides considerable background for the student and discusses techniques that are applicable to complex geometry, partial differential equations, harmonic analysis, differential geometry, and many other parts of mathematics. Topics include the deformation theorem, the area and coareas formulas, the compactness theorem, the slicing theorem and applications to minimal surfaces. Motivating key ideas with examples and figures, Geometric Integration Theory is a comprehensive introduction ideal for both self-study and for use in the classroom. The exposition demands minimal background, is self-contained and accessible, and thus is ideal for both graduate students and researchers. 2008. Approx. 380 p. 10 illus. (Cornerstones) Hardcover ISBN 978-0-8176-4676-9 $69.95

2008. Approx. 350 p. 25 illus. (Cornerstones) Hardcover ISBN 978-0-8176-4672-1 $59.95

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Analysis / Operator Theory




A Handbook of Real Variables With Applications to Differential Equations and Fourier Analysis S. G. Krantz, Washington University, St.Louis, MO, USA 2004. XII, 201 p. 30 illus. Hardcover ISBN 978-0-8176-4329-4 $62.95

Geometric Function Theory Explorations in Complex Analysis S. G. Krantz, Washington University, St. Louis, MO, USA “The geometric point of view is the unifying theme in this fine textbook in complex function theory. But the author also studies byways that come from analysis and algebra.... Altogether, the author treats advanced topics that lead the reader to modern areas of research. And what is important, the topics are presented with an explanation of their interaction with other important parts of mathematics. The presentations of the topics are clear and the text makes [for] very good reading; basic ideas of many concepts and proofs are carefully described, non-formal introductions to each chapter are very helpful, a rich collection of exercises is well composed and helps the student to understand the subject. The book under review leads the student to see what complex function theory has to offer and thereby gives him or her a taste of some of the areas of current research. As such it is a welcome addition to the existing literature in complex function theory.... In this reviewer’s opinion, the book can warmly be recommended both to experts and to a new generation of mathematicians.”— Zentralblatt MATH 2006. XIV, 314 p. 41 illus. (Cornerstones) Hardcover ISBN 978-0-8176-4339-3 $69.95

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A Primer of Real Analytic Functions




Second Edition S. G. Krantz, Washington University, St. Louis, MO, USA; H. R. Parks, Oregon State University, Corvallis, OR, USA “This is the second, improved edition of the only existing monograph devoted to realanalytic functions, whose theory is rightly considered in the preface ‘the wellspring of mathematical analysis.’ Organized in six parts, [with] a very rich bibliography and an index, this book is both a map of the subject and its history. Proceeding from the most elementary to the most advanced aspects, it is useful for both beginners and advanced researchers. Names such as CauchyKowalewsky (Kovalevskaya), Weierstrass, Borel, Hadamard, Puiseux, Pringsheim, Besicovitch, Bernstein, Denjoy-Carleman, Paley-Wiener, Whitney, Gevrey, Lojasiewicz, Grauert and many others are involved either by their results or by their concepts.” —Mathematical Reviews 2nd ed. 2002. XIII, 205 p. 5 illus. (Birkhäuser Advanced Texts) Hardcover ISBN 978-0-8176-4264-8 $79.95

The Implicit Function Theorem History, Theory, and Applications S. G. Krantz, Washington University, St.Louis, MO, USA; H. R. Parks, Oregon State University, Corvallis, OR, USA “This small book consists of six chapters and is entirely devoted to one of the most

important results in analysis - the implicit function theorem and its variations. The book starts with historical comments on the evolution of ideas leading to the theorem... The book will appeal to a large part of the mathematical community since everybody will find there some far going generalizations of classical results in a very readable form.” —EMS Newsletter 2002. XI, 163 p. Hardcover ISBN 978-0-8176-4285-3 $59.95

Second Edition

Gradient Flows In Metric Spaces and in the Space of Probability Measures

Vanishing and Finiteness Results in Geometric Analysis A Generalization of the Bochner Technique S. Pigola, Università dell’Insubria, Como, M. Rigoli, Università di Milano; A. G. Setti, Università dell’Insubria, Como The aim of the book is to describe very recent results involving an extensive use of analytical tools in the study of geometrical and topological properties of complete Riemannian manifolds. An extension of the Bochner technique to the non compact setting is analyzed in detail, yielding conditions which ensure that solutions of geometrically significant differential equations either are trivial (vanishing results) or give rise to finite dimensional vector spaces (finiteness results). To make up for the lack of compactness, a range of methods, from spectral theory and qualitative properties of solutions of PDEs, to comparison theorems in Riemannian geometry and potential theory, are developed. All needed tools are described in detail, often with an original approach. Some of the applications presented concern the topology at infinity of submanifolds, Lp cohomology, metric rigidity of manifolds with positive spectrum, and structure theorems for Kälher manifolds. 2008. Approx. 300 p. (Progress in Mathematics, Volume 266) Hardcover ISBN 978-3-7643-8641-2 $69.95

L. Ambrosio, N. Gigli, Scuola Normale Superiore, Pisa, Italy; G. Savaré, University of Pavia, Italy This book is devoted to a theory of gradient flows in spaces which are not necessarily endowed with a natural linear or differentiable structure. It consists of two parts, the first one concerning gradient flows in metric spaces and the second one devoted to gradient flows in the space of probability measures on a separable Hilbert space, endowed with the KantorovichRubinstein-Wasserstein distance. The two parts have some connections, due to the fact that the space of probability measures provides an important model to which the “metric” theory applies, but the book is conceived in such a way that the two parts can be read independently, the first one by the reader more interested in non-smooth analysis and analysis in metric spaces, and the second one by the reader more orientated towards the applications in partial differential equations, measure theory and probability. 2nd ed. 2008. Approx. 360 p. (Lectures in Mathematics. ETH Zürich) Softcover ISBN 978-3-7643-8721-1 $54.95

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Analysis / Operator Theory

Polynomial Convexity E. L. Stout, University of Washington, Seattle, USA This comprehensive monograph is devoted to the study of polynomially convex sets, which play an important role in the theory of functions of several complex variables. Important features of Polynomial Convexity: *Presents the general properties of polynomially convex sets with particular attention to the theory of the hulls of onedimensional sets. *Motivates the theory with numerous examples and counterexamples, which serve to illustrate the general theory and to delineate its boundaries. *Examines in considerable detail questions of uniform approximation, especially on totally real sets, for the most part on compact sets but with some attention to questions of global approximation on noncompact sets. *Discusses important applications, e.g., to the study of analytic varieties and to the theory of removable singularities for CR functions. This beautiful exposition of a rich and complex theory, which contains much material not available in other texts, is destined to be the standard reference for many years, and will appeal to all those with an interest in multivariate complex analysis. 2007. X, 439 p. (Progress in Mathematics, Volume 261) Hardcover ISBN 978-0-8176-4537-3 $79.95

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Holomorphic Morse Inequalities and Bergman Kernels Winner of the Ferran Sunyer i Balaguer Prize 2006 X. Ma, Ecole Polytechnique, Paris, France; G. Marinescu, University of Köln, Germany This book gives for the first time a selfcontained and unified approach to holomorphic Morse inequalities and the asymptotic expansion of the Bergman kernel on manifolds by using the heat kernel, and presents also various applications. The main analytic tool is the analytic localization technique in local index theory developed by Bismut-Lebeau. The book includes the most recent results in the field and therefore opens perspectives on several active areas of research in complex, Kähler and symplectic geometry. A large number of applications are included, e.g., an analytic proof of the Kodaira embedding theorem, a solution of the GrauertRiemenschneider and Shiffman conjectures, a compactification of complete Kähler manifolds of pinched negative curvature, the Berezin-Toeplitz quantization, weak Lefschetz theorems, and the asymptotics of the Ray-Singer analytic torsion. 2007. XIII, 422 p. (Progress in Mathematics, Volume 254) Hardcover ISBN 978-3-7643-8096-0 $79.95




Mathematical Analysis




An Introduction to Functions of Several Variables M. Giaquinta, Scuola Normale Superiore, Pisa, Italy; G. Modica, Università degli Studi di Firenze, Italy

A Geometric Approach to Differential Forms D. Bachman, Pitzer College, Claremont, CA, USA “[The author’s] idea is to use geometric intuition to alleviate some of the algebraic difficulties...The emphasis is on understanding rather than on detailed derivations and proofs. This is definitely the right approach in a course at this level.”— MAA Reviews “This book is intended as an elementary introduction to the notion of differential forms, written at an undergraduate level. … The book certainly has its merits and is very nicely illustrated … . It should be noted that the material, which has been tested already in the classroom, aims at three potential course tracks: a course in multivariable calculus, a course in vector calculus and a course for more advanced undergraduates (and beginning graduates).”—Mathematical Reviews 2006. XVI, 133 p. 39 illus. Softcover ISBN 978-0-8176-4499-4 $39.95

This self-contained work is an introductory presentation of basic ideas, structures, and results of differential and integral calculus for functions of several variables. The wide range of topics covered include: differential calculus of several variables, including differential calculus of Banach spaces, the relevant results of Lebesgue integration theory, differential forms on curves, a general introduction to holomorphic functions, including singularities and residues, surfaces and level sets, and systems and stability of ordinary differential equations. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis. Mathematical Analysis: An Introduction to Functions of Several Variables motivates the study of the analysis of several variables with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering. 2008. Approx. 330 p. 111 illus. Hardcover ISBN 978-0-8176-4509-0 $129.00

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Analysis / Operator Theory

Mathematical Analysis







Linear and Metric Structures and Continuity M. Giaquinta, Scuola Normale Superiore, Pisa, Italy; G. Modica, Università degli Studi di Firenze, Italy This self-contained work on linear and metric structures focuses on studying continuity and its applications to finite- and infinite-dimensional spaces. The book is divided into three parts. The first part introduces the basic ideas of linear and metric spaces, including the Jordan canonical form of matrices and the spectral theorem for self-adjoint and normal operators. The second part examines the role of general topology in the context of metric spaces and includes the notions of homotopy and degree. The third and final part is a discussion on Banach spaces of continuous functions, Hilbert spaces and the spectral theory of compact operators. Mathematical Analysis: Linear and Metric Structures and Continuity motivates the study of linear and metric structures with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering.

Functions of One Variable M. Giaquinta, Scuola Normale Superiore, Pisa, Italy; G. Modica, Università degli Studi di Firenze, Italy 2003. XII, 353 p. 196 illus. Hardcover ISBN 978-0-8176-4312-6 $94.95

Maps into manifolds and currents: area and W1,2-, W1/2-, BV-energies M. Giaquinta, Scuola Normale Superiore, Italy; D. Mucci, Università di Parma, Italy

2007. XVIII, 470 p. 128 illus. Softcover ISBN 978-0-8176-4375-1 $69.95

This volume deals with the problem of characterizing the limit points of sequences of smooth maps from the unit ball of Rn with values into a smooth boundaryless Riemannian manifold and with equibounded “integral energies”. After surveying some known results about Cartesian currents and graphs with finite area and finite boundary area, we do characterize, as in the title, weak limits of sequences of smooth maps with equibounded W 1,2-, W 1/2-, or BV-energies.

Mathematical Analysis

2006. XXII, 391 p. (Publications of the Scuola Normale Superiore / CRM Series, Volume 3) Softcover ISBN 978-88-7642-200-3 $34.95




Approximation and Discrete Processes M. Giaquinta, Scuola Normale Superiore, Pisa, Italy; G. Modica, Università degli Studi di Firenze, Italy 2005. XII, 388 p. 152 illus. Softcover ISBN 978-0-8176-4337-9 $69.95

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Mathematical Analysis




Analysis II H. Amann, Universität Zürich, Switzerland; J. Escher, Universität Hannover, Germany The second volume of this introduction into analysis deals with the integration theory of functions of one variable, the multidimensional differential calculus and the theory of curves and line integrals. The modern and clear development that started in Volume I is continued. In this way a sustainable basis is created which allows the reader to deal with interesting applications that sometimes go beyond material represented in traditional textbooks. This applies, for instance, to the exploration of Nemytskii operators which enable a transparent introduction into the calculus of variations and the derivation of the Euler-Lagrange equations. 2007. Approx. 425 p. Softcover ISBN 978-3-7643-7472-3 $79.95

Analysis I

Lecture Notes of a CIMPA Summer School held at Galatasaray University, Istanbul, 2005 R. Holzapfel, Humboldt University Berlin, Germany; A. M. Uludag, Galatasaray University, Istanbul, Turkey; M. Yoshida, Kyushu University, Fukuoka, Japan (Eds.) Contributions by D. Allcock, F. Beukers, J.A. Carlson, I.V. Dolgachev, A. Dzambic, R.-P. Holzapfel, A.N. Kochubei, S. Kondo, E. Looijenga, K. Matsumoto, T. Riedel, H. Shiga, J. Stienstra, D. Toledo, A.M. Uludag, J. Wolfart, M. Yoshida 2007. VIII, 437 p. 58 illus. (PM, Volume 260) Hardcover ISBN 978-3-7643-8283-4 $109.00

Methods of Nonlinear Analysis


H. Amann, University of Zürich, Switzerland; J. Escher, University of Hannover, Germany “It is a wonderful book that distinguishes itself by the clarity of presentation, but the fact that it is self-contained and has many exercises at various degrees of difficulty (among many other great qualities.)...” —MAA Reviews 2005. XV, 426 p. Softcover ISBN 978-3-7643-7153-1 $79.95

Arithmetic and Geometry Around Hypergeometric Functions




Applications to Differential Equations P. Drábek, University West Bohemia, Plzen, Czech Republic; J. Milota, Charles University Prague, Czech Republic In this book, the basic methods of nonlinear analysis are emphasized and illustrated in simple examples. Every considered method is motivated, explained in a general form but in the simplest possible abstract framework, and its applications are shown, particularly to boundary value problems for elementary ordinary or partial differential equations. 2007. XII, 568 p. 78 illus. (BAT) Hardcover ISBN 978-3-7643-8146-2 $89.95

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Analysis / Operator Theory

Shape-Preserving Approximation by Real and Complex Polynomials




S. G. Gal, University of Oradea, Romania This monograph presents the first comprehensive treatment in book form of shape-preserving approximation by real or complex polynomials in one or several variables. Such approximation methods are useful in many problems arising in science and engineering requiring an optimal mathematical representation of physical reality. Three different constructive methods are applicable to all four categories of shape-preserving approximation by polynomials and thus serve as ‘red lines’ for the book: Bernstein-type, Shisha-type, and convolution-type. Containing many open problems at the end of each chapter to spur future research as well as a rich and updated bibliography surveying the vast literature, the text will be useful to graduate students and researchers interested in approximation theory, mathematical analysis, numerical analysis, Computer Aided Geometric Design, robotics, data fitting, chemistry, fluid mechanics, and engineering. 2008. Approx. 340 p. Hardcover ISBN 978-0-8176-4702-5 $99.00

Holomorphic Functions in the Plane and n-dimensional Space K. Gürlebeck, Bauhaus University Weimar, Germany; K. Habetha, RWTH Aachen, Germany; W. Sprößig, TU Freiberg, Germany “The present book is very well and enthusiastically written and in many details marvellously elaborated. This is in particular the case for the typographically exposed historical remarks including photos of some of the main initiators of the number systems etc. involved. [...] This book is recommended as a text book for basic courses in complex analysis and also for self studies.” —Zentralblatt MATH 2008. Approx. 410 p. With CD-ROM. Softcover ISBN 978-3-7643-8271-1 $39.95

The Bartle-Dunford-Schwartz Integral T. V. Panchapagesan, Bangalore, India

Global Smoothness and Shape Preserving Interpolation by Classical Operators S. G. Gal, University of Oradea, Romania 2005. XIII, 146 p. 20 illus. Hardcover ISBN 978-0-8176-4387-4 $89.95

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This volume is a thorough and comprehensive treatise on vector measures. The functions to be integrated can be either [0,infinity]- or real- or complex-valued and the vector measure can take its values in arbitrary locally convex Hausdorff spaces. Moreover, the domian of the vector measure does not have to be a sigma-algebra: it can also be a delta-ring. The book contains not only a large amount of new material but also corrects various errors in well-known results available in the literature. $SSUR[S0RQRJUDßH0DWHPDW\F]QH Volume 69) Hardcover ISBN 978-3-7643-8601-6 $109.00

Recent Advances in Matrix and Operator Theory

Operator Algebras, Operator Theory and Applications

J. A. Ball, Virginia Tech, Blacksburg, VA, USA; Y. Eidelman, Tel Aviv University, Israel; W. Helton, University of California San Diego, CA, USA; V. Olshevsky, University of Connecticut, Storrs, CT, USA; J. Rovnyak, University of Virginia, Charlottesville, VA, USA (Eds.)

A. Bastos, Technical University of Lisbon, Portugal; I. Gohberg, Tel Aviv University, Ramat Aviv, Israel; A. B. Lebre, F. Speck, Technical University of Lisbon, Portugal (Eds.)

This volume comprises the proceedings of the International Workshop on Operator Theory and Its Applications held at the University of Connecticut in July 2005. 2008. Approx. 350 p. (Operator Theory: Advances and Applications, Volume 179) Hardcover ISBN 978-3-7643-8538-5 $209.00

This book is composed of three survey lecture courses and some twenty invited research papers presented to WOAT 2006 - the International Summer School and Workshop on Operator Algebras, Operator Theory and Applications, which was held at Lisbon in September 2006. The volume reflects recent developments in the area of operator algebras and their interaction with research fields in complex analysis and operator theory.

Factorization of Matrix and Operator Functions: The State Space Method

2008. Approx. 450 p. (Operator Theory: Advances and Applications, Volume 181) Hardcover ISBN 978-3-7643-8683-2 $229.00

H. Bart, Erasmus University Rotterdam, The Netherlands; I. Gohberg, Tel Aviv University, Israel; M. A. Kaashoek, A. C. Ran, Vrije Universiteit Amsterdam, The Netherlands

The Maximum Principle

This book delineates the various types of factorization problems for matrix and operator functions. The problems originate from, or are motivated by, the theory of non-selfadjoint operators, the theory of matrix polynomials, mathematical systems and control theory, the theory of Riccati equations, inversion of convolution operators, and the theory of job scheduling in operations research. The book presents a geometric principle of factorization which has its origins in the state space theory of linear input-output systems and in the theory of characteristic operator functions. 2008. XII, 409 p. (Operator Theory: Advances and Applications, Linear Operators and Linear Systems, Volume 178) Hardcover ISBN 978-3-7643-8267-4 $169.00

P. Pucci, Università degli Studi di Perugia, Italy; J. Serrin, University of Minnesota, MN, USA Maximum principles are bedrock results in the theory of second order elliptic equations. This principle, simple enough in essence, lends itself to a quite remarkable number of subtle uses when combined appropriately with other notions. Intended for a wide audience, the book provides a clear and comprehensive explanation of the various maximum principles available in elliptic theory, from their beginning for linear equations to recent work on nonlinear and singular equations. 2007. X, 234 p. (Progress in Nonlinear Differential Equations and Their Applications, Volume 73) Hardcover ISBN 978-3-7643-8144-8 $64.95

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Analysis / Operator Theory




C*-algebras and Elliptic Theory II

Nonstandard Analysis

D. Burghelea, Ohio State University, Columbus, OH, USA; R. Melrose, MIT, Cambridge, CA, USA; A. Mishchenko, E. Troitsky, Moscow State University, Russia (Eds.)

M. Väth, Freie Universität Berlin, Germany

This book consists of a collection of original, refereed research and expository articles on elliptic aspects of geometric analysis on manifolds, including singular, foliated and non-commutative spaces. The topics covered include the index of operators, torsion invariants, K-theory of operator algebras and L2-invariants. The results presented in this book, which is largely inspired and stimulated by the Atiyah-Singer index theorem, should be of interest to graduates and researchers in mathematical physics, differential topology and differential analysis. 2008. Approx. 320 p. (Trends in Mathematics) Hardcover ISBN 978-3-7643-8603-0 $139.00

This book presents an introduction into Robinson‘s nonstandard analysis. Nonstandard analysis is the application of model theory in analysis. However, the reader is not expected to have any background in model theory; instead, some background in analysis, topology, or functional analysis would be useful although the book is as much self-contained as possible and can be understood after a basic calculus course. Unlike some other texts, it does not attempt to teach elementary calculus on the basis of nonstandard analysis, but it points to some applications in more advanced analysis. Such applications can hardly be obtained by standard methods such as a deeper investigation of Hahn-Banach limits or of finitely additive measures. 2007. VIII, 252 p. Hardcover ISBN 978-3-7643-7773-1 $49.95

On the Topology of Isolated Singularities in Analytic Spaces Winner of the Ferran Sunyer i Balaguer 2005 prize J. Seade, Universidad Nacional Autónoma de México This book gives an overview of selected topics on the topology of real and complex isolated singularities, with emphasis on its relations to other branches of geometry

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and topology. The first chapters are mostly devoted to complex singularities and a myriad of results spread in a vast literature, which are presented here in a unified way, accessible to non-specialists. Among the topics are the fibration theorems of Milnor; the relation with 3-dimensional Lie groups; exotic spheres; spin structures and 3-manifold invariants; the geometry of quadrics and Arnold’s theorem which states that the complex projective plane modulo conjugation is the 4-sphere. The second part of the book studies pioneer work about real analytic singularities which arise from the topological and geometric study of holomorphic vector fields and foliations. In the low dimensional case these turn out to be related to fibred links in the 3-sphere defined by meromorphic functions. This provides new methods for constructing manifolds equipped with a rich geometry. 2006. XIV, 238 p. (Progress in Mathematics, Volume 241) Hardcover ISBN 978-3-7643-7322-1 $64.95

and exercises, motivating not only understanding on the part of the reader, but also developing the tools needed to think critically about mathematical problems. The material includes numerous examples and applications relevant to engineering students, along with some techniques to evaluate various types of integrals. “A good point of the book is the selections of questions and exercises at the end of each section. They are very carefully selected and will help students with reading comprehension and with application of the material of the current section. Most of the time the exercises progress nicely from simple applications of concepts to problems that will expand the student’s horizons.” —MAA Reviews 2006. XIII, 513 p. 109 illus. Hardcover ISBN 978-0-8176-4457-4 $59.95

Infinite Matrices and their Finite Sections

Complex Variables with Applications

An Introduction to the Limit Operator Method

S. Ponnusamy, Indian Institute of Technology, Madras, Chennai, India; H. Silverman, College of Charleston, SC, USA

M. Lindner, University of Reading, UK

Complex numbers can be viewed in several ways: as an element in a field, as a point in the plane, and as a twodimensional vector. Examined properly, each perspective provides crucial insight into the interrelations between the complex number system and its parent, the real number system. The authors explore these relationships by adopting both generalization and specialization methods to move from real variables to complex variables, and vice versa, while simultaneously examining their analytic and geometric characteristics. The engaging exposition is replete with discussions, remarks, questions,

This book is concerned with the study of infinite matrices and their approximation by matrices of finite size. The main concepts presented are invertibility at infinity (closely related to Fredholmness), limit operators, and the stability and convergence of finite matrix approximations. Concrete examples are used to illustrate the results throughout, including discrete Schrödinger operators and integral and boundary integral operators arising in mathematical physics and engineering. 2006. XV, 191 p. 12 illus. (Frontiers in Mathematics) Softcover ISBN 978-3-7643-7766-3 $49.95

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Analysis / Operator Theory

Lectures on complex analysis and analytic geometry




G. Della Sala, A. Saracco, A. Simioniuc, G. Tomassini, Scuola Normale Superiore, Italy This book is an introduction to the theory of holomorphic functions of several complex variables. It is based on the courses attended by students of mathematics at Scuola Normale Superiore of Pisa. The book is largely divided into three parts. The first one, perhaps the most curricular, deals with the domains of holomorphy and their characterizations, through different notions of convexity (holomorphic convexity, Leviconvexity and pseudoconvexity) and the Cauchy-Riemann equation. The extension of this matter to complex spaces, known as the Oka-Cartan theory, is the content of the second part. This theory systematically makes use of the local analytic geometry and of the theory of sheaves and cohomology. The last part deals with the interplay between the theory of topological algebras and the theory of holomorphic functions. Some of the advanced results in the field are overviewed, sometimes without detailed proofs, and (still) open problems are discussed. 2006. XIX, 430 p. (Publications of the Scuola Normale Superiore / Lecture Notes, Volume 3) Softcover ISBN 978-88-7642-199-0 $34.95

Extremum Problems for Eigenvalues of Elliptic Operators A. Henrot, Université Henri Poincaré, Vandoeuvre-les-Nancy, France

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“The book is a good collection of extremal problems for eigenvalues of elliptic operators and it gives a good account of the present state of research. It presents 30 open problems and is an absolutely necessary starting point for research work in this field. All proofs are strictly rigorous and the

author refers for some other proofs to the bibliography, which contains 215 references. The material is interesting for specialists in both pure and applied mathematics, and can also be used in students’ work.” —Mathematical Reviews 2006. X, 202 p. (Frontiers in Mathematics) Softcover ISBN 978-3-7643-7705-2 $49.95

Shift-invariant Uniform Algebras on Groups S. A. Grigoryan, Kazan State University, Russia; T. V. Tonev, University of Montana, Missoula, MT, USA “…this book will be useful for a wide range of analysts: the first chapters introduce basic tools of classical analysis (harmonic functions, almost periodic functions), of uniform algebras, of abstract harmonic analysis, and will be useful for beginning graduate students; the more advanced parts will interest research mathematicians and graduate students.” Zentralblatt MATH ,;S0RQRJUDßH0DWHPDW\F]QH9ROXPH  Hardcover ISBN 978-3-7643-7606-2 $99.00

Theory of Function Spaces III H. Triebel, University of Jena, Germany “This book can be considered the third volume in an impressive series of books on theory of function spaces…but at the same time it is quite self-contained…The book is…extremely well-written, and readerfriendly, and it contains an enormous amount of deep and interesting material. It is strongly recommended to anybody interested in function spaces or in any of the related areas.”—Mathematical Reviews 2006. XII, 426 p. (Monographs in Mathematics, Volume 100) Hardcover ISBN 978-3-7643-7581-2 $169.00

complete solutions for most of the problems Because they focus on what every young mathematician needs to know about real analysis, the books are ideal both as course texts and for self-study, especially for graduate students preparing for qualifying examinations. Their scope and approach will appeal to instructors and professors in nearly all areas of pure mathematics, as well as applied mathematicians working in analytic areas such as statistics, mathematical physics, and differential equations. Indeed, their clarity and breadth make them a welcome addition to the personal library of every mathematician.




Basic Real Analysis A. W. Knapp, State University of New York at Stony Brook, NY, USA 2005. XXIV, 656 p. 10 illus. (Cornerstones) Hardcover ISBN 978-0-8176-3250-2 $69.95

Advanced Real Analysis




A. W. Knapp, State University of New York at Stony Brook, NY, USA 2005. XXIV, 468 p. 6 illus. (Cornerstones) Hardcover ISBN 978-0-8176-4382-9 $59.95

Basic Real Analysis and Advanced Real Analysis systematically develop those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. These works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics. Key topics and features: * The development proceeds from the particular to the general, often introducing examples well before a theory that incorporates them * Incorporates, in the text and especially in the problems, material in which real analysis is used in algebra, in topology, in complex analysis, in probability, in differential geometry, and in applied mathematics of various kinds * The texts include many examples and hundreds of problems, and each provides a lengthy separate section giving hints or

“Basic Real Analysis and Advanced Real Analysis are two companion volumes of a comprehensive treatment unifying numerous branches of classical and functional analysis that can, with more or less assurance, be named as Real Analysis... Summing I can repeat that this volume is useful and interesting for all who deal with analysis and its applications. I suppose, any mathematical library must have a copy of this book and can recommend it for students and lecturers.” —Zentrablatt MATH 2005. XLVIII, 1176 p. 16 illus. (Cornerstones) ISBN 978-0-8176-4407-9 $89.95

Basic Real Analysis and Advanced Real Analysis Set




2005. 2 Vols. (Cornerstones) ISBN 978-0-8176-4407-9 $89.95

55

Analysis / Operator Theory

Singular Sets of Minimizers for the Mumford-Shah Functional

Indefinite Linear Algebra and Applications

Winner of the Ferran Sunyer i Balaguer prize 2004

I. Gohberg, Tel Aviv University, Israel; P. Lancaster, University of Calgary, Canada; L. Rodman, College of William and Mary, Williamsburg, USA

G. David, Université de Paris-Sud, France The Mumford-Shah functional was introduced in the 1980s as a tool for automatic image segmentation, but its study gave rise to many interesting questions of analysis and geometric measure theory. The main object under scrutiny is a free boundary K where the minimizer may have jumps. The book presents an extensive description of the known regularity properties of the singular sets K, and the techniques to get them. It is largely selfcontained, and should be accessible to graduate students in analysis. The core of the book is composed of regularity results that were proved in the last ten years and which are presented in a more detailed and unified way. 2005. XIV, 581 p. (Progress in Mathematics, Volume 233) Hardcover ISBN 978-3-7643-7182-1 $149.00

Ramsey Methods in Analysis S. A. Argyros, National Technical University, Athens, Greece; S. Todorcevic, Université Paris VII - CNRS, France, and University of Toronto, Canada “The book is carefully written with clear exposition of the material. It can be studied by graduate students who had a first course in functional analysis and are interested in either functional analysis or Ramsey theory.” —Zentralblatt MATH 2005. VI, 257 p. (Advanced Courses in Mathematics CRM Barcelona) Softcover ISBN 978-3-7643-7264-4 $54.95

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“This is a splendidly written book, one of a number by three of the world’s leading linear algebraists, that collects many results on indefinite linear algebra from the literature and puts them all in a single place. The book is based in part on a 1983 book titled Matrices and Indefinite Scalar Products by the same authors and publisher but includes many contemporary results from the journal literature and elsewhere. In fact, the ends of many of the chapters provide a guide to sources where further materials are to be found. There are some excellent exercises collected at the end of each chapter making the book ideal as a graduate-level textbook.” —SIAM Review 2005. XII, 357 p. Softcover ISBN 978-3-7643-7349-8 $59.95

Basic Classes of Linear Operators




I. Gohberg, University of Tel Aviv, Israel; S. Goldberg, University of Maryland, College Park, MD, USA; M. A. Kaashoek, Vrije Universiteit Amsterdam, The Netherlands “With a name like Gohberg–Goldberg– Kaashoek, it has got to be good. But let me count the ways. If you are interested in learning the basic theories of Hilbert and Banach spaces together with the wellknown operators that act on them, this book is for you. It is intended for advanced undergraduate and beginning graduate students in mathematics.... The volume is actually a second edition of Basic Operator Theory by Gohberg and Goldberg.... Exercises and examples have been added.... The text is well written, clear, and readable.... A student

at the specified level will have no difficulty understanding the presentation.” —SIAM Review

A Topological Introduction to Nonlinear Analysis

2003. XVII, 423 p. Softcover ISBN 978-3-7643-6930-9 $109.00

R. F. Brown, University of California, Los Angeles, USA

Harmonic Analysis, Signal Processing, and Complexity Festschrift in Honor of the 60th Birthday of Carlos A. Berenstein I. Sabadini, Politecnico di Milano, Milano, Italy; D. C. Struppa, D. F. Walnut, George Mason University, Fairfax, VA, USA (Eds.) Contributors: C.A. Berenstein; R.W. Braun; O. Calin; D-C. Chang; G. Dafni; L. Ehrenpreis; G. Kaiser; C.O. Kiselman; P. Krishnaprasad; B.Q. Li; B. Matt; R. Meise; D. Napoletani; R. Poovendran; Y. Qiao; J. Ryan; C. Sadosky; D.C. Struppa; B.A. Taylor; J. Tie; D.F. Walnut; and A. Yger. 2005. XI, 162 p. 15 illus. (Progress in Mathematics, Volume 238) Hardcover ISBN 978-0-8176-4358-4 $79.95




Second Edition

“The book is highly recommended as a text for an introductory course in nonlinear analysis and bifurcation theory... reading is fluid and very pleasant... style is informal but far from being imprecise.” Mathematical Reviews (review of the first edition) “For the topology-minded reader, the book indeed has a lot to offer: written in a very personal, eloquent and instructive style it makes one of the highlights of nonlinear analysis accessible to a wide audience.” —Monatshefte für Mathematik 2nd ed. 2004. XI, 184 p. 35 illus. Softcover ISBN 978-0-8176-3258-8 $44.95

Noncommutative Harmonic Analysis In Honor of Jacques Carmona

Introduction to Complex Analysis in Several Variables

P. Delorme, Institut de Mathématiques de Luminy, Marseille, France; M. Vergne, Ecole Polytechnique, Palaiseau, France (Eds.)

