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Cornerstones is a new Birkhäuser series that is comprised of textbooks focusing on “what students need to know” and Advanced Algebra “what faculty should teach” in various selected topics in pure Anthony W. Knapp, State University of New York, Stony Brook, NY mathematics and related subjects. Basic Algebra and Advanced Algebra systematically develop Series Editors: concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together the two Charles L. Epstein, University of Pennsylvania, Philadelphia, PA books give the reader a global view of algebra and its role in math- Steven G. Krantz, Washington University, St. Louis, MO ematics as a whole.

Basic Algebra Key Topics and Features of Advanced Algebra: Anthony W. Knapp, State University of • Topics build upon the linear algebra, group theory, factoriza- New York at Stony Brook, NY tions of ideals, structure of fields, Galois theory, and elementary theory of modules as developed in Basic Algebra Basic Algebra and Advanced Algebra systematically develop concepts and tools • Chapters on modern algebra treat various topics in commuta- in algebra that are vital to every mathema- tive and noncommutative algebra and povide introductions to tician, whether pure or applied,, aspiring the theory of associative algebras, homological algebras, alge- or established. Together, the two books braic number theory, and algebraic geometry give the reader a global view of algebra • Continues to carry on the three prominent themes recurring in and its role in mathematics as a whole. Basic Algebra: the anaology between integers and polynomials in one variable over a field, the interplay between linear algebra and group theory, and the relationship between number theory Key Topics and Features of Basic Algebra: and geometry • Linear algebra and group theory build on each other continually • Many examples and hundreds of problems are included, along • Chapters on modern algebra treat groups, rings, fields, modules, with hints or complete solutions for most of the problems and Galois groups with emphasis on methods of computation • The exposition proceeds from the particular to the general, throughout often providing examples well before a theory that incorporates • Three prominent themes recur and blend together at times: the them; it includes blocks of problems that introduce additional analogy between integers and polynomials in one variable over topics and applications for futher study a field, the interplay between linear algebra and group theory, Advanced Algebra presents its subject matter in a forward-look- and the relationship between number theory and geometry ing way that takes into accoutn the historical development of the • Many examples and hundreds of problems are included, along subject. It is suitable as a text in a two-semester advanced under- with a separate 90-page section giving hints or complete solu- graduated or first-year graduate sequence in algebra, possibly sup- tions for most of the problems plemented for a graduate sequence by some material from Basic • The exposition proceeds from the particular to the general, of- Algebra. It requires of the reader only familiarity with matrix algebra, ten providing examples well before a theory that incorporates an understanding of the geometry and reduction of linear equa- them; includes blocks of problems that introduce additional tions, and an acquantance with proofs. topics and applications for future study Contents: Preface. • Guide for the Reader. • Transition to Modern • Applications to science and engineering (e.g., the fast Fourier Number Theory. • Wedderburn-Artin Ring Theory. • Brauer Group. transform, the theory of error-correcting codes, the use of the • Homological Algebra. • Three Theorems in Algebraic Number Theory. Jordan canonical form in solving linear systems of ordinary dif- • Reinterpretation with Adeles and Ideles. • Infinite Field Extensions. ferential equations, and constructions of interest in mathemati- • Background for Algebraic Geometry. • The Number Theory of cal physics) appear in sequences of problems Algebraic Curves. • Methods of Algebraic Geometry. • Index 2007 / APPROX. 650 PP., 10 ILLUS. / HARDCOVER / $69.95 Basic Algebra presents the subject matter in a forward-looking way ISBN_13 978-0-8176-4533-5 that takes into account its historical development. It is suitable as a ISBN_10 0-8176-4533-0 text in a two-semester advanced undergraduate or first-year graduate CORNERSTONES sequence in algebra, possibly supplemented by some material from Advanced Algebra at the graduate level. It requires of the reader only familiarity with matrix algebra, an understanding of the geometry and reduction of linear equations, and an acquaintance with proofs. Set of Basic Algebra Contents: Preface. • Guide for the Reader • Preliminaries about the and Advanced Algebra Integers, Polynomials, and Matrices. • Vector Spaces over Q R and C. 2007/$89.95 (TENT.) ISBN_13 978-0-8176-4533-5 • Inner-Product Spaces. • Group and Group Actions. • Theory of a Single ISBN_10 0-8176-4533-0 Linear Transformation. • Multilinear Algebra. • Advanced Group Theory. CORNERSTONES • Commutative Rings and Their Modules. • Fields and Galois Theory. • Modules over Noncommutative Rings. • Appendix. • Index See pages 28 and 30 for additional titles in the Cornerstones Series 2006 / 718 PP., 42 ILLUS. / HARDCOVER / $69.95 ISBN_13 978-0-8176-3248-9 ISBN_10 0-8176-3248-4 CORNERSTONES

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Representation Theory and Artinian Modules Over Group Automorphic Forms Rings Toshiyuki Kobayashi, Kyoto University, RIMS, Kyoto, Japan; Leonid Kurdachenko, Dnipropetrovsk National University, Ukraine; Wilfried Schmid, Harvard University, Cambridge, MA; Javier Otal, University of Zaragoza, Spain; Jae-Hyun Yang, Inha University, Incheon, Korea (Eds.) Igor Ya. Subbotin, National University, Los Angeles, CA This volume uses a unified approach to representation theory and This book highlights important developments on artinian modules automorphic forms. The invited papers, written by leading mathema- over group rings of generalized nilpotent groups. Along with tradi- ticians in related fields, track recent progress in the ever expanding tional topics such as direct decompositions of artinian modules, fields of representation theory and automorphic forms, and their as- criteria of complementability for some important modules, and cri- sociation with number theory and differential geometry. teria of semisimplicity of artinian modules, it also focuses on recent Contributors: T. Ikeda, T. Kobayashi, S. Miller, D. Ramakrishnan, advanced results. W. Schmid, F. Shahidi, K. Yoshikawa The theory of modules over groups has its own specific character 2007 / APPROX. 310 PP., 10 ILLUS. / HARDCOVER / $89.95 (TENT.) that plays an imperative role here and, for example, allows for a ISBN_13 978-0-8176-4505-2 significant generalization of the classical Maschke Theorem on ISBN_10 0-8176-4505-5 PROGRESS IN MATHEMATICS, VOL. 255 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. Schubert Varieties As self-contained as possible, this book will be useful for students as V. Lakshmibai, Northeastern University, Boston, MA; well as for experts in group theory, ring theory, and module theory. Peter Littelmann, Bergische Universität, Wuppertal, Germany; 2007 / APPROX. 264 PP. / SOFTCOVER / $49.95 (TENT.) C.S. Seshadri, Chennai Mathematical Institute, Chennai, India ISBN_13 978-3-7643-7764-9 ISBN_10 3-7643-7764-X Over the past two decades, and more intensely in recent years, the FRONTIERS IN MATHEMATICS algebro-geometric study of Schubert Varieties has had considerable impact on the theory of algebraic groups. One of the most interesting developments in the theory has been the construction of natural bases of representations of the full linear group, the orthogonal The Geometry of the group, and the symplectic group. This construction gives character Word Problem for Finitely formulas of these representations which are quite different in spirit from the famous character formulas of H. Weyl. In fact, they connect Generated Groups to monomial theory and the work of Hodge which was done more Noel Brady, University of Oklahoma, Norman, OK; than fifty years ago, and to the very recent developments in path Hamish Short, Université de Provence, Marseille, France; models, Frobenius splittings, and quantum groups. Tim Riley, Cornell University, Ithaca, NY Written by three of the world’s leading mathematicians in algebraic The origins of the word problem in group theory are decidability geometry, group theory, and combinatorics, this excellent self- con- and complexity, but through the vision of M. Gromov and the lan- tained exposition on Schubert Varieties unfolds systematically, from guage of filling functions, the topic now impacts the world of large- relevant introductory material on commutative algebra and algebra- scale geometry, including topics such as soap films, isoperimetry, ic geometry. First-rate text for a graduate course or for self-study. coarse invariants and curvature. 2007 / APPROX 400 PP. / HARDCOVER / $79.95 (TENT.) ISBN_13 978-0-8176-4153-5 The first part of this book introduces van Kampen diagrams in Cay- ISBN_10 0-8176-4153-X ley graphs of finitely generated, infinite groups; it discusses the van PROGRESS IN MATHEMATICS, Vol. 257 Kampen lemma, the isoperimetric functions or Dehn functions, the theory of small cancellation groups and gives 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. Rings, Modules, and the Total The second part is thus dedicated to Dehn functions, negatively Friedrich Kasch, Universität München, Germany and curved groups, in particular, CAT(0) groups, cubings and cubical Adolf Mader, University of Hawaii, Honolulu complexes. “The book is self-contained, well organized and nicely written, mak- In the last part, filling functions are presented from geometric, alge- ing it a very effective introduction to the subject at hand: the to- braic and algorithmic points of view. How filling functions interact is tal.”—MAA REVIEWS discussed, and applications to nilpotent groups, hyperbolic groups 2005 / 136 PP. / SOFTCOVERÂ/ $49.95 and asymptotic cones are given. Many examples and open prob- ISBN_13 978-3-7643-7125-8 lems are included. ISBN_10 3-7643-7125-0 FRONTIERS IN MATHEMATICS 2007 / APPROX. 200 PP. / SOFTCOVER / $39.95 ISBN_13 978-3-7643-7949-0 ISBN_10 3-7643-7949-9 ADVANCED COURSES IN MATHEMATICS–CRM BARCELONA

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Lifting Modules Introduction to Plane Supplements and Projectivity Algebraic Curves in Module Theory Ernst Kunz, Universität Regensburg, Germany John Clark, University of Otago, New Zealand; Richard G. Belshoff, Southwest Missouri Christian Lomp, Universidade di Porto, State University, Springfield, MO (Translator) Portugal; Narayanaswami Vanaja, “[T]he reader is invited to learn some top- Mumbai University, India; ics from commutative ring theory by mainly Robert Wisbauer, Universität Düsseldorf, studying their illustrations and applications Germany in plane curve theory. This methodical approach is certainly very enlightening and ef- Extending modules are generalizations of in- ficient for both teachers and students…The jective modules and, dually, lifting modules generalize projective supple- whole text is a real masterpiece of clarity, rigor, comprehension, me- mented modules. There is a certain asymmetry in this duality. While the thodical skill, algebraic and geometric motivation…highly enlighten- theory of extending modules is well documented in monographs and ing, motivating and entertaining at the same time…One simply can- text books, the purpose of this monograph is to provide a thorough study not do better in writing such a textbook.” —ZENTRALBLATT MATH (From a review of supplements and projectivity conditions needed to investigate classes of the German edition) of modules related to lifting modules. “The translation of the book is impeccable …the exposition is very The text begins with an introduction to small submodules, the radical, clear and the reading flows nicely. The book is a very good choice for variations on projectivity, and hollow dimension. The subsequent chap- a first course in algebraic geometry.”— MAA REVIEWS ters consider preradicals and torsion theories (in particular related to small modules), decompositions of modules (including the exchange This work is an introduction to commutative ring theory and algebraic property and local semi-T-nilpotency), supplements in modules (with plane curves, requiring only a basic knowledge of algebra. The exposi- specific emphasis on semilocal endomorphism rings), finishing with a tion focuses on the purely algebraic aspects of plane curve theory, leav- long chapter on lifting modules, leading up their use in the theory of ing the topological and analytical viewpoints in the background, with perfect rings, Harada rings, and quasi-Frobenius rings. only casual references to these subjects and suggestions for further reading. Examples, exercises, figures, and suggestions for further study Most of the material in the monograph appears in book form for the round out this fairly self-contained textbook. first time. The main text is augmented by a plentiful supply of exercises 2005 / 300 PP., 40 ILLUS. / HARDCOVER / $59.95 together with comments on further related material and on how the ISBN_13 978-0-8176-4381-2 theory has evolved. ISBN_10 0-8176-4381-8 2006 / 394 PP. / SOFTCOVER / $59.95 ISBN_13 978-3-7643-7572-0 ISBN_10 3-7643-7572-8 FRONTIERS IN MATHEMATICS Introduction to Commutative Algebra and Algebraic Geometry Infinite Groups Ernst Kunz, Universität Regensburg, Germany “An excellent text for a student who wants to learn the basic facts from com- Geometric, mutative algebra and algebraic geometry . . . Many examples and exercises Combinatorial and Dynamical Aspects complete the text.”—REVUE ROUMANIE DE MATHÉMATIQUES PURES ET APPLIQUÉES Laurent Bartholdi, Ecole Polytechnique Fédérale, Lausanne, Switzerland; “An excellent introduction to the subject . . . The center of gravity lies Tullio Ceccherini-Silberstein, Università degli Studi del Sannio, in commutative algebra, and this book can serve as a preparation for Benevento, Italy; more advanced topics. The presentation is very clear and the theory Tatiana Smirnova-Nagnibeda, University of Geneva, Switzerland; is accompanied by numerous interesting exercises . . . This is a highly Andrzej Zuk, Université Pierre et Marie Curie, Paris, France (Eds.) recommended text for students and lecturers.”—MATHEMATICA This book offers a panorama of recent advances in the theory of infinite 1997 / 256 PP. / HARDCOVER / $59.95 groups. It contains survey papers contributed by leading specialists in ISBN_13 978-0-8176-3065-2 ISBN_10 0-8176-3065-1 group theory and other areas of mathematics. Topics addressed in the book include amenable groups, Kähler groups, automorphism groups of rooted trees, rigidity, C*-algebras, random walks on groups, pro-p groups, Burnside groups, parafree groups, and Fuchsian groups. The Categorical Closure Operators accent is put on strong connections between group theory and other Gabriele Castellini, University of Puerto Rico, Mayaguez, Puerto Rico areas of mathematics, such as dynamical systems, geometry, operator algebras, probability theory, and others. “The book … presents the contemporary theory of categorical clo- Contributors: G. Baumslag, A.V. Borovik, T. Delzant, W. Dicks, sure operators, one of the main branches of categorical topol- E. Formanek, R. Grigorchuk, M. Gromov, P. de la Harper, A. Lubotzky, ogy. The purpose of the theory is to develop a categorical charac- W. Lück, A.G. Myasnikov, C. Pache, G. Pisier, A. Shalev, S. Sidki, E. Zelmanov terization of the classical topological concepts. It provides a tool 2005 / 413 PP., 26 ILLUS. / HARDCOVER / $109.00 that allows us to extend these concepts to an arbitrary category ISBN_13 978-3-7643-7446-4 so that the results of the theory have many applications in other ISBN_10 3-7643-7446-2 fields of mathematics, particularly topology, algebra, and discrete PROGRESS IN MATHEMATICS, VOL. 248 mathematics.”—INTERNATIONALE MATHEMATISCHE NACHRICHTEN 2003 / 300 PP., 100 ILLUS. / HARDCOVER / $69.95 ISBN_13 978-0-8176-4250-1 ISBN_10 0-8176-4250-1 MATHEMATICS: THEORY AND APPLICATIONS