V. Scheidemann, Marburg, Germany “This is a book written with the student in mind: it offers a concise treatment of complex analysis in several variables, by focusing on special topics rather than trying to be a comprehensive treatment of the subject. (...) The main importance of this book is the fact that it fills a void: there are relatively few books on several complex variables. Any (graduate) student beginning work in this area and any instructor considering teaching a course in several complex variables should definitely take a look at Professor Scheidemann’s work.” —MAA Reviews 2005. VIII, 171 p. Softcover ISBN 978-3-7643-7490-7 $34.95

Contributors: V. Baldoni-Silva; D. Barbasch; P. Bieliavsky; N. Bopp; A. Bouaziz; P. Delorme; P. Harinck; A. Hersant; M.S. Khalgui; A.W. Knapp; B. Kostant; J. Kuttler; M. Libine; J.D. Lorch; L.A. Mantini; S.D. Miller; J.D. Novak; M.-N. Panichi; M. Pevzner; W. Rossmann; H. Rubenthaler; W. Schmid; P. Torasso; C. Torossian; E.P. van den Ban; M. Vergne; and N.R. Wallach. 2004. XVI, 509 p. 15 illus. (Progress in Mathematics, Volume 220) Hardcover ISBN 978-0-8176-3207-6 $94.00

57

Analysis / Operator Theory

An Introduction to the Uncertainty Principle Hardy’s Theorem on Lie Groups S. Thangavelu, Indian Statistical Institute, Bangalore, India “This nicely written book by Thangavelu is concerned with extensions of Hardy’s theorem to settings that arise from noncommutative harmonic analysis.... Each chapter contains several applications to the heat equation in various settings and ends with an extensive presentation of related topics, current research, detailed references to the literature, and lists of open problems. This makes the book an invaluable resource for graduate students and researchers in harmonic analysis and applied mathematics.”—SIAM Review 2004. XII, 174 p. (Progress in Mathematics, Volume 217) Hardcover ISBN 978-0-8176-4330-0 $69.95

3rd ed. 2004. XX, 476 p. 41 illus. Softcover ISBN 978-0-8176-4343-0 $89.95

Linear Integral Equations




Second Edition R. P. Kanwal, Pennsylvania State University, University Park, PA, USA 2nd ed. 1996. 332 p. Hardcover ISBN 978-0-8176-3940-2 $89.95

Reconstructive Integral Geometry V. Palamodov, Tel Aviv University, Israel

Theory and Applications

“This book is an excellent overview of the field of integral geometry with emphasis on the functional analytic and differential geometric aspects. The author proves theorems for some of the most important Radon transforms, including transforms on hyperplanes, k-planes, lines, and spheres, and he investigates incomplete (limited) data problems including microlocal analytic issues…This book contains many treasures in integral geometry…and it belongs on the shelf of any analyst or geometer who would like to see how deep functional analysis and differential geometry are used to solve important problems in integral geometry.” —Mathematical Reviews

Third Edition R. P. Kanwal, Pennsylvania State University, University Park, PA, USA

2004. IX, 164 p. (Monographs in Mathematics, Volume 98) Hardcover ISBN 978-3-7643-7129-6 $109.00

Harmonic Analysis on the Heisenberg Group S. Thangavelu, Indian Statistical Institute, Bangalore, India (Ed.) 1998. IX, 192 p. (Progress in Mathematics, Volume 159) Hardcover ISBN 978-0-8176-4050-7 $89.95

Generalized Functions

58

many new topics and [features] driven by additional examples and exercises... It presents a wealth of applications that connot be found in any other single source.” —Educational Book Review




“This fully revised edition of well-received book expands the treatment of fundamental concepts and theoretical background material delineates connections to a variety of applications in mathematical physics, elasticity, wave propagation, magnetohydrodynamics, linear systems, probability and statistics, optical control problems in economics, and more. It has

Geometry of State Spaces of Operator Algebras




E. M. Alfsen, University of Oslo, Norway; F. W. Shultz, Wellesley College, Wellesley, MA, USA “Notable results…are presented in this book in a unified way, with complete

and enlightening proofs and comments. The authors have done fine work for the mathematical community, providing a valuable toolkit for researchers interested in non-associative structures, self-adjoint operator algebras, or areas of functional analysis or mathematical physics where aspects related to convexity and ordered spaces appear….”—Zentralblatt MATH 2003. 488 p. (Mathematics: Theory & Applications) Hardcover ISBN 978-0-8176-4319-5 $89.95

State Spaces of Operator Algebras

Basic Real Analysis




H. Sohrab, Towson University, Towson, MD, USA 2003. XII, 559 p. Hardcover ISBN 978-0-8176-4211-2 $64.95

Automorphic Pseudodifferential Analysis and Higher Level Weyl Calculi A. Unterberger, Université de Reims, France




Winner of the Ferran Sunyer i Balaguer Prize 2002 2003. VIII, 246 p. (Progress in Mathematics, Volume 209) Hardcover ISBN 978-3-7643-6909-5 $114.00

Basic Theory, Orientations, and C*products E. M. Alfsen, University of Oslo, Norway; F. W. Shultz, Wellesley College, Wellesley, MA, USA

Hilbert Space Operators




A Problem Solving Approach 2001. XII, 350 p. (Mathematics: Theory & Applications) Hardcover ISBN 978-0-8176-3890-0 $79.95

C. S. Kubrusly, Catholic University of Rio de Janeiro, RJ, Brazil 2003. XIII, 149 p. Softcover ISBN 978-0-8176-3242-7 $69.95

Derivatives and Integrals of Multivariable Functions




A. Guzman, The City College of New York, NY, USA

Elements of Operator Theory

2003. X, 319 p. 41 illus. Softcover ISBN 978-0-8176-4274-7 $69.95

C. S. Kubrusly, Catholic University of Rio de Janeiro, Brazil




2001. XIII, 527 p. Hardcover ISBN 978-0-8176-4174-0 $79.95

Continuous Functions of Vector Variables




A. Guzman, The City College of New York, NY, USA 2002. X, 207 p. 26 illus. Softcover ISBN 978-0-8176-4273-0 $44.95

Global Riemannian Geometry: Curvature and Topology




S. Markvorsen, Technical University of Denmark, Lyngby, Denmark; M. Min-Oo, McMaster University, Hamilton, Ontario, Canada 2003. 100 p. (Advanced Courses in Mathematics CRM Barcelona) Softcover ISBN 978-3-7643-2170-3 $34.95

59

Analysis / Operator Theory

Real Analysis




E. DiBenedetto, Vanderbilt University, Nashville, TN USA “This is a very good book. It begins with the standard material, but also includes chapters dealing with distributions and weak derivatives, special topics (e.g., the Calderón-Zygmund decomposition theorem, the Marcinkiewicz interpolation theorem), and Sobolev spaces ... The Lebesgue integral is done in Rn and compared to the integral of Riemann... abstract measure theory and the Radon-Nykodym theorem are also treated... The author weaves together standard and non-standard material. I think this book would be of value to anyone with a serious interest in analysis. It is also suitable as a textbook.”—SIAM Review 2002. XXIV, 516 p. (Birkhäuser Advanced Texts) Hardcover ISBN 978-0-8176-4231-0 $89.95

The Radon Transform




Second Edition S. Helgason, MIT, Cambridge, MA, USA 2nd ed. 1999. XII, 188 p. 18 illus. (Progress in Mathematics, Volume 5) Hardcover ISBN 978-0-8176-4109-2 $39.95

A Concise Introduction to the Theory of Integration Third Edition D. W. Stroock, Massachusetts Institute of Technology, Cambridge, MA, USA

course and advanced calculus can be done. Strongly recommended to students as well as to teachers.”—EMS Newsletter (review of the second edition) 1998. 220 p. Hardcover ISBN 978-0-8176-4073-6 $29.95

Measure Theory and Probability




M. Adams, University of Georgia, Athens, GA, USA; V. Guillemin, MIT, Cambridge, MA, USA 1996. 228 p. Hardcover ISBN 978-0-8176-3884-9 $44.95

Advanced Calculus




A Differential Forms Approach H. M. Edwards, New York University, NY, USA “An inviting, unusual, high-level introduction to vector calculus, based solidly on differential forms. Superb exposition: informal but sophisticated, down-to-earth but general, geometrically and physically intuitive but mathematically rigorous, entertaining but serious. Remarkably diverse applications, physical and mathematical.” —The American Mathematical Monthly 1994. 528 p. Hardcover ISBN 978-0-8176-3707-1 $54.95

Measure Theory




D. L. Cohn “A number of valuable applications and a good collection of problems... A very interesting, well-informed book which draws on recent approaches not found in several commonly used texts.”—Zentralblatt MATH (review of the second edition)

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“The author succeeded in choosing the right level of generality and showed how a good combination of a measure and integration

“This book is a comprehensive and clearly written textbook on measure and integration. In the first six chapters the reader finds those basic knowledge, which form the general measure-theoretic background for analysis and probability.” —Zentralblatt MATH 1980. 388 p. Hardcover ISBN 978-0-8176-3003-4 $49.95

Differential Equations / Dynamical Systems




Vortices in the Magnetic Ginzburg-Landau Model

Vortices in Bose-Einstein Condensates

E. Sandier, Université Paris-XII Val-deMarne, Créteil, France; S. Serfaty, Courant Institute of Mathematical Sciences, New York, NY, USA

A. Aftalion, CNRS, Laboratoire JacquesLouis Lions, Paris, France

This book presents the mathematical study of vortices of the two-dimensional Ginzburg-Landau model, an important phenomenological model used to describe superconductivity. The vortices, identified as quantized amounts of vorticity of the superconducting current localized near points, are the objects of many observational and experimental studies, both past and present. The GinzburgLandau functionals considered include both the model cases with and without a magnetic field. The book acts a guide to the various branches of Ginzburg-Landau studies, provides context for the study of vortices, and presents a list of open problems in the field. Sylvia Serfaty is Winner of the European Young Investigator Award (EURYI) 2007. “All parts of this interesting book are clearly and rigorously written. A consistent bibliography is given and several open problems are detailed. This work has to be recommended.”—Zentralblatt MATH

One of the key issues related to superfluidity is the existence of vortices. In very recent experiments on Bose–Einstein condensates, vortices have been observed by rotating the trap holding the atoms. In contrast to a classical fluid for which the equilibrium velocity corresponds to solid body rotation, a quantum fluid such as a Bose–Einstein condensate can rotate only through the nucleation of quantized vortices. This monograph is dedicated to the mathematical modelling of these phenomena. The mathematical tools employed are energy estimates, Gamma convergence, and homogenization techniques. The mathematical analysis is made in the framework of the Gross–Pitaevskii energy. Results are presented and open problems related to recent experiments are explained. 2006. XII, 203 p. 18 illus. (Progress in Nonlinear Differential Equations and Their Applications, Volume 67) Hardcover ISBN 978-0-8176-4392-8 $99.00

2007. XII, 322 p. 13 illus. (Progress in Nonlinear Differential Equations and Their Applications, Volume 70) Hardcover ISBN 978-0-8176-4316-4 $119.00

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Differential Equations / Dynamical Systems

Partial Differential Equations




Second Edition

E. DiBenedetto, Vanderbilt University, Nashville, TN, USA This self-contained text offers an elementary introduction to partial differential equations (pdes), primarily focusing on linear equations, but also providing some perspective on nonlinear equations. The classical treatment is mathematically rigorous with a generally theoretical layout, though indications to some of the physical origins of pdes are made throughout. Large parts of this revised second edition have been streamlined and rewritten to incorporate years of classroom feedback, correct errors, and improve clarity. Most of the necessary background material has been incorporated into the complements and certain nonessential topics have been given reduced attention (noticeably, numerical methods) to improve the flow of presentation. The exposition is replete with examples, problems and solutions that complement the material to enhance understanding and solidify comprehension. The only prerequisites are advanced differential calculus and some basic Lp theory. The work can serve as a text for advanced undergraduates and graduate students in mathematics, physics, engineering, and the natural sciences, as well as an excellent reference for applied mathematicians and mathematical physicists. “This is a well-written, self-contained, elementary introduction to linear, partial differential equations.”—Zentralblatt MATH (review of the first edition)

62

“The author’s intent is to present an elementary introduction to pdes... In contrast to other elementary textbooks on pdes...much more material is presented

on the three basic equations: Laplace’s equation, the heat and wave equations...The presentation is clear and well organized...The text is complemented by numerous exercises and hints to proofs.” —Mathematical Reviews 2nd ed. 2008. Approx. 340 p. 10 illus. (Cornerstones) Hardcover ISBN 978-0-8176-4551-9 approx. $59.95

Functional Analysis and Evolution Equations The Günter Lumer Volume H. Amann, Universität Zürich, Switzerland; W. Arendt, Universität Ulm, Germany; M. Hieber, TU Darmstadt, Germany; F. Neubrander, Lousiana State University, Baton Rouge, LA, USA; S. Nicaise, Université Valenciennes, France; J. von Below, Université du Littoral, Calais, France (Eds.) Günter Lumer was an outstanding mathematician whose work has great influence on the research community in mathematical analysis and evolution equations. He was at the origin of the breath-taking development the theory of semigroups saw after the pioneering book of Hille and Phillips of 1957. This volume contains invited contributions presenting the state of the art of these topics and reflecting the broad interests of Günter Lumer. 2008. Approx. 660 p. Hardcover ISBN 978-3-7643-7793-9 $139.00




Dynamical Systems with Applications using Mathematica® S. Lynch, Manchester Metropolitan University, Manchester, UK The book provides an introduction to the theory of dynamical systems with the aid of the Mathematica computer algebra package. It has a very hands-on approach and takes the reader from basic theory to recently published research material. Emphasized throughout are numerous applications to biology, chemical kinetics, economics, electronics, epidemiology, nonlinear optics, mechanics, population dynamics, and neural networks. Mathematica’s symbolic, numerical, and graphical capabilities make it ideal for the study of nonlinear dynamical systems. An introductory chapter provides complete tutorials on how to use Mathematica’s text-based input commands and palettes, enabling new users to become familiar with the program, while providing a good reference source for experts. Working Mathematica notebooks will be available at http://library.wolfram.com/infocenter/ Books/AppliedMathematics/. Throughout the book, the author has focused on breadth of coverage rather than fine detail, with theorems and proofs being kept to a minimum. The first part of the book deals with continuous systems using ordinary differential equations, while the second part is devoted to the study of discrete dynamical systems. Some of the material presented is at the postgraduate level and has been influenced by the

author’s own research interests. Exercises are included at the end of every chapter. A comprehensive bibliography including textbooks and research papers rounds out the work. The book is intended for senior undergraduate and graduate students as well as working scientists in applied mathematics, the natural sciences, and engineering. Many chapters of the book are especially useful as reference material for senior undergraduate independent project work. 2007. XV, 484 p. 211 illus. Softcover ISBN 978-0-8176-4482-6 $59.95

Dynamical Systems with Applications using MAPLE




Second Edition

S. Lynch, Manchester Metropolitan University, Manchester, UK “This book covers standard material for an introduction to dynamical systems theory. Written for both advanced undergraduates and new postgraduate students, this book is split into two distinctive parts: continuous systems using ordinary differential equations and discrete dynamical systems. Lynch uses the Maple package as a tool throughout the text to help with the understanding of the subject. The book contains over 250 examples and exercises with solutions and takes a hands-on approach. There are over 300 individual figures including about 200 Maple plots, with simple commands and programs listed at the end of each chapter... This publication will provide a solid basis for both research and education in nonlinear dynamical systems.”—The Maple Reporter (review of the first edition) 2nd ed. 2008. Approx. 500 p. 350 illus. Softcover ISBN 978-0-8176-4389-8 approx. $59.95

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Differential Equations / Dynamical Systems

Dynamical Systems with Applications using MATLAB®




S. Lynch, Manchester Metropolitan University, Manchester, UK “The book is a good introduction to dynamical systems theory. ...The theory and applications are presented with the aid of the MATLAB package. Throughout the book, MATLAB is viewed as a tool for solving systems or producing exciting graphics....The MATLAB programs are kept as simple as possible and the author’s experience has shown that this method of teaching using MATLAB works well with computer laboratory classes of small sizes. I recommend ‘Dynamical Systems with Applications using MATLAB’ as a good handbook for a diverse readership: graduates and professionals in mathematics, physics, science and engineering.”—Mathematica 2004. XVIII, 462 p. 330 illus. Softcover ISBN 978-0-8176-4321-8 $59.95

Introduction to stochastic analysis and Malliavin calculus




G. D. Prato, Scuola Normale Superiore, Pisa, Italy From the contents: 1. Gaussian measures in Hilbert spaces.- 2. L2 and Sobolev spaces w.r.t. a Gaussian measure.3. Brownian Motion.- 4. Markov property of the Brownian motion.- 5. The Itô integral.6. The Itô formula.- 7. Stochastic differential equations.- 8. Transition evolution operators.- 9. Formulae of Feynman–Kac and Girsanov.- 10. One dimensional Malliavin calculus.- 11. Malliavin calculus in more dimensions.- 12. Asymptotic behaviour of the transition semigroup. 2008. Approx. 150 p. (Publications of the Scuola Normale Superiore / Lecture Notes, Volume 6) Softcover ISBN 978-88-7642-313-0 $34.95

Self-Dual Gauge Field Vortices Kolmogorov Equations for Stochastic PDEs G. Da Prato, Centre de Recerca Matemàtica, Barcelona, Spain “Many of the results presented here are appearing in book form for the first time. (...) The writing style is clear. Needless to say, the level of mathematics is high and will no doubt tax the average mathematics and physics graduate student. For the devoted student, however, this book offers an excellent basis for a 1-year course on the subject. It is definitely recommended.” —JASA Reviews 2004. VII, 182 p. (Advanced Courses in Mathematics CRM Barcelona) Softcover ISBN 978-3-7643-7216-3 $49.95

An Analytical Approach G. Tarantello, Università di Roma “Tor Vergata”, Italy In modern theoretical physics, gauge field theories are of great importance since they keep internal symmetries and account for phenomena such as spontaneous symmetry breaking, the quantum Hall effect, charge fractionalization, superconductivity and supergravity. This monograph discusses specific examples of self-dual gauge field structures, including the Chern–Simons model, the abelian–Higgs model, and Yang–Mills gauge field theory. Many open questions still remain in the field and are examined in this work in connection with Liouville-type equations and systems. 2008. Approx. 350 p. (Progress in Nonlinear Differential Equations and Their Applications, Volume 72) Hardcover ISBN 978-0-8176-4310-2 approx. $79.95

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Differential Equations, Chaos and Variational Problems V. Staicu, University of Aveiro, Portugal (Ed.) This collection of original articles and surveys written by leading experts in their fields is dedicated to Arrigo Cellina and James A. Yorke on the occasion of their 65th birthday. The volume brings the reader to the border of research in differential equations, a fast evolving branch of mathematics that, besides being a main subject for mathematicians, is one of the mathematical tools most used both by scientists and engineers. 2008. Approx. 445 p. (Progress in Nonlinear Differential Equations and Their Applications, Volume 75) Hardcover ISBN 978-3-7643-8481-4 $199.00

An Invitation to Variational Methods in Differential Equations




D. G. Costa, University of Nevada, Las Vegas, NV, USA This book is a short introductory text to variational techniques with applications to differential equations. It presents a sampling of topics in critical point theory with applications to existence and multiplicity of solutions in nonlinear problems involving ordinary differential equations (ODEs) and partial differential equations (PDEs). The concise, straightforward, user-friendly approach of this textbook will appeal to graduate students and researchers interested in differential equations, analysis, and functional analysis. 2007. XII, 138 p. 9 illus. Softcover ISBN 978-0-8176-4535-9 $49.95

Spectral Theory of Infinite-Area Hyperbolic Surfaces D. Borthwick, Emory University, Atlanta, GA, USA This book introduces geometric spectral theory in the context of infinitearea Riemann surfaces, providing a comprehensive account of dramatic recent developments in the field. These developments were prompted by advances in geometric scattering theory in the early 1990s which provided new tools for the study of resonances. Hyperbolic surfaces provide an ideal context in which to introduce these new ideas, with technical difficulties kept to a minimum. The spectral theory of hyperbolic surfaces is a point of intersection for a great variety of areas, including quantum physics, discrete groups, differential geometry, number theory, complex analysis, spectral theory, and ergodic theory. The book highlights these connections, at a level accessible to graduate students and researchers from a wide range of fields. Topics covered include an introduction to the geometry of hyperbolic surfaces, analysis of the resolvent of the Laplacian, characterization of the spectrum, scattering theory, resonances and scattering poles, the Selberg zeta function, the Poisson formula, distribution of resonances, the inverse scattering problem, Patterson-Sullivan theory, and the dynamical approach to the zeta function. 2007. XII, 356 p. 10 illus. (Progress in Mathematics, Volume 256) Hardcover ISBN 978-0-8176-4524-3 $59.95

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Differential Equations / Dynamical Systems




Fourth Edition

Linear Partial Differential Equations for Scientists and Engineers T. Myint-U, Manhattan College, New York, NY, USA; L. Debnath, University of Texas Pan-American, Edinburgh, TX, USA This significantly expanded fourth edition is designed as an introduction to the theory and applications of linear PDEs. The authors provide fundamental concepts, underlying principles, a wide range of applications, and various methods of solutions to PDEs. In addition to essential standard material on the subject, the book contains new material that is not usually covered in similar texts and reference books, including conservation laws, the spherical wave equation, the cylindrical wave equation, higherdimensional boundary-value problems, the finite element method, fractional partial differential equations, and nonlinear partial differential equations with applications. Linear Partial Differential Equations for Scientists and Engineers, Fourth Edition will primarily serve as a textbook for the first two courses in PDEs, or in a course on advanced engineering mathematics. The book may also be used as a reference for graduate students, researchers, and professionals in modern applied mathematics, mathematical physics, and engineering. Readers will gain a solid mathematical background in PDEs, sufficient to start interdisciplinary collaborative research in a variety of fields. 4th ed. 2007. XXII, 778 p. 79 illus. Hardcover ISBN 978-0-8176-4393-5 $89.95

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Nonlinear Partial Differential Equations for Scientists and Engineers




Second Edition L. Debnath, University of Texas Pan American, Edinburg, TX, USA “Nonlinear partial differential equations is an old and vast area of research. There is a big and well-developed theory as well as a huge variety of applications. It seems to be impossible to embrace this subject in a single monograph. The book of Lokenath Debnath is a quite successful attempt. It is a second edition of the book, considerably extended and revised. The author is trying to balance the deep and rigorous theory and a variety of approaches and often seminal examples. To examples, he gives the leading, more than just an illustrative, role.... The book could serve as a good selection of choices for a kernel of a graduate or even undergraduate module in Applied Mathematics or Engineering Sciences. For more fundamental courses the book is also useful, since it contains a lot of motivations and well elaborated exercises.... Overall, it is a useful book for teaching, a rich source of examples, and I am happy to have it on a shelf of my library.”—UK Nonlinear News (review of the second edition) “An exceptionally complete overview of the latest developments in the field of PDEs. There are numerous examples and the emphasis is on applications to almost all areas of science and engineering. There is truly something for everyone here... The style is clear and to the point... This is a very useful book for all scientists dealing with nonlinear phenomena. This reviewer feels that it is a very hard act to follow, and recommends it strongly for individual students, practitioners, and libraries alike. The reviewer seldom gets so enthusiastic about the books he is asked to review, but [this book] is a jewel.” —Applied Mechanics Review (review of the first edition) 2nd ed. 2005. XXII, 737 p. 77 illus. Hardcover ISBN 978-0-8176-4323-2 $79.95




Fuchsian Reduction Applications to Geometry, Cosmology and Mathematical Physics S. Kichenassamy, Université de Reims Champagne-Ardenne, Reims, France Fuchsian reduction is a method for representing solutions of nonlinear PDEs near singularities. The technique has multiple applications including soliton theory, Einstein’s equations and cosmology, stellar models, laser collapse, conformal geometry and combustion. Developed in the 1990s for semilinear wave equations, Fuchsian reduction research has grown in response to those problems in pure and applied mathematics where numerical computations fail. This work unfolds systematically in four parts, interweaving theory and applications. The case studies examined in Part III illustrate the impact of reduction techniques, and may serve as prototypes for future new applications. In the same spirit, most chapters include a problem section. Background results and solutions to selected problems close the volume. 2007. XVI, 296 p. (Progress in Nonlinear Differential Equations and Their Applications, Volume 71) Hardcover ISBN 978-0-8176-4352-2 $99.00

Nonlinear Oscillations of Hamiltonian PDEs M. Berti, Università degli Studi di Napoli “Federico II”, Italia Many partial differential equations (PDEs) that arise in physics can be viewed as

infinite-dimensional Hamiltonian systems. This monograph presents recent existence results of nonlinear oscillations of Hamiltonian PDEs, particularly of periodic solutions for completely resonant nonlinear wave equations. After introducing the reader to classical finite-dimensional dynamical system theory, including the Weinstein–Moser and Fadell–Rabinowitz bifurcation results, the author develops the analogous theory for nonlinear wave equations. The theory and applications of the Nash–Moser theorem to a class of nonlinear wave equations is also discussed together with other basic notions of Hamiltonian PDEs and number theory. The main examples of Hamiltonian PDEs presented include: the nonlinear wave equation, the nonlinear Schrödinger equation, beam equations, and the Euler equations of hydrodynamics. 2007. XIV, 180 p. 10 illus. (Progress in Nonlinear Differential Equations and Their Applications, Volume 74) Hardcover ISBN 978-0-8176-4680-6 $69.95

Phase Space Analysis of Partial Differential Equations A. Bove, Università di Bologna, Italy; F. Colombini, Università di Pisa, Italy; D. Del Santo, Università di Trieste, Italy (Eds.) This collection of original articles and surveys treats the linear and nonlinear aspects of the theory of partial differential equations. Original articles are selfcontained with full proofs; survey articles give a quick and direct introduction to selected topics evolving at a fast pace. Phase space analysis methods, including microlocal analysis, have yielded striking results in past years and have become one of the main tools of investigation. Equally important is their role in many applications to physics, for example, in quantum and spectral theories. 2007. XIV, 329 p. (Progress in Nonlinear Differential Equations and Their Applications, Volume 69) Hardcover ISBN 978-0-8176-4511-3 $139.00

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topics are related to the authors’ interests in Hilbert’s sixteenth problem, but would also be of interest to those working more generally in the qualitative theory of dynamical systems.