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Congruences of Linear Algebra Finite Lattices Second Edition Jin Ho Kwak and Sungpyo Hong, both, A Proof-by-Picture Approach Pohang University of Science and Technology, George Grätzer, University of Manitoba, Pohang, Republic of South Korea Winnipeg, Canada “The emphasis is on computational skills “The book is self-contained, with many along with mathematical abstractions; basic detailed proofs presented that can be fol- concepts are introduced by means of ma- lowed step-by-step … I believe that this trices and the solution of systems of linear book is a much-needed tool for any math- equations. Many illustrative examples are ematician wishing a gentle introduction to given and all the usual advanced topics are the field of congruence representations treated … The second edition has been sub- of finite lattices, with emphasis on the more `geometric’ aspects.” stantially revised and new sections have been added.”— ZENTRALBLATT MATH — MATHEMATICAL REVIEWS This clear and rigorous presentation of the fundamentals of linear al- One of the world’s leading experts in lattice theory, George Grätzer, gebra is unique in its emphasis and integration of computational skills presents major results on the subject using his unique, “Proof by and mathematical abstractions. The power and utility of the subject is Picture” method. The book is appropriate for a one-semester graduate demonstrated, in particular, through the book’s focus on linear recur- course, and will also be of interest to researchers studying lattices. rence, difference and differential equations that affect applications in 2005 /300 PP.,100 ILLUS./HARDCOVER/$59.95 physics, computer science, and economics. ISBN_13 978-0-8176-3224-3 ISBN_10 0-8176-3224-7 This book can serve as a text for both theoretical and applied courses, and is ideal for self-study. 2004 / 392 PP. / SOFTCOVER / $59.95 ISBN_13 978-0-8176-4294-5 General Lattice Theory ISBN_10 0-8176-4294-3 Second Edition George Grätzer, University of Manitoba, Winnipeg, Canada “Grätzer’s General Lattice Theory has become the lattice theorist’s A Path to bible. Now…we have the second edition, in which the old testament Combinatorics for is augmented by a new testament … . The new testament gospel is provided by leading and acknowledged experts in their fields … . Each Undergraduates [of these eight contributions] is itself a gold mine. This is an excellent Counting Strategies and engaging second edition that will long remain a standard refer- Titu Andreescu, University of Texas, ence.”—MATHEMATICAL REVIEWS Dallas, TX and 2003 / 684 PP. / SOFTCOVER / $92.00 Zuming Feng, Phillips Exeter Academy, ISBN_13 978-3-7643-6996-5 ISBN_10 3-7643-6996-5 Exeter, NH “A good foundation in combinatorics is provided in the early chapters that cover Polynomial Identity Rings ideas in combinatorial geometry …. This book serves as a solid stepping stone for more advanced combina- Vesselin Drensky, Bulgarian Academy of Sciences, Sofia and torics studies in related mathematical science fields or in computer Edward Formanek, Pennsylvania State University, PA science.” —L’ENSEIGNEMENT MATHÉMATIQUE “The book under review consists of two excellent monographs on “This book is an introduction to counting strategies in combinatorial the PI-theory by two leading researchers, V. Drensky and E. For- theory. The main mathematical ideas are carefully worked into orga- manek … In summary, both expositions are very well written, and the nized, challenging, and instructive examples given in the nine chap- book is recommended both for graduate students and researchers.” ters of this book. In the last chapter we find 111 problems (without — MATHEMATICAL REVIEWS solutions) …. The…experience of the authors in preparing students for This book treats polynomial identity rings from both the combinatorial various mathematical competitions allowed them to present a big col- and structural points of view. The greater part of recent research in poly- lection of beautiful problems. By studying this book, undergraduates nomial identity rings concerns combinatorial questions, and the combi- will be well-equipped to further their knowledge in more abstract com- natorial part of the book gives an up-to-date account of recent research. binatorics and its related fields.”—MAA ONLINE 2004 / 200 PP. / SOFTCOVER / $39.95 A Path to Combinatorics for Undergraduates is a lively introduction not ISBN_13 978-3-7643-7126-5 ISBN_10 3-7643-7126-9 only to combinatorics, but also to mathematical ingenuity, rigor, and the ADVANCED COURSES IN MATHEMATICS–CRM BARCELONA joy of solving puzzles. Topics encompass permutations and combinations, binomial coefficients and their applications, bijections, inclusions and ex- clusions, and generating functions. Each chapter features fully-worked problems, as well as a number of problems original to the authors; at the end of each chapter are further exercises to reinforce understanding, encourage creativity, and build a repertory of problem-solving techniques. 2004 / 228 PP., 40 ILLUS. / SOFTCOVER / $39.95 ISBN_13 978-0-8176-4288-4 ISBN_10 0-8176-4288-9

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102 Combinatorial A Beginner’s Guide to Discrete Problems Mathematics From the Training of the USA W.D. Wallis, Southern Illinois University, Carbondale, IL IMO Team “Wallis’s book on discrete mathematics is a resource for an introducto- Titu Andreescu, University of Texas, Dallas, TX ry course in a subject fundamental to both mathematics and computer and Zuming Feng, Phillips Exeter Academy, science, a course that is expected not only to cover certain specific Exeter, NH topics but also to introduce students to important modes of thought specific to each discipline . . . Lower-division undergraduates through “51 ‘introductory problems’ and 51 ‘advanced graduate students.”—CHOICE problems,’ all novel, would nicely supplement any university course in combinatorics or dis- “Very appropriately entitled as a ‘beginner’s guide’, this textbook crete mathematics. This volume contains presents itself as the first exposure to discrete mathematics and detailed solutions, sometimes multiple solutions, for all the problems, and rigorous proof for the mathematics or computer science student.” some solutions offer additional twists for further thought .”—CHOICE —ZENTRALBLATT MATH “Another excellent effort towards building combinatorial skills especially This introduction to discrete mathematics is aimed primarily at under- for students engaged in mathematical competitions is presented in this graduates in mathematics and computer science at the freshmen and book through 102 selected combinatorial problems.” — ZENTRALBLATT MATH sophomore levels. The text has a distinctly applied orientation and begins with a survey of number systems and elementary set theory. Ad- “Each solution is given in full, and often with alternative versions as well. ditional chapters treat: data structures, counting, probability, relations Some solutions introduce standard combinatorial tools like inclusion-exclu- and functions, graph theory, matrices, number theory and cryptography. sion, generating functions, and graphs. Others stray into probability, num- Good examples occur throughout and there are problem sets with se- ber theory, complex numbers, inequalities and functional equations. The lected solutions at the end of each section. book will be useful for teachers looking for challenging problems for able 2002 / 384 PP., 43 ILLUS ./ SOFTCOVER / $39.95 students and for those preparing for Olympiads.”—THE MATHEMATICAL GAZETTE ISBN_13 978-0-8176-4269-3 2002 / 128 PP., 40 ILLUS. / SOFTCOVER / $29.95 ISBN_10 0-8176-4269-2 ISBN_13 978-0-8176-4317-1 ISBN_10 0-8176-4317-6 A Beginner’s Guide to Graph Theory A Beginner’s Second Edition Guide to Finite W.D. Wallis, Southern Illinois University, Carbondale, IL “Altogether the book gives a comprehensive introduction to Mathematics graphs, their theory and their application … The use of the text is For Business, Management, optimized when the exercises are solved. The obtained skills im- and the Social Sciences prove understanding of graph theory as well … It is very useful that the solutions of these exercises are collected in an appendix.” W.D. Wallis, Southern Illinois University, —SIMULATION NEWS EUROPE Carbondale, IL This concisely written textbook intended for a first course in graph the- “Requiring little mathematical background ory for undergraduate mathematics majors, is also accessible to other beyond high school algebra, the text will students at the same level. The work strikes a balance between a theo- be especially useful for business and liberal retical and practical approach. arts majors. Its straightforward treatment of This second edition includes new chapters on labeling and communica- the essential concepts in finite mathematics will appeal to a wide audi- tions networks and small worlds, as well as expanded beginner’s mate- ence of students and teachers.”—ZENTRALBLATT MATH rial in the early chapters, including more examples, exercises, hints and This concise text takes a distinctly applied approach to finite mathemat- solutions to key problems. Many additional changes, improvements, ics at the freshman and sophomore level. Topics are presented se- and corrections resulting from classroom use and feedback have been quentially: the book opens with a brief review of sets and numbers, fol- added throughout. lowed by an introduction to data sets, histograms, means and medians. Counting techniques and the Binomial Theorem are covered, which With a distinctly applied flavor, this gentle introduction to graph theory provides the foundation for elementary probability theory; this, in turn, consists of carefully chosen topics to develop graph-theoretic reasoning leads to basic statistics. for a mixed audience. Familiarity with the basic concepts of set theory, along with some background in matrices and algebra, and a little math- Graph theory is defined, with particular emphasis on its use in mathe- ematical maturity are the only prerequisites. matical modeling. Matrices and vectors are discussed, along with several 2007 2nd ed. / APPROX. 300 PP., 120 ILLUS. / SOFTCOVER/$39.95 elementary commercial applications. The book concludes with an intro- ISBN_13 978-0-8176-4484-0 duction to linear programming, including the simplex method and duality. ISBN_10 0-8176-4484-9 Ample examples and illustrations are provided throughout; each section contains two sets of problems, with solutions provided for the first set. 2004 / 354 PP., 100 ILLUS. / SOFTCOVER / $49.95 ISBN_13 978-0-8176-4270-9 ISBN_10 0-8176-4270-6

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Magic Graphs Fields and Models W.D. Wallis, Southern Illinois University, Carbondale, IL From Sturm to Tarski and Robinson “The book is a beautiful collection of recent results on the topic of Hourya Benis Sinaceur, CNRS, Paris, France; and Rabat, Morocco ‘magic labelings’.”—MATHEMATICAL REVIEWS Translated by Fred Bourgoin, “The book should be accessible to advanced undergraduates or University of California, Berkeley, CA beginning graduate students. It might serve as inspiration for an This unique work, equal parts history, philosophy, and mathematics, REU program or as a source for senior undergraduate research traces the intertwined development of logic and algebra, particularly projects, particularly if supervised by a mathematician who is truly Tarski’s model theory and Artin’s and Schrier’s algebra of closed real ‘up’ on what is going on in this field.”—MAA REVIEWS fields. A number of pivotal results are woven into this collaboration Magic squares are among the more popular mathematical across disciplines: Sturm’s theorem on the location of roots of real recreations. This concise, self-contained exposition is unique in its polynomials, which is the unifying theme, as well as Artin’s solution focus on the theory of magic graphs and labeling, and has applica- to Hilbert’s 17th problem, Tarski’s decision procedure for the field tions to a number of new areas. It may serve as a graduate text for of real numbers, and research into quadratic forms. a special topics seminar in mathematics or computer science, or as Drawing extensively on original sources, Hourya Sinaceur discusses a professional text for the researcher. not only the evolution of new mathematical ideas, but also their 2001 / 160 PP., 21 ILLUS. / SOFTCOVER / $59.95 epistemological foundations and the ways in which mathematical ISBN_13 978-0-8176-4252-5 ISBN_10 0-8176-4252-8 subdisciplines influence one another. 2007 / APPROX. 446 PP., 5 ILLUS. / HARDCOVER / $99.00 (TENT.) ISBN_13 978-0-8176-4114-6 ISBN_10 0-8176-4114-9 Coxeter Matroids Alexandre V. Borovik, UMIST, Manchester, UK; Proofs and Israel M. Gelfand, Rutgers University, Piscataway, NJ; and Fundamentals Neil White, University of Florida, A First Course in Abstract Gainesville, FL Mathematics “This largely self-contained text pro- Ethan D. Bloch, Bard College, Annan- vides an intuitive and interdisciplin- dale-on-Hudson, NY ary treatment of Coxeter matroids, a new and beautiful generalization of “Proofs and Fundamentals has many matroids which is based on a finite strengths. One notable strength is its excellent organization. The book begins Coxeter group.”—ZENTRALBLATT MATH with a three-part preface which makes “This accessible and well-written book, intended to be ‘a cross its aims very clear. There are large ex- between a postgraduate text and a research monograph,’ is well ercise sets throughout the book . . . Exercises are well integrated worth reading and makes a good case for doing matroids with with the text and vary appropriately from easy to hard … Topics mirrors.”—SIAM REVIEW in Part III are quite varied, mostly independent from each other, “This accessible and well-written book, designed to be ‘a cross be- and truly dependent on Parts I and II. … there are useful hints to tween a postgraduate text and a research monograph’, should win selected exercises. many converts.”—MATHEMATICAL REVIEWS “Perhaps the book’s greatest strength is the author’s zeal and skill Key topics and features: for helping students write mathematics better. Careful guidance is given throughout. Basic issues like not abusing equal signs are • Systematic, clearly written exposition with ample references to treated explicitly. Attention is given to even relatively small issues, current research like not placing a mathematical symbol directly after a punctuation • Matroids are examined in terms of symmetric and finite mark. Throughout the book, theorems are often followed first by in- relection groups formative ‘scratch work’ and only then by proofs. Thus students can • The Gelfand-Serganove theorem is presented, allowing for a see many examples of what they should think, what they should geometric interpretation of matroids and Coxeter matroids as write, and how these are usually not the same.”—MAA ONLINE convex polytopes with certain symmetry properties 2000 / 448 PP., 39 ILLUS. / HARDCOVER / $49.95 ISBN_13 978-0-8176-4111-5 • Matroid representations in building and combinatorial flag ISBN_10 0-8176-4111-4 varieties are studied in the final chapter • Many exercies throughout 2003 / 264 PP., 65 ILLUS ./ HARDCOVER / $79.95 ISBN_13 978-0-8176-3764-4 ISBN_10 0-8176-3764-8 PROGRESS IN MATHEMATICS, VOL. 216

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Ordered Sets Logica Universalis An Introduction Towards a General Theory Bernd S.W. Schroeder, Louisiana Tech of Logic University, Ruston, LA Jean-Yves Beziau, University of Neuchâtel, Switzerland (Ed.) “The author has done the field a service by producing an excellent text strong in the pre- Universal Logic is not a new logic, but a sentation of certain topological aspects of the general theory of logics, considered as underlying diagrams, e.g., which should serve mathematical structures. The name was the developing community and field well and introduced about ten years ago, but the which can be recommended without reser- subject is as old as the beginning of mod- vations as one of the volumes which should ern logic: Alfred Tarski and other Polish grace a poseteer’s library whether she is in- logicians such as Adolf Lindenbaum devel- terested only or mainly in the theory of these objects or has directed her oped a general theory of logics at the end of the 1920s based on con- gaze towards applications. As a sourcebook of ideas and understanding it sequence operations and logical matrices. The subject was revived after will make its mark. And deservedly so.” —ZENTRALBLATT MATH the flowering of thousands of new logics during the last thirty years: “This book is a most successful introduction to the theory of ordered there was a need for a systematic theory of logics to put some order sets. The range of topics covered is wide yet the exposition is self- in this chaotic multiplicity. This book contains recent works on universal contained … The focus on open problems makes for enthusiastic logic by first-class researchers from all around the world. writing and provides continuity among the diverse topics that are The book is full of new and challenging ideas that will guide the future discussed … in each chapter the author proves a solid collection of of this exciting subject. It will be of interest for people who want to bet- basic results, presents one or more major theorems with detailed ter understand what logic is. Tools and concepts are provided here for and nontrivial proofs, and states without proof one or two other im- those who want to study classes of already existing logics or want to portant results. At the end of every chapter is an ample collection of design and build new ones. exercises … A novel aspect of [the twelfth] chapter is the presentation 2005 X / 228 PP. / SOFTCOVER / $69.95 of much of the material in terms of constraint satisfaction problems.” ISBN_13 978-3-7643-7259-0 —MATHEMATICAL REVIEWS ISBN_10 3-7643-7259-1 “Surprisingly, despite the extremely basic nature of the subject, this monograph has essentially no competition. But fortunately the first entry proves a gem. Undergraduate mathematics and computer science Foundations of Logic majors will find the first chapters offering background that will serve them well in many courses. The rest of the book, which features many and Mathematics open problems, constitutes an accessible and stimulating invitation to Applications to Computer Science research … Highly recommended.” —CHOICE and Cryptography 2003 / 416 PP., 35 ILLUS. / HARDCOVER / $59.95 Yves Nievergelt, Eastern Washington ISBN_13 978-0-8176-4128-3 University, Cheney, WA ISBN_10 0-8176-4128-9 “The way [the topics] are presented is highly original . . . The author has chosen a strictly formal and axiomatic approach. Logic for Computer Scientists All the results are proved in full detail from Uwe Schöning, Universität Ulm, Germany first principles…remarkably, the arithmetic “Contains examples and 126 interesting exercises which put the stu- laws on the rational numbers are proved, dent in an active reading mode … Would provide a good university step after step, starting from the very definitions! … This is a valuable short course introducing computer science students to theorem prov- reference text and a useful companion for anybody wondering how basic mathematical concepts can be rigorously developed within set ing and logic programming.”—MATHEMATICAL REVIEWS theory. The author has managed to combine the foundational ap- 1994 / 172 PP. / HARDCOVER / $49.95 ISBN_13 978-0-8176-3453-7 proach with a careful treatment of many applications. More than ISBN_10 0-8176-3543-3 1000 exercises complete the text.”—MATHEMATICAL REVIEWS PROGRESS IN COMPUTER SCIENCE AND APPLIED LOGIC, VOL. 8 Solutions manual is available upon adoption of the text. 2001/432 PP., 22 ILLUS./HARDCOVER/$69.95 ISBN_13 978-0-8176-4249-5 ISBN_10 0-8176-4249-8 Handbook of Logic and Proof Techniques for Computer Science Steven Krantz, Washington University, St. Louis, MO “This is really what it promises to be—a good handbook: supple, self - contained, providing the necessary and sufficient working resources … it is more than [one] expect[s]: the rigour of usefulness and conciseness exceeds or equals … the pleasure of reading it.”—ZENTRALBLATT MATH 2002/272 PP., 16 ILLUS./HARDCOVER/$54.95 ISBN_13 978-0-8176-4220-4 ISBN_10 0-8176-4220-X CO-PUBLISHED WITH SPRINGER

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Number Theory Complex Numbers An Introduction via the from A to … Z Distribution of Primes Titu Andreescu, University of Texas, Dallas, TX; Benjamin Fine, Fairfield University, Dorin Andrica, “Babes-Bolyai” University, Fairfield, CT; Cluj-Napoca, Romania Gerhard Rosenberger, Universität “It is for the readers who seek to harness Dortmund, Germany new techniques and to polish their mastery This book provides an introduction and over- of the old ones. It is for somebody who view of number theory based on the distri- made it their business to be solving prob- bution and properties of primes. The unique lems on a regular basis. These readers will approach provides both a firm background in appreciate the scope of the methodologi- the standard material as well as an overview cal detail the authors of the book bring to of the whole discipline. All the essential topics are covered: fundamental their attention, they will appreciate the power of the methods and the theorem of arithmetic, theory of congruences, quadratic reciprocity, arith- intricacy of the problems.”—MAA REVIEWS metic functions, and the distribution of primes. Analytic number theory and It is impossible to imagine modern mathematics without complex algebraic number theory both receive a solid introductory treatment. numbers. Complex Numbers from A to…Z introduces the reader to The book’s user-friendly style, historical context, and wide range of ex- this fascinating subject, which from the time of L. Euler, has become ercises from simple to quite difficult (with solutions and hints provided one of the most utilized ideas in mathematics. for select ones) make it ideal for self study as well as classroom use. In- The exposition concentrates on key concepts and then elementary tended for upper level undergraduates and beginning graduate students, results concerning these numbers. The reader learns how complex the only prerequisites are a basic knowledge of calculus, multivariable numbers can be used to solve algebraic equations and to understand calculus, and some linear algebra. All necessary concepts from abstract the geometric interpretation of complex numbers and the operations algebra and complex analysis are introduced in the book. involving them. 2007 / 342 PP., 12 ILLUS. / SOFTCOVER / $59.95 ISBN_13 978-0-8176-4472-7 The theoretical parts of the book are augmented with rich exercises and ISBN_10 0-8176-4472-5 problems at various levels of difficulty. A special feature of the book is the last chapter, a selection of outstanding Olympiad and other important mathematical contest problems solved by employing the methods already presented. Set Theory 2005 / 344 PP., 82 ILLUS. / SOFTCOVER / $49.95 Second Edition ISBN_13 978-0-8176-4326-3 Robert Vaught, University of California, Berkeley, CA ISBN_10 0-8176-4326-5 “One of [the book’s] strengths is the author’s voice. His prose is clear and correct … The text is quite concise.”—MATHEMATICAL REVIEWS “The volume is in a clear and interesting style and is highly recom- 104 Number Theory Problems mended to undergraduate students of mathematics as well as phi- From the Training of the USA IMO Team losophy.”—Acta Sci. Math. (on the first edition) Titu Andreescu, University of Texas, Dallas, TX; An excellent undergraduate level text on set theory written in a lively, interest- Dorin Andrica, “Babes-Bolyai” University, Cluj-Napoca, Romania; ing and good-humored style. This book corresponds to a view of the subject Zuming Feng, Phillips Exeter Academy, Exeter, NH from someone who has thought deeply about this and many other aspects This challenging problem book by renowned US Olympiad coaches, of mathematical logic. The second edition has been expanded to include so- mathematics teachers, and researchers develops a multitude of prob- lutions to the problems,, increasing the book’s usefulness as teaching tool. lem-solving skills needed to excel in mathematical contests and in 2001 / 184 PP. / Softcover / $69.95 mathematical research in number theory. Applying specific techniques ISBN_13 978-0-8176-4256-3 ISBN_10 0-8176-4256-0 and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory. The presentation begins by familiarizing students with typical examples that illustrate central themes, followed by numerous carefully selected problems and extensive discussions of their solutions. Engaging students in creative thinking and stimulating them to express their comprehension and mastery of the material beyond the classroom, 104 Num- ber Theory Problems is a valuable resource for advanced high school students, undergraduates, instructors, mathematics coaches preparing to participate in mathematical contents, and those contemplating future research in number theory and its related areas. 2007/204 PP./SOFTCOVER/$39.95 ISBN_13 978-0-8176-4527-4 ISBN_10 0-8176-4527-6

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Introduction to Diophantine Eisenstein Series and Applications Equations Wee Teck Gan, UCSD, La Jolla, CA; Stephen S. Kudla, University of Maryland, College Park, MD; Titu Andreescu, University of Texas, Dallas, TX; Yuri Tschinkel, Courant Institute of Mathematical Sciences / NYU, New Dorin Andrica, “Babes-Bolyai” University, Cluj-Napoca, Romania; York, NY, (Eds.) Ion Cucurezeanu, Revista de matematica si informatica din Constanta, Romania Eisenstein series are an essential ingredient in the spectral theory of automorphic forms and an important tool in the theory of L-functions. This book is an introduction to the study of Diophantine equations, a They have also been exploited extensively by number theorists for class of equations in which only integer solutions are allowed. The ma- many arithmetic purposes. terial is organized in two parts. Part I introduces the reader to elementary methods necessary in solving Diophantine equations, such as the The central theme of the exposition focuses on the common structural decomposition method, inequalities, the parametric method, modular properties of Eisenstein series occurring in many related applications arithmetic, mathematical induction, Fermat’s method of infinite de- that have arisen in several recent developments in arithmetic: Arakelov scent, and the method of quadratic fields. The presentation includes intersection theory on Shimura varieties, special values of L-functions some classical Diophantine equations, including linear, Pythagorean and Iwasawa theory, and equidistribution of rational/integer points on and some higher degree equations, as well as exponential Diophantine homogeneous varieties. equations. Part II contains complete solutions to all exercises featured Contributors: D. Bump, M. Emerton, W. T. Gan, S. Kudla, E. Lapid, in Part I. J. Schwermer, C. M. Skinner, R. Takloo-Bighush Many of the selected exercises and problems are original or are present- 2007/APPROX. 350 PP., 20 ILLUS./HARDCOVER/$69.95 (TENT.) ISBN_13 978-0-8176-4496-3 ed with original solutions. This work is intended for undergraduates, high ISBN_10 0-8176-4496-2 school students and their teachers, mathematics contests participants PROGRESS IN MATHEMATICS, vol 258 (including Olympiad and Putnam competitors), as well as any person interested in essential mathematics. This work uniquely presents uncon- ventional and non-routine examples, ideas, and techniques. 2007 / APPROX. 250 PP., 20 ILLUS. / SOFTCOVER / $49.95 (TENT.) Number Theory ISBN_13 978-0-8176-4548-9 ISBN_10 0-8176-4548-9 A Problem-Solving Approach Titu Andreescu, University of Texas, Dallas, TX; Dorin Andrica, “Babes-Bolyai” University, Cluj-Napoca, Romania Topics in the One of the oldest, liveliest branches of mathematics, number theory is noted for its theoretical depth and applications to other fields, including Theory of Algebraic representation theory, physics, and cryptography. The forefront of num- Function Fields ber theory is replete with sophisticated and famous open problems; at its foundation, however, are basic, elementary ideas that can stimulate Gabriel Daniel Villa Salvador, and challenge beginning students. CINVESTAV del IPN, Mexico City, Mexico Starting with the essentials, this introductory text covers divisibility, Fields of algebraic functions of one variable unique factorization, modular arithmetic and the Chinese Remainder appear in several areas of mathematics: Theorem, Diophantine equations, binomial coefficients, Fermat and complex analysis, algebraic geometry, and Mersenne primes and other special numbers, special sequences, and number theory. This text adopts the latter problems of density. Included are sections on mathematical induction perspective by applying an arithmetic-alge- and the pigeonhole principle, as well as a discussion of other number braic viewpoint to the study of function fields as part of the algebraic systems. theory of numbers. By emphasizing examples and applications, and by introducing and The examination explains both the similarities and fundamental dif- reinforcing every idea with an exercise, the authors motivate and en- ferences between function fields and number fields, including many gage readers. exercises and examples to enhance understanding and motivate further study. The only prerequisites are a basic knowledge of field theory, Written by distinguished research mathematicians and renowned complex analysis, and some commutative algebra. teachers, Number Theory: A Problem-Solving Approach will appeal to senior high school and undergraduate students and instructors. It is a The book can serve as a text for a graduate course in number theory or clear, accessible introduction to the subject and a source of fascinating an advanced graduate topics course. Researchers interested in number problems and puzzles for readers at all levels. theory, field theory, and their interactions will also find the workan 2008 / APPROX. 300 PP., 150 ILLUS. / HARDCOVER / $49.95 (TENT.) excellent reference. ISBN_13 978-0-8176-3245-8 2006/ 652 PP., 20 ILLUS. / HARDCOVER/$89.95 ISBN_10 0-8176-3245-X ISBN_13 978-0-8176-4480-2 ISBN_10 0-8176-4480-6 MATHEMATICS: THEORY & APPLICATIONS

10 Order By Phone: 1-800-777-4643 • Fax: 201-348-4505 • Or Online: www.birkhauser.com number theory

Value Distribution Theory Related An Introduction to Number Theory to the Langlands Pei-Chu Hu, Shandong University, China; Program Chung-Chun Yang, Hong Kong University of Science and Technology, China Joseph Bernstein, Tel Aviv University, The subject of the book is Diophantine approximation and Nevan- Israel; and linna theory. Not only does the text provide new results and direc- Stephen Gelbart, The Weizmann tions, it also challenges open problems and collects latest research Institute of Science, Rehovot, Israel (Eds.) activities on these subjects made by the authors over the past eight years. Some of the significant findings are the proof of the Green- “The six chapters of this monograph Griffiths conjecture by using meromorphic connections and Jacobian give a broad, user-friendly introduction sections, and a generalized abc-conjecture. to the Langlands program, that is, the theory of automorphic forms and its The book also presents state of the art studies of the analogues be- connection with the theory of L-functions and other fields of math- tween Diophantine approximation (in number theory) and value dis- ematics. First-year graduate students and researchers will benefit tribution theory (in complex analysis), with a method based on Vojta’s from this beautiful text.”—ZENTRALBLATT MATH dictionary for the terms of these two fields. It is self-contained and appended with a comprehensive and up-to-date list of references. “The present volume constitutes the most readable entree into the subject to date, suitable both for serious reading and for 2006 / 543 PP. / HARDCOVER / $125.00 ISBN_13 978-3-7643-7568-3 browsing, and should attract a new generation to this exciting ISBN_10 3-7643-7568-X subject … Recommended.”—CHOICE “I suspect this book will find its way into the hands of many graduate students. Perhaps it will also motivate a few of them Arithmetic of Higher-Dimensional to learn more, get involved, and make their own contributions.” —MAA REVIEWS Algebraic Varieties For the past several decades the theory of automorphic forms has Bjorn Poonen, University of California, Berkeley, CA and become a major focal point of development in number theory and Yuri Tschinkel, Princeton University, Princeton, NJ (Eds.) algebraic geometry, with applications in many diverse areas, includ- This text takes an interdisciplinary view of the study of higher ing combinatorics and mathematical phyiscs. dimensional varieties. A digest of research and survey papers by The six chapters of this monograph present a broad, user-friendly leading specialists, the work documents current knowledge in high- introduction to the Langlands program: that is, the theory of auto- er-dimensional arithmetic and gives indications for future research. morphic forms and its connection with the theory of L-functions and Contributors: V.V. Batyrev, N. Broberg, J-L Colliot-Thélène, other fields of mathematics. J.S.Ellenberg, P. Gille, T. Graber, D. Harari, J. Harris, B. Hassett, R. Key features: Heath-Brown, B. Mazur, E. Peyre, B. Poonen, O.N. Popov, W. Raskind, P.Salberger, V. Scharaschkin, J. Shalika, J. Starr, P. Swinnerton-Dyer, R. • A variety of areas in number theory from the classical zeta function Takloo-Bighash, Y. Tschinkel, J.F. Voloch, O. Wittenberg. up to the Langlands program are covered 2004 / 287 PP., 10 ILLUS. / HARDCOVER / $74.95 • The exposition is systematic, with each chapter focusing on a par- ISBN_13 978-0-8176-3259-5 ticular topic devoted to special cases of the program: Basic zeta ISBN_10 0-8176-3259-X function of Riemann and its generalizations to Dirichlet and Hecke L- PROGRESS IN MATHEMATICS, VOL. 226 function, class field theory and some topics on classical automorphic functions (E. Kowalski) • A study of the conjectures of Artin and Shimura-Taniyama-Weil Geometric Methods in Algebra (E. de Shalit) and Number Theory • An examination of classical modular (automorphic) L-functions Fedor Bogomolov, New York University, New York, NY, and as GL2 functions, bringing into play the theory of representations Yuri Tschinkel, Princeton University, Princeton, NJ (Eds.) (S. Kudla) • Selberg’s theory of the trace formula, which is a way to study This volume contains a selection of articles exploring geometric ap- automorphic representation (D. Bump) proaches to problems in algebra, algebraic geometry, and number theory. Specific topics covered: moduli spaces, Shimura varieties, D- • Discussion of cuspidal automorphic representations of GL2 modules, p-adic methods (motivic integration), and number theo- leads to Langlands theory for GLn and the importance of the retic applications (rational points). The text can serve as an intense Langlands’ dual group (J. Cogdell) introduction for graduate students and those wishing to pursue re- • An introduction to the geometric Langlands program, a new search in algebraic and arithmetic geometry. and active area of research that permits using powerful methods Contributors: I. Bauer, F. Bogomolov, N. Budur, F. Catanese, of algebraic geometry to construct automorphic sheaves (D. Gaitsgory). C.-L. Chai, R. Cluckers, C. De Concini, J.S. Ellenberg, F. Grunewald, B. Hassett, T. Hausel, F. Loeser, J. Pineiro, R. Pink, C. Procesi, Graduate students and researchers will benefit from this beautiful text. M. Spitzweck, P. Swinnerton-Dyer, L. Szpiro, H. Tamvakis, Y. Tschinkel, 2003 / 281 PP., 5 ILLUS. / SOFTCOVER/$42.95 ISBN_13 978-0-8176-3211-3 T.J. Tucker, A. Venkatesh, and Y.G. Zarhin. ISBN_10 0-8176-3211-5 2004 / 366 PP., 6 ILLUS. / HARDCOVER / $69.95 ISBN_13 978-0-8176-4349-2 ISBN_10 0-8176-4349-4 PROGRESS IN MATHEMATICS, VOL. 235

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Geometric Problems An Invitation to on Maxima and Quantum Minima Cohomology Titu Andreescu, University of Texas, Dallas, TX; Kontsevich’s Formula for Oleg Muskarov, Institute for Mathemat- Rational Plane Curves ics, Bulgarian Academy of Sciences, Sofia; and Joachim Kock, Universitat Autònoma de Barce- Luchezar Stoyanov, lona, Barcelona, Spain; University of Western Australia, Crawley Israel Vainsencher, Universidade Federal de “As an avid problem solver with a strong Minas Gerais, Pampulha-Belo Horizonte, Brazil interest in inequalities, particularly algebraic and analytic inequalities, I am delighted to This book is an elementary introduction to sta- supplement my repertoire with the techniques illustrated in this volume. ble maps and quantum cohomology, starting Over the years, Titu Andreescu and various collaborators have used with an introduction to stable pointed curves, and culminating with a proof of their experiences as teachers and as Olympiad coaches to produce a the associativity of the quantum product. series of excellent problem solving manuals, as a quick MAA Reviews Emphasis is given throughout the exposition to examples, heuristic discus- search on ‘Andreescu’ will reveal. The present volume continues that sions, and simple applications of the basic tools to best convey the intuition tradition and should appeal to a wide audience ranging from advanced behind the subject. The book demystifies these new quantum techniques high school students to professional mathematicians.”—MAA REVIEWS by showing how they fit into classical algebraic geometry. Questions of maxima and minima have great practical significance, with Each chapter concludes with some historical comments and an outline of applications to physics, engineering, and economics; they have also given key topics and themes as a guide for further study, followed by a collection rise to theoretical advances, notably in calculus and optimization. Indeed, of exercises that complement the material covered and reinforce computa- while most texts view the study of extrema within the context of calculus, tional skills. this carefully constructed problem book takes a uniquely intuitive ap- As such, the book is ideal for self-study, as a text for a mini-course in quan- proach to the subject: it presents hundreds of extreme value problems, tum cohomology, or as a special topics text in a standard course in intersec- examples, and solutions primarily through Euclidean geometry. tion theory. 2005 / 320 PP., 160 ILLUS. / SOFTCOVER / $69.95 2007/ 160 PP. / HARDCOVER / $49.95 ISBN_13 978-0-8176-3517-6 ISBN_13 978-0-8176-4456-7 ISBN_10 0-8176-3517-3 ISBN_10 0-8176-4456-3 PROGRESS IN MATHEMATICS, VOL. 249