2007. VIII, 171 p. 12 illus. (Advanced Courses in Mathematics - CRM Barcelona) Softcover ISBN 978-3-7643-8409-8 $39.95

Superlinear Parabolic Problems Blow-up, Global Existence and Steady States P. Quittner, University of Bratislava, Slovakia; P. Souplet, Université Paris XIII, France This book is devoted to the qualitative study of solutions of superlinear elliptic and parabolic partial differential equations and systems. This class of problems contains, in particular, a number of reaction-diffusion systems which arise in various mathematical models, especially in chemistry, physics and biology. The book is self-contained and up-to-date, taking special care on the didactical preparation of the material. It is devoted to problems that are intensively studied but have not been treated thus far in depth in the book literature. 2007. XI, 584 p. (Birkhäuser Advanced Texts) Hardcover ISBN 978-3-7643-8441-8 $89.95

Limit Cycles of Differential Equations




C. Christopher, Plymouth University, UK; C. Li, Beijing University, China

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This textbook contains the lecture series originally delivered at the “Advanced Course on Limit Cycles of Differential Equations” in the Centre de Rechercha Mathematica Barcelona in 2006. The topics covered are the center-focus problem for polynomial vector fields, and the application of abelian integrals to limit cycle bifurcations. Both

Analysis and Simulation of Fluid Dynamics C. Calgaro, J. Coulombel, T. Goudon, Université Lille, Villeneuve, France (Eds.) This volume collects the contributions of a Conference held in June 2005 at the laboratoire Paul Painleve (UMR CNRS 8524) in Lille, France. The meeting was intended to review hot topics and future trends in fluid dynamics, with the objective to foster exchanges of various viewpoints (e.g. theoretical, and numerical) on the addressed questions. It comprises a collection of research articles on recent advances in the analysis and simulation of fluid dynamics. 2007. VIII, 246 p. 55 illus. (Advances in Mathematical Fluid Mechanics) Hardcover ISBN 978-3-7643-7741-0 $89.95

Singularly Perturbed BoundaryValue Problems L. Barbu, Constanta, Romania; G. Morosanu, Central European University, Budapest, Hungary 2007. XIII, 230 p. (International Series of Numerical Mathematics, Volume 156) Hardcover ISBN 978-3-7643-8330-5 $119.00

Control of Coupled Partial Differential Equations K. Kunisch, Universität Graz, Austria; G. Leugering, Universität ErlangenNürnberg, Germany; J. Sprekels, HumboldtUniversität zu Berlin, Germany; F. Tröltzsch, Technische Universität Berlin, Germany (Eds.) 2007. VI, 382 p. 54 illus. (International Series of Numerical Mathematics, Volume 155) Hardcover ISBN 978-3-7643-7720-5 $129.00

Surface Evolution Equations A Level Set Approach Y. Giga, University of Tokyo, Japan “In view of its detailed and thorough presentation this book will be a valuable source for everyone interested in the level set approach to surface evolution equations.” —Zentralblatt MATH 2006. XII, 264 p. (Monographs in Mathematics, Volume 99) Hardcover ISBN 978-3-7643-2430-8 $119.00

semilinear elliptic cproblems on Rn, bifurcation from the essential spectrum, the prescribed scalar curvature problem, nonlinear Schrödinger equations, and singularly perturbed elliptic problems in domains. These topics are presented in a systematic and unified way. 2006. IX, 183 p. (Progress in Mathematics, Volume 240) Hardcover ISBN 978-3-7643-7321-4 $59.95

Variational Problems in Materials Science G. Dal Maso, A. DeSimone, SISSA, Trieste, Italy; F. Tomarelli, Politecnico di Milano, Italy (Eds.) Contributions by K. Barmak, A. Braides, G. Buttazzo, V. Chiadò Piat, G. De Matteis, G. Del Piero, N. Desenzani, I. Fragalà, G. Francfort, A. Garroni, D. Kinderlehrer, I. Livshits, G. Palatucci, D. Percivale, P. Podio-Guidugli, M.O. Rieger, S. Ta’asan, F. Tomarelli, E. Virga, A. Visintin. 2006. X, 159 p. (Progress in Nonlinear Differential Equations and Their Applications, Volume 68) Hardcover ISBN 978-3-7643-7564-5 $119.00

Perturbation Methods and Semilinear Elliptic Problems on Rn Winner of the Ferran Sunyer i Balaguer Prize 2005

Conformal and Potential Analysis in Hele-Shaw Cells

A. Ambrosetti, A. Malchiodi, SISSA, Trieste

B. Gustafsson, Royal Institute of Technology, Stockholm, Sweden; A. Vasil’ev, University of Bergen, Norway

The aim of this monograph is to discuss several elliptic problems on Rn with two main features: they are variational and perturbative in nature, and standard tools of nonlinear analysis based on compactness arguments cannot be used in general. For these problems, a more specific approach that takes advantage of such a perturbative setting seems to be the most appropriate. The first part of the book is devoted to these abstract tools, which provide a unified frame for several applications, often considered different in nature. Such applications are discussed in the second part, and include

This monograph presents recent and new ideas arising from the study of problems of planar fluid dynamics, and which are interesting from the point of view of geometric function theory and potential theory. 2006. X, 231 p. 34 illus. (Advances in Mathematical Fluid Mechanics) Hardcover ISBN 978-3-7643-7703-8 $89.95

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Differential Equations / Dynamical Systems

Variational Methods in Shape Optimization Problems




D. Bucur, Université de Metz, Metz, France; G. Buttazzo, Università di Pisa, Pisa, Italy “The book under review deals with some variational methods to treat shape optimization problems … . The book contains a complete study of mathematical problems for scalar equations and eigenvalues, in particular regarding the existence of solutions in shape optimization. … The main goal of the book is to focus on the existence of an optimal shape, necessary conditions of optimality, and stability of optimal solutions under some prescribed kind of perturbations.”—Mathematical Reviews 2005. VIII, 216 p. 19 illus. (Progress in Nonlinear Differential Equations and Their Applications, Volume 65) Hardcover ISBN 978-0-8176-4359-1 $69.95

Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control




P. Cannarsa, C. Sinestrari, Università di Roma “Tor Vergata”, Roma, Italy 2005. XII, 306 p. (Progress in Nonlinear Differential Equations and Their Applications, Volume 58) Softcover ISBN 978-0-8176-4336-2 $69.95

Free Energy and Self-Interacting Particles T. Suzuki, Osaka University, Osaka, Toyonaka-shi, Japan The work describes the mathematical and physical principles: derivation of a series of equations, biological modeling based on biased random walks, the study of equilibrium states via the variational structure derived from the free energy, and the quantized blowup mechanism based on several PDE techniques. Suitable for researchers and graduate students of math and applied math interested in nonlinear

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PDEs in stochastic processes, cellular automatons, variational methods, and their applications to natural sciences. 2005. XIV, 366 p. 7 illus. (Progress in Nonlinear Differential Equations and Their Applications, Volume 62) Hardcover ISBN 978-0-8176-4302-7 $129.00

An introduction to the regularity theory for elliptic systems, harmonic maps and minimal graphs




M. Giaquinta, Scuola Normale Superiore, Italy; L. Martinazzi, ETH-Zentrum, Switzerland 2005. XI, 302 p. (Publications of the Scuola Normale Superiore / Lecture Notes, Volume 2) Softcover ISBN 978-88-7642-168-6 $34.95

Nonlinear Partial Differential Equations with Applications




T. Roubicek, Charles University, Praha, Czech Republic 2005. XVIII, 405 p. (International Series of Numerical Mathematics, Volume 153) Hardcover ISBN 978-3-7643-7293-4 $149.00

Parabolic Quasilinear Equations Minimizing Linear Growth Functionals Winner of the Ferran Sunyer i Balaguer Prize 2003 F. Andreu-Vaillo, Universidad de Valencia, Burjassot, Spain; V. Caselles, Universidad Pompeu Fabra, Barcelona, Spain; J. M. Mazon, Universidad de Valencia, Burjassot, Spain “This book is well written…[and] should be of interest to anyone studying image reconstruction and to anyone in PDEs trying to see what kinds of modern applications abound for the subject.”—Mathematical Reviews

“This book is devoted to PDE’s of elliptic and parabolic type associated to functionals having a linear growth in the gradient, with a special emphasis on the applications related to image restoration and nonlinear filters.... The book is written with great care, paying also a lot of attention to the bibliographical and historical notes. It is a recommended reading for all researchers interested in this field.”—Zentralblatt MATH 2004. XIV, 340 p. (Progress in Mathematics, Volume 223) Hardcover ISBN 978-3-7643-6619-3 $119.00

A Stability Technique for Evolution Partial Differential Equations A Dynamical Systems Approach V. A. Galaktionov, University of Bath, UK; J. L. Vázquez, Universidad Autonoma de Madrid, Spain 2004. XIX, 377 p. 10 illus. (Progress in Nonlinear Differential Equations and Their Applications, Volume 56) Hardcover ISBN 978-0-8176-4146-7 $99.00

Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation Laws and Well-Balanced Schemes for Sources F. Bouchut, CNRS & Ecole Normale Supérieure, Paris, France 2004. VIII, 134 p. (Frontiers in Mathematics) Softcover ISBN 978-3-7643-6665-0 $39.95

Adaptive Finite Element Methods for Differential Equations W. Bangerth, The University of Texas at Austin, TX, USA; R. Rannacher, University of Heidelberg, Germany “Most graduate students in engineering and physical sciences should be able to handle the material without excessive difficulty. The presentation is very much a tutorial approach promoting a handson experience, reinforced with practical exercises at the end of each chapter, aimed towards practitioners.... [The] present book provides a gentler introduction for the beginning graduate student or nonspecialist practitioner.”— SIAM Review 2003. VIII, 207 p. (Lectures in Mathematics. ETH Zürich) Softcover ISBN 978-3-7643-7009-1 $34.95

The Symmetry Perspective




From Equilibrium to Chaos in Phase Space and Physical Space Winner of the Ferran Sunyer i Balaguer Prize 2000 M. Golubitsky, University of Houston, TX, USA; I. Stewart, University of Warwick, Coventry, UK “[The] rich collection of examples makes the book … extremely useful for motivation and for spreading the ideas to a large Community. This [review] is far from complete and cannot reflect the authors’ unique way of presenting examples, asking questions, giving answers or forming an intuition.”—Mathematical Reviews 1st ed. 2002. Corr. 2nd printing 2003. XVII, 325 p. Softcover ISBN 978-3-7643-2171-0 $59.95

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The Symmetry Perspective From Equilibrium to Chaos in Phase Space and Physical Space M. Golubitsky, University of Houston, TX, USA; I. Stewart, University of Warwick, Coventry, UK 2002. XVII, 325 p. (Progress in Mathematics, Volume 200) Hardcover ISBN 978-3-7643-6609-4 $103.00

Advances in Dynamic Equations on Time Scales




M. Bohner, A. C. Peterson, Florida Institute of Technology, Melbourne, FL, USA (Eds.) 2003. 368 p. Hardcover ISBN 978-0-8176-4293-8 $79.95

Dynamic Equations on Time Scales




M. Bohner, University of Missouri-Rolla, Rolla, MO, USA; A. Peterson, University of Nebraska, Lincoln, NE, USA




M. Chipot, University of Zurich, Switzerland This book provides proofs of the asymptotic behaviour of solutions to various important cases of linear and nonlinear problems in the theory of elliptic and parabolic partial differential equations. It is a valuable resource for graduates and researchers in applied mathematics. Many results presented here are original and have not been published elsewhere.

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M. Chipot, University of Zurich, Switzerland “This book covers some of the main aspects of nonlinear analysis. It concentrates on stressing the fundamental ideas instead of elaborating on the intricacies of them more esoteric ones…it encompass[es] many methods of dynamical systems in quite simple and original settings. I recommend this book to anyone interested in the main and essential concepts of nonlinear analysis as well as the relevant methodologies and applications.”—Mathematical Reviews 2000. VII, 256 p. (Birkhäuser Advanced Texts) Hardcover ISBN 978-3-7643-6406-9 $67.95

Hyperbolic Systems of Conservation Laws

P. G. LeFloch, Ecole Polytechnique, Palaiseau, France 2002. X, 294 p. (Lectures in Mathematics. ETH Zürich) Softcover ISBN 978-3-7643-6687-2 $39.95

2001. X, 358 p. Hardcover ISBN 978-0-8176-4225-9 $69.95

2002. (Birkhäuser Advanced Texts) Hardcover ISBN 978-3-7643-6646-9 $59.95




The Theory of Classical and Nonclassical Shock Waves

An Introduction with Applications

l goes to plus Infinity

Elements of Nonlinear Analysis

Introduction to Partial Differential Equations with MATLAB




J. M. Cooper, University of Maryland, College Park, MD, USA “Cooper’s book stands out among a host of PDE works. It not only adequately treats traditional core partial differential equation methods but also integrates analytic solutions with numerical schemes through the implementation of Matlab routines. As an application-oriented book that provides the basic definitions, theorems, and analyses of the solutions, it contains the core topics needed for a sound background in partial differential equations.... One of the book’s

excellent features is the availability of illustrative and challenging problems, some of which have been cast in the form of MATLAB projects. Such features undoubtedly make this a suitable work for a laboratory component of an introductory PDEs course. Recommended. Undergraduates through faculty.”—Choice 1st ed. 1998. Corr. 2nd printing 2000. 556 p. 50 illus. (Applied and Numerical Harmonic Analysis) Hardcover ISBN 978-0-8176-3967-9 $64.95

Differential Galois Theory and Non-Integrability of Hamiltonian Systems Winner of the Ferran Sunyer i Balaguer Prize 1998

Numerical Methods for Conservation Laws




Second Edition R. J. LeVeque, University of Washington, Seattle, WA, USA “The computing community needs a good text on modern methods for conservation laws, and these notes provide an excellent start on that text. Equally important, LeVeque’s perspective and writing style make for wonderful reading and learning. (How often do we find important content and good writing in one book?)”—SIAM Review 2nd ed. 1992. 214 p. (Lectures in Mathematics. ETH Zürich) Softcover ISBN 978-3-7643-2723-1 $37.95

J. J. Morales Ruiz, Universitat Politecnica de Catalunya, Barcelona, Spain “...[an] account of recent work of the author and co-workers on obstructions to the complete integrability of complex Hamiltonian systems. The methods are of considerable importance to practitioners... The book provides all the needed background...and presents concrete examples in considerable detail... The final chapter...includes a fascinating account of work-in-progress by the author and his collaborators... Of particular interest...is the program of extending the differential Galois theory to higher-order variational equations... [an] excellent introduction to non-integrability methods in Hamiltonian mechanics [that] brings the reader to the forefront of research in the area.” —Mathematical Reviews 1999. 182 p. (Progress in Mathematics, Volume 179) Hardcover ISBN 978-3-7643-6078-8 $107.00

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Mathematical Physics / Physics




Integrable Systems in Celestial Mechanics D. Ó’Mathúna, Dublin Institute for Advanced Studies, Dublin, Ireland

Conformal Groups in Geometry and Spin Structures P. Anglès, Universite Paul Sabatier, Toulouse, France Conformal groups play a key role in geometry and spin structures. This book provides a self-contained overview of this important area of mathematical physics, beginning with its origins in the works of Cartan and Chevalley and progressing to recent research in spinors and conformal geometry. Key topics and features: * Focuses initially on the basics of Clifford algebras * Studies the spaces of spinors for some even Clifford algebras * Examines conformal spin geometry, beginning with an elementary study of the conformal group of the Euclidean plane * Treats covering groups of the conformal group of a regular pseudo-Euclidean space, including a section on the complex conformal group * Introduces conformal flat geometry and conformal spinoriality groups, followed by a systematic development of riemannian or pseudo-riemannian manifolds having a conformal spin structure * Examines pseudo-unitary spin structures and pseudo-unitary conformal spin structures using the Clifford algebra associated with the classical pseudounitary space * Ample exercises with many hints for solutions

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2008. XXVIII, 284 p. 40 illus. (Progress in Mathematical Physics, Volume 50) Hardcover ISBN 978-0-8176-3512-1 $99.00

This work focuses on the two integrable systems of relevance to celestial mechanics, both of which date back to the 18th century. Under discussion are the Kepler (two-body) problem and the Euler (two-fixed center) problem. The book includes a full analysis of the planar Euler problem via a clear generalization of the form of the solution in the Kepler case. It contains original insights that have hitherto not appeared in book form. 2008. 240p. (Progress in Mathematical Physics, Volume 51) Hardcover ISBN 978-0-8176-4096-5 approx. $89.95

Lectures on the ElectroWeak Interactions




R. Barbieri, Scuola Normale Superiore, Pisa, Italy The lectures presented in this book introduce students and interested readers to the entire subject in a compact way. It details the current theory of ElectroWeak interactions after one year of operation of the Large Hadron Collider at CERN in Geneva, focusing on open questions that the experiments might allow to answer. 2008. Approx. 80 p. (Publications of the Scuola Normale Superiore / Lecture Notes, Volume 5) Softcover ISBN 978-88-7642-311-6 $22.95




Planar Ising Correlations J. Palmer, University of Arizona, Tucson, AZ, USA Steady progress in recent years has been made in understanding the special mathematical features of certain exactly solvable models in statistical mechanics and quantum field theory, including the scaling limits of the 2-D Ising (lattice) model, and more generally, a class of 2-D quantum fields known as holonomic fields. New results have made it possible to obtain a detailed nonperturbative analysis of the multi-spin correlations. In particular, the book focuses on deformation analysis of the scaling functions of the Ising model, and will appeal to graduate students, mathematicians, and physicists interested in the mathematics of statistical mechanics and quantum field theory. 2007. XII, 372 p. 30 illus. (Progress in Mathematical Physics, Volume 49) Hardcover ISBN 978-0-8176-4248-8 $99.00

Rigorous Quantum Field Theory A Festschrift for Jacques Bros A. Boutet de Monvel, Université Paris VII, France; D. Buchholz, Universität Göttingen, Germany; D. Iagolnitzer, CEA/Saclay, Gifsur-Yvette, France; U. Moschella, Università dell’Insubria, Como, Italy (Eds.) Jacques Bros has greatly advanced our present understanding of rigorous quantum field theory through numerous contributions; this book arose from an international symposium held in honour of Bros on the occasion of his 70th birthday.

Key topics in this volume include: Analytic structures of Quantum Field Theory (QFT), renormalization group methods, gauge QFT, stability properties and extension of the axiomatic framework, QFT on models of curved spacetimes, QFT on noncommutative Minkowski spacetime. 2007. VI, 326 p. (Progress in Mathematics, Volume 251) Hardcover ISBN 978-3-7643-7433-4 $99.00

Quantum Spaces Poincaré Seminar 2007 B. Duplantier, CEA Saclay, Gif-sur-Yvette, France; V. Rivasseau, Université de Paris Sud, Orsay, France (Eds.) This book starts with an introduction by V. Pasquier on the usefulness of noncommutative geometry, especially in the condensed matter context of the Hall effect. This theme is further developed by A. Polychronakos, who together with L. Susskind introduced the concept of non-commutative fluids. Jean-Michel Maillet compares the experimental results on one dimensional magnetic chains to the theoretical predictions based on the algebraic Bethe Ansatz and related to quantum group symmetries that he actively developed with many collaborators. On the high energy side of noncommutative geometry the book includes two complementary reviews. A. Connes describes the striking progress recently made in gathering all the interactions and fields of the standard model into a noncommutative geometry on a simple internal space, while V. Rivasseau describes in a large review the very recent technique of renormalization of quantum field theories on non-commutative space-time, which lead to the surprising discovery of their improved short-distance behavior. 2007. IX, 227 p. 33 illus. (Progress in Mathematical Physics, Volume 53) Hardcover ISBN 978-3-7643-8521-7 $109.00

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Gravitation and Experiment

Quantum Gravity

Poincaré Seminar 2006

Mathematical Models and Experimental Bounds

T. Damour, IHES, Bures-sur-Yvette, France; B. Duplantier, CEA Saclay, Gif-sur-Yvette, France; V. Rivasseau, Université de ParisSud, Orsay, France (Eds.) This book starts with a detailed introduction to general relativity by world expert T. Damour. It includes a review of what may lie beyond by string theorist I. Antoniadis, and collects up-to-date essays on the experimental tests of this theory. Contrary to some beliefs, general relativity is now a theory extremely well confirmed by detailed experiments, including the precise timing of the double pulsar J0737-3039 explained by M. Kramer, member of the team which discovered it in 2003, and satellite missions such as Gravity Probe B described by leading team member J. Mester. The search for detecting gravitational waves is also very much under way as reviewed by J.-Y. Vinet.

The construction of a quantum theory of gravity is the most fundamental challenge confronting contemporary theoretical physics. The different physical ideas evolved in developing a theory of quantum gravity require highly advanced mathematical methods. This book provides the reader with an overview of the different mathematical attempts to quantize gravity written by leading experts in this field. Also discussed are the possible experimental bounds on quantum gravity effects. All of the contributions have been strictly refereed. The present volume emerged from the 2nd Blaubeuren Workshop “Mathematical and Physical Aspects of Quantum Gravity’’.

2007. VII, 138 p. 35 illus. (Progress in Mathematical Physics, Volume 52) Hardcover ISBN 978-3-7643-8523-1 $109.00

2007. XVI, 336 p. Hardcover ISBN 978-3-7643-7977-3 $119.00

Einstein, 1905-2005 Poincaré Seminar 2005 T. Damour, IHÉS, Bures-sur-Yvette, France; O. Darrigol, Université Denis Diderot, Paris, France; B. Duplantier, CEA - Saclay, Gif-surYvette, France; V. Rivasseau, Université Paris XI, Orsay, France (Eds.) 2006. VIII, 293 p. (Progress in Mathematical Physics, Volume 47) Hardcover ISBN 978-3-7643-7435-8 $99.00

Quantum Decoherence Poincaré Seminar 2005 B. Duplantier, CEA Saclay, Gif-sur-Yvette, France; J. Raimond, ENS Paris, France; V. Rivasseau, Université Paris XI, France (Eds.)

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B. Fauser, J. Tolksdorf, E. Zeidler, MPI for Mathematics in the Sciences, Leipzig, Germany (Eds.)

2007. VIII, 192 p. (Progress in Mathematical Physics, Volume 48) Hardcover ISBN 978-3-7643-7807-3 $89.95

Molecular Gas Dynamics Theory, Techniques, and Applications Y. Sone, Kyoto University, Kyoto, Japan “In this book the author presents a good review of the theory and the modeling of molecular gas dynamics, together with applications, based on his work with his collaborators. This book is a good reference for researchers interested in applications to kinetic theory and fluid dynamics.” —MathSciNet 2007. XII, 658 p. 179 illus. (Modeling and Simulation in Science, Engineering and Technology) Hardcover ISBN 978-0-8176-4345-4 $119.00

Continuum Mechanics using Mathematica® Fundamentals, Applications and Scientific Computing A. Romano, Università degli Studi di Napoli “Federico II”, Italy; R. Lancellotta, Politecnico di Torino, Italy; A. Marasco, Università degli Studi di Napoli “Federico II”, Italy “The book will be an invaluable reference for all those with active interest in the areas of continuum mechanics and its fundamental applications: balance laws, constitutive axioms, linear elasticity, fluid dynamics, waves, etc. It may serve as a supplement to any of the standard textbooks for undergraduate students, graduate students, and researchers in applied mathematics, mathematical physics, and engineering.” —Zentralblatt MATH 2006. XII, 388 p. 66 illus. With CD-ROM. (Modeling and Simulation in Science, Engineering and Technology) Hardcover ISBN 978-0-8176-3240-3 $79.95

Slow Rarefied Flows Theory and Application to MicroElectro-Mechanical Systems C. Cercignani, Politecnico di Milano, Italy 2006. XI, 166 p. (Progress in Mathematical Physics, Volume 41) Hardcover ISBN 978-3-7643-7534-8 $74.95

Handbook of Normal Frames and Coordinates

full, and in some cases new, proofs. A large number of examples and exercises illustrate the material. 2006. XV, 441 p. (Progress in Mathematical Physics, Volume 42) Hardcover ISBN 978-3-7643-7618-5 $125.00

Modern Differential Geometry in Gauge Theories Maxwell Fields, Volume I A. Mallios, University of Athens Panepistimioupolis, Athens, Greece This 2-volume research monograph presents a new kind of modern differential geometry approach to such physical theories as gauge theory. Sheaf theory (geometry) and sheaf cohomology (analysis) are used to explain all the machinary of classical differential geometry without any notion of smoothness. Beginning with Volume 1, the focus is on Maxwell fields. All the basic concepts of this mathematical approach are formulated and used thereafter to describe elementary particles, electromagnetism, and geometric prequantization. Maxwell fields are fully examined and classified in the language of sheaf theory and sheaf cohomology. Together the new volumes present Maxwell fields, Yang–Mills fields and general relativity. These texts contains a treasure trove of minutely detailed and rigorous computations. 2006. XVII, 293 p. Softcover ISBN 978-0-8176-4378-2 $119.00 Set price 7 approx. $99.50

B. Z. Iliev, Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria This book provides the first comprehensive and complete overview on results and methods concerning normal frames and coordinates in differential geometry. Practically all existing essential results and methods concerning normal frames and coordinates can be found in the book. Most of the results are presented in detail with

Homogenization of Partial Differential Equations V. A. Marchenko, E. Y. Khruslov, B.Verkin Institute for Low Temperature Physics and Engineering, Kharkov, Ukraine 2006. XII, 398 p. 28 illus. (Progress in Mathematical Physics, Volume 46) Hardcover ISBN 978-0-8176-4351-5 $139.00

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Mathematical Physics / Physics

Many-body physics in condensed matter systems




M. Polini, M. Tosi, Scuola Normale Superiore, Italy This volume collects the lecture notes of an introductory course on the theory of many-body systems, held at the Scuola Normale Superiore di Pisa. The book is divided into seven chapters and includes 18 appendices on specialized topics. The introductory chapter illustrates some of the longstanding problems in many-body physics. Chapters 2, 3 and 4 are mainly devoted to topics concerning electron fluids. A formal presentation of the theory of Green’s functions and linear response functions for fermions in chapter 2 is followed by a chapter on electron liquids in the normal state and by a further chapter on the magnetism of conduction electrons and strongly correlated electron fluids. Chapter 5 turns to the formal theory of Green’s functions and linear response functions for bosons. And finally, Chapters 6 and 7 are on trapped boson gases and on confined fermion gases and gaseous boson-fermion mixtures. 2006. IX, 320 p. (Publications of the Scuola Normale Superiore / Lecture Notes, Volume 4) Softcover ISBN 978-88-7642-192-1 $34.95

Computer Algebra Recipes for Mathematical Physics




R. H. Enns, Simon Fraser University, Burnaby, Canada “This textbook shows in an easy-to-read way how a computer algebra system, in this case Maple, can be used to solve problems from physics. It is suitable for undergraduate students and requires no previous knowledge of Maple.… It is a nice complement to a traditional mathematical methods in physics course, with plenty of problems for the teacher to choose from.”—Monatshefte für Mathematik

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2005. XIV, 390 p. 106 illus. With CD-ROM. Softcover ISBN 978-0-8176-3223-6 $69.95

Computer Algebra Recipes for Classical Mechanics




R. H. Enns, Simon Fraser University, Burnaby, BC, Canada; G. C. McGuire, University College of the Fraser Valley, Abbotsford, BC, Canada 2003. 280 p. 100 illus. With CD-ROM. Softcover ISBN 978-0-8176-4291-4 $59.95

Nonlinear Physics with Mathematica for Scientists and Engineers




R. H. Enns, Simon Fraser University, Burnaby, BC, Canada; G. C. McGuire, University College of the Fraser Valley, Abbotsford, BC, Canada “This book is a revision of an earlier work that looked at nonlinear physics using MAPLE® software. As with that work, Enns and McGuire incorporate theory, experiment, and numerical applications in a thorough introduction to a wide range of nonlinear topics. Also included is a CD-ROM with the needed MATHEMATICA® files. The book assumes no familiarity with nonlinear physics or MATHEMATICA® ... The authors do an extraordinary job of integrating application and theory. They provide applications from a variety of disciplines throughout the sections that introduce the theory and that look at methods of analysis and consider the various approaches to addressing nonlinear problems. It is not an exaggeration to say that this book considers all areas of interest in nonlinear analysis with solid introductions. (This reviewer, having taught the basics of nonlinear physics over the last 15 years, wishes he had had this book as a tutor.) Added to this are 33 experimental activities using MATHEMATICA® that demonstrate concepts and applied examples.”—Choice 2001. XV, 691 p. 282 illus. With CD-ROM. Hardcover ISBN 978-0-8176-4223-5 $89.95

Nonlinear Physics with MAPLE for Scientists and Engineers




R. H. Enns, Simon Fraser University, Burnaby, BC, Canada; G. C. McGuire, University College of the Fraser Valley, Abbotsford, BC, Canada “In this second edition extensive use is made of the computer algebra system, Maple® V. No prior knowledge of Maple® or of programming is assumed.” —Zentralblatt MATH 2nd ed. 2000. XV, 661 p. 282 illus. With CD-ROM. Hardcover ISBN 978-0-8176-4119-1 $89.95

Determining Spectra in Quantum Theory M. Demuth, Technische Universität Clausthal, Clausthal-Zellerfeld, Germany; M. Krishna, Institute of Mathematical Sciences, Chennai, India The spectral theory of Schrödinger operators, particularly those with random potentials, continues to be a very active field of research. This work focuses on various known criteria in the spectral theory of selfadjoint operators. Concise unified presentation is aimed at graduate students and researchers working in the spectral theory of Schrödinger operators with either fixed or random potentials. However, given the large gap that this book fills in the literature, it will serve a wider audience of mathematical physicists in its contribution to works in spectral theory.

will prove extremely useful for its target audience (advanced graduate students with an interest in this area). Moreover, it will also very much feel at home on the bookshelf of an expert.”—Mathematical Reviews 2005. X, 219 p. (Progress in Mathematical Physics, Volume 44) Hardcover ISBN 978-0-8176-4366-9 $99.00

The Quantum Hall Effect Poincaré Seminar 2004 B. Douçot, CNRS and Universités Paris VI/ VII, France; B. Duplantier, V. Pasquier, CEA - Saclay, France; V. Rivasseau, Université Parix XI, France (Eds.) 2005. 197 p. (Progress in Mathematical Physics, Volume 45) Hardcover ISBN 978-3-7643-7300-9 $94.95

Continuum Thermomechanics




A. Bermúdez de Castro, University of Santiago de Compostela, Spain 2005. XII, 209 p. (Progress in Mathematical Physics, Volume 43) Hardcover ISBN 978-3-7643-7265-1 $79.95

Quantum-Statistical Models of Hot Dense Matter Methods for Computation Opacity and Equation of State A. F. Nikiforov, V. G. Novikov, V. B. Uvarov 2005. XVII, 428 p. (Progress in Mathematical Physics, Volume 37) Hardcover ISBN 978-3-7643-2183-3 $189.00