Algebraic Geometry and Number Theory Introduction to Classical Geometries Ana Irene Ramirez Galarza, Universidad Nacional Autónoma de México; In Honor of José Seade, Universidad Nacional Autónoma de México Vladimir Drinfeld’s 50th Birthday 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 Victor Ginzburg, University of Chicago, the classical geometries are studied: Euclidean, affine, elliptic, projective IL (Ed.) and hyperbolic. For simplicity the focus is on the two-dimensional case, One of the most creative mathematicians which is already rich enough, though some aspects of the 3–dimen- of our times, Vladimir Drinfeld received the sional geometries are included. The book appeals to, and develops, the Fields Medal in 1990 for his groundbreaking geometric intuition of the reader. Some basic notions of algebra and contributions to the Langlands program and analysis are also used to get better understandings of various concepts to the theory of quantum groups. These ten original articles by promi- and results. nent mathematicians, dedicated to Drinfeld on the occasion of his 50th 2006 / APPROX. 264 PP. / SOFTCOVER / $39.95 birthday, broadly reflect the range of Drinfeld’s own interests in algebra, ISBN_13 978-3-7643-7517-1 ISBN_10 3-7643-7517-5 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, M. A. Tsfasman 2006/ 644 PP., 19 ILLUS. / HARDCOVER / $129.00 ISBN_13 978-0-8176-4471-0 ISBN_10 0-8176-4471-7 PROGRESS IN MATHEMATICS, VOL. 253

12 Order By Phone: 1-800-777-4643 • Fax: 201-348-4505 • Or Online: www.birkhauser.com Geometry / Topology

The Geometry of Complex From Geometry to Quantum Domains Mechanics Robert E. Greene, UCLA, Los Angeles, CA; In Honor of Hideki Omori Kang-Tae Kim, Pohang University of Science and Technology, Yoshiaki Maeda, Keio University, Yokohama-shi, Japan; Pohang, South Korea; Peter Michor, Universität Wien, Austria; Steven G. Krantz, Washington University, St. Louis, MO Takushiro Ochiai, Nippon Sport Science University, Tokyo, Japan; This work examines a rich tapestry of themes and concepts that pro- Akira Yoshioka, Tokyo University of Science, Tokyo, Japan (Eds.) vides a comprehensive treatment of an important area of mathemat- This volume is composed of invited expository articles by well- ics, while simultaneously covering a broader area of the geometry of known mathematicians in differential geometry and mathematical domains in complex space. At once authoritative and accessible, this text physics that have been arranged in celebration of Hideki Omori’s touches upon many important parts of modern mathematics: complex recent retirement from Tokyo University of Science and in honor of geometry, Finsler metrics, Bergman and Kahler geometry, curvatures, dif- his fundamental contributions to these areas. ferential invariants, boundary asymptotics of geometries, group actions, and moduli spaces. This text can serve as a “coming of age” book for a The papers focus on recent trends and future directions in symplectic graduate student who has completed at least one semester or more of and Poisson geometry, global analysis, infinite-dimensional Lie group complex analysis, and will be most welcomed by analysts and geom- theory, quantizations and noncommutative geometry, as well as ap- eters engaged in current research. plications of partial differential equations and variational methods to 2007 / APPROX. 400 PP., 20 ILLUS. / HARDCOVER/$79.95 (TENT.) geometry. ISBN_13 978-0-8176-4139-9 ISBN_10 0-8176-4139-4 These articles will appeal to graduate students in mathematics and BIRKHAUSER ADVANCED TEXTS quantum mechanics, as well as researchers, differential geometers, and mathematical physicists. Contributors include: M. Cahen, D. Elworthy, A. Fujioka, M. Goto, J. Grabowski, S. Gutt, J. Inoguchi, M. Karasev, O. Kobayashi, Y. Maeda, K. A Geometric Mikami, N. Miyazaki, T. Mizutani, H. Moriyoshi, H. Omori, T. Sasai, Approach to D. Sternheimer, A. Weinstein, K. Yamaguchi, T. Yatsui, and A. Yoshioka. 2007/324 PP./HARDCOVER/$99.00 Differential Forms ISBN_13 978-0-8176-4512-0 David Bachman, Pitzer College, ISBN_10 0-8176-4512-8 PROGRESS IN MATHEMATICS, VOL. 252 Claremont, CA The modern subject of differential forms subsumes classical vector calculus. This text presents differential forms from a Near Polygons geometric perspective accessible at the Bart De Bruyn, Gent University, Belgium undergraduate level. The book begins Near polygons were introduced about 25 years ago and studied with basic concepts such as partial dif- intensively in the 1980s. In recent years the subject has regained ferentiation and multiple integration and gently develops the entire interest. This monograph gives an extensive overview of the basic machinery of differential forms. theory of general near polygons. The first part of the book includes The author approaches the subject with the idea that complex con- a discussion of the classes of dense near polygons, regular near cepts can be built up by analogy from simpler cases, which, being polygons, and glued near polygons. Also valuations, one of the most inherently geometric, often can be best understood visually. Each important tools for classifying dense near polygons, are treated in new concept is presented with a natural picture that students can detail. The second part of the book discusses the classification of easily grasp. Algebraic properties then follow. This facilitates the de- dense near polygons with three points per line. velopment of differential forms without assuming a background in The book is self-contained and almost all theorems are accompanied linear algebra. with proofs. Several new results are presented. Many known results Containing excellent motivation, numerous illustrations and solu- occur in a more general form and the proofs are often more stream- tions to selected problems in an appendix, the material has been lined than their original versions. The volume is aimed at advanced tested in the classroom. graduate students and researchers in the fields of combinatorics and 2006/ 134 PP., 39 ILLUS. / SOFTCOVER / $39.95 finite geometry. ISBN_13 978-0-8176-4499-4 2006/ 263 PP. / SOFTCOVER / $54.95 ISBN_10 0-8176-4499-7 ISBN_13 978-3-7643-7552-2 ISBN_10 3-7643-7552-3 FRONTIERS IN MATHEMATICS

Visit www.birkhauser.com For Monthly Series Sales and Other Promotions 13 Geometry / Topology

Cycle Spaces of Flag String Topology and Cyclic Domains Homology A Complex Geometric Ralph L. Cohen, Stanford University, USA; Viewpoint Kathryn Hess, EPFL Lausanne, Switzerland; Alexander A. Voronov, University of Minnesota, Minneapolis, MN Gregor Fels, University of Tübingen, Germany; Alan Huckleberry, University of The subject of this book is string topology, Hochschild and cyclic ho- Bochum, Germany; mology. The first part consists of an excellent exposition of various ap- Joseph A. Wolf, University of California, proaches to string topology and the Chas-Sullivan loop product. The Berkeley, CA second gives a complete and clear construction of an algebraic model for computing topological cyclic homology. It is certainly the best source This monograph, divided into four parts, of much information that was until now available only to specialists presents a comprehensive treatment and and covers material from the elementary bases to the most recent systematic examination of cycle spaces of flag domains. Assuming only developments. a basic familiarity with the concepts of Lie theory and geometry, this 2006 VI / 163 PP., 29 ILLUS. / SOFTCOVER / $29.95 work presents a complete structure theory for these cycle spaces, as ISBN_13 978-3-7643-2182-6 well as their applications to harmonic analysis and algebraic geometry. ISBN_10 3-7643-2182-2 ADVANCED COURSES IN MATHEMATICS–CRM BARCELONA Key features: • Accessible to readers from a wide range of fields, with all the necessary background material provided for the nonspecialist Complex, Contact and Symmetric • Many new results presented for the first time • Driven by numerous examples Manifolds • The exposition is presented from the complex geometric viewpoint, In Honor of L. Vanhecke but the methods, applications and much of the motivation also Oldrich Kowalski, Charles University, Prague, Czech Republic; come from real and complex algebraic groups and their representa- Emilio E. Musso, Università di L’Aquila, Coppito, Italy; and tions, as well as other areas of geometry Domenico Perrone, Università di Lecce, Italy (Eds.) • Comparisons with classical Barlet cycle spaces are given This volume contains research and survey articles by well-known and • Good bibliography and index. respected mathematicians on differential geometry and topology that have been collected and dedicated in honor of Lieven Vanhecke, as a Researchers and graduate students in differential geometry, complex analy- tribute to his many fruitful and inspiring contributions to these fields. sis, harmonic analysis, representation theory, transformation groups, algebraic geometry, and areas of global geometric analysis will benefit from this work. Contributors: D. E. Blair, E. Boeckx. A. A. Borisenko, G. Calvaruso, V. Cortés, P. de Bartolomeis, J. C. Díaz-Ramos, M. Djori , C. Dunn, 2006/ 339 PP. / HARDCOVER / $74.95 ć ISBN_13 978-0-8176-4391-1 M. Fernández, A. Fujuki, E. Garcia-Río, P. B. Gilkey, O. Gil-Medrano, ISBN_10 0-8176-4391-5 L. Hervella, O. Kowalski, V. Muñoz, A. M. Naveira, T. Oguro, PROGRESS IN MATHEMATICS, VOL. 245 M. Pontecorvo, L. Schäfer, K. Sekigawa, C.-L. Terng, K. Tsukuda, Z. Vlášek, E. Wang, J. A. Wang 2005 / 278 PP. / HARDCOVER / $99.00 ISBN_13 978-0-8176-3850-4 Classical Geometries in ISBN_10 0-8176-3850-4 Modern Contexts PROGRESS IN MATHEMATICS, VOL. 234 Geometry of Real Inner Product Spaces Walter Benz, University of Hamburg, Germany The Algebra of Secondary This book is based on real inner product spaces X of arbitrary (finite or Cohomology Operations infinite) dimension greater than or equal to 2. With natural properties of Hans-Joachim Baues, Max-Planck-Institut für Mathematik, Bonn, (general) translations and general distances of X Euclidean, hyperbolic Germany translations and distances, respectively, are characterized. For these spaces the sphere geometries of Möbius and Lie are studied (besides The algebra of primary cohomology operations computed by the well- Euclidean and hyperbolic geometry), as well as geometries where known Steenrod algebra is one of the most powerful tools of algebraic Lorentz transformations play the key role. The geometrical notions of topology. This book computes the algebra of secondary cohomology this book are based on general spaces X as described. This implies that operations which enriches the structure of the Steenrod algebra in a also mathematicians who have not so far been especially interested in new and unexpected way. The book solves a long-standing problem geometry may study and understand great ideas of classical geometries on the algebra of secondary cohomology operations by developing a in modern and general contexts. new algebraic theory of such operations. The results have strong impact Proofs of newer theorems, characterizing isometries and Lorentz trans- on the Adams spectral sequence and hence on the computation of formations under mild hypotheses are included, like for instance infi- homotopy groups of spheres. nite dimensional versions of famous theorems of A.D. Alexandrov on 2006/ 483 PP. / HARDCOVER / $149.00 ISBN_13 978-3-7643-7448-8 Lorentz transformations. A real benefit is the dimension-free approach ISBN_10 3-7643-7448-9 to important geometrical theories. PROGRESS IN MATHEMATICS, VOL. 247 2005 / 244 PP. / HARDCOVER / $99.00 ISBN_13 978-3-7643-7371-9 ISBN_10 3-7643-7371-7

14 Order By Phone: 1-800-777-4643 • Fax: 201-348-4505 • Or Online: www.birkhauser.com Geometry / Topology

Differential Geometric Mechanics on Geometry of Curves Riemannian Manifolds and Surfaces Applications to Partial Differential Equations A Concise Guide Ovidiu Calin, Eastern Michigan University, East Lansing and Der-Chen Chang, Georgetown University, Washington Victor A. Toponogov, Sobolev Insti- tute of Mathematics, Novosibirsk, Russia “This book contains old and new basic results from a significant With the editorial assistance of part of the modern theory of partial differential equations on Ri- Vladimir Y. Rovenski, University of emannian manifolds. All results are presented in an elementary Haifa, Israel way. Only a basic knowledge of basic functional analysis, mechanics and analysis is assumed. The book is well written and con- This book presents traditional material tains a wealth of material …. To conclude, this book provides the of curves and surfaces related to differ- reader with an in-depth introduction to a rich and rapidly develop- ential geometry along with important ideas of Riemannian geom- ing research area that has already produced remarkable results.” etry. The book weaves together standard theoretical material with —ZENTRALBLATT MATH more difficult theorems and complex problems while maintaining This work presents a purely geometric treatment of problems in phys- an easy separation between the two. One of the striking features ics involving quantum harmonic oscillators, quartic oscillators, mini- of this presentation is the large number of nontrivial and original mal surfaces, and Schrödinger’s, Einstein’s and Newton’s equations. problems, some with useful hints and solutions, which introduce a 2004 / 280 PP., 26 ILLUS. / HARDCOVER / $79.95 motivated student into the real world of geometry. Another strong ISBN_13 978-0-8176-4354-6 point is the nontrivial material connected with the Aleksandrov glob- ISBN_10 0-8176-4354-0 al angle comparison theorem—one of the cornerstones of modern APPLIED AND NUMERICAL HARMONIC ANALYSIS Riemannian geometry. This rigorous exposition, with well-motivated topics, is ideal for advanced undergraduate students and first-year graduate students. 2005 / 200 PP., 40 ILLUS. / SOFTCOVER / $59.95 Lines and Curves ISBN_13 978-0-8176-4384-3 A Practical Geometry ISBN_10 0-8176-4384-2 Handbook Victor Gutenmacher, VISTAGY, Inc., Waltham, MA and N.B. Vasilyev, Differential Geometry and University of Moscow, Russia Analysis on CR Manifolds Based on an English translation of the Russian edition by A. Kundu, Saha Sorin Dragomir, Università della Basilicata, Romana, Potenza, Italy; Institute of Nuclear Physics, Calcutta, India Giuseppe Tomassini, Scuola Normale Superiore, Pisa, Italy The study of CR manifolds lies at the intersection of three main Lines and Curves is a unique adventure mathematical disciplines: partial differential equations, complex in geometry. Originally written in Rus- analysis in several complex variables, and differential geometry. sian and used in the Gelfand Correspondence School, the book While the PDE and complex analytic aspects have been intensely has since become a classic: unlike standard geometry textbooks studied in the last fifty years, much effort has recently been made that primarily introduce axiomatic reasoning, this book maintains to understand the differential geometric aspects in the theory of CR solid rigor but strikes a balance between artistry, storytelling, and manifolds and tangential Cauchy-Riemann equations. surprising examples of geometric properties. This newly revised and expanded edition includes more than 200 theoretical and practical Motivated by clear exposition, many examples, explicitly worked- problems in which formal geometry provides simple and elegant out geometric results, and stimulating unproved statements and insight, and the book points the reader toward important areas of comments referring to the most recent aspects of the theory, this modern mathematics. monograph is suitable for researchers and graduate students in differential geometry, complex analysis, and PDEs. The text focuses on the geometrical properties of paths traced by moving points, the sets of points satisfying given geometric con- 2005 / 530 PP. / HARDCOVER / $109.00 ISBN_13 978-0-8176-4388-1 straints, and questions of maxima and minima; it is, therefore, well ISBN_10 0-8176-4388-5 positioned for companion use with software packages like Geometry PROGRESS IN MATHEMATICS, VOL. 246 Sketchpad, and can serve as a guidebook for engineers. Its deeper, interdisciplinary treatment of geometry also makes it ideal for those interested in the subject purely for its beauty, and the development of Lines and Curves from first principles makes it accessible to high school students, teachers, and puzzle enthusiasts alike. A wide audience will profit from its careful treatment of geometry and its synthesis of many branches of mathematics. 2004 / 200 PP., 350 ILLUS. / SOFTCOVER / $44.95 ISBN_13 978-0-8176-4161-0 ISBN_10 0-8176-4161-0