“In my opinion, the basic idea of the monograph is to help graduate students working on spectral theory and beginning researchers in the field to build a toolkit. The book definitely has more than enough material for this purpose, some of which is quite advanced, and it is very up to date. ... In conclusion, I believe that this book

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Mathematical Physics / Physics

The Mathematics of the Bose Gas and its Condensation







E. H. Lieb, R. Seiringer, Princeton University, USA; J. P. Solovej, University of Copenhagen, Denmark; J. Yngvason, University of Vienna, Austria

F. Colombo, I. Sabadini, Politecnico di Milano, Italy; F. Sommen, Ghent University, Belgium; D. C. Struppa, George Mason University, Fairfax, USA

“The presentation provides significant insight into a large part of the current issues of interest in the physics of Bose systems and especially into the “kitchen” of several relevant mathematical techniques. As such, it is highly recommended to both advanced researchers and students preparing to work in this field.”—Mathematical Reviews

“Altogether the book is a pioneering, and quite successful, attempt to apply computational and algebraic techniques to several branches of hypercomplex analysis … The book provides a very different way to look at some important questions which arise when one tries to develop multidimensional theories.”—Mathematical Reviews

2005. VIII, 208 p. (Oberwolfach Seminars, Volume 34) Softcover ISBN 978-3-7643-7336-8 $39.95

Lectures on Clifford (Geometric) Algebras and Applications

2004. XVI, 336 p. 6 illus. (Progress in Mathematical Physics, Volume 39) Hardcover ISBN 978-0-8176-4255-6 $94.95




R. Ablamowicz, Tennessee Technological University, Cookeville, TN, USA; G. Sobczyk, Universidad de las Americas, Puebla, Mexico (Eds.) “This text contains a set of lectures presented by P. Lounesto, Introduction to Clifford Algebras; I. Porteous, Mathematical Structure of Clifford Algebras; J. Ryan, Clifford Analysis; W.E. Baylis, Applications of Clifford Algebras in Physics; J.M. Selig, Clifford Algebras in Engineering; T. Branson, Clifford Bundles and Clifford Algebras; and an appendix by R. Ablamowicz and G. Sobczyk describing software for solving different kinds of problems involving computations with Clifford algebras. Each one of the lectures is a jewel and will be appreciated [by] newcomers wanting an introduction to a rapidly developing field as well [as] by practitioners, [who] for pleasure certainly will enjoy reading the texts of those well-known experts....”—Zentralblatt MATH

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Analysis of Dirac Systems and Computational Algebra

2004. XVII, 221 p. 25 illus. Softcover ISBN 978-0-8176-3257-1 $34.95

Mathematical Theory of Diffraction A. Sommerfeld Translated by: R. Nagem, Boston University, MA, USA; M. Zampolli, NATO SACLANT Undersea Research Centre, La Spezia, Italy; G. Sandri, Boston University, MA, USA 2004. VII, 157 p. 38 illus. (Progress in Mathematical Physics, Volume 35) Hardcover ISBN 978-0-8176-3604-3 $64.95

Foundations of Classical Electrodynamics




Charge, Flux, and Metric F. W. Hehl, University of Cologne, Germany and University of Missouri, Columbia, MO; Y. N. Obukhov, University of Cologne, Germany and Moscow State University, Russia “Throughout this book, the rationalized MKS system of units is used, making analysis more intelligible, and there are many diagrams which are of great help in understanding the text. Each part of the book is followed by a copious list of references.... Also, in appropriate places there are

indications how computer algebra (REDUCE/ EXCALC) can be used.... The printing and appearance of the book are excellent.... It can be warmly recommended.” —Zentralblatt MATH 2003. XIV, 410 p. (Progress in Mathematical Physics, Volume 33) Hardcover ISBN 978-0-8176-4222-8 $79.95

A. O. Petters, Duke University, Durham, NC, USA; H. Levine, Brandeis University, Waltham, MA, USA; J. Wambsganss, University of Potsdam, Germany 2001. XXV, 603 p. 184 illus. (Progress in Mathematical Physics, Volume 21) Hardcover ISBN 978-0-8176-3668-5 $84.95

An Introduction to Dirac Operators on Manifolds J. Cnops, Gent Polytechnic, Gent, Belgium

Symmetry in Mechanics




A Gentle, Modern Introduction S. F. Singer, Haverford College, Haverford, PA, USA

2002. X, 211 p. (Progress in Mathematical Physics, Volume 24) Hardcover ISBN 978-0-8176-4298-3 $74.95

The Evolution Problem in General Relativity S. Klainerman, F. Nicolo 2002. 400 p. 20 illus. (Progress in Mathematical Physics, Volume 25) Hardcover ISBN 978-0-8176-4254-9 $89.95

Electrodynamics

Singularity Theory and Gravitational Lensing




A Modern Geometric Approach W. E. Baylis “[The book has] a nice blend of mathematical physics, fundamentals of electromagnetic theory and practical applications... It is extremely well written and contains numerous exercises and problems to help the reader gain familiarity with new concepts. Throughout... the author emphasizes the conceptual framework of electromagnetism so that the reader does not get lost in details. Such a style is very valuable in a textbook. ... The book simultaneously teaches the reader electromagnetic theory and more advanced mathematical concepts in a very concrete physical context."—Current Science 1st ed. 1998. Corr. 2nd printing 2001. 404 p. 43 illus. (Progress in Mathematical Physics, Volume 17) Hardcover ISBN 978-0-8176-4025-5 $64.95

“’Symmetry in Mechanics’ is directed to students at the undergraduate level and beyond, and offers a lovely presentation of the subject ... The book contains 122 student exercises, many of which are solved in an appendix. The solutions, especially, are valuable for showing how a mathematician approaches and solves specific problems. Using this presentation, the book removes some of the language barriers that divide the worlds of mathematics and physics.” —Physics Today 2001. XII, 193 p. 30 illus. Softcover ISBN 978-0-8176-4145-0 $39.95

Caught by Disorder Bound States in Random Media P. Stollmann, Technical University of Chemnitz, Germany 2001. XVII, 166 p. 24 illus. (Progress in Mathematical Physics, Volume 20) Hardcover ISBN 978-0-8176-4210-5 $79.95

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Probability and Statistics

An Introduction to

Queueing Theory




MODELING AND ANALYSIS IN APPLICATIONS

U. Narayan Bhat

An Introduction to Queueing Theory

Introduction to Queueing Theory may be used as a textbook by first-year graduate students and upper-level undergraduate students. With its rigorous coverage of basic material and extensive bibliography of the queueing literature, the work may also be useful to applied scientists and practitioners as a self-study reference for applications and further research. 2008. Approx. 290 p. 5 illus. (Statistics for Industry and Technology) Hardcover ISBN 978-0-8176-4724-7 $59.95

Modeling and Analysis in Applications U. N. Bhat, Professor Emeritus, Southern Methodist University, Dallas, TX, USA This introductory textbook is designed for a one-semester course on queueing theory that does not require a course in stochastic processes as a prerequisite. By integrating the necessary background on stochastic processes with the analysis of models, this book provides a sound foundational introduction to the modeling and analysis of queueing systems for a broad interdisciplinary audience of students coming from diverse disciplines, including applied mathematics, statistics, computer science, operations research, and industrial, systems, manufacturing, and communications engineering. Key features include an introductory chapter, which contains a historical account of the growth of queueing theory in the last 100 years; rigorous treatment of the foundations of basic models commonly used in applications with appropriate references for advanced topics; a chapter on modeling and analysis using computational tools; modeling exercises as a motivational tool, and review exercises covering background material on statistical distributions; minimal prerequisites: calculus with some differential equations and an undergraduate course in probability and statistics; and appendices containing essential background material.

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Introduction to Probability with Statistical Applications




G. Schay, University of Massachusetts, Boston, MA, USA Introduction to Probability with Statistical Applications targets non-mathematics students, undergraduates and graduates, who do not need an exhaustive treatment of the subject. While the presentation is rigorous and contains theorems and proofs, linear algebra is largely avoided and only a minimal amount of multivariable calculus is needed. Carefully balancing theory and applications, the exposition is motivated by clear definitions, simplified notation and techniques of statistical analysis, combined with well-chosen examples and exercises. The book is aimed at students in a variety of disciplines, including computer science, engineering, natural and social sciences. 2007. X, 318 p. 44 illus. Softcover ISBN 978-0-8176-4497-0 $39.95




Third Edition

Statistical Analysis of Extreme Values with Applications to Insurance, Finance, Hydrology and Other Fields R. Reiss, M. Thomas, University of Siegen, Germany This book provides a self-contained introduction to the parametric modeling, exploratory analysis and statistical interference for extreme values. The entire text of this third edition has been thoroughly updated and rearranged to meet the new requirements. Additional sections and chapters, elaborated on more than 100 pages, are particularly concerned with topics like dependencies, the conditional analysis and the multivariate modeling of extreme data. Parts I–III about the basic extreme value methodology remain unchanged to some larger extent, yet notable are, e.g., the new sections about “An Overview of Reduced-Bias Estimation”, “The Spectral Decomposition Methodology”, and “About Tail Independence”, and the new chapter about “Extreme Value Statistics of Dependent Random Variables”. Other new topics, e.g., a chapter about “Environmental Sciences”, are collected within Parts IV–VI. “The book is well written. It assumes a knowledge of statistics, but many of the ideas and techniques can be used by a nonstatistician. As a handbook for XTREMES, it is excellent, and I recommend it highly.” —Computing Reviews 3rd ed. 2007. XVII, 511 p. Softcover ISBN 978-3-7643-7230-9 $79.95

Advances in Mathematical and Statistical Modeling B. C. Arnold, University of California, Riverside, CA, USA; N. Balakrishnan, McMaster University, Hamilton, ON, Canada; J. M. Sarabia, University of Cantabria, Santander, Spain; R. Mínguez, University of Castilla-La Mancha, Ciudad Real, Spain (Eds.) This volume is an outgrowth of the “International Conference on Mathematical and Statistical Modeling” and covers recent advances in mathematical and statistical modeling. Applications to safety, reliability and life testing, financial modeling, quality control, general inference, as well as neural networks and computational techniques are presented. The book is divided into seven main sections, which include distribution theory and order statistics, extreme value theory, modeling in engineering, fatigue models, modeling in business and economics, optimization, and computing. The book will serve as a comprehensive reference text for the statistical, applied mathematics, engineering, and economics communities. Practitioners, researchers, and graduate students in mathematical and statistical modeling, optimization, and computing will benefit from this work. 2008. Approx. 410 p. 56 illus. (Statistics for Industry and Technology) Hardcover ISBN 978-0-8176-4625-7 $99.00

Statistical Models and Methods for Biomedical and Technical Systems F. Vonta, University of Cyprus, Nicosia, Cyprus; M. Nikulin, Université Victor Segalen Bordeaux 2, Bordeaux, France; N. Limnios, Université de Technologie de Compiègne, Compiègne, France; C. Huber-Carol, Université Paris V, Paris, France (Eds.) This book deals with the mathematical aspects of survival analysis and reliability as well as other topics, reflecting recent

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Probability and Statistics

developments in the following areas: applications in epidemiology; probabilistic and statistical models and methods in reliability; models and methods in survival analysis, longevity, aging, and degradation; accelerated life models; quality of life; new statistical challenges in genomics.

also an excellent resource of educational and training material for scientists and engineers working in research laboratories.

2008. Approx. 600 p. 55 illus. (Statistics for Industry and Technology) Hardcover ISBN 978-0-8176-4464-2 $139.00

Point Process Theory and Applications

2006. XII, 206 p. 65 illus. Softcover ISBN 978-0-8176-4398-0 $39.95




Marked Point and Piecewise Deterministic Processes

A First Course in Statistics for Signal Analysis




W. A. Woyczynski, Case Western Reserve University, Cleveland, OH, USA This essentially self-contained, deliberately compact, and user-friendly textbook is designed for a first, one-semester course in statistical signal analysis for a broad audience of students in engineering and the physical sciences. The emphasis throughout is on fundamental concepts and relationships in the statistical theory of stationary random signals, explained in a concise, yet fairly rigorous presentation. Topics and Features: Fourier series and transforms are developed from scratch, emphasizing the time-domain vs. frequency-domain duality. Basic concepts of probability theory, laws of large numbers, the stability of fluctuations law, and statistical parametric inference procedures are presented. Introduction of the fundamental concept of a stationary random signal and its autocorrelation structure. Many diverse examples as well as end-of-chapter problems and exercises. Developed by the author over the course of several years of classroom use, A First Course in Statistics for Signal Analysis may be used by junior/senior undergraduates or graduate students in electrical, systems, computer, and biomedical engineering, as well as the physical sciences. The work is

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M. Jacobsen, University of Copenhagen, Denmark “This book consists of three parts: (I) Theory, (II) Applications and (III) Appendices, that concisely summarize necessary mathematical concepts which are often found scattered among numerous texts. … The most remarkable aspect of the book is its reader-friendly structure and the style in which it has been written. The importance of this book, both from the practical and from the theoretical standpoint, is unquestionable. It will be an essential part of every mathematical library.” —Mathematical Reviews 2006. X, 328 p. (Probability and its Applications) Hardcover ISBN 978-0-8176-4215-0 $59.95

Lagrangian Probability Distributions




P. C. Consul, University of Calgary, AB, Canada; F. Famoye, Central Michigan University, Mount Pleasant, MI, USA Foreword by: S. Kotz, George Washington University, Washington, DC This book presents a comprehensive, systematic treatment of the class of Lagrangian probability distributions, along with some of its families, their properties, and important applications. Lagrangian expansions can be used to obtain numerous

useful probability models, which have been applied to real life situations including, but not limited to: branching processes, queuing processes, stochastic processes, environmental toxicology, diffusion of information, ecology, strikes in industries, sales of new products, and production targets for optimum profits. Graduate students, applied scientists and researchers in environmental statistics, reliability, sales management, epidemiology, operations research, optimization in manufacturing and marketing, and infectious disease control will benefit immensely from the various applications in the book. 2006. XX, 352 p. Hardcover ISBN 978-0-8176-4365-2 $79.95

Resampling Methods




A Practical Guide to Data Analysis Third Edition

An Introduction to Continuous-Time Stochastic Processes




Theory, Models, and Applications to Finance, Biology, and Medicine V. Capasso, D. Bakstein, Miriam Research Centre for Industrial and Applied Mathematics, Milan, Italy “This is an introductory text on continuous time stochastic processes and their applications to finance and biology. The first part of the book reviews basic probability and then covers the basic continuous time processes such as Brownian motion, point processes, etc.... The book will be useful for applied mathematicians who are not probabilists to get a quick flavour of the techniques of stochastic calculus, and for professional probabilists to get a quick flavour of the applications.” —Mathematical Reviews

P. I. Good “[The book] has a 309-item bibliography, a glossary, and author and subject indices.… [It] provides much greater depth on the methods [than other books on the same subject]. Software support is broad.” — Pharmaceutical Statistics “I enjoyed this book. The style of writing suggests that statistics is fun and exploratory (which it often is). The reader is helped and encouraged to understand the problem (how the data were obtained) and how they might analyze it using resampling methods.”—The American Statistician (review of the second edition) 3rd ed. 2005. XX, 218 p. 40 illus. Hardcover ISBN 978-0-8176-4386-7 $79.95

“The style of the text...is concise and rigorous.... Each chapter concludes with a set of exercises inviting readers to prove supplementary results and review particular aspects of the theory.... In summary, I have found this to be a useful reference text, and would recommend it to those wishing to delve in to the mathematical theory of stochastic processes.”—UK Nonlinear News 2005. XI, 343 p. 13 illus. (Modeling and Simulation in Science, Engineering and Technology) Hardcover ISBN 978-0-8176-3234-2 $79.95

Invariant Probabilities of Markov-Feller Operators and Their Supports R. Zaharopol, Mathematical Reviews, Ann Arbor, USA 2005. XII, 108 p. (Frontiers in Mathematics) Softcover ISBN 978-3-7643-7134-0 $39.95

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Laws of Small Numbers: Extremes and Rare Events Second Edition M. Falk, University of Würzburg, Germany; J. Hüsler, Universität Bern, Switzerland; R. Reiss, Universität-Gesamthochschule Siegen, Germany This book gives a mathematically oriented development of the theory of rare events underlying various applications. The second edition incorporates various new results on about 130 additional pages. Part II, added in the second edition, discusses recent developments in multivariate extreme value theory.

“A splendid book to bring home the value and importance of stochastic processes. Highly recommended.”—Choice “There are so many good introductory texts on [stochastic processes] that one can hardly hope to write a better or more attractive one. This book, however, convinced the reviewer that it very likely that the Adventures will become a widely used, popular first year graduate text on stochastic processes. The book is flexible, the motivations of deep theories are clear, the examples and exercises are interesting.” —Zentralblatt MATH 1992. 640 p. Hardcover ISBN 978-0-8176-3591-6 $69.95

2nd ed. 2004. XIII, 376 p. Softcover ISBN 978-3-7643-2416-2 $54.95

Stochastic Calculus A Probability Path




S. Resnick, Cornell University, Ithaca, NY, USA

M. Grigoriu, Cornell University, Ithaca, NY, USA

“This book is a rather comfortable probability path leading from fundamental notions of measure theory and probability theory to martingale theory, since fundamental concepts and basic theorems are always illustrated by important examples and results of additional theoretical value.” —Statistics & Decision 1st ed. 1998. 3rd printing 2003. XII, 460 p. 10 illus. Hardcover ISBN 978-0-8176-4055-2 $64.95

Adventures in Stochastic Processes




S. I. Resnick, Cornell University, Ithaca, NY, USA “Definitely the best textbook for a second course in probability now available. Written with excruciating lucidity, and with an excellent choice of exercises.”—Gian-Carlo Rota, The Bulletin of Mathematics Books

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Applications in Science and Engineering

“When familiar at least with the basics of measure theoretic probability, one may use this book to get a feel for the type of problems one tackles with the given methods and the type of results one can expect and then proceed to more detailed expositions.... The book is an impressive achievement.” —Mathematical Reviews 2003. XII, 774 p. 177 illus. Hardcover ISBN 978-0-8176-4242-6 $79.95

A Natural Introduction to Probability Theory




R. Meester, Vrije Universiteit Amsterdam, The Netherlands “Most textbooks designed for a one-year course in mathematical statistics cover probability in the first few chapters as preparation for the statistics to come. This book in some ways resembles the first

part of such textbooks: it’s all probability, no statistics. But it does the probability more fully than usual, spending lots of time on motivation, explanation, and rigorous development of the mathematics…. The exposition is usually clear and eloquent…. Overall, this is a five-star book on probability that could be used as a textbook or as a supplement.”—MAA Online 2003. XI, 191 p. Softcover ISBN 978-3-7643-2188-8 $34.95

Mathematical Finance and Probability




P. Koch Medina, SwissRe, Zürich, Switzerland; S. Merino, UBS, Zürich, Switzerland “The style of presentation will appeal to anyone who is seeking an elementary but rigorous introduction to the pricing of derivative securities. The book is written carefully and is very readable.” —Mathematical Reviews 2003. VIII, 328 p. Softcover ISBN 978-3-7643-6921-7 $59.95

Counting, Sampling and Integrating: Algorithms and Complexity M. Jerrum, University of Edinburgh, UK 2003. XI, 112 p. (Lectures in Mathematics. ETH Zürich) Softcover ISBN 978-3-7643-6946-0 $34.95

Theory and Applications of Long-Range Dependence




P. Doukhan, Université de Cergy-Pontoise, France; G. Oppenheim, Université Paris-Sud, France; M. S. Taqqu, Boston University MA, USA (Eds.) “This book is a valuable and unique collection of material on LRD. It gathers together a large amount of material; the papers and their extensive references here give a broad and current summary of the research on the topic of long-range dependence.” —Journal of Statistical Physics 2003. 736 p. 72 illus. Hardcover ISBN 978-0-8176-4168-9 $99.00

Markov Chains and Invariant Probabilities O. Hernández-Lerma, CINVESTAV-IPN, Mexico; J. B. Lasserre, LAAS-CNRS, Toulouse, France “It should be stressed that an important part of the results presented is due to the authors. . . . In the reviewer’s opinion, this is an elegant and most welcome addition to the rich literature of Markov processes.” —MathSciNet 2003. XVI, 208 p. (Progress in Mathematics, Volume 211) Hardcover ISBN 978-3-7643-7000-8 $84.95

A Stochastic Control Framework for Real Options in Strategic Valuation A. Vollert, Universität Karlsruhe (TH), Germany “The book is written in a quite self-contained manner, and gives a nice survey of the results on the subject, old and new. Many graphics are provided along with theoretical illustrations to help explain the materials throughout the book. Numerical analysis

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Probability and Statistics

as well as simulation are also provided in Chapter 6, which is particularly useful for both academic researchers and real world practitioners. Various examples are provided in the book in order to show the potential of the new framework. …Could also be used as a reference book or as a source of problems for stochastic controlists.”—Mathematical Reviews 2003. 288 p. 77 illus. Hardcover ISBN 978-0-8176-4258-7 $99.00

Handbook of Brownian Motion Facts and Formulae A. N. Borodin, Steklov Mathematical Institute, St. Petersburg, Russia; P. Salminen, Abo Akademi University, Turku, Finland 2nd ed. 2002. XV, 672 p. (Probability and its Applications) Hardcover ISBN 978-3-7643-6705-3 $176.00

Empirical Process Techniques for Dependent Data H. Dehling, University of Bochum, Germany; T. Mikosch, M. Sörensen, University of Copenhagen, Denmark (Eds.) 2002. 400 p. 2 illus. Hardcover ISBN 978-0-8176-4201-3 $98.00

Foundations of Statistical Analyses and Applications with SAS




M. Falk, University of Würzburg, Germany; F. Marohn, B. Tewes, Catholic University of Eichstätt-Ingolstadt, Eichstätt, Germany 2002. X, 402 p. Softcover ISBN 978-3-7643-6893-7 $74.95

Lévy Processes Theory and Applications O. E. Barndorff-Nielsen, University of Aarhus, Denmark; T. Mikosch, University of Copenhagen, Denmark; S. I. Resnick, Cornell University, Ithaca, NY, USA (Eds.) “This volume presents a useful summary of some of the recent scientific developments concerning Lévy processes. Both introductory and more advanced articles are included. The interested researcher will get a good overview of ‘where the action is’ whereas students will find numerous interesting research topics to work on . . . I am convinced that the text will contribute further to making stochastic models based on general Lévy processes even more popular. I, therefore, take pleasure in recommending this volume to all interested readers.”—ISI Short Book Reviews 2001. X, 415 p. 32 illus. Hardcover ISBN 978-0-8176-4167-2 $99.00

The Laplace Distribution and Generalizations A Revisit with Applications to Communications, Economics, Engineering, and Finance

S. Kotz, George Washington University, Washington, DC, USA; T. Kozubowski, University of Nevada, Reno, NV, USA; K. Podgorski, Indiana University-Purdue University, Indianapolis, IN, USA “This book is devoted to presenting properties, generalizations and applications of the Laplace distribution … This distribution is a natural and sometimes superior alternative to the normal distribution … The rich set of exercises is an integral part of the discussion.”—Zentralblatt MATH 2001. XVIII, 349 p. 37 illus. Hardcover ISBN 978-0-8176-4166-5 $89.95

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Probability with Statistical Applications




R. B. Schinazi, University of Colorado, Colorado Springs, CO, USA “This book is well-written and the presentation is clear and concise. The textbook is an introduction to probability theory and statistics. The text is intended for a one-semester course for undergraduates, but it can also serve as a basis for a highschool course. The level of the book is very elementary and in most of the chapters of the book only basic calculus is required. As promised by the author ‘theory is kept to a minimum’ and it is successfully tried to ‘minimize the difficulties students often have with calculus’.”—Zentralblatt MATH

in parallel…. The book employs several devices to aid readability…. In summary, the text is…a valuable source for the practitioner and nonstatistics major… It is well organized and well written at a difficulty level that precisely meets the target audience’s needs.” —JASA 2000. XXXV, 784 p. 13 illus. Hardcover ISBN 978-0-8176-4012-5 $89.95

Parametric Statistical Change Point Analysis J. Chen, University of Missouri-Kansas City, MO, USA; A. Gupta, Bowling Green State University, OH, USA 2000. VIII, 184 p. Hardcover ISBN 978-0-8176-4169-6 $99.00

2001. XIII, 218 p. 25 illus. Softcover ISBN 978-0-8176-4247-1 $59.95

Classical and Spatial Stochastic Processes




R. Schinazi, University of Colorado, Colorado Springs, CO, USA 1999. 190 p. Hardcover ISBN 978-0-8176-4081-1 $59.95

Analysis of Variance




Fixed, Random and Mixed Models H. Sahai, University of Puerto Rico, San Juan, Puerto Rico; M. I. Ageel, King Saud University, Abha Campus, Saudi Arabia “Intended as a text for an introductory analysis of variance service course, it requires little more than a precalculus understanding of probability, estimation, and hypothesis testing…. The student and practitioner will benefit from a well-balanced mixture of statistical theory, formulas, and explanations and the great care exercised by the authors in discussing properties and analysis of fixed, random, and mixed models

A Modern Approach to Probability Theory




B. E. Fristedt, L. F. Gray, University of Minnesota, Minneapolis, MN, USA “The book takes the reader from a relatively low level.... To the point where he or she can specialize in research topics of current interest. ...an outstanding basis for teaching a graduate course in probability theory. The exhaustive compilation of results and detailed index also make it a very useful reference text for the more advanced probabilist... a good buy for anyone looking for a very accessible and complete mathematical account of modern probability theory.”—Journal of the American Statistical Association 1996. 780 p. (Probability and its Applications) Hardcover ISBN 978-0-8176-3807-8 $79.95

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Applications / Computational Sciences and Engineering




Ideal Sequence Design in TimeFrequency Space Applications to Radar, Sonar, and Communication Systems M. An, Prometheus, Inc., Newport, RI, USA; A. K. Brodzik, The MITRE Corporation, Bedford, MA, USA; R. Tolimieri, Prometheus, Inc., Newport, RI, USA

A Software-Defined GPS and Galileo Receiver A Single-Frequency Approach K. Borre, Aalborg University, Aalborg, Denmark; D. M. Akos, University of Colorado, Boulder, CO, USA; N. Bertelsen, Klarup, Denmark; P. Rinder, Aalborg, Denmark; S. H. Jensen, Aalborg University, Aalborg, Denmark

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This book develops theory and algorithms leading to systematic waveform design in time-frequency space. The key tool employed in the work is the Zak transform, which provides a two-dimensional image for sequences, the Fourier transform, convolution, and correlation, and allows for the design of sequences directly in Zak space.

This book and companion DVD provide hands-on exploration of new technologies in the rapidly growing field of satellite navigation receivers. One of the unique features of the work is the interactive approach used, giving readers the ability to construct their own Global Navigation Systems (GNSS) receivers. A complete GPS software receiver implemented using MATLAB code as well as GPS and GIOVE-A signal records – available on the companion cross-platform DVD – allows readers to change various parameters and immediately see their effects. Optional, supplementary front-end hardware equipment may be purchased at http://ccar.colorado.edu/gnss. Supplementary course material for instructors is available at http://gps.aau.dk/softgps.

Topics and features include a rigorous mathematical development of the theory, illustrated by many examples; numerous tables, which compare signal sets satisfying good correlation properties attainable by standard communication theory methods versus Zak space methods; applications in pulse radars and sonars, multibeam radar and sonar imaging systems, remote dielectric material identification, and code division multiple-access communication systems; and a variety of mathematical and application-oriented open problems.

“The work of this platform is described in a MATLAB coding language...It is worthy to mention that Windows and LINUX can be used. The book is intended for applied mathematicians, electrical engineers, geodesists and graduate students as a reference book as well for self-study.” —Zentralblatt MATH

2008. Approx. 210 p. 40 illus. (Applied and Numerical Harmonic Analysis) Hardcover ISBN 978-0-8176-4737-7 approx. $59.95

2007. XXI, 176 p. 98 illus. With DVD. (Applied and Numerical Harmonic Analysis) Softcover ISBN 978-0-8176-4390-4 $79.95

Ideal Sequence Design in Time-Frequency Space is an excellent reference text for graduate students, researchers, and engineers in radar, sonar, and communication systems.




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Ole Christensen

Frames and Bases in Mathematics and Engineering An Introductory Course O. Christensen, Technical University of Denmark, Lyngby, Denmark Based on a streamlined presentation of the author’s successful work ‘An Introduction to Frames and Riesz Bases’, this new textbook fills a gap in the literature, developing frame theory as part of a dialogue between mathematicians and engineers. Newly added sections on applications will help mathematically oriented readers to see where frames are used in practice and engineers to discover the mathematical background for applications in their field. The primary focus of the work is on basic topics without too many side remarks making it easier for students to follow the presentation. An introductory chapter presents basic results in finite-dimensional vector spaces, enabling readers with a basic knowledge of linear algebra to understand the idea behind frames without the technical complications in infinite-dimensional spaces. Extensive exercises make the work suitable as a textbook for use in theoretical graduate courses on bases and frames or applications-oriented courses focusing on either Gabor analysis or wavelets. Frames and Bases in Mathematics and Engineering will be an excellent textbook for graduate students as well as a good reference for researchers working in pure and applied mathematics, mathematical

physics, and engineering. Practitioners working in digital signal processing who wish to understand the theory behind many modern signal processing tools may also find the book a useful self-study resource. 2008. Approx. 330 p. 14 illus. (Applied and Numerical Harmonic Analysis) Softcover ISBN 978-0-8176-4677-6 approx. $42.95

An Introduction to Frames and Riesz Bases




O. Christensen, Technical University of Denmark, Lyngby, Denmark “The book is a well-written and detailed course into the theory of bases and frames in Hilbert spaces. The composition is very clear, and the proofs are well achieved…. In the basic chapters, a large number of carefully chosen examples and exercises are included. That first part can be used in a graduate course. The material of the later chapters is more in the line of current research”—ZAA 2003. 464 p. 16 illus. (Applied and Numerical Harmonic Analysis) Hardcover ISBN 978-0-8176-4295-2 $69.95

Approximation Theory




From Taylor Polynomials to Wavelets O. Christensen, K. L. Christensen, Technical University of Denmark, Lyngby, Denmark “The authors concentrate on the presentation of main ideas and demonstrate the great influence of classical approximation theory on modern applied mathematics. This book, with many illustrative examples, is easy to read…[and] will be very useful for anyone interested in approximation theory and wavelets.” —Zentralblatt MATH 1st ed. 2004., Corr. 2nd printing 2005, Corr. 3rd printing 2006. XI, 165 p. 40 illus. (Applied and Numerical Harmonic Analysis) Softcover ISBN 978-0-8176-3600-5 $34.95

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Applications / Computational Sciences and Engineering

Representations, Wavelets and Frames A Celebration of the Mathematical Work of Lawrence Baggett P. E. Jorgensen, University of Iowa, IA, USA; K. Merrill, Colorado College, CO, USA; K. Merrill, Colorado College, CO, USA; J. Packer, University of Colorado at Boulder, CO, USA (Eds.) The work of Lawrence Baggett has had a profound impact on the field of abstract harmonic analysis and the many areas of mathematics that use its techniques. His sphere of influence ranges from purely theoretical results regarding the representations of locally compact groups to recent applications of wavelets and frames to problems in sampling theory and image compression. Contributors include: Marcin Bownik, Victor Guillemin, Bin Han, Christopher Heil, Jeff Hogan, Palle Jorgensen, Joe Lakey, Dave Larson, Gail Ratcliff, Daniel Stroock, Keith Taylor. 2009. 350 p. 10 illus. (Applied and Numerical Harmonic Analysis) Hardcover ISBN 978-0-8176-4682-0 approx. $79.95

Wavelets Through a Looking Glass




The World of the Spectrum O. Bratteli, University of Oslo, Blindern, Norway; P. Jorgensen, University of Iowa, Iowa City, IA, USA “Mere words cannot adequately describe all the great features of the book...which has something for everyone of all mathematical persuasions.... This book has quite a different perspective from the other monographs on wavelets...mainly because it emphasizes the Fourier domain as the proper “window” or “looking glass” from which one can most easily study wavelet theory.... Whatever his

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or her level of expertise with the subject, a reader of this book will never be bored.... Each chapter begins with an introductory section accessible to the layperson, often containing some historical background, and often extremely entertaining.... This is a fun book, full of exciting new results, written by two world-renowned experts in the field, which makes connections between a variety of important areas in pure and applied mathematics.”—SIAM Review 2002. XX, 424 p. 122 illus. (Applied and Numerical Harmonic Analysis) Hardcover ISBN 978-0-8176-4280-8 $69.95

Advances in Discrete Tomography and Its Applications G. T. Herman, The City University of New York, New York, NY, USA; A. Kuba, deceased (Eds.) This book provides a unified presentation of new methods, algorithms, and select applications that are the foundations of multidimensional image construction and reconstruction. The self-contained survey chapters, written by leading mathematicians, engineers, and computer scientists, present cutting-edge research and results in the field. Three main areas are covered: theoretical results, algorithms, and practical applications. Following an historical and introductory overview of the field, the book explores the various mathematical and computational problems of discrete tomography with an emphasis on new applications. 2007. XX, 392 p. 140 illus. (Applied and Numerical Harmonic Analysis) Hardcover ISBN 978-0-8176-3614-2 $99.00

Harmonic Analysis and Applications In Honor of John J. Benedetto C. Heil, Georgia Institute of Technology, Atlanta, GA, USA (Ed.) Contributors: A. Aldroubi, L. Baggett, G. Benke, C. Cabrelli, P.G. Casazza, O. Christensen, W. Czaja, M. Fickus, J.-P. Gabardo, K. Gröchenig, K. Guo, E. Hayashi, C. Heil, H.P. Heinig, J.A. Hogan, E. Kovacevic, D. Labate, J.D. Lakey, D. Larson, M.T. Leon, S. Li, W.-Q Lim, A. Lindner, U. Molter, A.M. Powell, B. Rom, E. Schulz, T. Sorrells, D. Speegle, K.F. Taylor, J. Tremain, D. Walnut, G. Weiss, E. Wilson, G. Zimmermann. 2006. XXVIII, 374 p. 13 illus. (Applied and Numerical Harmonic Analysis) Hardcover ISBN 978-0-8176-3778-1 $89.95

Time-Frequency and Time-Scale Methods Adaptive Decompositions, Uncertainty Principles, and Sampling J. A. Hogan, University of Arkansas, Fayetteville, AR, USA; J. D. Lakey, New Mexico State University, Las Cruces, NM, USA “[This book] covers an enormous range in time-frequency analysis and time-scale analysis…. [It] is about methods and ideas. The main goal is to motivate, discuss, and describe important results and new developments in time-frequency and timescale analysis. Full proofs are rarely given, but insightful sketches of proofs or at least descriptions of the underlying ideas are given for most results. This style makes it possible to cover an enormous amount of material, and indeed the book reviews the main results of (an estimated) 200 articles in some detail. ...The resulting book is like a gigantic mosaic. Each facet describes an interesting result. While neighboring facets are not necessarily

related in any formal way, the entire mosaic, when viewed from a distance, displays a coherent and magnificent picture, the picture of time-frequency and time-scale analysis.” —Bulletin of the AMS 2005. XXII, 390 p. 22 illus. (Applied and Numerical Harmonic Analysis) Hardcover ISBN 978-0-8176-4276-1 $74.95

Sampling, Wavelets, and Tomography J. J. Benedetto, University of Maryland, College Park, MD, USA; A. Zayed, DePaul University, Chicago, IL, USA (Eds.) “This volume has been compiled by the editors with a readership of mathematicians, scientists, and engineers working in signal and image processing. It is a collection of invited articles on sampling, wavelets, and tomography, three active areas in contemporary mathematics having Fourier analysis as a common root. This state-ofthe-art book not only presents new results in these research areas, but also demonstrates the role of sampling in both wavelet theory and tomography. One key feature of the book is an introductory chapter stressing the interdependence of the three main areas covered.”—Int. Mathem. Nachrichten 2004. XXI, 344 p. 50 illus. (Applied and Numerical Harmonic Analysis) Hardcover ISBN 978-0-8176-4304-1 $79.95

Modern Sampling Theory Mathematics and Applications J. J. Benedetto, University of Maryland, College Park, MD, USA; P. J. Ferreira, University of Aveiro, Portugal (Eds.) 2001. XVI, 417 p. 30 illus. (Applied and Numerical Harmonic Analysis) Hardcover ISBN 978-0-8176-4023-1 $99.00

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Applications / Computational Sciences and Engineering

Transforms and Fast Algorithms for Signal Analysis and Representations




G. Bi, Nanyang Technical University, Singapore; Y. Zeng, The University of Hong Kong “This is perhaps the best text on transforms for signal processing since Nussbaumer’s Fast Fourier Transform and Convolution Algorithms (Springer, 1982) and Elliott and Rao’s, Fast Transforms: Algorithms, Analyses, Applications (Academic Press, 1982). Its nine chapters encompass almost all the knowledge needed to apply signal processing transforms successfully in practice. It is expected that the reader has had some exposure to transforms, so the first introductory chapter is very short; it mainly provides a sort of plan of things to come.... The authors have chosen to provide proofs only to essential theorems, like the Chinese remainder theorem, a good decision for a reference book, but perhaps not so good for a textbook. However, this book does lean more towards serving as a professional reference than does the more academic Nussbaumer text. The lack of proofs felt by some readers is largely offset by an abundance of concrete examples.... In conclusion, this book is a highly practical and very welcome addition to the collection of texts on signal processing techniques and applications.”—Analog Dialogue 2004. XVIII, 422 p. 92 illus. (Applied and Numerical Harmonic Analysis) Hardcover ISBN 978-0-8176-4279-2 $79.95

Multiscale Potential Theory




With Applications to Geoscience W. Freeden, V. Michel, Technische Universität Kaiserslautern, Germany

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“The book is devoted to well-posed and ill-posed boundary-value problems arising in geoscience, elasticity, gravimetry and other areas, including satellite problems.

New mathematical methods and fast computational schemes based on harmonic analysis and wavelet transforms are developed…. The book may be used for graduate-level courses in geomathematics, applied mathematics, and geophysics. It is also an up-to-date reference text for geoscientists, applied mathematicians, and engineers.”—Zentralblatt MATH 2004. XVIII, 510 p. 127 illus. (Applied and Numerical Harmonic Analysis) Hardcover ISBN 978-0-8176-4105-4 $89.95

An Introduction to Wavelet Analysis




D. F. Walnut, George Mason University, Fairfax, VA, USA “D. Walnut’s lovely book aims at the upper undergraduate level, and so it includes relatively more preliminary material ...than is typically the case in a graduate text. It goes from Haar systems to multiresolutions, and then the discrete wavelet transform ...The applications to image compression are wonderful, and the best I have seen in books at this level. I also found the analysis of the best choice of basis, and wavelet packet, especially attractive. The later chapters include MATLAB codes. Highly recommended!”—Bulletin of the AMS Corrected 2nd printing, 2003. 2001. XII, 452 p. 66 illus. (Applied and Numerical Harmonic Analysis) Hardcover ISBN 978-0-8176-3962-4 $69.95

Foundations of Time-Frequency Analysis K. Gröchenig, University of Vienna, Vienna, Austria “Foundations of Time-Frequency Analysis provides a clear and thorough exposition of some of the fundamental results in the theory and gives some important perspectives on a rapidly growing field . . .

An important feature of the book is complete, detailed proofs of all claims and extensive motivation of topics . . . The author has chosen topics that illuminate a path toward some of the most interesting and challenging research areas in mathematical timefrequency analysis. A graduate student or researcher seeking research problems in this area can come to no better source . . . The book is definitely suitable for a graduatelevel course in mathematical time-frequency analysis. It assumes a background in real analysis, Fourier analysis and Hilbert spaces. It is also suitable for self-study, as the exposition is superb.”—Mathematical Reviews

function, statistical testing, and Bayesian methods.... The book could conveniently be used by scientists who wish to apply wavelet methods to data analysis and by graduate students as a supplementary text. Recommended. Graduates through faculty and professionals.”—Choice

2001. XV, 359 p. 14 illus. (Applied and Numerical Harmonic Analysis) Hardcover ISBN 978-0-8176-4022-4 $79.95

“This book provides an expository treatment of wavelets from a signal processing perspective. The focus is on the expansion of signals in overcomplete wavelet systems. All illustrations of the theory are generated in the framework of the Matlab toolbox wavelet signal processing workstation (WSPW) made publicly available by the author.... The last chapter is a manual for WSPW, and the whole book serves as an extended manual.” —Mathematical Reviews

Wavelets Made Easy




Y. Nievergelt, Eastern Washington University, Cheney, WA, USA 1st ed. 1999. Corr. 2nd printing 2001. 312 p. 53 illus. Hardcover ISBN 978-0-8176-4061-3 $49.95

Essential Wavelets for Data Analysis T. Ogden, Columbia University, New York, USA “As an accessible work that explains the decomposition and reconstruction of wavelet algorithms as applied to statistical data, Ogden’s book is one of the growing number on wavelets. But this book is in a class of its own: it concentrates solely on the application of wavelets to statistics and data analysis. Ogden gives a brief introduction to basic theory, and then provides generous examples of wavelets and how they are constructed. He briefly compares Fourier methods, then discusses statistical applications, such as density estimation, estimation of regression functions through the application of the convolution-type kernel

1997. 224 p. Hardcover ISBN 978-0-8176-3864-1 $67.95

Computational Signal Processing with Wavelets A. Teolis, US Naval Research Laboratory, Washington, DC

1996. 352 p. 128 illus. (Applied and Numerical Harmonic Analysis) Hardcover ISBN 978-0-8176-3909-9 $59.95

A Friendly Guide to Wavelets G. Kaiser, Center for Signals and Waves, Austin, TX, USA “The book is indeed what its title promises: A friendly guide to wavelets...In short, Kaiser’s book is excellently written and can be considered as one of the best textbooks on this topic presently available...it will enjoy wide distribution among mathematicians and physicists interested in wavelet analysis.”—Int. Math. Nachrichten 1994. 324 p. Hardcover ISBN 978-0-8176-3711-8 $49.95

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Applications / Computational Sciences and Engineering Mathematical Biology

Generalized Collocation Methods




Solutions to Nonlinear Problems N. Bellomo, Politecnico di Torino, Italia; B. Lods, Université Blaisé Pascal, Aubière, France; R. Revelli, L. Ridolfi, Politecnico di Torino, Italia

Modeling Complex Living Systems A Kinetic Theory and Stochastic Game Approach N. Bellomo, Politecnico di Torino, Italia Using tools from mathematical kinetic theory and stochastic game theory, this work deals with the modeling of large complex systems in the applied sciences, particularly those comprised of several interacting individuals whose dynamics follow rules determined by some organized, or even “intelligent” ability. The author develops new mathematical methods and tools – hopefully a “new” mathematics – toward the modeling of living systems. Such tools need to be far more complex than those dealing with systems of inert matter. The first part of the book deals with deriving general evolution equations that can be customized to particular systems of interest in the applied sciences. The second part of the book deals with various models and applications related to immunology, transportation engineering, and economics. 2008. XII, 220 p. 37 illus. (Modeling and Simulation in Science, Engineering and Technology) Hardcover ISBN 978-0-8176-4510-6 $69.95

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This book examines various mathematical tools – based on generalized collocation methods – to solve nonlinear problems related to partial differential and integrodifferential equations. Covered are specific problems and models related to vehicular traffic flow, population dynamics, wave phenomena, heat convection and diffusion, transport phenomena, and pollution. Based on a unified approach combining modeling, mathematical methods, and scientific computation, each chapter begins with several examples and problems solved by computational methods; full details of the solution techniques used are given. The last section of each chapter provides problems and exercises giving readers the opportunity to practice using the mathematical tools already presented. Although the authors make use of Mathematica®, readers may use other packages such as MATLAB® or Maple™ depending on their specific needs and software preferences. Generalized Collocation Methods is written for an interdisciplinary audience of graduate students, engineers, scientists, and applied mathematicians with an interest in modeling real-world systems by differential or operator equations. 2008. XII, 196 p. 62 illus. (Modeling and Simulation in Science, Engineering and Technology) Hardcover ISBN 978-0-8176-4525-0 $69.95

Selected Topics in Cancer Modeling Genesis, Evolution, Immune Competition, and Therapy N. Bellomo, Politecnico di Torino, Italy; M. Chaplain, University of Dundee, Scotland; E. De Angelis, Politecnico di Torino, Italy (Eds.) Applied mathematicians are becoming increasingly involved in the modeling and simulation of tumor growth, reducing the amount of experimentation necessary for drug and therapy development and shedding light on aspects of cancer dynamics that are difficult to assess experimentally. This collection of selected chapters offers a comprehensive overview of state-of-the-art mathematical methods and tools for modeling and analyzing cancer phenomena. Topics covered include stochastic evolutionary models of cancer initiation and progression, tumor cords and their response to anticancer agents, and immune competition in tumor progression and prevention Selected Topics in Cancer Modeling is an excellent reference guide for applied mathematicians, physicists, biologists, and economists interested in the modeling of complex social systems and living matter. 2008. Approx. 400 p. 100 illus. (Modeling and Simulation in Science, Engineering and Technology) Hardcover ISBN 978-0-8176-4712-4 approx. $95.00

Mathematical Methods in Biomedical Imaging and IntensityModulated Radiation Therapy (IMRT) Y. Censor, University of Haifa, Israel; M. Jiang, Peking University, Beijing, China; A. K. Louis, Universität des Saarlandes, Saarbrücken, Germany (Eds.) This book consists of research and review papers by leading experts and practitioners

in biomedical imaging and intensitymodulated radiation therapy (IMRT). The topics include mathematical aspects and practical problems in current major and emerging technologies for the diagnostic and therapeutic medicine and biology research. The contributed work signifies the interdisciplinary cooperation between mathematicians and scientists from medical physics, engineering, clinical medicine and biology, that leads to mathematically-based better solutions of practical problems in biomedical imaging and IMRT. This book is also a survey of important research directions and opportunities in mathematics induced by problems in biomedical imaging and radiation planning applications. 2008. Approx. 400 p. (Publications of the Scuola Normale Superiore / CRM Series, 6) Softcover ISBN 978-88-7642-314-7 $39.95

Mathematical Modeling of Biological Systems, Volume I Cellular Biophysics, Regulatory Networks, Development, Biomedicine, and Data Analysis A. Deutsch, L. Brusch, Technical University of Dresden, Germany; H. Byrne, University of Nottingham, UK; G. de Vries, University of Alberta, Edmonton, Canada; H. Herzel, Humboldt-Universität zu Berlin, Berlin, Germany (Eds.) This two-volume, interdisciplinary work is a unified presentation of a broad range of state-of-the-art topics in the rapidly growing field of mathematical modeling in the biological sciences. Highlighted throughout the work are mathematical and computational approaches to solving central problems in the life sciences, ranging from the organizational principles of individual cells to the dynamics of large populations. 2007. XVIII, 382 p. 120 illus. (Modeling and Simulation in Science, Engineering and Technology) Hardcover ISBN 978-0-8176-4557-1 $109.00

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Applications / Computational Sciences and Engineering

Mathematical Modeling of Biological Systems, Volume II Epidemiology, Evolution and Ecology, Immunology, Neural Systems and the Brain, and Innovative Mathematical Methods A. Deutsch, Technical University of Dresden, Germany; R. Bravo de la Parra, University of Alcala, Madrid, Spain; R. J. de Boer, O. Diekmann, Utrecht University, The Netherlands; P. Jagers, Chalmers University of Technology, Göteborg, Sweden; E. Kisdi, University of Helsinki, Finland; M. Kretzschmar, University of Bielefeld, Germany; P. Lansky, Academy of Sciences of the Czech Republic, Prague, Czech Republic; H. Metz, University of Leiden, The Netherlands (Eds.) 2008. XVIII, 390 p. 119 illus. (Modeling and Simulation in Science, Engineering and Technology) Hardcover ISBN 978-0-8176-4555-7 $109.00

Cellular Automaton Modeling of Biological Pattern Formation Characterization, Applications, and Analysis A. Deutsch, Technical University of Dresden, Germany; S. Dormann, University of Osnabrück, Germany “The book is a good starting point for scientists and students [who] would like to move into the field of studying effects of spatial pattern formation in biology. The introductory chapters are fun reading.... The introduction to the lattice-gas method is thorough and sound, and the array of applications of the method to systems of biological pattern formation is impressive and inspiring.... ”—Mathematical Biosciences 2005. XXVI, 334 p. 131 illus. (Modeling and Simulation in Science, Engineering and Technology) Hardcover ISBN 978-0-8176-4281-5 $89.95

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Modeling of Biological Materials F. Mollica, Universita di Ferrara, Ferrara, Italy; L. Preziosi, Politecnico di Torino, Torino, Italy; K. Rajagopal, University of Texas A&M, College Station, TX, USA (Eds.) This unique collection highlights the central role played by modeling in general, and the modeling of mechanical considerations that have an effect on living matter. The volume collects several survey papers by actively working specialists, dealing with some of the most important problems – both theoretical and practical – in biomechanics. Written in a user-friendly style, these papers clearly explain both the biomedical and mechanical backgrounds associated with complex phenomena. This book may be used in interdisciplinary introductory courses covering various biomechanical topics for graduate students in applied mathematics, engineering, and biomedicine. 2007. XV, 357 p. 71 illus. (Modeling and Simulation in Science, Engineering and Technology) Hardcover ISBN 978-0-8176-4410-9 $89.95

Mathematical Modeling of Complex Biological Systems A Kinetic Theory Approach A. Bellouquid, University Cadi Ayad, Ecole Nationale des Sciences Appliquées, Safi, Morocco; M. Delitala, Politecnico di Torino, Italy 2006. X, 188 p. 47 illus. (Modeling and Simulation in Science, Engineering and Technology) Hardcover ISBN 978-0-8176-4395-9 $79.95

Variational problems in transport theory with mass concentration F. Santambrogio, Université Paris Dauphine, Paris, France This book examines variational problems involving optimal transportation of probability measures, in competition

with concentration effects. It presents some problems where measures have to be selected minimizing transport costs between them, but satisfying some concentration criteria, with possible applications to urban planning. The book also covers optimization problems where the concentration or diffusion phenomena occurs directly at the level of the transportation structure. 2008. Approx. 225 p. (Publications of the Scuola Normale Superiore / Theses, Volume 4) Softcover ISBN 978-88-7642-312-3 $24.95

engineering, meteorology, biology, chemistry, materials science, nanotechnology, and pharmacy. Written by leading specialists in their respective fields, this book presents an overview of recent developments in the field of mathematical kinetic theory with a focus on modeling complex systems, emphasizing both mathematical properties and their physical meaning. 2007. XIII, 271 p. 26 illus. (Modeling and Simulation in Science, Engineering and Technology) Hardcover ISBN 978-0-8176-4489-5 $79.95

Hemodynamical Flows Transport Equations in Biology B. Perthame, Ecole Normale Supérieure, Paris, France This book presents models written as partial differential equations and originating from various questions in population biology, such as physiologically structured equations, adaptive dynamics, and bacterial movement. Its purpose is to derive appropriate mathematical tools and qualitative properties of the solutions. The book further contains many original PDE problems originating in biosciences. 2007. VIII, 198 p. 28 illus. (Frontiers in Mathematics) Softcover ISBN 978-3-7643-7841-7 $49.95

Transport Phenomena and Kinetic Theory Applications to Gases, Semiconductors, Photons, and Biological Systems C. Cercignani, Politecnico di Milano, Milano, Italy; E. Gabetta, Università degli Studi di Pavia, Pavia, Italy (Eds.)




Modeling, Analysis and Simulation G. P. Galdi, University of Pittsburgh, PA, USA; R. Rannacher, Universität Heidelberg, Germany; A. M. Robertson, University of Pittsburgh, PA, USA; S. Turek, Universität Dortmund, Germany This book surveys results on the physical and mathematical modeling as well as the numerical simulation of hemodynamical flows, i.e., of fluid and structural mechanical processes occurring in the human blood circuit. The topics treated are continuum mechanical description, choice of suitable liquid and wall models, mathematical analysis of coupled models, numerical methods for flow simulation, parameter identification and model calibration, fluidsolid interaction, mathematical analysis of piping systems, particle transport in channels and pipes, artificial boundary conditions, and many more. Hemodynamics is an area of active current research, and this book provides an entry into the field for graduate students and researchers. 2007. Approx. 510 p. (Oberwolfach Seminars, Volume 37) Softcover ISBN 978-3-7643-7805-9 $49.95

The study of kinetic equations related to gases, semiconductors, photons, traffic flow, and other systems has developed rapidly in recent years because of its role as a mathematical tool in areas such as

99

Applications / Computational Sciences and Engineering Mathematical Finance

finance have been studied intensively in recent years, many theoretical and practical financial aspects have yet to be explored. This volume presents current research and survey articles focusing on various numerical methods in finance. The book is designed for the academic community and will also serve professional investors. 2004. VI, 435 p. 15 illus. Hardcover ISBN 978-0-8176-3219-9 $89.95

Advances in Mathematical Finance M. C. Fu, University of Maryland, College Park, MD, USA; R. A. Jarrow, Cornell University, Ithaca, NY, USA; J. J. Yen, Vanderbilt University, Nashville, TN, USA; R. J. Elliott, University of Calgary, AB, Canada (Eds.) Contributors: H. Albrecher, D.C. Brody, P. Carr, E. Eberlein, R.J. Elliott, M.C. Fu, H. Geman, M. Heidari, A. Hirsa, L.P. Hughston, R.A. Jarrow, X. Jin, W. Kluge, S.A. Ladoucette, A. Macrina, D.B. Madan, F. Milne, M. Musiela, P. Protter, W. Schoutens, E. Seneta, K. Shimbo, R. Sircar, J. van der Hoek, M.Yor, T. Zariphopoulou 2007. XXVIII, 340 p. 41 illus. (Applied and Numerical Harmonic Analysis) Hardcover ISBN 978-0-8176-4544-1 $79.95

Handbook of Computational and Numerical Methods in Finance S. T. Rachev, University of California, Santa Barbara, CA, USA (Ed.)

100

The subject of numerical methods in finance is a discipline at the intersection of probability theory, finance, and numerical analysis. The methods employed bridge the gap between financial theory and computational practice, and provide solutions for complex problems that are difficult to solve by traditional analytical methods. Although numerical methods in

Computational Financial Mathematics using MATHEMATICA®




Optimal Trading in Stocks and Options S. Stojanovic, University of Cincinnati, OH, USA “It is an innovative approach and is very useful for students and practitioners in finance to learn how to use mathematics for investment analysis.”—Mathematical Reviews 2003. XI, 481 p. 250 illus. Hardcover ISBN 978-0-8176-4197-9 $79.95

Advances in Dynamic Games Applications to Economics, Management Science, Engineering, and Environmental Management A. Haurie, ORDECSYS, Chêne-Bougeries, Switzerland; S. Muto, Institute of Technology of Tokyo, Japan; L. A. Petrosjan, State University of St. Petersburg, Russia; T. Raghavan, University of Illinois at Chicago, IL, USA (Eds.) The paradigms of dynamic games play an important role in the development of multiagent models in engineering, economics, and management science. The applicability of their concepts stems from the ability to encompass situations with uncertainty, incomplete information, fluctuating coalition structure, and coupled constraints imposed

on the strategies of all the players. This book – an outgrowth of the 10th International Symposium on Dynamic Games – presents current developments of the theory of dynamic games and its applications to various domains, in particular energyenvironment economics and management sciences. 2006. XIX, 420 p. 55 illus. (Annals of the International Society of Dynamic Games, Volume 8) Hardcover ISBN 978-0-8176-4500-7 $99.00

numerical examples, complete with Maple code.... In summary, this book seems like an essential reference for the experts (which I’m not). More importantly, this is an interesting book for the curious (which I am). In this case, you’ll probably learn many interesting things from this book. If you teach numerical analysis or approximation theory, then this book will give you some good examples to discuss in class.”—MAA Reviews (review of second edition) 2nd ed. 2006. XXII, 266 p. 36 illus. Hardcover ISBN 978-0-8176-4372-0 $59.95

Numerical-Computational Math Symbolic-Numeric Computation D. Wang, Beihang University, Beijing, China and Université Pierre et Marie Curie, Paris; L. Zhi, Chinese Academy of Sciences, Beijing (Eds.) 2007. VIII, 394 p. 38 illus. (Trends in Mathematics) Hardcover ISBN 978-3-7643-7983-4 $99.00

Nexus Network Journal 9,2 Architecture and Mathematics Editor-in-chief: K. Williams, Torino, Italy 2008. 382 p. (Nexus Network Journal, Volume 9,2) Softcover ISBN 978-3-7643-8444-9 $64.95

Elementary Functions

Methods of Applied Mathematics with a MATLAB Overview




J. H. Davis, Queen’s University, Kingston, ON, Canada “Overall, this textbook has an attractive format with lots of figures, programs, and formulas, and it presents, in a very traditional way, a body of material that is fundamental in applied mathematics, science, and engineering. It would make an excellent textbook for courses focused around Fourier analysis and applications to differential equations.”—SIAM Review 2004. XII, 721 p. 246 illus. (Applied and Numerical Harmonic Analysis) Hardcover ISBN 978-0-8176-4331-7 $89.95




Algorithms and Implementation Second Edition J. Muller, CNRS-Laboratoire LIP, Lyon, France “There a few classic books on algorithms for computing elementary functions.... These books focused on software implementation using polynomial approximations. Perhaps Muller’s book is destined to become a new classic in this subject, but only time will tell.... Muller’s book contains few theorems and even fewer proofs. It does contain many

Statistics and Analysis of Shapes




H. Krim, North Carolina State University, Raleigh, NC, USA; A. Yezzi, Jr., Georgia Institute of Technology, Atlanta, GA, USA (Eds.) The subject of pattern analysis and recognition pervades many aspects of our daily lives, including user authentication in banking, object retrieval from databases in the consumer sector, and the omnipresent

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surveillance and security measures around sensitive areas. Shape analysis, a fundamental building block in many approaches to these applications, is also used in statistics, biomedical applications (Magnetic Resonance Imaging), and many other related disciplines. With contributions from some of the leading experts and pioneers in the field, this self-contained, unified volume is the first comprehensive treatment of theory, methods, and algorithms available in a single resource. Developments are discussed from a rapidly increasing number of research papers in diverse fields, including the mathematical and physical sciences, engineering, and medicine. 2006. XI, 395 p. 143 illus. (Modeling and Simulation in Science, Engineering and Technology) Hardcover ISBN 978-0-8176-4376-8 $79.95

Neural Networks and Sea Time Series Reconstruction and Extreme-Event Analysis B. Tirozzi, University of Rome “La Sapienza,” Rome, Italy; S. Puca, European Meteorological Satellite Org., Rome, Italy; S. Pittalis, A. Bruschi, S. Morucci, E. Ferraro, University of Rome “La Sapienza,” Rome, Italy; S. Corsini, Agenzia per la Protezione dell’Ambiente e per i Servizi Tecnici, Rome, Italy Increasingly, neural networks are used and implemented in a wide range of fields and have become useful tools in probabilistic analysis and prediction theory. This book – unique in the literature – studies the application of neural networks to the analysis of time series of sea data, namely significant wave heights and sea levels. The particular problem examined as a starting point is the reconstruction of missing data, a general problem that appears in many cases of data analysis.This careful blend of theory

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and applications is an excellent introduction to the use of artificial neural networks, which may encourage readers to try analogous approaches in other important application areas. 2006. XII, 180 p. 64 illus. (Modeling and Simulation in Science, Engineering and Technology) Hardcover ISBN 978-0-8176-4347-8 $89.95