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The Breadth of The Topology of Torus Actions Symplectic and on Symplectic Manifolds Poisson Geometry Second Edition Michèle Audin, Université Louis Pasteur et CNRS, Strasbourg, France Festschrift in Honor of Alan Weinstein “Through careful writing, this revised edition achieves much more than that volume, and can be considered, in fact, a new and improved book. Jerrold E. Marsden, California Institute The second edition contains more material, and includes several new of Technology, Pasadena, CA results and techniques. Topics included in the first edition are now pre- Tudor S. Ratiu, Ecole Polytechnique Fédérale sented more thoroughly, with more results, illustrated by well-chosen de Lausanne, Lausanne, Switzerland (Eds.) examples, and many new exercises. The author has systematically ad- One of the world’s foremost geometers, dressed suggestions made in the review of the first edition. The book Alan Weinstein has made deep contribu- is nicely written, and is a good reference book. By including detailed tions to symplectic and differential geometry, Lie theory, mechanics, and proofs, illuminating examples and figures, and numerous exercises, the a number of related fields. Written in his honor, the invited papers in this author has made this book a suitable text for a graduate course, espe- volume reflect the active and vibrant research in these areas and are a cially one centered on Hamiltonian torus actions and their applications.” tribute to Weinstein’s ongoing legacy. —MATHEMATICAL REVIEWS The well-recognized contributors to this text cover a broad range of This is a revised and expanded second edition of The Topology of Torus topics: Induction and reduction for systems with symmetry, symplectic Actions on Symplectic Manifolds published in 1991. Symplectic mani- geometry and topology, geometric quantization, the Weinstein Con- folds and torus actions are investigated, with numerous examples of jecture, Poisson algebra and geometry, Dirac structures, deformations torus actions, for example, on some moduli spaces. Although the book for Lie group actions, Kähler geometry of moduli spaces, theory and is still centered on convexity theorems, it contains many more results, applications of Lagrangian and Hamiltonian mechanics and dynamics, proofs, and examples. symplectic and Poisson groupoids, and quantum representations. 2005 / 332 PP. / HARDCOVER / $99.00 Contributors: H. Bursztyn, M. Cahen, M. Crainic, J. J. Duistermaat, ISBN_13 978-3-7643-2176-5 ISBN_10 3-7643-2176-8 K. Ehlers, S. Evens, V. L. Ginzburg, A. B. Givental, S. Gutt, D. D. Holm, PROGRESS IN MATHEMATICS, VOL. 93 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, Tubes P. M. Rios, L. Schwachhöfer, J. Stasheff, I. Vaisman, A. Yoshioka, P. Xu, S. Zelditch. Second Edition 2005 / 65 PP., 30 ILLUS. / HARDCOVER / $99.00 Alfred Gray, University of Maryland, College Park, MD ISBN_13 978-0-8176-3565-7 ISBN_10 0-8176-3565-3 “The new book by Alfred Gray will do much to make Weyl’s tube for- PROGRESS IN MATHEMATICS, VOL. 232 mula more accessible to modern readers. The first five chapters give a careful and thorough discussion of each step in the derivation and its application to the Gauss–Bonnet formula. Gray’s pace is quite lei- The Novikov Conjecture surely, and a gradualte student who has completed a basic differential geometry course will have little difficulty following the presentation. Geometry and Algebra In the remaining chapters of the book, one can find an extension Matthias Kreck, Universität Heidelberg, of Weyl’s tube formula to complex submanifolds of complex projec- Germany and tive space, power series expansions for tube volumes, and the ‘half- Wolfgang Lück, Universität Münster, Germany tube formula’ for hypersurfaces. A high point is the presentation of “Overall, the book is very suitable both as estimates for the volumes of tubes in ambient Riemannian manifolds an introduction and as a reference, and whose curvature is bounded above or below.”—BULLETIN OF THE AMS finds exactly the right balance between (review of the first edition) detail, comprehensiveness and length of This second edition, which consists of newly added historical notes and the presentation. It is recommended to figures in Mathematica®, is a comprehensive examination of Weyl’s for- everyone with a background in algebra- mula for the volume of a tube, its roots, and its implications. Graduate ic topology who wants to learn about one or some of the aspects students with a basic knowledge of differential geometry, as well as re- covered.”—MATHEMATICAL REVIEWS searchers and instructors in the areas of analysis, differential geometry, This book contains a guided tour to the Novikov Conjecture and related con- topology, and mathematical physics, will benefit from this excellent text. jectures due to Baum–Connes, Borel, and Farrell-Jones. Beginning with the 2004 / 280 PP., 12 ILLUS. / HARDCOVER/$89.95 basics of higher signatures, Whitehead torsion, and the s-Cobordism Theorem, ISBN_13 978-3-7643-6907-1 ISBN_10 3-7643-6907-8 the authors then present an introduction to surgery theory and a version of PROGRESS IN MATHEMATICS, VOL. 221 the assembly map. Using the solution of the Novikov conjecture for special groups, some applications to the classification of low-dimensional manifolds are given. The most recent developments concerning these conjectures are surveyed, including a detailed status report. Prerequisites consist of a solid knowledge of the basics about manifolds, vector bundles, (co-) homology, and characteristic classes. 2005 / 276 PP. / SOFTCOVER / $49.95 ISBN_13 978-3-7643-7141-8 ISBN_10 3-7643-7141-2 OBERWOLFACH SEMINARS, VOL. 33

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A Topological Rigid Analytic Geometry and its Introduction to Applications Nonlinear Analysis Jean Fresnel, Université de Bordeaux I, Talence, France Marius van der Put, Rijksuniversiteit Groningen, The Netherlands Second Edition Robert F. Brown, University of Califor- “Beginners will appreciate the numerous exercises and the gentle nia, Los Angeles, CA progression of the first four chapters, from the one-variable calculus on the projective line, through the algebraic study of general af- “The book is highly recommended finoid algebras, to the definition of general rigid varieties and their as a text for an introductory course in analytic reductions. And each of the last five chapters can be used nonlinear analysis and bifurcation the- as the basis for a student workshop at the advanced graduate level.” ory … reading is fluid and very pleasant — MATHEMATICAL REVIEWS …style is informal but far from being 2003 / 300 PP., 2 ILLUS. / HARDCOVER / $79.95 imprecise.”—MATHEMATICAL REVIEWS (review of the first edition) ISBN_13 978-0-8176-4206-8 ISBN_10 0-8176-4206-4 “For the topology-minded reader, the book indeed has a lot to PROGRESS IN MATHEMATICS, VOL. 218 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 Here is a book that will be a joy to the mathematician or graduate Hyperbolic Manifolds and student of mathematics—or even the well-prepared undergradu- Discrete Groups ate—who would like, with a minimum of background and prepara- Michael Kapovich, University of Utah, Salt Lake City, UT tion, to understand some of the beautiful results at the heart of nonlinear analysis. “This book can act as source material for a postgraduate course and as a reference text on the topic as the references are full and extensive … The Based on carefully-expounded ideas from several branches of to- text is self-contained and very well illustrated.”—ASLIB BOOK GUIDE pology, and illustrated by a wealth of figures that attest to the geometric nature of the exposition, the book will be of immense help in “The book is very clearly written and fairly self-contained. It will be providing its readers with an understanding of the mathematics of useful to researchers and advanced graduate students in the field the nonlinear phenomena that characterize our real world. and can serve as an ideal guide to Thurston’s work and its recent developments.”—MATHEMATICAL REVIEWS New to the second edition: New chapters supply additional ap- 2001 / 486 PP., 75 ILLUS. / HARDCOVER / $89.95 plications of the theory and techniques presented in the book. ISBN_13 978-0-8176-3904-4 2004 / 184 PP., 35 ILLUS. / SOFTCOVER / $42.95 ISBN_10 0-8176-3904-7 ISBN_13 978-0-8176-3258-8 PROGRESS IN MATHEMATICS, VOL. 183 ISBN_10 0-8176-3258-1

Symmetry in Finite Generalized Symplectic Geometry of Integrable Hamiltonian Systems Quadrangles Michèle Audin, Université Louis Pasteur et CNRS, Strasbourg, France; Koen Thas, Ghent University, Belgium Ana Cannas da Silva, Lisboa, Portugal; and In this monograph, finite generalized quadrangles are classified by Eugene Lerman, University of Illinois at Urbana-Champaign, IL symmetry, generalizing the celebrated Lenz–Barlotti classification “This book, an expanded version of the lectures delivered by the for projective planes. The book is self-contained and serves as an authors at the ‘Centre de Recerca Matemàtica’ Barcelona in July introduction to the combinatorial, geometrical, and group-theoreti- 2001, is designed for a modern introduction to symplectic and cal concepts that arise in the classification and the general theory contact geometry to graduate students. It can also be useful to of finite generalized quadrangles, including automorphism groups, research mathematicians interested in integrable systems. The elation and translation generalized quadrangles, generalized ovals text includes up-to-date references, and has three parts. The first and generalized ovoids, span-symmetric generalized quadrangles, part, by Michèle Audin, contains an introduction to Lagrangian and flock geometry and property (G), regularity and nets, split BN-pairs special Lagrangian submanifolds in symplectic and Calabi-Yau of rank 1, and the Moufang property. manifolds . … The second part, by Ana Cannas da Silva, provides 2004 / 214 PP. / SOFTCOVER / $59.95 an elementary introduction to toric manifolds (i.e. smooth toric ISBN_13 978-3-7643-6158-7 ISBN_10 3-7643-6158-1 varieties) . … In these first two parts, there are exercises designed to FRONTIERS IN MATHEMATICS complement the exposition or extend the reader’s understanding . … The last part, by Eugene Lerman, is devoted to the topological study of these manifolds.”—ZENTRALBLATT MATH 2003 / 236 PP. / SOFTCOVER / $39.95 ISBN_13 978-3-7643-2167-3 ISBN_10 3-7643-2167-9 ADVANCED COURSES IN MATHEMATICS–CRM BARCELONA

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Global Riemannian Geometry Riemannian Geometry of Contact Curvature and Topology and Symplectic Manifolds Steen Markvorsen, Technical University of Denmark, Lyngby, Denmark and David E. Blair, Michigan State University, East Lansing, MI Maung Min-Oo, McMaster University, Hamilton, Ontario, Canada “The book … supplies a lot of examples, and includes many recent re- The book contains a clear exposition of two contemporary topics in sults. It can be used either as an introduction to the subject or as a ref- modern differential geometry: erence for students and researchers … [it] gives a clear and complete • Distance geometric analysis on manifolds, in particular, comparison account of the main ideas … and studies a vast amount of related theory for distance functions in spaces which have well defined subjects such as integral submanifolds, symplectic structure of tangent bounds on their curvature bundles, curvature of contact metric manifolds and curvature functionals on spaces of associated metrics.”—MATHEMATICAL REVIEWS • The application of the Lichnerowicz formula for Dirac operators 2002 / 260 PP., 5 ILLUS. / HARDCOVER / $69.95 to the study of Gromov’s invariants to measure the K-theoretic ISBN_13 978-0-8176-4261-7 size of a Riemannian manifold. ISBN_10 0-8176-4261-7 PROGRESS IN MATHEMATICS, VOL. 203 It is intended for both graduate students and researchers who want to get a quick and modern introduction to these topics. 2003 / 100 PP. / SOFTCOVER / $39.95 ISBN_13 978-3-7643-2170-3 Torsions of 3-Dimensional ISBN_10 3-7643-2170-9 ADVANCED COURSES IN MATHEMATICS–CRM BARCELONA Manifolds Vladimir Turaev, CNRS, Strasbourg, France “This is an excellent exposition about abelian Reidemeister torsions for Elements of three-manifolds.”—ZENTRALBLATT MATH Noncommutative “This monograph contains a wealth of information many topologists Geometry will find very handy”.—MATHEMATICAL REVIEWS J.M. Gracia-Bondía, The book is concerned with one of the most interesting and important J.C. Várilly, and topological invariants of 3-dimensional manifolds based on an original H. Figueroa, all, Universidad de Costa Rica, idea of Kurt Reidemeister (1935). The purpose of the book is to give San José a systematic exposition of the theory of maximal abelian torsions of 3-manifolds. “The material is collected from an enormous 2002 / 208 PP. / HARDCOVER / $114.00 number of sources … All of it is carefully ISBN_13 978-3-7643-6911-8 worked out and serves as a highly recom- ISBN_10 0-8176-4261-7 PROGRESS IN MATHEMATICS, VOL. 208 mendable introduction to the vital field of noncommutative geometry.”—ZENTRALBLATT MATH “In collecting the material in a coherent form, the authors have performed a valuable service and this book will no doubt open noncom- Proper Group Actions and the mutative geometry to a wider audience … [A] large number of meta- phorical and mathematical remarks embedded in the text … highlight Baum-Connes Conjecture the plethora of connections between the material of the book and Guido Mislin, ETH Zürich, Switzerland Alain Valette, University of Neuchâtel, Switzerland other areas of mathematics.”—MATHEMATICAL REVIEWS “The style of the book is lively, exempt of the stereotypes one en- This book contains a concise introduction to the techniques used to counters rather often in the mathematical literature. The authors prove the Baum-Connes conjecture. The approach is expository, but it know how to tell stories and enjoy doing it. The friendly tone could contains proofs of many basic results on topological K-homology and be of some help for an hypothetical inexperienced reader confronted the K-theory of C*-algebras. It features a detailed discussion of naturality with almost 700 pages of rather difficult and delicate mathematics.” questions concerning the assembly map, a topic not well documented — JOURNAL OF OPERATOR THEORY in the literature. The book is aimed at advanced graduate students and 2001 / 704 PP. / HARDCOVER / $69.95 researchers in the area, leading to current research problems. ISBN_13 978-0-8176-4124-5 2003 / 131 PP / SOFTCOVER / $44.95 ISBN_10 0-8176-4124-6 ISBN_13 978-3-7643-0408-9 BIRKHÄUSER ADVANCED TEXTS ISBN_10 3-7643-0408-1 ADVANCED COURSES IN MATHEMATICS–CRM BARCELONA

18 Order By Phone: 1-800-777-4643 • Fax: 201-348-4505 • Or Online: www.birkhauser.com Geometry / Topology

Introduction to the Baum-Connes Riemannian Conjecture Geometry Alain Valette, University of Neuchâtel, Switzerland Manfredo P. Do Carmo, Instituto de Matematica Pura e Aplicada (IMPA), Rio de “Overall, the book is a very valuable addition to the literature on the Janeiro, Brazil Baum-Connes conjecture. It is highly recommended reading for anyone interested in learning more about the conjecture, or who does Translated by F. Flaherty, Oregon State research in areas related to it. Of course, the reader who wants to University, Corvallis, OR be an expert will eventually have to consult the original literature, but “This is one of the best (if even not just such is inevitable in a book of this size (around 100 pages) and not the best) book for those who want to get necessarily a bad thing.”—MATHEMATICAL REVIEWS a good, smooth and quick, but yet thor- 2002 / 116 PP. / SOFTCOVER / $29.95 ough introduction to modern Riemannian ISBN_13 978-3-7643-6706-0 ISBN_10 3-7643-6706-7 geometry.”—PUBLICATIONES MATHEMATICAE LECTURES IN MATHEMATICS. ETH ZÜRICH “This is a very nice introduction to global Riemannian geometry, which leads the reader quickly to the heart of the topic. Neverthe- less, classical results are also discussed on many occasions, and Differentiable almost 60 pages are devoted to exercises.”—NEWSLETTER OF THE AMS 1992 / 320 PP., 53 ILLUS. / HARDCOVER / $49.95 Manifolds ISBN_13 978-0-8176-3490-2 ISBN_10 0-8176-3490-8 Second Edition MATHEMATICS: THEORY & APPLICATIONS Lawrence Conlon, Washington University, St. Louis, MO “This second edition contains a significant Textbook Adoption Policy amount of new material, which, in addition to classroom use, will make it a useful Textbook evaluation copies are available on a 60-day ap- reference text. Topics that can be omitted proval basis. If you request a book under the 60-day ap- safely in a first course are clearly marked, proval and decide to adopt it, simply return the invoice making this edition easier to use for such a that came with your order and indicate the course name and course, as well as for private study by non- number, the expected enrollment, the name of the bookstore specialists wishing to survey the field.” L’ENSEIGNEMENT— MATHÉMATIQUE where the adoption order will be placed, and the number of copies ordered. At that time, the invoice charge will be cancelled. “This is a carefully written and wide-ranging textbook suitable mainly If you do not adopt the book, you must either purchase it if you for graduate courses, although some advanced undergraduate cours- wish to keep it, or return it via a traceable method of delivery es may benefit from the early chapters. The subject matter is differen- (or contact us for a call-tag) to cancel the invoice. tial topology and geometry, that is, the study of curves, surfaces and manifolds where the assumption of differentiability adds the tools of To request evaluation copies, please go to differentiable and integral calculus to those of topology. Within this www.birkhauser.com/textbooks, mail or fax your request on area, the book is unusually comprehensive . … The style is clear and letterhead, indicating the book title and ISBN, the course precise, and this makes the book a good reference text. There are name and number, and the expected enrollment to: many good exercises.”—THE MATHEMATICAL GAZETTE Birkhäuser Text Sales, Order Department, P.O. Box 2485, Secaucus, NJ 07096-2485, fax: 212-533-3503. Or send us “This is a well-organized and nicely written text containing the ba- an e-mail with this information to [email protected]. sic topics needed for further work in differential geometry and global To expedite your order, please add code Y2655 to your request. analysis . … This book is very suitable for students wishing to learn the subject, and interested teachers can find well-chosen and nicely presented materials for their courses.”—EMS NEWSLETTER 2001 / 432 PP., 48 ILLUS. / HARDCOVER / $59.95 ISBN_13 978-0-8176-4134-4 ISBN_10 0-8176-4134-3 BIRKHÄUSER ADVANCED TEXTS