Optimal Stopping and FreeBoundary Problems G. Peskir, The University of Manchester, UK; A. Shiryaev, Steklov Mathematical Institute, Moscow, Russia This book discloses a fascinating connection between optimal stopping problems in probability and free-boundary problems. It focuses on key examples and the theory of optimal stopping is exposed at its basic principles in discrete and continuous time covering martingale and Markovian methods. Methods of solution explained range from change of time, space, and measure, to more recent ones such as local time-space calculus and nonlinear integral equations. A chapter on stochastic processes makes the material more accessible. 2006. XXII, 500 p. (Lectures in Mathematics. ETH Zürich) Hardcover ISBN 978-3-7643-2419-3 $59.95

Applied Laplace Transforms and z-Transforms for Scientists and Engineers




Engineering


A Computational Approach Using a Mathematica Package U. Graf, Hochschule für Technik und Architektur, Biel, Switzerland “This book is a very good tool for scientists and engineers that work in the fields of applications, especially on practical problems leading to ordinary differential equations which could be solved through Laplace transformation.”—Zentralblatt MATH 2004. X, 500 p. With CD-ROM. Hardcover ISBN 978-3-7643-2427-8 $119.00

Numerical Methods for Scientists and Engineers




H. Antia, Tata Institute of Fundamental Research, Mumbai, India 2nd ed. 2002. XXII, 842 p. With CD-ROM. Hardcover ISBN 978-3-7643-6715-2 $69.95

Numerical Analysis




W. Gautschi “The book reads like an unfolding story... Topics are motivated with great care and ingenuity that might be given to establishing the drive behind characters in a good novel... Clarity is never sacrificed for elegance. Above all, the pace is always lively and brisk, the writing concise, and the author never lets the exposition bog down... Both the theoretical problems and machine assignments are a great resource... This is a stylish, lucid, and engaging book... [It] successfully conveys the author’s interest and experience in the subject to the reader.”—SIAM Review 1996. 524 p. Hardcover ISBN 978-0-8176-3895-5 $84.95

Algebra and Analysis for Engineers and Scientists A. N. Michel, University of Notre Dame, IN, USA; C. J. Herget, Herget Associates, Alameda, CA, USA Written for graduate and advanced undergraduate students in engineering and science, this classic book focuses primarily on set theory, algebra, and analysis. Useful as a course textbook, for self-study, or as a reference, the work is intended to familiarize engineering and science students with a great deal of pertinent and applicable mathematics in a rapid and efficient manner without sacrificing rigor. The book is divided into three parts: set theory, algebra, and analysis. It offers a generous number of exercises integrated into the text and features applications of algebra and analysis that have a broad appeal. Supplementary material for students and instructors is available at http://Michel.Herget.net “This book is a useful compendium of the mathematics of (mostly) finite-dimensional linear vector spaces (plus two final chapters on infinite-dimensional spaces), which do find increasing application in many branches of engineering and science…. The treatment is thorough; the book will certainly serve as a valuable reference.”—American Scientist 2007. XIV, 486 p. 48 illus. Softcover ISBN 978-0-8176-4706-3 $49.95

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Integral Methods in Science and Engineering




Techniques and Applications C. Constanda, University of Tulsa, OK, USA; S. Potapenko, University of Waterloo, ON, Canada (Eds.) This self-contained work illustrates the application of integral methods to diverse problems in mathematics, physics, biology, and engineering. The thirty two chapters of the book contain state-of-the-art information on current research in a variety of important practical disciplines. The problems examined arise in real-life processes and phenomena, and the solution techniques range from theoretical integral equations to finite and boundary elements. Specific topics covered include spectral computations, atmospheric pollutant dispersion, vibration of drilling masts, bending of thermoelastic plates, homogenization, equilibria in nonlinear elasticity, modeling of syringomyelia, fractional diffusion equations, operators on Lipschitz domains, systems with concentrated masses, transmission problems, equilibrium shape of axisymmetric vesicles, boundary layer theory, and many more. Integral Methods in Science and Engineering is a useful and practical guide to a variety of topics of interest to pure and applied mathematicians, physicists, biologists, and civil and mechanical engineers, at both the professional and graduate student level. 2008. XVI, 298 p. 62 illus. Hardcover ISBN 978-0-8176-4670-7 $89.95

Atmospheric and Space Flight Dynamics Modeling and Simulation with MATLAB® and Simulink® A. Tewari, Indian Institute of Technology, Kanpur, India Modern aerospace vehicles, such as the space shuttle, other launch vehicles, and long-range ballistic missiles, do not discriminate between atmospheric and space flight. Most texts on flight dynamics, however, make this artificial distinction and therefore do not simultaneously cover aircraft and spacecraft. Bridging this gap in the literature, Atmospheric and Space Flight Dynamics is a unified presentation, demonstrating that the two disciplines have actually evolved from the same set of physical principles. 2007. XX, 556 p. 207 illus. (Modeling and Simulation in Science, Engineering and Technology) Hardcover ISBN 978-0-8176-4437-6 $89.95 Softcover Edition ISBN 978-0-8176-4373-7 $59.95

Fundamentals of Multibody Dynamics




Theory and Applications

Engineering and Scientific Computing with Scilab Gomez, C. (Ed.) ;;9SRYHUßJVZLWK&'520+DUGFRYHU ISBN 978-0-8176-4009-5 $79.95

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F. Amirouche, University of Illinois, Chicago, USA “This textbook offers a comprehensive exposition of contemporary multibody dynamics elaborated by an expert in and an experienced teacher of the field. There are five features that distinguish this publication:

comprehensivity, orientation towards computer implementation, utilization of matrix algebra, teaching-by-examples methodology, and embedding in the author’s own research accomplishments.... [T]his is an excellent textbook for undergraduate, graduate, and doctoral students of mechanical engineering, industrial physics and robotics; it may also be recommended as a reference text for researchers in these areas.”—Mathematical Reviews 2006. XVIII, 686 p. 216 illus. Hardcover ISBN 978-0-8176-4236-5 $129.00

Analytical Methods in Anisotropic Elasticity




with Symbolic Computational Tools O. Rand, Technion - Israel Institute of Technology, Haifa, Israel; V. Y. Rovenski, University of Haifa, Israel

J. Abonyi, B. Feil, Pannon University, Hungary The aim of this book is to illustrate that advanced fuzzy clustering algorithms can be used not only for partitioning the data. They can also be used for visualization, regression, classification and time-series analysis, hence fuzzy cluster analysis is a good approach to solve complex data mining and system identification problems. This book is oriented towards undergraduate and postgraduate students and is well suited for teaching purposes.

A Graph-Theoretic Approach to Enterprise Network Dynamics


W. S. Slaughter, University of Pittsburgh, PA, USA “There is a good balance between theory and practical applications…[the] approach acknowledges the basic concepts of continuum mechanics without burdening the presentation with excessive generalities. The assumptions required to obtain linear results from nonlinear results are clearly described. This enables students to clearly understand the limitations of linear results…the book includes a good range of discussion and examples…to motivate and complement the theory…[it] is written in a clear style…[and] can be recommended as a good example of a modern textbook in this field.” —Applied Mechanics Review 2002. XVI, 543 p. 36 illus. Hardcover ISBN 978-0-8176-4117-7 $89.95

Cluster Analysis for Data Mining and System Identification

2007. XVIII, 303 p. 120 illus. Hardcover ISBN 978-3-7643-7987-2 $129.00

2005. XVIII, 451 p. 167 illus. With CD-ROM. Softcover ISBN 978-0-8176-4272-3 $79.95

The Linearized Theory of Elasticity

Computer Science

H. Bunke, University of Bern, Switzerland; P. J. Dickinson, M. Kraetzl, Defense Science and Technology Organization, Adelaide, SA, Australia; W. D. Wallis, Southern Illinois University, Carbondale, IL, USA This monograph treats the application of numerous graph-theoretic algorithms to a comprehensive analysis of dynamic enterprise networks. Network dynamics analysis yields valuable information about network performance, efficiency, fault prediction, cost optimization, indicators and warnings. Based on many years of applied research of generic network dynamics, this work covers a number of elegant applications (including many new and experimental results) to motivate network analysts, practitioners and researchers alike. The material is also suitable for graduate courses addressing state-of-theart applications of graph theory in analysis

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of dynamic communication networks, dynamic databasing, and knowledge management.

cryptography, provable security for public key schemes, and efficient and secure public-key cryptosystems.

2007. XIII, 225 p. 110 illus. (Progress in Computer Science and Applied Logic (PCS), Volume 24) Hardcover ISBN 978-0-8176-4485-7 $69.95

2005. VIII, 237 p. (Advanced Courses in Mathematics CRM Barcelona) Softcover ISBN 978-3-7643-7294-1 $49.95

Quantum Information and Many Body Quantum Systems

An Introduction to Data Structures and Algorithms

M. Ericsson, University of Cambridge, UK (Ed.)

J. Storer, Brandeis University, Waltham, MA, USA

In the last years a growing attention has been dedicated to many body quantum systems from the point of view of quantum information. Indeed, the need of understanding the characteristics of a realistic quantum information device leads necessarily to the study of many body quantum systems. This book gives a selection of current research topics in the field of quantum information for many body quantum systems together with open problems.

“Intended as a teaching aid for college and graduate-level courses on data structures, the material in this book has been aligned to support the lecture style. All the algorithms in the book are provided in pseudocode, so that students can implement the algorithms in a programming language of their choice. The book addresses basic as well as advanced algorithms in data structures, with introductory but adequate material about parallel computing models also provided... At the end of each chapter, there are sample exercises with solutions that help students to test their understanding of the book. There are also unsolved exercises that can be of use to instructors for course assignments... Each chapter also includes notes at the end, providing a good summary of the topics covered, which is very useful for students taking the course. The author has done a commendable job in outlining various algorithms for a problem, and also in comparing their merits... [The] approach of the book is easy to understand for students with a strong mathematical background.” —ACM Computing Reviews

2008. Approx. 400 p. (Publications of the Scuola Normale Superiore / CRM Series, Volume 5) Softcover ISBN 978-88-7642-307-9 $39.95

Contemporary Cryptology




D. Catalano, Ecole Normale Supérieure, Paris, France; R. Cramer, CWI, Amsterdam, The Netherlands; I. Damgard, University of Aarhus, Denmark; G. Di Crescenzo, Telcorida Technologies, Inc., Morristown, NJ, USA; D. Pointcheval, Ecole Normale Supérieure, Paris, France; T. Takagi, Future University Hakodate, Hokkaiodo, Japan The aim of this text is to treat selected topics of the subject of contemporary cryptology, structured in five quite independent but related themes: Efficient distributed computation modulo a shared secret, multiparty computation, modern

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2002. XVII, 599 p. 186 illus. Hardcover ISBN 978-0-8176-4253-2 $79.95




An Introduction to Quantum Computing Algorithms




A. O. Pittenger, University of Maryland, Baltimore, MD, USA “If you have a general (fuzzy) background on quantum physics and on computer science, I recommend reading this book.... It is well written, easy to read, with many illustrating examples, and many exercises.” —Zentralblatt MATH 1st ed. 2000. Corr. 2nd printing 2001. XII, 138 p. (Progress in Computer Science and Applied Logic, Volume 19) Hardcover ISBN 978-0-8176-4127-6 $54.95

Automata Theory and its Applications




B. Khoussainov, University of Auckland, New Zealand; A. Nerode, Cornell University, Ithaca, NY, USAQ “The aim of this book is to present a theory of several types of automata and applications of these facts in logic, concurrency and algebra. ...The book contains suitable material for a two-semester course for students of computer science or mathematics. It is completely self-contained and one can really enjoy reading it. It is strongly recommended for researchers and postgraduate students interested in logic, automata and/or concurrency.”—Bulletin of the EMS 2001. XIV, 430 p. 111 illus. (Progress in Computer Science and Applied Logic, Volume 21) Hardcover ISBN 978-0-8176-4207-5 $89.95

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Systems and Control




Linear Systems




P. J. Antsaklis, A. N. Michel, University of Notre Dame, IN, USA

A Linear Systems Primer P. J. Antsaklis, A. N. Michel, University of Notre Dame, IN, USA Based on a streamlined presentation of the authors’ successful work Linear Systems, this textbook provides an introduction to systems theory with an emphasis on control. The material presented is broad enough to give the reader a clear picture of the dynamical behavior of linear systems as well as their advantages and limitations. The emphasis throughout is on time-invariant systems, both continuous- and discretetime. For full coverage of time-variant systems, the reader is encouraged to see the companion book Linear Systems, which contains more detailed descriptions and additional material, including all the proofs of the results presented here. A Linear Systems Primer is geared towards senior undergraduate and first-year graduate students in a typical one-semester introductory course on systems and control; a solutions manual is available to instructors upon adoption of the text. It may also serve as an excellent reference or self-study guide for electrical, mechanical, chemical, and aerospace engineers, applied mathematicians, and researchers working in control, communications, and signal processing. 2007. XVI, 520 p. 61 illus. Softcover ISBN 978-0-8176-4460-4 $59.95

“There are three words that characterize this work: thoroughness, completeness and clarity. The authors are congratulated for taking the time to write an excellent linear systems textbook!”—IEEE Transactions on Automatic Control 1st ed. 1997. Corr. 2nd printing 2006. XVIII, 670 p. 85 illus. Hardcover ISBN 978-0-8176-4434-5 $89.95

Numerical Methods for Controlled Stochastic Delay Systems

H. J. Kushner, Brown University, Providence, RI, USA This book is the first to extend the Markov chain approximation method – typically used for stochastic control and optimal stochastic control problems in continuous time – to stochastic control problems for systems with delays. Numerical methods presented here provide a practical and efficient approach to both the investigation and design of such systems. The book’s main focus is on the development of robust and intuitive algorithms that can be conveniently programmed and have good numerical properties. An excellent resource for graduate students, researchers, and practitioners in stochastic systems and communications, the text is aimed at those whose main interest is in the use of algorithms, as well as those whose primary focus is on the mathematics of stochastic systems with delays. The work may be used as a graduate-level textbook for a special topics course or seminar on numerical methods in stochastic control. 2008. Approx. 250 p. 25 illus. (Systems & Control: Foundations & Applications) Hardcover ISBN 978-0-8176-4534-2 approx. $69.95

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defined on general metric spaces * Specialization of this stability theory to finite-dimensional dynamical systems * Specialization of this stability theory to infinite-dimensional dynamical systems Replete with exercises and requiring basic knowledge of linear algebra, analysis, and differential equations, the work may be used as a textbook for graduate courses in stability theory of dynamical systems.

Stability of Dynamical Systems Continuous, Discontinuous, and Discrete Systems A. N. Michel, University of Notre Dame, Notre Dame, IN, USA; L. Hou, St. Cloud State University, Saint Cloud, MN, USA; D. Liu, University of Illinois, Chicago, IL, USA Filling a gap in the literature, this textbook presents the first comprehensive stability analysis of all the major types of system models: finite-dimensional and infinitedimensional systems; continuous-time and discrete-time systems; continuous continuous-time and discontinuous continuous-time systems; and hybrid systems involving a mixture of continuous and discrete dynamics. Throughout the book, the applicability of the developed theory is demonstrated by means of many specific examples and applications to important classes of systems, including digital control systems, nonlinear regulator systems, pulse-width-modulated feedback control systems, artificial neural networks (with and without time delays), digital signal processing, a class of discrete-event systems (with applications to manufacturing and computer load balancing problems) and a multicore nuclear reactor model. The book covers the following four general topics: * Representation and modeling of dynamical systems of the types described above * Presentation of Lyapunov and Lagrange stability theory for dynamical systems

2008. XII, 508 p. 44 illus. (Systems & Control: Foundations & Applications) Hardcover ISBN 978-0-8176-4486-4 $79.95

Control of Turbulent and Magnetohydrodynamic Channel Flows Boundary Stabilization and State Estimation R. Vazquez, University of Seville, Seville, Spain; M. Krstic, University of California, San Diego, CA, USA This monograph presents new constructive design methods for boundary stabilization and boundary estimation for several classes of benchmark problems in flow control, with potential applications to turbulence control, weather forecasting, and plasma control. One of the main features of the book is a unique “backstepping” approach to parabolic partial differential equations, which yields not only the stabilization of the flow, but also the explicit solvability of the closed-loop system. The work is an excellent reference for a broad, interdisciplinary engineering and mathematics audience: control theorists, fluid mechanicists, mechanical engineers, aerospace engineers, chemical engineers, electrical engineers, applied mathematicians, as well as research and graduate students in these fields. 2008. X, 214 p. 14 illus. (Systems & Control: Foundations & Applications) Hardcover ISBN 978-0-8176-4698-1 $69.95

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Systems and Control

Set-Theoretic Methods in Control F. Blanchini, S. Miani, Università di Udine, Italy This self-contained monograph describes basic set-theoretic methods and provides a discussion of their links to fundamental problems in control. The work presents several established and potentially new applications, along with numerical examples and case studies. Mathematical language is kept to a minimum necessary for the adequate formulation and statement of main concepts. Set-Theoretic Methods in Control is accessible to readers familiar with the basics of systems and control theory. The text provides a solid foundation of mathematical techniques and applications and also features avenues for further theoretical study. Aimed primarily at graduate students and researchers in applied mathematics and engineering, the book will also appeal to practitioners since it contains extensive references to the literature and supplies many recipes for solving significant control problems. 2008. XVI, 488 p. 119 illus. (Systems & Control: Foundations & Applications) Hardcover ISBN 978-0-8176-3255-7 $89.95

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Representation and Control of Infinite Dimensional Systems Second Edition A. Bensoussan, University of Texas Richardson, TX, USA; G. Da Prato, Scuola Normale Superiore, Pisa, Italy; M. C. Delfour, Université de Montréal, Montreal, QC, Canada; S. K. Mitter, Massachusetts Institute of Technology, Cambridge, MA, USA This reorganized, revised, and expanded edition of a two-volume set is a selfcontained account of quadratic cost optimal control for a large class of infinite dimensional systems. The study of this problem shows the beautiful interplay between optimality and the qualitative properties of systems such as controllability, observability, stabilizability, and detectability. New material includes an expanded chapter on the control of linear systems and a chapter on linear quadratic twoperson zero-sum differential games. A unique chapter on semigroup theory and interpolation of linear operators brings together advanced concepts and techniques that are usually treated independently. The material on delay systems and structural operators is not available elsewhere in book form. “We state at the outset that this book is a most welcome addition to the literature of this field, where it serves the need for a modern treatment on topics that only very recently have found a satisfactory solution.

...Many readers will appreciate the concise exposition.... The book makes a worthwhile effort to be accessible and relatively selfcontained. [It] should prove to be a valuable source for mathematicians who want to learn more about aspects of deterministic control theory as well as theoretical engineers willing to learn the mathematical tools necessary to give precise formulations and solutions to problems arising from applications.”—Mathematical Reviews (review of Vol. I of the first edition) 2nd ed. 2007. XXVI, 575 p. 5 illus. (Systems & Control: Foundations & Applications) Hardcover ISBN 978-0-8176-4461-1 $89.95

Introduction to Mathematical Systems Theory




Linear Systems, Identification and Control C. Heij, Erasmus University Rotterdam, The Netherlands; A. C. Ran, F. v. Schagen, Vrije Universiteit Amsterdam, The Netherlands This book provides an introduction to the theory of linear systems and control for students in business mathematics, econometrics, computer science, and engineering; the focus is on discrete time systems. The subjects treated are among the central topics of deterministic linear system theory: controllability, observability, realization theory, stability and stabilization by feedback, LQ-optimal control theory. Kalman filtering and LQC-control of stochastic systems are also discussed, as are modeling, time series analysis and model specification, along with model validation. Exercises using MATLAB, presented on an accompanying CD, enhance the main concepts and techniques in the text.

Filtering Theory With Applications to Fault Detection, Isolation, and Estimation A. Saberi, Washington State University, Pullman, WA, USA; A. A. Stoorvogel, Eindhoven University of Technology, Eindhoven, The Netherlands; P. Sannuti, Rutgers University, Piscataway, NJ, USA The focus of this book is on filtering for linear processes, and its primary goal is to design linear stable unbiased filters that yield an estimation error with the lowest root-mean-square (RMS) norm. Various hierarchical classes of filtering problems are defined based on the availability of statistical knowledge regarding noise, disturbances, and other uncertainties. The authors employ a structural approach for several aspects of filter analysis and design, revealing an inherent freedom to incorporate other classical secondary engineering constraints in filter design. This approach requires an understanding of powerful tools that then may be used in several engineering applications besides filtering. Filtering Theory is aimed at a broad audience of practicing engineers, graduate students, and researchers in filtering, signal processing, and control. The book may serve as an advanced graduate text for a course or seminar in filtering theory in applied mathematics or engineering departments. 2007. XIV, 723 p. 44 illus. (Systems & Control: Foundations & Applications) Hardcover ISBN 978-0-8176-4301-0 $129.00

2007. VII, 166 p. With CD-ROM. Softcover ISBN 978-3-7643-7548-5 $49.95

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Systems and Control

Max-Plus Methods for Nonlinear Control and Estimation

be used as a textbook for a graduate course on nonlinear control.”—Zentralblatt MATH

W. M. McEneaney, University of California at San Diego, La Jolla, CA, USA

2006. IX, 172 p. 38 illus. (Systems & Control: Foundations & Applications) Hardcover ISBN 978-0-8176-4445-1 $59.95

“This outstanding book discusses new theoretical approaches to the study of the control and estimation of continuous-time/ continuous-space nonlinear systems to be a challenging problem. … This book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of the max-plus algebra and some basics of functional analysis over the maxplus algebra. … The volume is primarily addressed to applied mathematicians … . will also be useful for scientists from the application areas, in particular, applied scientists from engineering and physics.” —Zentralblatt MATH 2006. XIII, 241 p. 17 illus. (Systems & Control: Foundations & Applications) Hardcover ISBN 978-0-8176-3534-3 $79.95

Uniform Output Regulation of Nonlinear Systems A Convergent Dynamics Approach A. Pavlov, Norwegian University of Science and Technology, Trondheim, Norway; N. v. Wouw, H. Nijmeijer, Eindhoven University of Technology, Eindhoven, The Netherlands “The book is one of the first systematic studies on the nonlinear output regulating problem that embraces both the local and global solvability analysis, covering such aspects as solvability conditions, controller design, and practical implementation issues...In addition to being an excellent reference for the uniform output regulation problem, the book has a tutorial value on convergent systems. The work will be of interest to control engineers to control engineers, theorists, and students, and may

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Supervisory Control of Concurrent Systems A Petri Net Structural Approach M. V. Iordache, LeTourneau University, Longview, TX, USA; P. J. Antsaklis, University of Notre Dame, IN, USA “This book is an excellent monograph that approaches, in the Petri nets context, the supervisory control of concurrent systems.” —Mathematical Reviews 2006. XIV, 281 p. 100 illus. (Systems & Control: Foundations & Applications) Hardcover ISBN 978-0-8176-4357-7 $79.95

Handbook of Networked and Embedded Control Systems D. Hristu-Varsakelis, University of Macedonia, Thessaloniki, Greece; W. S. Levine, University of Maryland, College Park, MD, USA (Eds.) This handbook, the first of its kind, provides engineers, computer scientists, mathematicians, and students a broad, comprehensive source of information and technology to address many questions and aspects of embedded and networked control. Separated into six main sections – Fundamentals, Hardware, Software, Theory, Networking, and Applications – this work unifies into a single reference many scattered articles, websites, and specification sheets. Also included are case studies, experiments, and examples that give a multifaceted view of the subject, encompassing computation and communication considerations. 2005. X, 822 p. 256 illus. (Control Engineering) Hardcover ISBN 978-0-8176-3239-7 $89.95

Convex Functional Analysis




A. J. Kurdila, M. Zabarankin, University of Florida, Shalimar, FL, USA “The book provides not only the bare minimum of the theory required to understand the principles of functional, convex and set-valued analysis, but also a concise summary of definitions and theorems so that the text is self-contained.” —Zentralblatt MATH 2005. XIV, 228 p. (Systems & Control: Foundations & Applications) Hardcover ISBN 978-3-7643-2198-7 $109.00

The Mathematics of Internet Congestion Control R. Srikant, University of Illinois, Urbana, IL, USA “This first book on the mathematics of congestion control [is] very useful for both students and researchers, but also for system engineers developing new Internet protocols. This is an elementary book for graduate students that uses a rich pallet of mathematical tools: convex optimization and control theory (Lyapunov stability and Nyquist criteria and stochastic processes). The tools are summarized well in appendices which makes the book self-contained and easy to read. The book is very well written and will undoubtedly remain a major reference on the topic for years to come.” —Mathematical Reviews 2004. XII, 164 p. 19 illus. (Systems & Control: Foundations & Applications) Hardcover ISBN 978-0-8176-3227-4 $54.95

Stability of Time-Delay Systems K. Gu, Southern Illinois University at Edwardsville, IL, USA; V. L. Kharitonov, CINVESTAV-IPN, Mexico, Mexico; J. Chen, University of California at Riverside, Riverside, CA, USA “This book is written by famous scientists in the area of time-delay systems. It presents a systematic treatment of the theory of such systems and their stability. It is devoted to the study of the stability of time-delay systems, an area long pursued by mathematicians, physical and life scientists, engineers, and economists.... The book is well written and contains a number of examples.” —Zentralblatt MATH 2003. XXII, 354 p. 16 illus. (Control Engineering) Hardcover ISBN 978-0-8176-4212-9 $79.95

Switching in Systems and Control




D. Liberzon, University of Illinois, Urbana, IL, USA “This book is a well-structured and clearly written text addressing pertinent issues on stability and control for switched systems. These are regarded as a collection of individual dynamic systems, which are selected to drive the state according to a switching policy…. The book also includes two appendices succinctly covering some basic facts on stability and Lie algebras. Interesting notes and additional references complementing the main text on a chapterby-chapter basis are also included. The book serves well the purpose stated by the author of supporting research and advanced graduate courses on switched systems and control.”—Mathematical Reviews 2003. XII, 234 p. 43 illus. (Systems & Control: Foundations & Applications) Hardcover ISBN 978-0-8176-4297-6 $69.95

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Optimal Control




An Introduction A. Locatelli, Politecnico di Milano, Italy “The style of the book reflects the author’s wish to assist in the effective learning of optimal control by suitable choice of topics, the mathematical level used, and by including numerous illustrated examples. The book has been written for undergraduate and postgraduate students who already know control theory, basic linear systems and possess a background in calculus…. In my view the book suits its function and purpose, in that it gives a student a comprehensive coverage of optimal control in an easy-toread fashion.”—Measurement and Control 2001. VIII, 294 p. Hardcover ISBN 978-3-7643-6408-3 $64.95

Optimal Control R. Vinter, Imperial College of Science, Technology, and Medicine London, UK “In this self-contained monograph the author brings us right to the frontier of the research on necessary optimality conditions using the methodology of nonsmooth analysis and variational methods. He also presents a new perspective on the regularity of minimizers and discusses some of the recent progress on dynamic programming…. Each chapter contains a well-written introduction and notes. They include the author’s deep insights on the subject matter and provide historical comments and guidance to related literature. This book may well become an important milestone in the literature of optimal control.”—Mathematical Reviews 2000. XVII, 507 p. 13 illus. (Systems & Control: Foundations & Applications) Hardcover ISBN 978-0-8176-4075-0 $89.95

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Of General Interest

Mathematical Bridges




T. Andreescu, University of Texas at Dallas, Richardson, TX, USA; C. Mortici, University of Targoviste, Romania Building bridges between classical results and contemporary nonstandard problems, Mathematical Bridges embraces important topics in analysis and algebra from a problem-solving perspective. Blending old and new techniques, tactics and strategies used in solving challenging mathematical problems, readers will discover numerous genuine mathematical gems throughout that will heighten their appreciation of the inherent beauty of mathematics. Most of the problems are original to the authors and are intertwined in a well-motivated exposition driven by representative examples. The book is structured to assist the reader in formulating and proving conjectures, as well as devising solutions to important mathematical problems by making connections between various concepts and ideas from different areas of mathematics. 2008. Approx. 300 p. 20 illus. Softcover ISBN 978-0-8176-4394-2 approx. $59.95

Mathematical Olympiad Challenges T. Andreescu, University of Texas at Dallas, Richardson, TX, USA; R. Gelca, Texas Tech University, Lubbock, TX, USA

Second Edition




This significantly revised and expanded second edition of Mathematical Olympiad Challenges is a rich collection of problems put together by two experienced and wellknown professors and coaches of the U.S. International Mathematical Olympiad Team. Hundreds of beautiful, challenging, and instructive problems from algebra, geometry, trigonometry, combinatorics, and number theory from numerous mathematical

competitions and journals have been selected and updated. The problems are clustered by topic into self-contained sections with solutions provided separately. Historical insights and asides are presented to stimulate further inquiry. The emphasis throughout is on creative solutions to openended problems. With many new or expanded examples, problems, and solutions, this second edition includes completely rewritten discussions preceding each of the 30 units, as well as a more user-friendly style with more accessible and inviting examples. Featuring enhanced motivation for advanced high school and beginning college students, as well as instructors and Olympiad coaches, this text can be used for creative problemsolving courses, for professional teacher development seminars and workshops, for self-study, or as a resource for training for mathematical competitions. “This [book] is…much more than just another collection of interesting, challenging problems, but is instead organized specifically for learning. The book expertly weaves together related problems, so that insights gradually become techniques, tricks slowly become methods, and methods eventually evolve into mastery…. I strongly recommend this book for anyone interested in creative problem-solving in mathematics…. It has already taken up a prized position in my personal library, and is bound to provide me with many hours of intellectual pleasure.” —The Mathematical Gazette 2nd ed. 2008. 320 p. Softcover ISBN 978-0-8176-4528-1 approx. $29.95

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Of General Interest







103 Trigonometry Problems

The Math Problems Notebook

From the Training of the USA IMO Team

V. Boju, MontrealTech, Institute de Technologie de Montreal, QC, Canada; L. Funar, CNRS, Université de Grenoble I, France

T. Andreescu, The University of Texas at Dallas, Richardson, TX, USA; Z. Feng, Phillips Exeter Academy, Exeter, USA “The title of this book already says everything about the content: 103 trigonometry problems that were given in the training and testing of the US International Mathematical Olympiad team are presented along with their solutions. … The presentation is clear, accurate and extensive. For these reasons the book is very easy to read and leads the reader to astonishing insights in an elementary field of mathematics. It is therefore also very appropriate as a textboook.”—Monatshefte für Mathematik 2005. XII, 214 p. Softcover ISBN 978-0-8176-4334-8 $49.95

Mathematical Olympiad Treasures




T. Andreescu, The University of Texas at Dallas, Richardson, TX, USA; B. Enescu, B.P. Hasdeu National College, Buzau, Romania “All featured solutions are interesting, given in increasing level of difficulty; some of them are real gems that will give great satisfaction to any math lover attempting to solve the problems—or even extend them. I believe strongly that Mathematical Olympiad Treasures will reveal the beauty of mathematics to all students, teachers and all math lovers.”—MAA Online

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2004. VI, 234 p. 99 illus. Softcover ISBN 978-0-8176-4305-8 $29.95

The Math Problems Notebook is a collection of nontrivial, unconventional problems requiring deep insight and imagination reminiscent of those discussed at Sunday Math Circles. These circles have become a place for disseminating beautiful mathematics at an elementary level for college students who have a common passion for mathematics. The problems cover many topics, including number theory, algebra, combinatorics, geometry and analysis, of varying levels of difficulty. The presentation of each topic begins with simple exercises and follows with more difficult problems, challenging enough even for the experienced problem solver. The easier problems focus on basic methods and tools, while the more advanced problems develop problemsolving techniques, intuition and promote further research. Undergraduates and teachers of advanced mathematics, as well as the casual mathematician will mutually enjoy The Math Problems Notebook. 2007. XII, 236 p. 21 illus. Softcover ISBN 978-0-8176-4546-5 $39.95




Colloquium De Giorgi 2006 U. Zannier, Scuola Normale Superiore, Pisa, Italy (Ed.)

Symmetry Cultural-historical and Ontological Aspects of Science-Arts Relations; the Natural and Man-made World in an Interdisciplinary Approach G. Darvas, Hungarian Academy of Sciences, Budapest, Hungary The first comprehensive book on the topic in half a century explores recent symmetry – and symmetry breaking – related discoveries, and discusses the questions and answers they raise in diverse disciplines: particle and high-energy physics, structural chemistry and the biochemistry of proteins, in genetic code study, in brain research, and also in architectural structures, and business decision making, to mention only a few examples.

This book contains expositions of talks of the Colloquio De Giorgi, given by eminent experts and addressed to a ‘general’ public (audience) of mathematicians. The topics are prepared in such a way that readers will get some idea of recent progress in several mathematical fields. 2006. 57 p. (Publications of the Scuola Normale Superiore / Colloquia, Volume 1) Softcover ISBN 978-88-7642-212-6 $24.95

Exploring, Investigating and Discovering in Mathematics




V. Berinde, University Baia Mare, Romania

Contributors: Alessio Ageno, Jean-Pierre Antoine, Sandro Caparrini, Frans A. Cerulus, Sidney D. Drell, David Ritz Finkelstein, Laszlo Grenacs, Donal Hurley, Giuseppe La Rocca, Siegmund Levarie, Bernd Lindemann, Giulio Maltese, Wolfgang K.H. Panofsky, Orietta Pedemonte, Patricia Radelet-de Grave, Luigi A. Radicati di Brozolo, Michael Vandyck, Piero Villaggio, Kim Williams

“In the spirit of George Polya’s classic treatise How to Solve It: A New Aspect of Mathematical Method, this book is Vasile Berinde’s attempt to “algorithmetize” the creative process involved in problemsolving.... The author’s stated goals are twofold. The most obvious aim is to provide methods for solving some difficult problems. But on a deeper level, he is trying to grow new research mathematicians by planting the seeds that will develop into the skills they will need to do original research.... Each of the 24 chapters begins with a source or starting problem and its solution. Then the fun begins! Remarks about the “essence” of the problem and its solution suggest new directions to explore, and these investigations lead to generalizations and the formulation of related problems, sometimes building a “factory” of new problems. From the first page I eagerly grabbed my pencil and a stack of scratch paper, and set to work as I happily read along.... I recommend the book for all lovers of mathematics, but especially students and teachers who participate in mathematics contests and practice problem solving.”—MAA Online

2006. 201 p. Hardcover ISBN 978-3-7643-7186-9 $89.95

2004. XIX, 246 p. Softcover ISBN 978-3-7643-7019-0 $49.95

2007. XI, 508 p. 420 illus., 66 in color. Softcover ISBN 978-3-7643-7554-6 $79.95

Two Cultures Essays in Honour of David Speiser K. Williams, Torino, Italy (Ed.)

117

Of General Interest

The Topos of Music

First Steps in LaTeX

Geometric Logic of Concepts, Theory, and Performance

G. Grätzer, University of Mannitoba, Winnipeg, Canada

G. Mazzola, University of Zurich, Switzerland In cooperation with: S. Göller, S. Müller, University of Zurich, Switzerland

1999. 152 p. Softcover ISBN 978-0-8176-4132-0 $29.95

“Topos of Music is an extensive and elaborate body of mathematical investigations into music and involves several and ontologically different levels of musical description. Albeit the author Guerino Mazzola lists 17 contributors and 2 collaborators, the book should be characterized as a monograph. Large portions of the content represent original research of Mazzola himself, and the material from other work is exposed from Mazzola’s point of view and is well referenced. The preface preintimates an intended double meaning of the term topos in the title. On the one hand, it provides a mathematical anchor, which is programmatic for the entire approach: the concept of a cartesian closed category with a subobject classifier. (...)”—Zentralblatt MATH

Beyond the Quartic Equation

2002. 1368 p. Hardcover ISBN 978-3-7643-5731-3 $169.00

Fibonacci Numbers N. N. Vorobiev “This is a wonderful book with a huge amount of information on Fibonacci numbers. First published in the 1950s for high school students enrolled in a mathematical circle at the Leningrad State University, the book only assumes knowledge of high school mathematics, but the reader will need the sophistication of a good upperlevel mathematics major. The warmth and enthusiasm of the late author comes through Mircea Martin‘s English translation.” —MAA Online 2002. X, 176 p. Softcover ISBN 978-3-7643-6135-8 $39.95

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B. King 1996. 164 p. Hardcover ISBN 978-0-8176-3776-7 $69.95

The Mathematical Experience, Study Edition P. J. Davis, Brown University, Providence, RI, USA; R. Hersh, The University of New Mexico, Albuquerque, NM, USA; E. A. Marchisotto, California State University, Northridge, CA, USA Introduction by: G. Rota, deceased “This is a people-centered book about mathematics, and as such it provides an opportunity to explore fundamental issues that are typically absent from the experience of most college and university students (as well as their teachers). This new edition provides an excellent initiation of students into some of the more challenging aspects of mathematics…The study edition of The Mathematical Experience will help its readers acquire a real understanding of mathematics.”—Notices of the AMS “Two distinguished mathematicians...have written a perfectly marvelous book about the Queen of Sciences, from which one will get a real feeling for what mathematicians do and who they are. The exposition is clear and full of wit and humor...”—The New Yorker (1984 American Book Award Edition) 1995. XXI, 487 p. 172 illus. Hardcover ISBN 978-0-8176-3739-2 $49.95

The Companion Guide to the Mathematical Experience, Study Edition P. J. Davis, Brown University, Providence, RI, USA; R. Hersh, University of New Mexico, NM, USA; E. A. Marchisotto, California State University, Northridge, CA, USA 1995. 128 p. Softcover ISBN 978-0-8176-3849-8 $24.95

Algebra

The Method of Coordinates I. Gelfand, Rutgers University, Piscataway, NJ, USA; E. Glagoleva, A. Kirilov, University of Moscow, Russia 1990. 84 p. Softcover ISBN 978-0-8176-3533-6 $24.95

Functions and Graphs




I. Gelfand, Rutgers University, Piscataway, NJ, USA; A. Shen, Institute of Problems of Information Transmission, Moscow, Russia “The idea behind teaching is to expect students to learn why things are true, rather than have them memorize ways of solving a few problems, as most of our books have done. [This] same philosophy lies behind the current text by Gelfand and Shen. There are specific ‚practical‘ problems but there is much more development of the ideas . . . [The authors] have shown how to write a serious yet lively look at algebra.” —The American Mathematics Monthly 1st ed. 1993. 4th printing 1993. 160 p. 27 illus. Softcover ISBN 978-0-8176-3677-7 $22.95

I. Gelfand, Rutgers University, Piscataway, NJ, USA; E. Glagoleva, E. Shnol, University of Moscow, Russia 1990. 170 illus. Softcover ISBN 978-0-8176-3532-9 $24.95

In Search of Infinity N. Vilenkin, York University, Ontario, Canada “In fewer than 150 pages Vilenkin has packed a whole course on infinity: its history, philosophy, and mathematical theory. Abe Shenitzer‘s translation is very smooth and natural... When fractals have gone out of style, and chaos is no longer the flavor of the month, some kind of ‚geometric set theory‘ or ‚set-theoretic geometry‘ may very well remain, and In Search of Infinity may still be the best introduction to it.” —American Mathematical Monthly 1995. 156 p. Hardcover ISBN 978-0-8176-3819-1 $37.95

Trigonometry




I. Gelfand, Rutgers University, Piscataway, NJ, USA; M. Saul, Bronxville Schools, Bronxville, NJ, USA 2001. X, 229 p. 185 illus. Softcover ISBN 978-0-8176-3914-3 $22.95

119

History of Science

Leonhard Euler

Leonhard Euler

E. A. Fellmann, Basel, Switzerland Translated by: E. Gautschi, W. Gautschi

A Man to Be Reckoned with

“This is the only biography of Leonhard Euler currently available in English, and it would be worth having for that reason alone. (...) The book is a good introductory biography of Euler, and it is handsomely produced, with nice paper and lots of illustrations. It is a welcome addition to the literature on Euler. Fellmann has chosen to make this a non-technical biography. There are no mathematical details and no formulas. Short accounts of Euler‘s work are included, but few details are given. Even then, the sections that go into Euler‘s work are marked with asterisks so that readers who are not willing to delve into specifics can skip them. With non-technical readers in mind, Fellmann privileges those aspects of Euler‘s work that are more accessible, so his music theory gets much more attention than his work on elliptic integrals and his lunar theory and optics more than the geometry or number theory.”—MAA Reviews 2007. XV, 179 p. 58 illus. Hardcover ISBN 978-3-7643-7538-6 $39.95

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A. K. Heyne, A. K. Heyne Illustrations by: E. S. Pini His ideas turned the mathematical world on its head. As a scientist he should be placed on the same level as Newton and Einstein. This account of Euler‘s life and livings is embedded in the great political developments of his time, particularly in Austria, Prussia and Russia. The comic by Elena Pini (illustrations) and Alice and Andreas K. Heyne (text) follows the life of the genius from Basel, who, born 300 years ago, would set out to change the scientific world. The book is completed by a short biography of Euler and relevant data of the most important politicians and contemporaries. 2007. 45 p. Hardcover ISBN 978-3-7643-8332-9 $19.95

The Legacy of Mario Pieri in Geometry and Arithmetic E. A. Marchisotto, California State University, Northridge, CA, USA; J. T. Smith, San Francisco State University, San Francisco, CA, USA “This book portrays Pieri as an individual of exceptional ability, who responded to the influence of many of his contemporaries; and they, in turn, acknowledged the quality of Pieri’s work. In fact, there is a sixty-page section in the first chapter containing biographical sketches of the lives and work of almost a hundred such mathematicians. Moreover, the general historical analysis and interpretative commentary, whilst focussing particularly upon the achievements of Mario Pieri, also extends to many of the general mathematical developments of his era. The book is very thoroughly documented and contains an abundance of photographic portraits. It culminates with an extensive bibliography and an accurately compiled index, and it will undoubtedly appeal to those concerned with the history of ‘modern mathematics’, as well as being of interest to the general readership specified by the authors.”—MAA Reviews 2007. XIX, 494 p. 67 illus. Hardcover ISBN 978-0-8176-3210-6 $129.00

A History of Abstract Algebra I. Kleiner, York University, Toronto, ON, Canada Prior to the nineteenth century, algebra meant the study of the solution of polynomial equations. By the twentieth century it came to encompass the study of abstract, axiomatic systems such as groups, rings, and fields. This presentation provides an account of the history of the basic concepts, results, and theories of abstract algebra. The development of abstract algebra was propelled by the need for new tools to address certain classical problems that appeared unsolvable by classical means. A major theme of the approach in this book is to show how abstract algebra has arisen in attempts to solve some of these classical problems, providing a context from which the reader may gain a deeper appreciation of the mathematics involved. Mathematics instructors, algebraists, and historians of science will find the work a valuable reference. The book may also serve as a supplemental text for courses in abstract algebra or the history of mathematics. 2007. XVI, 168 p. 24 illus. Softcover ISBN 978-0-8176-4684-4 $49.95

121

History of Science

Lacroix and the Calculus J. Caramalho Domingues, University of Minho, Braga, Portugal Silvestre François Lacroix (Paris, 1765 - ibid., 1843) was not a prominent mathematical researcher, but he was certainly a most influential mathematical book author. His most famous work is the three-volume Traité du calcul différentiel et du calcul intégral (1797-1800; 2nd ed. 1810-1819) – an encyclopedic appraisal of 18th-century calculus which remained the standard reference on the subject through much of the 19th century. The Calculus According to S.F. Lacroix (1765-1843) is a study of Lacroix’s large Traité, making use of its unique bibliography to explore late 18th-century calculus, and how it is reflected in Lacroix’s account. Its adaptation into the shorter, textbook version Traité élémentaire de calcul… (1802; several later editions) is also addressed. 2008. Approx. 470 p. (Science Networks. Historical Studies, Volume 35) Hardcover ISBN 978-3-7643-8637-5 $169.00

The Theory of the Top Volume I. Introduction to the Kinematics and Kinetics of the Top F. Klein, A. Sommerfeld Translated by: R. J. Nagem, , G. Sandri, Boston University, Boston, MA The lecture series on The Theory of the Top was originally given as a dedication to Göttingen University by Felix Klein in 1895, but has since found broader appeal. The Theory of the Top: Volume I. Introduction to the Kinematics and Kinetics of the Top is the first of a series of four self-contained English translations that provide insights into kinetic theory and kinematics.

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Key features: * Presentation of a historical nature complete with recent advances and additional notes * Annotated notes by translators provide insights into the nature of science and mathematics in the early 19th century *Each volume interweaves theory and applications * Volume I focuses on providing background material and basic theoretical concepts Graduates and researchers interested in the theories behind applied mechanics will find this an insightful and thorough account. Other topics in this series include the Development of the Theory for the Heavy Symmetric Top, Perturbations: Astronomical and Geophysical Applications, and Technical Applications of the Theory of the Top. 2008. Approx. 315 p. 159 illus. Hardcover ISBN 978-0-8176-4720-9 approx. $59.95

History of Banach Spaces and Linear Operators A. Pietsch, University of Jena, Germany Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. Banach space theory is presented as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. Equal emphasis is given to both spaces and operators. The book may serve as a reference for researchers and as an introduction for graduate students who want to learn Banach space theory with some historical flavor. 2007. XXIII, 855 p. 82 illus. Hardcover ISBN 978-0-8176-4367-6 $129.00

Discovering the Principles of Mechanics 1600-1800 Essays by David Speiser K. Williams, Kim Williams Books, Torino, Italy; S. Caparrini, Orbassano (Torino), Italy (Eds.) This book assembles 21 essays on the history of mechanics and mathematical physics written by David Speiser. Covering a period from the beginning of the seventeenth century to the eighteenth, the essays discuss developments in elasticity, rigid bodies, gravitation, the principle of relativity, optics, and first principles. They examine the work of Galileo, Huygens, Newton, Leibniz, the Bernoullis, Euler, Maupertuis, and Lambert. 2008. Approx. 300 p. Hardcover ISBN 978-3-7643-8564-4 $119.00

Geometry and Monadology Leibniz‘s Analysis Situs and Philosophy of Space V. De Risi, Scuola Normale Superiore, Pisa, Italy This book reconstructs, both from the historical and theoretical points of view, Leibniz’s geometrical studies, focusing in particular on the research Leibniz carried on in the last years of his life. The main purpose of the work is to offer a better understanding of the philosophy of space and in general of the mature Leibnizean metaphysics, through a pressing confrontation with the problems of geometric foundation. Regarding this scope of problems, the book also deals quite in depth with Leibniz’s theory of sensibility, thus favouring the comparison and contrast between Leibniz’s philosophy and Kant’s transcendentalist solution. The Appendix gives editing to a number of previously unpublished manuscripts on geometry from the Leibniz Archiv. 2007. XX, 658 p. (SNHS, Volume 33) Hardcover ISBN 978-3-7643-7985-8 $179.00

Second Edition

Labyrinth of Thought A History of Set Theory and Its Role in Modern Mathematics J. Ferreirós, Universidad de Sevilla, Spain “José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization.”—Bulletin of Symbolic Logic 2nd, revised ed. 2007. XXV, 466 p. 7 illus. Softcover ISBN 978-3-7643-8349-7 $79.95

Tool and Object A History and Philosophy of Category Theory R. Krömer, University of Nancy, France 2007. XXXVI, 367 p. (Science Networks. Historical Studies, Volume 32) Hardcover ISBN 978-3-7643-7523-2 $129.00

123

History of Science

Jacopo da Firenze‘s Tractatus Algorismi and Early Italian Abbacus Culture

Die Werke von Johann I und Nicolaus II Bernoulli

J. Høyrup, Roskilde University, Denmark

P. Villaggio, University of Pisa, Italy; P. Radelet-de Grave (Eds.)

The book deals with a Tractatus algorismi written in 1307 in Montpellier by a certain Jacopo da Firenze. This work is one of the earliest surviving „abbacus“ treatises, that is, textbooks for the vernacular school for merchant youth which sprung up in Northern Italy in the later 13th century, and by far more orderly than any of the extant predecessors. It is also the first to contain a presentation of algebra. The book contains an edition and an English translation of a manuscript from c. 1450 which is a meticulous copy of a meticulous copy; a critical edition of an abridged version of which two manuscripts exist, and an extensive discussion of the contents of the treatise and its location within early abbacus culture – including evidence that this culture was transnational and probably older in the Catalan-Provençal area than in Italy. 2007. XII, 482 p. (Science Networks. Historical Studies, Volume 34) Hardcover ISBN 978-3-7643-8390-9 $139.00

La correspondance entre Henri Poincaré et les physiciens, chimistes et ingénieurs S. Walter, E. Bolmont, A. Coret, Université Nancy 2, France (Eds.) Henri Poincaré, while well-known as the most brilliant mathematician at the close of the 19th century, is also a founder of 20thcentury physics, in virtue of his fundamental contributions to Maxwell‘s theory, systems dynamics, electron theory, relativity and quantum theory. These subjects and others are discussed in this critical edition of his correspondence with sixty physicists, chemists, and engineers.

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2007. 493 p. (Publications of the Henri Poincaré Archives) Hardcover ISBN 978-3-7643-7136-4 $299.00

Band 6: Mechanik I

This volume on mechanics of rigid and elastic bodies contains early papers concerning geometric statics, accompanied by works dealing with the motion of compound pendula and the deformation of beams. The papers on mechanics in this volume do not encompass the area of hydraulics, which occupies approximately one half of the papers dealing with mechanical problems and which are included in volume 7. This collection constitutes, roughly, one eighth of the entire work written by Bernoulli. 2008. XXII, 695 p. Cloth bound ISBN 978-3-7643-7367-2 $289.00

Lise Meitner and the Dawn of the Nuclear Age P. Rife, University of Maryland, Adelphi, MD, USA Foreword by: J. Wheeler “The dramatic tale of the discovery of nuclear fission on the eve of WWII has been told before, but never with such attention to the barriers formed by gender and racial discrimination… This is not just a story of ideas leading to nuclear fission, but also of the social and intellectual milieu in which these ideas were developed. It is also the story of how a shy, self-effacing young woman, through talent and hard work, became a world-class scientists… Rife tells this story very well.”—The Antioch Review 1st ed. 1999. 2nd printing 2007. XVIII, 432 p. 35 illus. Softcover ISBN 978-0-8176-4559-5 $49.95

Italian Mathematics Between the Two World Wars

The History of Approximation Theory

A. Guerraggio, Università Bocconi, Milano, Italy; P. Nastasi, Università di Palermo, Italy

From Euler to Bernstein

“What the book conveys is the richness of Italian mathematics throughout the period and, despite being expert in none of these fields, the authors captured my imagination and made me want to know more of such mathematical ideas … immensely enjoyable for all that.“—MAA Reviews

“This book aims to tell the historical evolution of the methods and results of approximation theory, starting from the work of Euler in 1777 on minimizing distance errors in maps of Russia, and of Laplace in 1843 on finding the best ellipsoid for the earth, and ending with the work of Bernstein. The central character in the book is Chebyshev (1821–1894) and the Saint Petersburg Mathematical School he created.... [The] book contains much interesting material and has certainly motivated me to learn more about the subject and its history. No book can wish for more and so I recommend the book to anyone interested in approximation theory or in the history of mathematics.”—MAA Reviews

2006. X, 299 p. (Science Networks. Historical Studies, Volume 29) Hardcover ISBN 978-3-7643-6555-4 $119.00

Expounding the Mathematical Seed. Vol. 1: The Translation A Translation of Bhaskara I on the Mathematical Chapter of the Aryabhatiya A. Keller 2006. LIII, 172 p. (Science Networks. Historical Studies, Volume 30) Hardcover ISBN 978-3-7643-7291-0 $109.00

K. Steffens, Kreuzau, Germany

2006. XIX, 219 p. 12 illus. Softcover ISBN 978-0-8176-4353-9 $79.95

6HWSULFH ÷' _÷$ _V)U

Through a Reporter‘s Eyes The Life of Stefan Banach

Expounding the Mathematical Seed. Vol. 2: The Supplements A Translation of Bhaskara I on the Mathematical Chapter of the Aryabhatiya A. Keller 2006. XI, 240 p. (Science Networks. Historical Studies, Volume 31) Hardcover ISBN 978-3-7643-7292-7 $109.00 6HWSULFH ÷' _÷$ _V)U

R. Kaluza 2005. X, 172 p. Softcover ISBN 978-0-8176-4371-3 $44.95

The Universe of General Relativity A. Kox, Universiteit van Amsterdam, The Netherlands; J. Eisenstaedt, Observatoire de Paris, France (Eds.) This volume from the Einstein Studies Series contains contributions from notable experts offering both new and historical insights on gravitation, general relativity, cosmology, unified field theory, and the history of science. 2005. X, 383 p. 17 illus. (Einstein Studies, Vol. 11) Hardcover ISBN 978-0-8176-4380-5 $99.00

125

History of Science

The Evolution of Applied Harmonic Analysis

Modern Algebra and the Rise of Mathematical Structures

Models of the Real World

Second Edition

E. Prestini, Università di Roma „Tor Vergata“, Italy

L. Corry, Tel Aviv University, Ramat Aviv, Israel

“For a little more than fifty years abstract modern harmonic analysis has evolved in ways independent of physical applications. It has become intertwined with abstract group theory and a host of modern analytical techniques. The broader subject has a much longer history, however, as a branch of applied mathematics, which dates back to the active period of the eighteenth century. The present book is concerned with this longer history as an applied science. In each of the application areas the author provides a sketch of the underlying mathematical tools borrowed from harmonic analysis. The first area is that of historical origins which dealt with waves and heat diffusion…. The author [also] discusses the topics of the fast Fourier transform, signal sampling, quantization, and filtering that are mainstays of modern digital communications as applied to telecommunications and astrophysics. The topics of sound and light provide graphic demonstrations of the role of the spectrum and higher-dimensional filtering. Perhaps the most important of all applications are the recent ones to medical technology. One example is provided by computerized axial tomography (CAT scans), which are two-dimensional images (density distributions) resulting from measuring the attenuation of x-rays along different paths and rotational angles perpendicular to the vertical axis of the human body. Building these images as well as combining them to obtain three- dimensional reconstructions requires harmonic analytical transform techniques.”—Zentralblatt MATH

2nd revised ed. 2004. 451 p. Softcover ISBN 978-3-7643-7002-2 $84.95

2004. XIX, 349 p. 169 illus. (Applied and Numerical Harmonic Analysis) Softcover ISBN 978-0-8176-4125-2 $59.95

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Gnomes in the Fog The Reception of Brouwer‘s Intuitionism in the 1920s D. E. Hesseling, Den Haag, The Netherlands “L.E.J. Brouwer is best known to many mathematicians for his seminal contributions to topology. He is also the founder of mathematical intuitionism, and a key player in the debate on foundations of mathematics that raged for a brief decade in the 1920s, and then subsided. Gnomes in the Fog tells the story of that important and influential episode in the history of mathematics, in fascinating and delicious detail.... [A]nyone with an interest in mathematics and its history and philosophy, should enjoy this book. Mathematicians (especially logicians) may find some surprises in the first chapter, on Brouwer‘s predecessors; philosophers and science study scholars should especially appreciate the final chapter on the cultural context of the debate.... One of the many treasures to be discovered in reading this book is the rich collection of original quotes in the many languages in which the debate took place, along with the author‘s translations.” —MAA Online 2003. XXIII, 447 p. (Science Networks. Historical Studies, Volume 28) Hardcover ISBN 978-3-7643-6536-3 $149.00

Writing the History of Mathematics - Its Historical Development J. W. Dauben, The Graduate Center, CUNY, New York, NY, USA; C. J. Scriba, University of Hamburg, Germany (Eds.) “This book, a historiographical one, is very useful as a reference.... The book is unique. It should be in all libraries that support graduate level history and philosophy of science and mathematics. Other libraries should consider purchasing it. Individuals familiar with the subject may wish to own it. Beginners should start with histories.” —Mathematical Reviews 2002. XIX, 689 p. (Science Networks. Historical Studies, Volume 27) Softcover ISBN 978-3-7643-6167-9 $119.00

Einstein from 'B' to 'Z' J. Stachel, Boston University, Boston, MA, USA “This book is really a collection of essays on Einstein‘s life and, as the title suggests, does not try to offer a complete picture of the great man. The essays are independent so you can read them in any order and, indeed, I found it easier to read them by looking at the essay titles and choosing the one that caught my eye.”—The Mathematical Gazette 2002. XI, 556 p. 5 illus. (Einstein Studies, Vol. 9) Hardcover ISBN 978-0-8176-4143-6 $79.95

A Mathematician Grappling with His Century L. Schwartz, Paris, France 2001. VIII, 490 p. Softcover ISBN 978-3-7643-6052-8 $52.95

Evariste Galois (1811-1832) L. Toti Rigatelli “This very pleasant, interesting and wellwritten biography is based on the analysis and interpretation of a series of hitherto neglected documents found by the author in the French archives. Certainly a book to recommend and that every mathematical library should have.”—Numerical Algorithms 1996. 163 p. (Vita Mathematica, Volume 11) Softcover ISBN 978-3-7643-5410-7 $49.95

Mach‘s Principle From Newton‘s Bucket to Quantum Gravity J. B. Barbour, College Farm, Banbury, Oxon, UK; H. Pfister, Universitat Tübingen, Tübingen, Germany (Eds.) 1995. 544 p. (Einstein Studies, Vol. 6) Hardcover ISBN 978-0-8176-3823-8 $89.00

A History of Algebraic and Differential Topology, 1900-1960 J. Dieudonné

Mathematics of the 19th Century Vol. I: Mathematical Logic – Algebra – Number Theory – Probability Theory Second Edition A. Kolmogorov, A. Yushkevich (Eds.) 2nd rev. ed. 2001. XIV, 308 p. Softcover ISBN 978-3-7643-6442-7 $52.95

“This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincaré and Brouwer to Serre, Adams, and Thom. …Within its chosen boundaries the coverage of this book is superb. Read it!”—Mathematical Reviews 1989. 676 p. Hardcover ISBN 978-0-8176-3388-2 $69.95

127

Series Index

For a complete description of all Birkhäuser series and a list of published books in each series, please visit birkhauser.com

Series in Pure and Applied Mathematics

Annals of the International Society of Dynamic Games Series Editor: Tamar Basar, University of Illinois, Urbana, USA

Advanced Courses in Mathematics - CRM Barcelona Series Editor: Manuel Castellet, Universitat Autònoma de Barcelona, Spain

Advances in Mathematical Fluid Mechanics Series Editors: Giovanni P. Galdi, University of Pittsburgh, USA John G. Heywood, University of British Columbia, Vancouver, Canada Rolf Rannacher, University of Heidelberg, Germany

Advances in Partial Differential Equations A subseries of: Operator Theory: Advances and Applications Subseries Editors: Bert-Wolfgang Schulze, University of Potsdam, Germany Sergio Albeverio, University of Bonn, Germany Michael Demuth, TU Clausthal, Germany Jerome A. Goldstein, University of Memphis, USA Nobuyuki Tose, Keio University, Yokohama, Japan

128

Applied and Numerical Harmonic Analysis Series Editor: John J. Benedetto, University of Maryland, College Park, USA

Birkhäuser Advanced Texts Series Editors: Herbert Amann, University of Zürich, Switzerland Steven G. Krantz, Washington University, St. Louis, USA Shrawan Kumar, University of North Carolina at Chapel Hill, Chapel Hill, USA Jan Nekovár, University Pierre et Marie Curie (Paris VI), France

Control Engineering Series Editor: William S. Levine, University of Maryland, College Park, USA

Cornerstones Series Editors: Charles L. Epstein, University of Pennsylvania, Philadelphia, USA Steven G. Krantz, Washington University, St. Louis, USA Editorial Advisory Board: Anthony W. Knapp, State University of New York at Stony Brook, Professor Emeritus, Stony Brook, USA

Edizioni della Normale Birkhäuser has taken over the international distribution of the English-language scientific titles of the Edizioni della Normale. The Edizioni della Normale are published by the Scuola Normale Superiore (SNS), the internationally renowned study and research centre in Pisa, Italy. See also www.birkhauser.ch/sns

Lectures in Mathematics – ETH Zürich Linear Operators and Linear Systems A subseries of: Operator Theory: Advances and Applications Subseries Editors: Daniel Alpay, Ben Gurion University of the Negev, Beer-Sheeva, Israel Joseph A. Ball, Virginia Tech, Blacksburg, USA André C. M. Ran, Vrije University of Amsterdam, The Netherlands

Mathematics: Theory & Applications Series Editor: Nolan Wallach, University of California, San Diego, USA

Frontiers in Mathematics Advisory Board: Luigi Ambrosio, Scuola Normale Superiore, Pisa, Italy Leonid A. Bunimovich, Georgia Institute of Technology, Atlanta, USA Benoît Perthame, Ecole Normale Supérieure, Paris, France Gennady Samorodnitsky, Cornell University, Ithaca, NY, USA Igor Shparlinski, Macquarie University, Australia Wolfgang Sprössig, TU Bergakademie Freiberg, Germany

International Series of Numerical Mathematics Managing Editors: Karl-Heinz Hoffmann, Technische Universität München, Germany Hans D. Mittelmann, Arizona State University, Tempe, USA

Modeling and Simulation in Science, Engineering and Technology Series Editor: Nicola Bellomo, Politecnico di Torino, Italy

Modern Birkhäuser Classics Many of the original research and survey monographs in pure and applied mathematics published by Birkhäuser in recent decades have been groundbreaking and have come to be regarded as foundational to the subject. Through the MBC Series, a select number of these modern classics, entirely uncorrected, are being re-released in paperback (and as eBooks) to ensure that these treasures remain accessible to new generations of students, scholars, and researchers.