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D-Modules, Poisson Structures and Their Perverse Sheaves, and Represen- Normal Forms tation Theory Jean-Paul Dufour, Université de Montpellier, France; Nguyen Tien Zung, Université Paul Sabatier, Toulouse, France Ryoshi Hotta, Okayama University of Science, Okayama, Japan; Poisson manifolds play a fundamental role in Hamiltonian dynamics, Kiyoshi Takeuchi, University of Tsukuba, Japan; where they serve as phase spaces. They also arise naturally in other Toshiyuki Tanisaki, Osaka City University, Osaka, Japan mathematical problems, and form a bridge from the “commutative Translated by K. Takeuchi world” to the “noncommutative world”. The aim of this book is twofold: On the one hand, it gives a quick, This work examines in detail the foundations of D-module theory and its self-contained introduction to Poisson geometry and related subjects, intersection with perverse sheaves and representation theory. This sys- including singular foliations, Lie groupoids and Lie algebroids. On the tematic and carefully written exposition begins in Part I with preliminary other hand, it presents a comprehensive treatment of the normal form concepts before focusing on some basic but important theories that have problem in Poisson geometry. Even when it comes to classical results, emerged in the last few decades. Part II is devoted to the applications of the book gives new insights. It contains results obtained over the past D-modules and perverse sheaves to representation theory. 10 years which are not available in other books. Significant topics that have emerged as studies in their own right include: 2005/ 321 PP. / HARDCOVER / $64.95 a treatment of the theory of holonomic D-modules, perverse sheaves, ISBN_13 978-3-7643-7334-4 the Riemann-Hilbert correspondence, Hodge modules, and Kazhdan- ISBN_10 3-7643-7334-2 PROGRESS IN MATHEMATICS, VOL. 242 Lusztig polynomials. To further aid the reader, appendices are provided as reviews for the theory of derived categories and algebraic varieties. D-modules, Perverse Sheaves, and Representation Theory is a unique and essential textbook at the graduate level for classroom use or self- The Unity of study. Graduate students and researchers in algebra and representation theory will benefit greatly from this work. Mathematics 2007 / 350 PP./ $89.95 (TENT.) In Honor of the Ninetieth ISBN_13 978-0-8176-4363-8 Birthday of I.M. Gelfand ISBN_10 0-8176-4363-X PROGRESS IN MATHEMATICS, VOL. 236 Pavel Etingof, Massachusetts Institute of Technology, Cambridge, MA; Vladimir S Retakh, Rutgers University, Piscataway, NJ; and Dirac Operators in I.M. Singer, Massachusetts Institute of Technology, Representation Theory Cambridge, MA (Eds.) Jing-Song Huang, University of Science and Technology, Hong Kong, China; A tribute to the vision and legacy of Israel Gelfand, the invited papers in Pavle PandŽic`, University of Zagreb, Croatia this volume reflect the unity of mathematics as a whole, with particular emphasis on the many connections among the fields of geometry, This monograph presents a comprehensive physics, and representation theory. Written by leading mathematicians, treatment of important new ideas on Dirac the text is broadly divided into two sections: the first is devoted to operators and Dirac cohomology. Dirac op- developments at the intersection of geometry and physics, and the erators are widely used in physics, differen- second to representation theory and algebraic geometry. tial geometry, and group-theoretic settings Contributors: M. Atiyah, A. Beilinson, J. Bernstein, A. Connes, P. Deligne, (particularly, the geometric construction of R. Dijkgraaf, D. Gaitsgory, M. Gromov, F. Hirzebruch, M. Hopkins, discrete series representations). The related D. Kazhdan, F. Kirwan, M. Kontsevich, B. Kostant, G. Lusztig, D. McDuff, concept of Dirac cohomology, which is defined using Dirac operators, is a H. Nakajima, S. Novikov, P. Sarnak, A. Schwartz, I. Singer, R. Taylor, C. Vafa, far-reaching generalization that connects index theory in differential geom- A. Vershik, E. Witten. etry to representation theory. 2005 / 464 PP., 20 ILLUS. / HARDCOVER / $115.00 Using Dirac operators as a unifying theme, the authors demonstrate ISBN_13 978-0-8176-4076-7 how some of the most important results in representation theory fit to- ISBN_10 0-8176-4076-2 gether when viewed from this perspective. An excellent contribution to PROGRESS IN MATHEMATICS, VOL. 244 the mathematical literature of representation theory, this self-contained exposition offers a systematic examination and panoramic view of the subject. The material will be of interest to researchers and graduate students in representation theory, differential geometry, and physics. 2006 X / 199 PP. / HARDCOVER / $59.95 ISBN_13 978-0-8176-3218-2 ISBN_10 0-8176-3218-2 MATHEMATICS: THEORY & APPLICATIONS

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Studies in Frobenius Splitting Lie Theory Methods in Geometry A. Joseph Festschrift and Representation Joseph Bernstein, Tel Aviv University, Israel; Vladimir Hinich, University of Haifa, Israel; Theory Anna Melnikov, University of Haifa, Israel Michel Brion, Université Grenoble, (Eds.) St.-Martin d’Hères, France and Shrawan Kumar, University of North Dedicated to Anthony Joseph in honor of Carolina, Chapel Hill, NC his 60th birthday, this volume contains two articles reviewing different aspects of Jo- “This is a truly fantastic book. It is the first seph’s impact on the theory of representa- comprehensive text on Frobenius splitting tions of Lie algebras and 17 original contributions from leading special- and its applications to geometry and rep- ists in the field. The book contains new results on different aspects of resentation theory. If this was a one-paragraph review, I would say Lie theory, including Lie superalgebras, quantum groups, crystal bases, ‘buy the book, study it carefully and then apply the contents to a re- representations of reductive groups in finite characteristic, and the geo- search project’. The readers (and the reviewer) are in the authors’ metric Langlands program. debt.”—MATHEMATICAL REVIEWS Contributors: J. Alev, A. Beilinson, A. Braverman, I. Cherednik, J. Dixmier, Key topics and features: F. Dumas, P. Etingof, D. Farkas, D. Gaitsgory, F. Ivorra, D. Joseph, • Concise, efficient exposition unfolds from basic introductory materi- M. Kashiwara, D. Kazhdan, A. Kirillov, B. Kostant, S. Kumar, G. Letzter, al on Frobenius splittings—definitions, properties and examples—to T. Levasseur, G. Lusztig, L. Makar-Limanov, W. McGovern, M. Nazarov, cutting-edge research K.-H. Neeb, L. Rybnikov, A. Sergeev, V. Schechtman, T. Stafford, Ya. Varshavsky, N. Wallach, I. Waschkies. • Studies in detail the geometry of Schubert varieties, their syzygies, equivariant embeddings of reductive groups, Hilbert Schemes, ca- 2005 / 400 PP., 10 ILLUS. / HARDCOVER / $99.00 ISBN_13 978-0-8176-4342-3 nonical splittings, good filtrations, among other topics ISBN_10 0-8176-4342-7 • Applies Frobenius splitting methods to algebraic geometry and vari- PROGRESS IN MATHEMATICS, vol 243 ous problems in representation theory • Many examples, exercises, and open problems suggested throughout. The Monodromy Group This book will be an excellent resource for mathematicians and graduate students in algebraic geometry and representation theory of algebraic groups. Henryk Zoladek, University of Warsaw, Poland 2005 / 258 PP. / HARDCOVER / $69.95 In singularity theory and algebraic geometry the monodromy group is ISBN_13 978-0-8176-4191-7 ISBN_10 0-8176-4191-2 embodied in the Picard-Lefschetz formula and the Picard-Fuchs equa- PROGRESS IN MATHEMATICS, VOL. 231 tions. 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 Rie- mann-Hilbert problem, the Stokes phenomena and the hypergeomet- Studies in Memory ric functions with their multidimensional generalizations. In the theory of Issai Schur of homomorphic foliations there appear the Ecalle-Voronin-Martinet- Anthony Joseph, Weizmann Institute of Ramis moduli. On the other hand, there is a deep connection of mono- Science, Rehovot, Israel; dromy theory with Galois theory of differential equations and algebraic Anna Melnikov, University of Haifa, Israel; and functions. All this is presented in this book, underlining the unifying role Rudolf Rentschler, Université Pierre et of the monodromy group. Marie Curie, Paris, France (Eds.) The material is addressed to a wide audience, ranging from specialists This volume is dedicated to the memory in the theory of ordinary differential equations to algebraic geometers. of Issai Schur. It features an extended bi- The book contains results which are usually spread in many sources. ography of Schur—written in collaboration Readers can quickly get introduced to modern and vital mathemati- with some of his former students—as well cal theories, such as singularity theory, analytic theory of ordinary dif- as survey articles covering many areas in- ferential equations, holomorphic foliations, Galois theory, and parts of spired by Schur’s work, as well as more recent developments involving algebraic geometry, without searching through vast literature. crystal and canonical bases, Hecke algebras, and the geometric ap- 2006/ 580 PP., 134 ILLUS. / HARDCOVER / $129.00 ISBN_13 978-3-7643-7535-5 proach linking orbits to representations. ISBN_10 3-7643-7535-3 Contributors: MONOGRAFIE MATEMATYCZNE, VOL. 67 BIOGRAPHY: W. Ledermann, B. Neumann, P.M. Neumann, H. Abelin- Schur; REVIEW OF WORK: H. Dym, V. Katznelson; ORIGINAL PAPERS: H. H. Andersen, A. Braverman, S. Donkin, V. Ivanov, D. Kazhdan, B. Kostant, A. Lascoux, N. Lauritzen, B. Leclerc, P. Littelmann, G. Luzstig, O. Mathieu, M. Nazarov, M. Reinek, J.-Y. Thibon, G. Olshanski, E. Opdam, A. Regev, C.S. Seshadri, M. Varagnolo, E. Vasserot, A. Vershik. 2002 / 560 PP., 30 ILLUS. / HARDCOVER / $103.00 ISBN_13 978-0-8176-4208-2 ISBN_10 0-8176-4208-0 PROGRESS IN MATHEMATICS, VOL. 210

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Lie Theory Lie Theory Jean-Philippe Anker, Université d’Orléans, Orléans, France and Unitary Representations and Compactifica- Bent Orsted, University of Southern Denmark, Odense, Denmark (Eds.) tions of Symmetric Spaces Semisimple Lie groups, and their algebraic analogues over fields This volume, a self-contained work by A. Borel, L. Ji, and T. Kobayashi, other than the reals, are of fundamental importance in geometry, focuses on two fundamental questions in the theory of semisimple analysis, and mathematical physics. Three independent, self-con- Lie groups: the geometry of Riemannian symmetric spaces and tained volumes, under the general title Lie Theory, feature survey their compactifications; and branching laws for unitary represen- work and original results by well-established researchers in key ar- tations, i.e., restricting unitary representations to (typically, but not eas of semisimple Lie theory. exclusively, symmetric) subgroups and decomposing the ensuing representations into irreducibles. Knowledge of basic representation theory of Lie groups as well as Lie Theory familiarity with semisimple Lie groups and symmetric spaces is re- Harmonic Analysis on quired of the reader. Symmetric Spaces— 2005 / 207 PP., 20 ILLUS. / HARDCOVER / $69.95 ISBN_13 978-0-8176-3526-8 General Plancherel Theorems ISBN_10 0-8176-3256-2 PROGRESS IN MATHEMATICS, VOL. 229 “This book is a remarkable and highly commendable effort by three leading experts, Erik P. van den Ban, Henrik Schlichtk- rull, and Patrick Delorme, to survey the fas- Lie Theory cinating progress made in the last decade on the Plancherel theorem for reductive Lie Algebras and Representations symmetric spaces.”—MATHEMATICAL REVIEWS This work contains J. C. Jantzen’s “Nilpotent Orbits in Representa- This work presents extensive surveys by tion Theory,” and K. H. Neeb’s “Infinite Dimensional Groups and E.P. van den Ban, H. Schlichtkrull, and P. Delorme of the spectacular their Representations.” Both are comprehensive treatments of the progress over the past decade in deriving the Plancherel theorem on re- relevant geometry of orbits in Lie algebras, or their duals, and the ductive symmetric spaces. correspondence to representations. Well suited for both graduate students and researchers in semi- Ideal for graduate students and researchers, Lie Theory provides a simple Lie theory and neighboring fields, possibly even -math broad, clearly focused examination of semisimple Lie groups and ematical cosmology, Harmonic Analysis on Symmetric Spaces — their integral importance to research in many branches of math- General Plancherel Theorems provides a broad, clearly focused ex- ematics. amination of semisimple Lie groups and their integral importance 2004 / 328 PP. / HARDCOVER / $69.95 and applications to research in many branches of mathematics and ISBN_13 978-0-8176-3373-8 ISBN_10 0-8176-3373-1 physics. Knowledge of basic representation theory of Lie groups as PROGRESS IN MATHEMATICS, VOL. 228 well as familiarity with semisimple Lie groups, symmetric spaces, and parabolic subgroups is required. 2005 / 175 PP., 3 ILLUS. / HARDCOVER / $69.95 ISBN_13 978-0-8176-3777-4 ISBN_10 0-8176-3777-X PROGRESS IN MATHEMATICS, VOL. 230

Introduction to searchers interested in the theory of vertex operator algebras and their applications.” —MATHEMATICAL REVIEWS Vertex Operator The deep and relatively new field of vertex operator algebras is inti- Algebras and Their mately related to a variety of areas in mathematics and physics: for example, the concepts of “monstrous moonshine,” infinite-dimensional Representations Lie theory, string theory, and conformal field theory. This book intro- James Lepowsky and Haisheng Li, duces the reader to the fundamental theory of vertex operator algebras both, Rutgers University, Piscataway, NJ and its basic techniques and examples. “[The] authors give a systematic introduction Requiring only a familiarity with basic algebra, the work will equip read- to the theory of vertex operator algebras ers to embark on many active research directions related to vertex op- and their representations. Particular empha- erator algebras, group theory, representation theory, and string theory. sis is put on the axiomatic development of 2004 / 316 PP. / HARDCOVER / $89.95 ISBN_13 978-0-8176-3408-7 the theory and the construction theorems ISBN_10 0-8176-3408-8 for vertex operator algebras and their modules. The book provides a PROGRESS IN MATHEMATICS, VOL. 227 detailed study of most basic families of vertex operator algebras and their representation theory. A number of new, original results are presented … . This excellent book is written in a self-contained manner with detailed proofs. It will be useful for graduate students and active re-

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2000 Ferran Sunyer i Balaguer 2002 Ferran Sunyer i Balaguer Prize Winner Prize Winner Momentum Maps Subgroup Growth and Hamiltonian Alexander Lubotzky, Hebrew University, Jerusalem, Israel and Dan Segal, All Souls College, Oxford, UK Reduction “[Subgroup growth] is one of the first books on Asymptotic Group The- Juan-Pablo Ortega, CNRS, Université de ory–a new, quickly developing direction in modern mathematics … The Franche-Comté, Besançon, France and book of A. Lubotzky and D.Segal, leading specialists in group theory, Tudor S. Ratiu, Ecole Polytechnique answers…questions in a beautiful way . … It was natural to expect a Fédérale de Lausanne, Switzerland text on the subject that would summarize the achievements in the “The present book offers a thorough de- field and we are very lucky to witness the appearance of this wonder- scription of [reduction] theory and a unified ful book . … Readers will be impressed with the encyclopedic scope treatment of most of its developments and generalizations, with a par- of the text. It includes all, or almost all, topics related to subgroup ticular emphasis on those due to the authors. It contains many impor- growth … . The book also includes plenty of general information on tant results which cannot be found in other books, and covers a large topics that are well known to algebraic audiences and should be part part of the recent developments related to momentum maps and re- of the background for every modern researcher in mathematics . …a duction. This book fills a need and will be appreciated by specialists as wonderful methodological tool introduced by the authors . … well as by persons new to the field … . ”—MATHEMATICAL REVIEWS The book ends [with] a section on open problems, which contains Momentum Maps and Hamiltonian Reduction may serve as a resource 35 problems related to subgroup growth. The list will be useful and for graduate courses and seminars in symplectic and Poisson geometry, interesting to both established mathematicians and young research- mechanics, Lie theory, mathematical physics, and as a comprehensive ers. There is no doubt that the list includes the most important and reference resource for researchers. illuminating problems in the area, and we eagerly anticipate solutions 2004 / 497 PP., 10 ILLUS. / HARDCOVER / $69.95 of at least some of them in the near future. ISBN_13 978-0-8176-4307-2 The book will surely have [a] big impact on all readers interested in ISBN_10 0-8176-4307-9 PROGRESS IN MATHEMATICS, VOL. 222 Group Theory, as well as in Algebra and Number Theory in general.” — BULLETIN OF THE AMS 2003 / 454 PP. / HARDCOVER / $137.00 ISBN_13 978-3-7643-6989-7 ISBN_10 3-7643-6989-2 Noncommutative Harmonic PROGRESS IN MATHEMATICS, VOL. 212 Analysis In Honor of Jacques Carmona Patrick Delorme, Institut de Mathématiques de Luminy, France and The Orbit Method in Geometry Michèle Vergne, Ecole Polytechnique, Palaiseau, France (Eds.) and Physics This volume is devoted to the theme of noncommutative harmonic In Honor of A.A. Kirillov analysis and honors Jacques Carmona, whose scientific interests range through all aspects of Lie group representations. Topics include: the Christian Duval, CNRS, Marseille, France; theory of representations of reductive Lie groups, and especially the Laurent Guieu, Universitée Montpelier II, Montpelier, France; and determination of the unitary dual, the problem of geometric realizations Valentin Ovsienko, Université Claude Bernard Lyon I, Villeurbanne, France of representations, harmonic analysis on reductive symmetric spaces, Among the distinguished names associated with the orbit method is the study of automorphic forms, and results in harmonic analysis that that of A.A. Kirillov, whose pioneering paper on nilpotent orbits (1962) apply to the Langlands program. places him as the founder of orbit theory. The original research papers General Lie groups are also discussed, particularly from the orbit meth- in this volume are written by prominent mathematicians and reflect re- od perspective, which has been a constant source of inspiration for cent achievements in orbit theory and other closely related areas such both the theory of reductive Lie groups and for general Lie groups. Also as harmonic analysis, classical representation theory, Lie superalgebras, covered is Kontsevich quantization, which has appeared in recent years Poisson geometry, and quantization. as a powerful tool. Contributors: A. Alekseev, J. Alev, V. Baranovksy, R. Brylinski, J. Dixmier, Contributors: V. Baldoni-Silva, D. Barbasch, P. Bieliavsky, N. Bopp, S. Evens, D.R. Farkas, V. Ginzburg, V. Gorbounov, P. Grozman, E. Gutkin, A. Bouaziz, P. Delorme, P. Harinck, A. Hersant, M. S. Khalgui, A. W. Knapp, A. Joseph, D. Kazhdan, A.A. Kirillov, B. Kostant, D. Leites, F. Malikov, B. Kostant, J. Kuttler, M. Libine, J. D. Lorch, L. A. Mantini, S. D. Miller, A. Melnikov, P.W. Michor, Y.A. Neretin, A. Okounkov, G. Olshanski, F. Petrov, J. D. Novak, M.-N. Panichi, M. Pevzner, W. Rossmann, H. Rubenthaler, A. Polishchuk, W. Rossmann, A. Sergeev, V. Schechtman, I. Shchepochkina. W. Schmid, P. Torasso, C. Torussian, E. P. van deu Ban, M. Vergne, 2003 / 472 PP., 1 ILLUS. / HARDCOVER / $114.00 N. R. Wallach ISBN_13 978-0-8176-4232-7 ISBN_10 0-8176-4232-3 2004 / 509 PP., 15 ILLUS. / HARDCOVER / $89.95 PROGRESS IN MATHEMATICS, VOL. 213 ISBN_13 978-0-8176-3207-6 ISBN_10 0-8176-3207-7 PROGRESS IN MATHEMATICS, VOL. 220

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Analysis on Lie Groups with Kac-Moody Groups, Polynomial Growth their Flag Varieties Nick Dungey, Australian National University, Canberra, Australia; and Representation A.F.M. ter Elst, Eindhoven University of Technology, Eindhoven, The Netherlands; and Theory Derek W. Robinson, Australian National University, Canberra, NSW, Shrawan Kumar, University of North Australia Carolina, Chapel Hill, NC “The book is written in a very concise, clear, and elegant way. Misprints “Most of these topics appear here for the are rare … There are no exercises, but the book is well equipped with first time in book form. Many of them are examples, which help to understand the assertions and are, as a rule, interesting even in the classical case of of independent interest. To sum up, the text presents an extremely semi-simple algebraic groups. Some ap- interesting account of some of the most important developments in pendices recall useful results from other the chosen direction.”—MATHEMATICAL REVIEWS areas, so the work may be considered self-contained, although some Analysis on Lie Groups with Polynomial Growth presents a method for familiarity with semi-simple Lie algebras or algebraic groups is helpful. examining the surprising connection between invariant differential op- It is clear that this book is a valuable reference for all those interested erators and almost periodic operators on a suitable nilpotent Lie group. in flag varieties and representation theory in the semi-simple or Kac- It deals with the theory of second-order, right invariant, elliptic opera- Moody case.”—MATHEMATICAL REVIEWS tors on a large class of manifolds: Lie groups with polynomial growth. “A lot of different topics are treated in this monumental work . … many Further, the text goes beyond the classical homogenization theory by of the topics of the book will be useful for those only interested in the converting an analytical problem into an algebraic one. finite-dimensional case. The book is self contained, but is on the level 2003 / 312 PP. / HARDCOVER / $79.95 of advanced graduate students . …For the motivated reader who is ISBN_13 978-0-8176-3225-0 willing to spend considerable time on the material, the book can be a ISBN_10 0-8176-3225-5 PROGRESS IN MATHEMATICS, VOL. 214 gold mine.”—ZENTRALBLATT MATH This comprehensive and self-contained text focuses on the study of Kac-Moody groups and their flag varieties. The theory is developed from scratch, and the reader is gently led to the forefront of the subject, Lie Groups Beyond treating the algebro-geometric, topological, and representation-theo- an Introduction retic aspects of the theory. Second Edition A number of examples, exercises, and challenging open problems are Anthony W. Knapp, State University of presented. Research mathematicians at the crossroads of representation New York, Stony Brook, NY theory, geometry, and topology will benefit greatly from this book. The work is also an excellent text for a graduate course in Kac-Moody theory. “The first edition of the present book ap- 2002 / 632 PP., 86 ILLUS. / HARDCOVER / $69.95 peared in 1996, and quickly became one of ISBN_13 978-0-8176-4227-3 the standard references on the subject … . The ISBN_10 0-8176-4227-7 present edition has been perfected even fur- PROGRESS IN MATHEMATICS, VOL. 204 ther, apart from straightening occasional er- rors … and making various revisions throughout, by adding a new introduction and two new chapters [IX and X] … . Chapter IX contains a treatment of induced Lectures on Algebraic representations and branching theorems … . Chapter X is largely about Quantum Groups actions of compact Lie groups on polynomial algebras, pointing toward Ken A. Brown, University of Glasgow, UK and invariant theory and some routes to infinite-dimensional representation Ken R. Goodearl, University of California, theory…. This is an excellent monograph, which, as with the previous edi- Santa Barbara, CA tion, can be recommended both as a textbook or for reference to anyone interested in Lie theory.” — MATHEMATICA BOHEMICA (review of the second edition) “The proofs, sketches of proofs, and quota- tions from the literature are carefully writ- Lie Groups Beyond an Introduction, takes the reader from the end of ten. Numerous examples and exercises are introductory Lie group theory to the threshold of infinite-dimensional included, and bibliographical notes con- group representations. Merging algebra and analysis throughout, the clude each chapter. The second and third author uses Lie-theoretic methods to develop a beautiful theory with parts end with a discussion of open prob- wide applications in mathematics and physics. lems and perspectives for further research.”—MATHEMATICAL REVIEWS 2002 / 816 PP., 8 ILLUS. / HARDCOVER / $69.95 2002 / 357 PP. / SOFTCOVER / $49.95 ISBN_13 978-0-8176-4259-4 ISBN_13 978-3-7643-6714-5 ISBN_10 0-8176-4259-5 ISBN_10 3-7643-6714-8 PROGRESS IN MATHEMATICS, VOL. 140 ADVANCED COURSES IN MATHEMATICS–CRM BARCELONA

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Compactifications Complex Variables of Symmetric and with Applications Locally Symmetric S. Ponnusamy, Indian Institute of Technology, Madras, Chennai, India; Spaces Herb Silverman, College of Charleston, SC Armand Borel, Institute for Advanced Complex numbers can be viewed in several Study, Princeton, NJ and ways: as an element in a field, as a point in Lizhen Ji, University of Michigan, Ann Arbor, MI the plane, and as a two-dimensional vector. Non-compact Riemannian symmetric spaces Examined properly, each perspective provides and their quotients by arithmetically defined crucial insight into the interrelations between groups of isometries occur in many parts the complex number system and its parent, of mathematics. For many purposes it has the real number system. The authors explore been necessary to compactify them. This monograph attempts to give these relationships by adopting both generalization and specialization meth- a systematic, and in part new exposition of these compactifications as ods to move from real variables to complex variables, and vice versa, while well as new ones, their interrelations, and the context out of which they simultaneously examining their analytic and geometric characteristics. arose. Compactifications of the more general semisimple symmetric The engaging exposition is replete with discussions, remarks, questions, spaces are also considered. and exercises, motivating not only understanding on the part of the 2005 / 400 PP. / HARDCOVER / $79.95 reader, but also developing the tools needed to think critically about ISBN_13 978-0-8176-3247-2 mathematical problems. The material includes numerous examples ISBN_10 0-8176-3247-6 MATHEMATICS: THEORY & APPLICATIONS and applications relevant to engineering students, along with some techniques to evaluate various types of integrals. The book may serve as a text for an undergraduate course in complex variables. The only prerequisite is a basic knowledge of advanced calculus. Polynomial Convexity 2006/ 514 PP., 109 ILLUS. / HARDCOVER/$59.95 Edgar Lee Stout, University of Washington, Seattle, WA ISBN_13 978-0-8176-4457-4 ISBN_10 0-8176-4457-1 This comprehensive monograph is devoted to the study of polynomially convex sets, which play a key role in the theory of functions of several complex variables. Important Features of Polynomial Convexity: Introduction to Complex Analysis • Presents the general properties of polynomially convex sets with in Several Variables particular attention to the theory of the hulls of one-dimensional- Volker Scheidemann, Marburg, Germany sets. • Motivates the theory with numerous examples and counterexam- This book gives a comprehensive introduction to complex analysis in sev- ples, which serve to illustrate the general theory and to delineate its eral variables. Many cross-references to other parts of mathematics, such boundaries. as functional analysis or algebras, are pointed out in order to broaden the view and the understanding of the chosen topics. The book primarily • Examines in considerable detail questions of uniform approxima- aims at students starting to work in the field of complex analysis in sev- tion, especially on totally real sets, for the most part on compact eral variables and teachers who want to prepare a course. To that end, sets but with some attention to questions of global approximation a lot of examples and supporting exercises are inserted throughout the on noncompact sets. text, which will help students to become acquainted with the subject. • Discusses important applications, e.g., to the study of analytic variet- 2005 VIII / 171 PP. / SOFTCOVER / $34.95 ies and to the theory of removable singularities for CR functions. ISBN_13 978-3-7643-7490-7 ISBN_10 3-7643-7490-X • Requires of the reader a solid background in real and complex analysis together with some previous experience with the theory of functions of several complex variables as well as the elements of functional analysis. This beautiful exposition of a rich and complex theory, The Functional Calculus for which contains much material not available in other texts and which Sectorial Operators is destined to be the standard reference for many years, will appeal to all those with an interest in multivariate complex analysis. Markus Haase, University of Leeds, U.K. 2007 / APPROX. 450 PP. / HARDCOVER / $69.95 (TENT.) This book contains a systematic (and partly axiomatic) treatment of holo- ISBN_13 978-0-8176-4537-3 morphic functional calculus for unbounded sectorial operators. The con- ISBN_10 0-8176-4537-3 PROGRESS IN MATHEMATICS nection of functional calculus with interpolation theory is developed to a considerable extent. One chapter is dedicated to the stunning relations between functional calculus, similarity questions and numerical range conditions for operators on Hilbert spaces. In the last chapter applications to PDE, evolution equations and approximation theory as well as the connection with harmonic analysis are described. 2006/ 392 PP., 8 ILLUS. / HARDCOVER / $99.00 ISBN_13 978-3-7643-7697-0 ISBN_10 3-7643-7697-X OPERATOR THEORY: ADVANCES AND APPLICATIONS, VOL. 169

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Ramsey Methods in Analysis Indefinite Linear Algebra and Spiros A. Argyros, National Technical University, Athens, Greece; Applications Stevo Todorcevic, Université Paris VII - CNRS, France, and University of Israel Gohberg, Tel Aviv University, Israel; Toronto, Canada Peter Lancaster, University of Calgary, Canada; This book introduces graduate students and researchers to the study of Leiba Rodman, College of William and Mary, Williamsburg the geometry of Banach spaces using combinatorial methods. The combinatorial, and in particular the Ramsey-theoretic, approach to Banach This graduate text provides a careful treatment of the theory and appli- space theory is not new, it can be traced back as early as the 1970s. Its cations of matrices in the presence of an indefinite inner product. The full appreciation, however, came only during the last decade or so, after theory is a natural extension of the classical theory of hermitian and uni- some of the most important problems in Banach space theory were tary matrices in linear algebra. Applications of the theory to differential solved, such as, for example, the distortion problem, the unconditional equations, difference equations and systems theory are included. basic sequence problem, and the homogeneous space problem. The 2005/ 357 PP. / SOFTCOVER / $59.95 ISBN_13 978-3-7643-7349-8 book covers most of these advances, but one of its primary purposes is ISBN_10 3-7643-7349-0 to discuss some of the recent advances that are not present in survey articles of these areas. 2005/ 257 PP. / SOFTCOVER / $49.95 ISBN_13 978-3-7643-7264-4 The Fourfold Way in ISBN_10 3-7643-7264-8 ADVANCED COURSES IN MATHEMATICS–CRM BARCELONA Real Analysis An Alternative to the Meta- 2005 Ferran Sunyer i Balaguer Prize plectic Representation Winner André Unterberger, Université de Reims, France On the Topology of The fourfold way starts with the consider- Isolated ation of entire functions of one variable satisfying specific estimates at infinity, both on Singularities in the real line and the pure imaginary line. A Analytic Spaces major part of classical analysis, mainly that which deals with Fourier analysis and related concepts, can then be José Seade, Universidad Nacional given a parameter-dependent analogue. In fourfold analysis, the spec- Autónoma de México trum of the harmonic oscillator can be an arbitrary class modulo the The aim of this book is to give an overview integers. Even though the whole development touches upon notions of of selected topics on the topology of real representation theory, pseudodifferential operator theory, and algebraic and complex isolated singularities, with emphasis on its relations to geometry, it remains completely elementary in all these aspects. The other branches of geometry and topology. book should be of interest to researchers working in analysis in general, The first chapters are devoted to complex singularities and a myriad of in harmonic analysis, or in mathematical physics. results spread in a vast literature, which are presented here in a unified 2006/ 220 PP. / HARDCOVER / $109.00 ISBN_13 978-3-7643-7544-7 way, accessible to non-specialists. Among the topics are the fibration ISBN_10 3-7643-7544-2 theorems of Milnor; the relation with 3-dimensional Lie groups; exotic PROGRESS IN MATHEMATICS, VOL. 250 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. Complex Convexity and Analytic The second part of the book studies pioneer work about real analytic singularities which arise from the topological and geometric study of Functionals holomorphic vector fields and foliations. In the low dimensional case Mats Andersson, Chalmers Tekniska Högskola, Göteborg, Sweden; these turn out to be related to fibred links in the 3-sphere defined by Mikael Passare, Stockholm University, Sweden; and meromorphic functions. This provides new methods for constructing Ragnar Sigurdsson, University of Iceland, Reykjavik, Iceland manifolds equipped with a rich geometry. 2006/ 238 PP. / HARDCOVER / $64.95 “This valuable monograph, which was in preparation for a ISBN_13 978-3-7643-7322-1 decade, … The book consists of four chapters, each of which begins ISBN_10 3-7643-7322-9 with a helpful summary and concludes with bibliographic references PROGRESS IN MATHEMATICS, VOL. 241 and historical comments.”—ZENTRALBLATT MATH 2004 / 164 PP. / HARDCOVER/$99.00 ISBN_13 978-3-7643-2420-9 ISBN_10 3-7643-2420-1 PROGRESS IN MATHEMATICS, VOL. 225