129

Series Index

Monografie Matematyczne

Probability and its Applications

Founded by: Banach, S., Knaster, B., Kuratowski, K., Mazurkiewicz, S., Sierpinski, Steinhaus, H. Originally published by Polish Scientific Publishers, Warsaw Managing Editor Przemyslaw Wojtaszczyk, IMPAN and Warsaw University, Poland Editorial Board Jean Bourgain, IAS, Princeton, USA Tadeusz Iwaniec, Syracuse University, USA Tom Körner, Cambridge, UK Krystyna Kuperberg, Auburn University, USA Tomasz Luczak, Poznan University, Poland Ludomir Newelski, Wroclaw University, Poland Gilles Pisier, Université Paris 6, France Piotr Pragacz, Institute of Mathematics, Polish Academy of Sciences Grzegorz Swiatek, Pennsylvania State University, USA Jerzy Zabczyk, Institute of Mathematics, Polish Academy of Sciences

Series Editors: C. Newman, New York University, USA S. I. Resnick, Cornell University, Ithaka, USA

Monographs in Mathematics Managing Editors: H. Amann, Universität Zürich, Switzerland J.-P. Bourguignon, IHES, Bures-sur-Yvette, France K. Grove, University of Maryland, College Park, USA P.-L. Lions, Université de Paris-Dauphine, France

Oberwolfach Seminars Originally published as “Seminare der Deutschen Mathematiker-Vereinigung”

Operator Theory: Advances and Applications Series Editor: Israel Gohberg, School of Mathematical Sciences, Tel Aviv University, Israel

130

Progress in Mathematical Physics Editors-in-chief: Anne Boutet de Monvel, Université Paris VII Denis Diderot, France Gerald Kaiser, The Center for Signals and Waves, Austin, TX, U.S.A. Editorial Board: C. Berenstein, University of Maryland, College Park, U.S.A. Sir M. Berry, University of Bristol, U.K. P. Blanchard, Universität Bielefeld, Germany M. Eastwood, The University of Adelaide, Australia A.S. Fokas, Imperial College of Science, Technology, and Medicine, London, U.K. D. Sternheimer, Université de Bourgogne, Dijon, France C. Tracy, University of California, Davis, U.S.A.

Progress in Mathematics Series Editors: Hyman Bass, University of Michigan, USA Joseph Oesterlé, Institut Henri Poincaré, Université Paris VI, France Alan Weinstein, University of California, Berkeley, USA

Progress in Nonlinear Differential Equations and Their Applications Series Editor: H. Brezis, Université de Paris, France, and Rutgers University, USA

Progress in Probability Series Editors: C. Newman, New York University, USA S. I. Resnick, Cornell University, Ithaca, USA

Statistics for Industry and Technology

Science Networks – Historical Studies

Series Editor: N. Balakrishnan, McMaster University, Hamilton, Canada

Founded by: Hiebert, E., Wußing, H. Series Editors: E. Knobloch, Technische Universität Berlin, Germany E. Scholz, Bergische Universität, Gesamthochschule Wuppertal, Germany H. Kragh, University of Aarhus, Denmark In cooperation with an international editorial board

Studies in Universal Logic Series Editor: Jean-Yves Beziau, Swiss National Science Foundation, Switzerland

Systems & Control: Foundations & Applications Series Editor: Tamer Basar, University of Illinois, UrbanaChampaign, IL, USA

Trends in Mathematics

Series in History of Mathematics

Vita Mathematica Series Editor: E.A. Fellmann, Basel, Switzerland

Leonhard Euler: Opera Omnia Edited by the Euler Committee of the Swiss Academy of Science in collaboration with numerous specialists Editorial Board of Series I–III: H.-C. Im Hof (Chief Editor) / Th. Steiner / G.A. Tammann Editorial Board of Series IV: A. Kleinert (Chief Editor) / S. Bodenmann / E.A. Fellmann / G. Frei / M. Mattmüller / G.K. Mikhajlov / Th. Steiner

Contemporary Mathematicians Series Editor: Joseph P. Kung, University of North Texas, Denton, USA

Einstein Studies

The Collected Scientific Papers of the Mathematicians and Physicists of the Bernoulli Family General Editor: Patricia Radelet-de Grave

Published under the sponsorship of the Center for Einstein Studies, Boston University, USA Series Editors: D. Howard, University of Kentucky, Lexington, USA, Center for Einstein Studies, Boston University, USA J. Stachel, Center for Einstein Studies, Boston University, USA

131

Journals

Qualitative Theory of Dynamical Systems Editors-in-Chief: J. Llibre and J. Giné, both Universitat de Lleida, Spain Print ISSN: 1661-8254 Electronic ISSN: 1662-3592 2008, Vol. 1 (2 issues) For more information on this journal please see birkhauser.com

NEW in 2008

Advances in Applied Clifford Algebras Managing Editor: J. Keller, Universidad Nacional Autonoma de Mexico Print ISSN: 0188-7009 Electronic ISSN: 1661-4909 2008, Vol. 18 (4 issues)

Aequationes Mathematicae Honorary Editor-in-Chief: J. Aczél, University of Waterloo, ON, Canada Editor-in-Chief: L. Reich, Universität Graz, Austria Managing Editor: D. Gronau, Universität Graz, Austria Associate Managing Editor: C.T. Ng, University of Waterloo, ON, Canada Print ISSN 0001-9054 Electronic ISSN 1420-8903 2008, Vols. 75-76 (3 issues per volume)

132

algebra universalis Honorary Editors-in-Chief: B. Jónsson, Vanderbilt University, Nashville, TN Editor-in-Chief: G. Grätzer, University of Manitoba, Winnipeg, MB, Canada Executive Editors: C.R. Platt and R.W. Quackenbush, both, University of Manitoba, Winnipeg, MB, Canada, B.A. Davey, La Trobe University, Victoria, Australia Print ISSN 0002-5240 Electronic ISSN 1420-8911 2008, Vols. 59-60 (4 issues per volume)

Annales Henri Poincaré A Journal of Theoretical and Mathematical Physics Chief Editor: V. Rivasseau, Université d’Orsay, France Print ISSN 1424-0637 Electronic ISSN 1424-0661 2008, Vol. 9 (8 issues)

Annals of Combinatorics Managing Editor: W.Y.C. Chen, Nankai University, Tianjin, China; G.E. Andrews, Pennsylvania State University, PA; P. Paule, University of Linz, Austria Print ISSN 0218-0006 Electronic ISSN 0219-3094 2008, Vol. 12 (4 issues)

133

Journals

Archiv der Mathematik Managing Editor: E.-U. Gekeler, Universität des Saarlandes, Saarbrücken, Germany Print ISSN 0003-889X Electronic ISSN 1420-8938 2008, Vols. 90-91 (6 issues per volume)

Circuits, Systems & Signal Processing Editor-in-Chief: M.N.S. Swamy, Concordia University, Montreal, Canada Print ISSN 0278-081X Electronic ISSN 1531-5878 2008, Vol. 27 (6 issues)

Complex Analysis and Operator Theory Managing Editor: D. Alpay, Ben Gurion University of the Negev, Be’er-Sheva, Israel Print ISSN: 1661-8254 Electronic ISSN: 1661-8262 2008, Vol. 2 (4 issues per volume)

134

computational complexity Editor-in-Chief: J. von zur Gathen, Universität Bonn, Germany Associate Editors: S. Arora, Princeton University, Princeton, NJ; P. Bürgisser, Universität Paderborn, Germany; O. Goldreich, The Weizmann Institute, Rehovot, Israel Print ISSN 1016-3328 Electronic ISSN 1420-8954 2008, Vol. 17 (4 issues)

Geometric and Functional Analysis (GAFA) Managing Editor: M. Hercberg, Tel Aviv University, Israel Print ISSN 1016-443X Electronic ISSN 1420-8970 2008, Vol. 18 (6 issues)

Integral Equations and Operator Theory Editors-in-Chief: I. Gohberg, Tel Aviv University, Israel and S.M. Verduyn Lunel , Leiden University, The Netherlands Print ISSN 0378-620X Electronic ISSN 1420-8989 2008, Vols. 60-63 (4 issues per volume)

135

Journals

Journal of Evolution Equations Editors-in Chief: W. Arendt , Universität Ulm, Germany and R. Nagel , Universität Tübingen, Germany Print ISSN 1424-3199 Electronic ISSN 1424-3202 2008, Vol. 8 (4 issues)

Journal of Fixed Point Theory and Applications Editor-in Chief: A. Granas, Université de Montreal, Montreal (Quebec) Canada Print ISSN: 1661-7738 Electronic ISSN: 1661-7746 2008, Vol. 2 (2 issues)

Journal of Fourier Analysis and Applications (JFAA) Editor-in-Chief: H.G. Feichtinger, University of Vienna, Austria Founding Editor-in-Chief: J.J. Benedetto, University of Maryland, College Park, MD Print ISSN 1069-5869 Electronic ISSN 1531-5851 2008, Vol. 14 (6 issues)

136

Journal of Geometry Managing Editor: H.-J. Kroll, Technical University of Munich, Germany Print ISSN 0047-2468 Electronic ISSN 1420-8997 2008, Vols. 91-93 (2 issues per volume)

Journal of Mathematical Fluid Mechanics (JMFM) Editors-in-Chief: G.P. Galdi (Managing editor), University of Pittsburgh, PA; J.G. Heywood, University of British Columbia, Vancouver, BC, Canada; and R. Rannacher,Universität Heidelberg, Germany Print ISSN 1422-6928 Electronic ISSN 1422-6952 2008, Vol. 10 (6 issues)

Logica Universalis Editor-in-Chief: J.-Y. Beziau, Swiss National Science Foundation, Switzerland Print ISSN: 1661-8297 Electronic ISSN: 1661-8300 2008, Vol. 2 (2 issues)

137

Journals

Mathematics in Computer Science Editors-in-Chief: D. Zeng (Managing editor), and Z. Zeng, both Beihang University, Beijing, China Print ISSN: 1661-8270 Electronic ISSN: 1661-8289 2008, Vol. 2 (4 issues)

Mediterranean Journal of Mathematics Editor-in-Chief: F. Altomare, Università degli Studi di Bari, Italy Print ISSN: 1660-5446 Electronic ISSN: 1660-5454 2008, Vol. 8 (4 issues)

Milan Journal of Mathematics Managing Editor: B. Ruf, Università degli Studi di Milano, Italy Print ISSN: 1424-9286 Electronic ISSN: 1424-9294 2008, Vol. 76 (1 issue)

138

Nexus Network Journal Architecture and Mathematics Editor-in-Chief: K. Williams Print ISSN: 1590-5896 Electronic ISSN: 1522-4600 2008, Vol. 10 (2 issues)

Nonlinear Differential Equations and Applications (NoDEA) Managing Editor: V. Coti Zelati, Università degli Studi di Roma “La Sapienza,” Rome, Italy Print ISSN 1021-9722 Electronic ISSN 1420-9004 2008, Vol. 15 (6 issues)

Physics in Perspective Editors-in-Chief: J.S. Rigden, Washington University, St. Louis, MO; and R.H. Stuewer, University of Minnesota, Minneapolis, MN Print ISSN 1422-6944 Electronic ISSN 1422-6960 2008, Vol. 10 (4 issues)

139

Journals

Positivity An International Mathematics Journal Devoted to the Theory and Applications of Positivity Editor-in-Chief: C. D. Aliprantis, Purdue University, West Lafayette, IN Print ISSN: 1385-1292 Electronic ISSN: 1572-9281 2008, Vol. 12 (4 issues)

Results in Mathematics H. Wefelscheid, Universitat Duisburg-Essen, Germany Print ISSN 1422-6383 Electronic ISSN 1422-9012 2008, Vols. 53-54 (4 issues per volume)

Selecta Mathematica, New Series Editor-in-Chief: I.M. Gelfand, Rutgers University, Piscataway, NJ Print ISSN 1022-1824 Electronic ISSN 1420-9020 2008, Vol. 14 (4 issues)

140

Transformation Groups Editor-in-Chief: E.B. Vinberg, Moscow State University, Russia Managing Editors: M. Brion, Institut Fourier, Saint-Martin d’Heres Cedex, France V. Ginzburg, University of Chicago, Chicago, IL H. Nakajima, Kyoto University, Kyoto, Japan R. Sjamaar, Cornell University, Ithaca, NY A. Zelevinsky, Northeastern University, Boston, MA Print ISSN 1083-4362 Electronic ISSN 1531-586X 2008, Vol. 13 (4 issues)

Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Journal of Applied Mathematics and Physics Managing Editor: K. Nipp, ETH Zentrum, Zürich, Switzerland Print ISSN 0044-2275 Electronic ISSN 1420-9039 2008, Vol. 59 (6 issues)

For more information on all journals please visit birkhauser.com

141

Authors and Editors Index

142

Ablamowicz 80 Abonyi 105 Aczél 132 Adams 60 Adamson 22, 35 Aftalion 61 Ageel 89 Akos 90 Albeverio 128 Alfsen 58, 59 Aliprantis 140 Alpay 129, 134 Altomare 138 Amann 49, 62, 128, 130, Ambrosetti 69 Ambrosio 45, 129 Amirouche 104 An 90 Andreescu 15, 16, 28, 115, 116 Andreu-Vaillo 70 Andrews 133 Andrica 15 Anglès 74 Anker 39 Antia 103 Antsaklis 108, 112 Arendt 62, 136 Argyros 56 Arnold 83 Arora 135 Audin 32 Bachman 47 Bakstein 85 Balakrishnan 83, 131 Ball 51, 129 Banach 130 Bangerth 71 Barbieri 74 Barbour 127 Barbu 68 Bardi 6 Barge 24 Barndorff-Nielsen 88 Bart 51 Bartholdi 40 Basar 6, 128, 131 Bass 42, 130 Bastos 51 Baues 28 Baylis 81 Bellomo 96, 97, 129

Bellouquid 98 Benedetto 93, 128, 136 Bensoussan 110 Benz 25 Berenstein 57, 130 Berinde 117 Bermúdez de Castro 79 Bernhard 5 Bernoulli 123 Berry 130 Bertelsen 90 Berti 67 Beziau 22, 131, 137 Bhat 82 Bi 94 Billey 14 Blair 33 Blanchard 130 Blanchini 110 Bloch 23, 34 Bobenko 26 Boccaletti 25 Bodenmann 131 Bogomolov 19 Bohner 72 Boju 116 Bolmont 124 Bondy 11 Borel 4, 38, 39 Borodin 88 Borovik 14, 40 Borre 90 Borthwick 65 Bouchut 71 Bourgain 130 Bourguignon 130 Boutet de Monvel 75, 130 Bove 67 Brady 36 Bratteli 92 Bravo de la Parra 98 Brešar 11 Brezis 130 Brion 39, 141 Brodzik 90 Brown 41, 57 Brusch 97 Bruschi 102 Brylinski 4 Buchholz 75 Bucur 70 Bunimovich 129

Bunke 105 Burghelea 52 Bürgisser 135 Buser 35 Buttazzo 69, 70 Byrne 97 Calgaro 68 Calin 31, 57 Cannarsa 70 Cannas da Silva 32 Cannata 25 Caparrini 117, 123 Capasso 85 Capogna 37 Capuzzo-Dolcetta 6 Caramalho Domingues 122 Cardinali 27 Cartier 6, 7 Caselles 70 Castellet 128 Castellini 14 Catalano 106 Catoni 25 Ceccherini-Silberstein 40 Censor 97 Cercignani 77, 99 Chang 31, 57 Chaplain 97 Chebotar 11 Chen 89, 113, 133 Cherix 42 Chipot 72 Christensen 91, 93 Christopher 68 Clark 12 Cnops 81 Cohen 30 Cohn 60 Colombini 67 Colombo 80 Conlon 4 Constanda 104 Consul 84 Cooper 72 Coret 124 Corry 126 Costa 65 Coti Zelati 139 Coulombel 68 Cowling 42 Cramer 106 Cuntz 27

Da Prato 64, 110 Dal Maso 69 Damgard 106 Damour 76 Danielli 37 Darrigol 76 Darvas 117 Dauben 127 Davey 18, 133 David 56 Davis 101,118, 119 De Angelis 97 de Boer 98 De Bruyn 12 de Gosson 39 De Risi 123 de Vries 97 Debnath 66 Dehling 88 Dehornoy 34 Del Santo 67 Delfour 110 Delitala 98 Della Sala 54 Delorme 57 Demuth 79, 128 DeSimone 69 Deutsch 97, 98 Di Crescenzo 106 Diaconescu 21 DiBenedetto 60, 62 Dickinson 105 Diekmann 98 Dieudonne 127 do Carmo 35 Dormann 98 Douçot 79 Doukhan 87 Drábek 49 Dragomir 28 Drensky 13 Drucker 5 Dufour 40 Duistermaat 30, 43 Dungey 41 Duplantier 75, 76, 79 Eastwood 130 Edwards 60 Eidelman 51 Eisenstaedt 125 Elliott 100 Enescu 116

Enns 78, 79 Epstein 129 Ericsson 106 Escher 49 Etingof 37 Facchini 12 Falk 86, 88 Famoye 84 Fargues 25 Fauser 76 Feichtinger 136 Feil 105 Fellmann 120, 131 Fels 29 Feng 15, 16, 116 Ferreira 93 Ferreirós 123 Figueroa 33 Fine 17 Fokas 130 Fonlupt 11 Formanek 13, 40 Fouquet 11 Fournier 11 Freeden 94 Freeman 6 Frei 131 Fresnel 32 Fristedt 89 Fu 100 Funar 116 Gaal 20 Gabetta 99 Gal 50 Galaktionov 71 Galdi 99, 128, 137 Gan 16 Gautschi 103, 120 Gekeler 134 Gelbart 20 Gelca 115 Gelfand 4, 14, 37, 119, 140 Genestier 25 Giaquinta 47, 48, 70 Giga 69 Gigli 45 Giné 132 Ginzburg 19, 30, 61, 141 Glagoleva 119 Goldberg 56 Goldreich 135 Goldstein 128

Golubitsky 71, 72 Gomez 104 Good 85 Goodearl 41 Goudon 68 Gracia-Bondia 33 Graf 103 Granas 136 Grätzer 11, 18, 118, 133 Gray 5, 31, 89 Greene 5 Grigoriu 86 Grigoryan 54 Gröchenig 93, 94 Gromov 7, 40 Gronau 132 Grove 130 Gu 113 Guerraggio 125 Guillemin 60, 92 Gupta 89 Gürlebeck 50 Gustafsson 69 Gutenmacher 32 Guzman 59 Habetha 50 Haurie 100 Hehl 80 Heij 111 Heil 92, 93 Helgason 60 Helmstetter 10 Helton 51 Henrot 54 Hercberg 135 Herget 103 Herman 92 Hernández-Lerma 87 Hersh 118, 119 Herzel 97 Hess 30 Hesseling 126 Heyne 120 Heywood 128, 137 Hieber 62 Hinich 37 Hofer 35 Hoffmann 129 Hogan 92, 93 Holzapfel 49 Hong 13 Hörmander 7

143

Authors and Editors Index

144

Hotta 8 Hou 109 Howard 131 Høyrup 124 Hristu-Varsakelis 112 Hu 19 Huang 38 Huber-Carol 83 Huckleberry 29 Hüsler 86 Iagolnitzer 75 Iliev 77 Illusie 6, 7 Im Hof 131 Iordache 112 Iwaniec 130 Jacobsen 84 Jagers 98 Jarrow 100 Jensen 90 Jerrum 87 Ji 38, 39 Jiang 16, 97 Jolissaint 42 Jónsson 133 Jorgensen 92 Joseph 37, 41 Juhl 34 Julg 42 Kaashoek 51, 56 Kac 5 Kaiser 57, 95, 130 Kaluza 125 Kanwal 58 Kapovich 33, 36 Kapranov 4, 36 Katz 6, 7 Keller 125, 132 Kharitonov 113 Khoussainov 107 Khruslov 77 Kichenassamy 67 King 118 Kirilov 119 Klainerman 81 Klein 122 Kleiner 121 Kleinert 131 Knapp 8, 41, 55, 57, 129 Knaster 130 Knobloch 131 Knudson 34

Knuth 5 Kobayashi 9, 39 Koch Medina 87 Kock 24 Kokotovic 6 Kolk 43 Kolmogorov 127 Kolyada 36 Körner 130 Kotz 84, 88 Kox 125 Kozubowski 88 Kraetzl 105 Krantz 23, 43, 44, 128, 129 Kreck 31 Krim 101 Krishna 79 Kroll 137 Krömer 123 Krstic 109 Kuba 92 Kubrusly 59 Kudla 16, 20 Kumar 37, 39, 41, 128 Kung 131 Kunisch 69 Kunz 13 Kuperberg 130 Kuratowski 130 Kurdachenko 10 Kurdila 113 Kushner 108 Kwak 13 Lafforgue 25 Lakey 92, 93 Lakshmibai 14 Lancaster 56 Lancellotta 77 Landsman 34 Lannes 24 Lasserre 87 Laugwitz 5 Laumon 6, 7, 19 Lebre 51 LeFloch 72 Lepowsky 40 Lerman 32 Leugering 69 LeVeque 73 Levine 81, 112, 128 Li 40, 57, 68, 93 Liberzon 113

Lieb 80 Limnios 83 Lindner 53, 93 Lions 61, 130 Liu 109 Llibre 132 Locatelli 114 Lods 96 Lomp 12 Louis 97 Lubotzky 40, 42 Lück 31, 40 Luczak 130 Lusztig 4, 37 Lynch 63, 64 Ma 46 Maeda 24, 31 Malchiodi 69 Mallios 77 Manin 6, 7, 19, 36 Marasco 77 Marchenko 77 Marchisotto 118, 119, 121 Marinescu 46 Markvorsen 59 Marohn 88 Marsden 30, 31 Martinazzi 70 Martindale III 11 Mattmüller 131 Mazon 70 Mazurkiewicz 130 Mazzola 118 McEneaney 112 McGuire 78, 79 Meester 86 Melnikov 37, 41 Melrose 52 Merino 87 Merrill 92 Meyer 27 Miani 110 Micali 10 Michel 94, 103, 108, 109 Michor 24 Migliore 12 Mikhajlov 131 Mikosch 88 Milota 49 Mínguez 83 Min-Oo 59 Miró-Roig 9

Mishchenko 52 Mittelmann 129 Mitter 110 Modica 47, 48 Mollica 98 Monastyrsky 5 Moonen 31 Morales Ruiz 73 Moree 36 Morosanu 68 Mortici 115 Morucci 102 Moschella 75 Moszynska 29 Mucci 48 Muller 101, 118 Mumford 7 Murasugi 4 Mushkarov 28 Muto 100 Myint-U 66 Nagel 136 Nakajima 141 Nastasi 125 Nekovár 128 Nerode 107 Neubrander 62 Newelski 130 Newman 130 Ng 132 Nicaise 62 Nichelatti 25 Nicolo 81 Nievergelt 23, 95 Nijmeijer 112 Nikiforov 79 Nikulin 83 Nipp 141 Novikov 79 Obukhov 80 Ochiai 24 Oesterlé 130 Ogden 95 Olshevsky 51 Ó'Mathúna 74 Oppenheim 87 Orsted 39 Ortega 31, 40 Otal 10, 36 Packer 92 Palamodov 58 Palmer 75

Panchapagesan 50 Pandzic 38 Parks 43, 44 Pasquier 75, 79 Paule 133 Pauls 37 Pavlov 112 Payne 27 Perthame 99, 129 Peskir 102 Peterson 72 Petrosjan 100 Petters 81 Pfister 127 Pflaum 34 Pietsch 122 Pigola 45 Pisier 40, 130 Pittalis 102 Pittenger 107 Platt 133 Podgorski 88 Pogorzelski 21 Pointcheval 106 Polini 78 Ponnusamy 53 Poonen 20 Potapenko 104 Potyagailo 36 Pragacz 26, 130 Prato 64, 110 Prestini 126 Preziosi 98 Puca 102 Pucci 51 Quackenbush 133 Quittner 68 Rachev 100 Radelet-de Grave 117, 124, 131 Raghavan 100 Raimond 76 Rajagopal 98 Ramírez Alfonsín 11 Ramírez Galarza 26 Ran 51, 111, 129 Rand 62, 105 Rannacher 71, 99, 128, 137 Ratiu 30, 31, 40 Reich 132 Reiss 83, 86 Rentschler 41

Resnick 86, 88, 130 Retakh 37 Revelli 96 Ridolfi 96 Rife 124 Rigden 139 Rigoli 45 Riley 36 Rinder 90 Rivasseau 75, 76, 79, 133 Robertson 99 Robinson 41 Rodman 56 Romano 77 Rose 14, 18 Rosenberg 27 Rosenberger 17 Rota 5, 118 Roubicek 70 Rovenski 105 Rovnyak 51 Ruf 138 Sabadini 57, 80 Saberi 111 Sahai 89 Salminen 88 Samorodnitsky 129 Sandier 61 Sannuti 111 Santambrogio 98 Sarabia 83 Saracco 54 Saul 119 Savaré 45 Schagen 111 Schay 82 Scheidemann 57 Schinazi 89 Schlichenmaier 34 Schmid 9, 57 Scholz 131 Schöning 5 Schoof 31 Schröder 23, 26 Schulze 128 Schwartz 5, 127 Scriba 127 Seade 26, 52 Segal 40 Seiringer 80 Serfaty 61 Serrin 51

145

146

Setti 45 Shen 5, 119 Shiryaev 102 Shnol 119 Short 36 Shultz 58, 59 Sierpinski 130 Silverman 53 Simioniuc 54 Sinestrari 70 Singer 37, 81 Sjamaar 141 Slaughter 105 Smirnova-Nagnibeda 40 Smith 121 Sobczyk 80 Sohrab 59 Solovej 80 Sommen 80 Sommerfeld 80, 122 Sone 76 Sörensen 88 Souplet 68 Speck 51 Sprekels 69 Springer 14 Sprößig 50 Srikant 113 Srinivas 4 Stachel 127, 131 Staicu 65 Stanley 20 Steffens 125 Steiner 131 Steinhaus 130 Sternheimer 130 Stewart 71, 72 Stojanovic 100 Stollmann 81 Stoorvogel 111 Storer 106 Stout 46 Stoyanov 28 Stroock 60, 92 Struppa 57, 80 Stuewer 139 Subbotin 10 Sullivan 26 Suris 14 Suzuki 70 Swamy 134 Swiatek 130

Takeuchi 8 Tammann 131 Tanisaki 8 Taqqu 87 Tarantello 64 Teolis 95 ter Elst 41 Tewari 104 Tewes 88 Thangavelu 58 Thomas 83 Tian 34 Tirozzi 102 Todorcevic 18, 56 Tolimieri 90 Tolksdorf 76 Tomarelli 69 Tomassini 28, 54 Tonev 54 Toponogov 29 Tose 128 Tosi 78 Toti Rigatelli 127 Tracy 130 Triebel 54 Troitsky 52 Tröltzsch 69 Trudeau 5 Tschinkel 16, 19, 20 Turaev 32 Turek 99 Tyson 37 Uludag 49 Unterberger 38, 59 Uvarov 79 Vainsencher 24 Valette 33, 42 van der Geer 31 van der Put 32 Vanaja 12 Varilly 33 Vasil'ev 69 Vasilyev 32 Väth 52 Vaught 23 Vazquez 109 Vázquez 71 Verduyn Lunel 135 Vergne 57 Vilenkin 119 Villa Salvador 19 Vinberg 141

Vinter 114 Vollert 87 von zur Gathen 135 Vonta 83 Vorobiev 118 Voronov 30 Wallach 37, 57, 129 Wallis 17, 22, 23, 105 Walnut 57, 93, 94 Walter 124 Wambsganss 81 Wang 101 Wefelscheid 140 Weil 7 Weinstein 130 White 14 Williams 101, 117, 123, 139 Wisbauer 12 Wojtaszczyk 130 Wojtylak 21 Wolf 29 Wouw 112 Woyczynski 84 Xiao 30 Yang 9, 19 Yen 10 Yezzi, Jr. 101 Yngvason 80 Yoshida 49 Yoshioka 24, 31 Yushkevich 127 Zabarankin 113 Zabczyk 6, 130 Zaharopol 85 Zannier 27, 117 Zayed 93 Zehnder 35 Zeidler 76 Zelevinsky 4, 141 Zeng 94, 138 Zhi 101 Ziegler 26 Zoladek 30 Zuk 40 Zung 40

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