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Shift-Invariant Analysis I Uniform Algebras on Herbert Amann, University of Zürich, Switzerland; Groups Joachim Escher, University of Suren A. Grigoryan, Kazan State University, Hannover, Germany Russia; This book is the first of a three volume in- Thomas V. Tonev, University of Montana, troduction to analysis. It is distinguished by Missoula, MT its modern and clear presentation, always The central subject of the book–the theory concentrating on essential concepts. In con- of shift-invariant algebras–is an outgrowth of trast to most other textbooks, there is no the established theory of generalized analytic artificial separation between the theories functions. Associated subalgebras of almost of one variable and that of many variables. periodic functions of real variables and of bounded analytic functions on Emphasis is placed on the early development of a solid foundation in the unit disc are carried along within the general framework. There are topology. As well, the basics of complex analysis are covered. given characterizations of semigroups such that classical theorems of 2005/ 426 PP. / SOFTCOVER / $79.95 complex analysis hold on the associated shift-invariant algebras. Bourgain ISBN_13 978-3-7643-7153-1 ISBN_10 3-7643-7153-6 algebras, orthogonal measures, and primary ideals of big disc algebras are described. The notion of a harmonic function is extended on compact abelian groups, and corresponding Fatou-type theorems are proven. Important classes of inductive limits of standard uniform algebras, includ- Analysis II ing Blasche algebras, are introduced and studied. Herbert Amann, Universität Zürich, Switzerland; 2006 / 284 PP. / HARDCOVER / $99.00 Joachim Escher, Universität Hannover, Germany ISBN_13 978-3-7643-7606-2 ISBN_10 3-7643-7606-6 The second volume of this introduction into analysis deals with the integra- MONOGRAFIE MATEMATYCZNE, VOL. 68 tion theory of functions of one variable, the multidimensional differential calculus and the theory of curves and line integrals. The modern and clear development that began in Volume I (3-7643-7153-6) continues. In this way a sustainable basis will be created which allows to deal with interesting Theory of Function applications that sometimes go considerably beyond the material that is Spaces III represented in traditional textbooks. This applies, for instance, to the explora- Hans Triebel, University of Jena, Germany tion of Nemytskii operators which enable a transparent introduction into the calculus of variations and the derivation of the Euler-Lagrange equations. This book deals with the recent theory 2006 / APPROX. 424 PP. / SOFTCOVER / $79.95 of function spaces as it stands now. Spe- ISBN_13 978-3-7643-7472-3 cial attention is paid to developments in ISBN_10 3-7643-7472-1 the last 10–15 years which are closely related to numerous applications of the theory of function spaces to some areas such as numerics, signal processing Nonstandard Analysis and fractal analysis. In particular, typical build- Martin Väth, Freie Universität Berlin, Germany ing blocks as (non-smooth) atoms, quarks, This book presents an introduction into Robinson‘s nonstandard analy- wavelet bases and wavelet frames are discussed in detail and applied sis. Nonstandard analysis is the application of model theory in analysis. afterwards to some outstanding problems of the recent theory of func- However, the reader is not expected to have any background in model tion spaces such as a local smoothness theory, fractal measures, fractal theory; instead, some background in analysis, topology, or functional analysis, spaces on Lipschitz domains and on quasi-metric spaces. analysis would be useful—although the book is as much self-contained The book is essentially self-contained, although it might also be consid- as possible and can be understood after a basic calculus course. Unlike ered as the continuation of the two previous books of the author with some other texts, it does not attempt to teach elementary calculus on the same title which appeared as volumes 78 and 84 in this book series. the basis of nonstandard analysis, but it points to some applications It is directed to mathematicians working in analysis, numerics and fractal in more advanced analysis. Such applications can hardly be obtained geometry, and to (theoretical) physicists interested in related subjects by standard methods such as a deeper investigation of Hahn-Banach such as signal processing. limits or of finitely additive measures. 2006 / 426 PP. / HARDCOVER / $169.00 2006 / APPROX. 260 PP. / HARDCOVER / $49.95 ISBN_13 978-3-7643-7581-2 ISBN_13 978-3-7643-7773-1 ISBN_10 3-7643-7581-7 ISBN_10 3-7643-7773-9 MONOGRAPHS IN MATHEMATICS, VOL. 100

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Geometric Qp Functions Geometric Function Jie Xiao, Memorial University of Newfoundland, St. John‘s, NF, Canada Theory This book documents the rich structure of the holomorphic Q functions Explorations in Complex which are geometric in the sense that they transform naturally under Analysis conformal mappings. Particular emphasis is placed on recent developments based on the interaction between geometric function / measure Steven G. Krantz, Washington University, theory and other branches of mathematical analysis, including potential St. Louis, MO theory, complex variables, harmonic analysis, functional analysis, and “The geometric point of view is the unify- operator theory. Largely self-contained, this book will be an instructional ing theme in this fine textbook in complex and reference work for advanced courses and research in conformal function theory. But the author also stud- analysis, geometry, and function spaces. ies byways that come from analysis and 2006 / APPROX. 252 PP. / SOFTCOVER / $49.95 algebra. What is important, the topics are ISBN_13 978-3-7643-7762-5 presented with an explanation of their interaction with other important ISBN_10 3-7643-7762-3 FRONTIERS IN MATHEMATICS parts of mathematics. The presentations of the topics are clear and the text makes a 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 Infinite Matrices and and helps the student to understand the subject. The book under review leads the student to see what complex function theory has to their Finite Sections offer and thereby give him or her a taste of some of the areas of An Introduction to the Limit current research. As such it is a welcome addition to the existing litera- Operator Method ture in complex function theory.In this reviewer’s opinion, the book can Marko Lindner, University of Reading, UK warmly be recommended both to experts and to a new generation of mathematicians.”—ZENTRALBLATT MATH This book is an introduction to a fascinating Complex variables is a precise, elegant, and captivating subject. Pre- topic at the interface of functional analysis, sented from a geometric analytical viewpoint, this work addresses algebra and numerical analysis, written for advanced topics in complex analysis that verge on modern areas of a broad audience of students, researchers research, including: invariant geometry, the Bergman metric, the au- and practitioners. It is concerned with the tomorphism groups of domains, extremal length, harmonic measure, study of infinite matrices and their approxi- boundary regularity of conformal maps, the inhomogeneous Cauchy- mation by matrices of finite size. The framework includes the simplest, Riemann equations, and the corona problem. important case where the matrix entries are numbers, but also the more general case where the entries are bounded linear operators. The author adroitly weaves these varied topics to reveal a number of delightful interactions. Perhaps more importantly, they are presented The main items and concepts studied are band-dominated operators, with an understanding and explanation of their interrelations with other invertibility at infinity, Fredholmness, the method of limit operators, and important parts of mathematics: harmonic analysis, differential geom- the stability and convergence of finite matrix approximations. Concrete etry, partial differential equations, potential theory, abstract algebra, and examples are used to illustrate the results throughout, including dis- invariant theory. crete Schrödinger operators and integral and boundary integral opera- 2005 / APPROX. 350 PP. / HARDCOVER / $69.95 tors arising in mathematical physics and engineering. ISBN_13 978-0-8176-4339-3 The main audience are those concerned with large finite matrices and ISBN_10 0-8176-4339-7 CORNERSTONES their infinite counterparts, for example in numerical linear algebra and mathematical physics. More generally, the book will be of interest to those working in operator theory and applications, for example studying integral operators or the application of operator algebra methods. Approximation Theory Using While some basic knowledge of functional analysis would be helpful, the presentation contains relevant preliminary material and is largely Positive Linear Operators self-contained. Radu Păltănea, “Transilvania” University of Brasov, Romania 2006 / 314 PP., 12 ILLUS. / SOFTCOVER / $49.95 ISBN_13 978-3-7643-7766-3 “This monograph will be of interest to those working in the field ISBN_10 3-7643-7766-6 of approximation, and it may serve as a good supplementary text FRONTIERS IN MATHEMATICS for courses in approximation theory, or as a reference text on the subject.” —ZENTRALBLATT MATH This work treats quantitative aspects of the approximation of functions using positive linear operators. The theory of these operators has been an important area of research in the last few decades, particularly as it affects computer-aided geometric design. In this book, the crucial role of the second order moduli of continuity in the study of such operators is emphasized. New and efficient methods, applicable to general operators and to diverse concrete moduli, are presented. The advantages of these methods consist in obtaining improved and even optimal estimates as well as in broadening the applicability of the results. 2004 / 202 PP. / SOFTCOVER / $74.95 ISBN_13 978-0-8176-4350-8 ISBN_10 0-8176-4350-8

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Harmonic Analysis, Signal Global Smoothness and Shape Processing, and Complexity Preserving Interpolation by Festschrift in Honor of the 60th Birthday of Classical Operators Carlos A. Berenstein Sorin G. Gal, University of Oradea, Romania Irene Sabadini, Politecnico di Milano, Italy; “This research monograph is a systematic treatment of the global Daniele C. Struppa and David F. Walnut, both, George Mason smoothness preservation and the shape preservation properties for University, Fairfax, VA (Eds.) classical univariate and bivariate interpolation operators of Lagrange, Carlos A. Berenstein has had a profound influence on scholars and Grünwald, Hermite-Fejér and Shepard type. Written in a clear and con- practitioners alike amid a distinguished mathematical career span- cise style, with numerous open problems supplementing each chapter ning nearly four decades. His uncommon capability of adroitly moving and up to date references, this book constitutes a valuable tool for between these parallel worlds is demonstrated by the breadth of his graduate students and researchers in approximation theory and its research interests, from his early theoretical work on interpolation in applications.”—ZENTRALBLATT MATH spaces of entire functions with growth conditions and residue theory to This monograph focuses on two aspects of the interpolations of func- his later work on deconvolution and its applications to issues ranging tions, namely the Global Smoothness Preservation Property (GSPP) from optics to the study of blood flow. This volume, which celebrates and the Shape Preservation Property (SPP) of well-known classical in- his sixtieth birthday, reflects the state-of-the-art in these areas. Original terpolation operators such as Lagrange, Grünwald, Hermite-Fejér and articles and survey articles, all refereed, cover topics in harmonic and Shepard type. For both aspects, the study is mainly developed in the complex analysis, as well as more applied work in signal processing. directions of univariate and bivariate cases with some exceptions. One Contributors: C.A. Berenstein, R.W. Braun, O. Calin, D-C. Chang, G. Dafni, of the first books on the subject, it presents recent work and features L. Ehrenpreis, G. Kaiser, C.O. Kiselman, P. Krishnaprasad, B.Q. Li, B. Matt, many new results as well as an excellent survey of past research. Re- R. Meise, D. Napoletani, R. Poovendran, Y. Qiao, J. Ryan, C. Sadosky, plete with open questions throughout, the work also contains twenty D.C. Struppa, B.A. Taylor, J. Tie, D.F. Walnut, A. Yger. very suggestive figures of nine types of Shepard surfaces, concerning 2005/162 PP., 15 ILLUS./HARDCOVER/$69.95 their shape preserving property. ISBN_13 978-0-8176-4358-4 ISBN_10 0-8176-4358-3 This unique, well-written text is best suited for graduate students and PROGRESS IN MATHEMATICS, VOL. 238 researchers in mathematical analysis, interpolation of functions, pure and applied mathematicians in numerical analysis, approximation theory, data fitting, computer aided geometric design, fluid mechanics, and 2004 Ferran Sunyer i Balaguer Prize engineering researchers. Winner 2005 / 160 PP., 20 ILLUS. / HARDCOVER / $79.95 ISBN_13 978-0-8176-4387-4 Singular Sets of ISBN_10 0-8176-4387-7 Minimizers for the Mumford–Shah Generalized Analytic Automorphic Functional Forms in Hypercomplex Spaces Guy David, Université de Paris-Sud, France Rolf S. Krausshar, Ghent University, Belgium “This monograph is the Ferran Sunyer i “Its remarkable feature is a masterful combination of deep and sophis- Balaguer 2004 prize winner.The book un- ticated results with very accessible form of presentation. I am sure the der review gives an excellent overview of book will have numerous and far-reaching consequences and reper- a part of the work done in recent years on this problem … and the cussions.”—ZENTRALBLATT MATH book is therefore a useful source for mathematicians working in this This book describes the basic theory of hypercomplex-analytic automor- field.”—MATHEMATICAL REVIEWS phic forms and functions for arithmetic subgroups of the Vahlen group This book studies regularity properties of Mumford–Shah minimizers. The in higher dimensional spaces. Hypercomplex analyticity generalizes the Mumford–Shah functional was introduced in the 1980s as a tool for au- concept of complex analyticity in the sense of considering null-solu- tomatic image segmentation, but its study gave rise to many interesting tions to higher dimensional Cauchy-Riemann type systems. Vector- and questions of analysis and geometric measure theory. The main object un- Clifford algebra-valued Eisenstein and Poincaré series are constructed der scrutiny is a free boundary K where the minimizer may have jumps. within this framework and a detailed description of their analytic and The book presents an extensive description of the known regularity proper- number theoretical properties is provided. Explicit relationships to gen- ties of the singular sets K, and the techniques to get them. eralized variants of the Riemann zeta function and Dirichlet L-series are Largely self-contained, the work is accessible to graduate students in established and a concept of hypercomplex multiplication of lattices is analysis. The core of the book is composed of regularity results that introduced. Applications to the theory of Hilbert spaces with reproduc- were proved in the last ten years and which are presented in a more ing kernels, to partial differential equations and index theory on some detailed and unified way. conformal manifolds are also described. 2005 / 581 PP. / HARDCOVER / $139.00 2004 / 167 PP. / SOFTCOVER / $49.95 ISBN_13 978-3-7643-7182-1 ISBN_13 978-3-7643-7059-6 ISBN_1- 3-7643-7182-X ISBN_10 3-7643-7059-9 PROGRESS IN MATHEMATICS, VOL. 233 FRONTIERS IN MATHEMATICS

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Basic Real Analysis Advanced Anthony W. Knapp, State University Real Analysis of New York at Stony Brook, NY Anthony W. Knapp, State University “The volume contains more than 300 of New York at Stony Brook, NY problems and a separate section gives hints or complete solutions to them. “It is useful both as a course text and for The book seems to be completely uni- self-study. One can see, that its content fied, carefully reasoned, rich in con- is near all areas of pure mathematics, cepts, methods and results, and indu- as well as applied mathematics, includ- bitably useful as for students in Real ing statistics, mathematical physics, Analysis so also for teachers in this and differential equations. I think that and this volume turns to be useful for field.”—ZENTRALBLATT MATH any mathematical library and can be Basic Real Analysis and its companion volume Advanced Real recommended to students and lecturers.”—ZENTRALBLATT MATH Analysis systematically develop the concepts and tools that are vital to every mathematician, whether pure or applied, aspiring or Advanced Real Analysis develops Fourier analysis and functional established. The two works are a comprehensive treatment with a analysis with an eye toward partial differential equations. Included global view of the subject, emphasizing the connections between are chapters on Sturm–Liouville theory, compact self-adjoint opera- real analysis and other branches of mathematics. tors, topics in Euclidean Fourier analysis, topological vector spaces and distributions, compact and locally compact groups, aspects In Basic Real Analysis, the subject of Fourier series is used as re- of linear partial differential equations, analysis on manifolds, and curring motivation for a number of theoretical developments. The foundations of probability. The work incorporates, in the text and treatment proceeds from fundamentals to more advanced topics, especially in the problems, material in which real analysis is used in from the particular to the general, often introducing examples well algebra, topology, complex analysis, probability, differential geom- before a theory that incorporates them. Included throughout are etry, and applied mathematics of various kinds. many examples and hundreds of problems (with hints or complete solutions given for most) making the text suitable for an advanced Featuring many examples and hundreds of problems (with hints undergraduate course in real variable theory and most basic gradu- and selected solutions), the book is suitable as a text in graduate ate courses in Lebesgue integration and related topics. courses such as Fourier and functional analysis, modern analysis, and partial differential equations. Because it focuses on what every young mathematician needs to 2005/468 PP., 6 ILLUS./HARDCOVER/$59.95 know about real analysis, the book may also be used for self-study, ISBN_13 978-0-8176-4382-9 particularly by graduate students preparing for qualifying examina- ISBN_10 0-8176-4382-6 tions. The scope and unique approach of the book will also appeal CORNERSTONES 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. Set of Basic and Advanced Real 2005/656 PP., 10 ILLUS./HARDCOVER/$69.95 ISBN_13 978-0-8176-3250-2 Analysis ISBN_10 0-8176-3250-6 2005/$89.95 CORNERSTONES ISBN_13 978-0-8176-4407-9 ISBN_10 0-8176-4407-5

“The collaboration of physicists or engineers and mathematicians, Theory and which is more and more popular and necessary in modern investiga- Applications of tions, requires … a common language. The book under review provides this language … . [It] is a well written book, most of the material Generalized Functions is accessible to senior undergraduate and graduate students in math- Third Edition ematical, physical and engineering sciences … . [The] book will [also] Ram P. Kanwal, Pennsylvania State be useful … for specialists in ODEs, PDEs, functional analysis, [and] University, University Park, PA physicists, engineers, and lecturers.”—ACTA Scientiarum Mathematicarum (Review of a previous edition) “This is the third edition of a textbook on generalized functions which appeals to a This third edition of Generalized Functions expands the treatment of fun- wide class of scientists and engineers. damental concepts and theoretical background material and delineates connections to a variety of applications in mathematical physics, elasticity, In summary, this book continues to be very wave propagation, magnetohydrodynamics, linear systems, probability useful to engineers, scientists and math- and statistics, optimal control problems in economics, and more. ematicians as a collection of examples and important applications, 2004 / 480 PP. / SOFTCOVER / $89.95 and to scientists and engineers as a concise introduction to the theory ISBN_13 978-0-8176-4343-0 of distributions.”—ZENTRALBLATT MATH ISBN_10 0-8176-4343-5

30 Order By Phone: 1-800-777-4643 • Fax: 201-348-4505 • Or Online: www.birkhauser.com Analysis / Operator Theory

Distance and Measure in Analysis A Handbook of and Partial Differential Equations Real Variables Hugo Aimar, Instituto de Matemàtica Aplicada del Litoral, Santa Fe, Argentina With Applications to This comprehensive exploration of a metric approach to some relevant Differential Equations and problems and techniques in analysis focuses on examining spaces of Fourier Analysis homogeneous type. Both the structural and analytical problems under Steven G. Krantz, Washington University, consideration reflect active areas of current research. St. Louis, MO The exposition, motivated by examples and details of which many cannot “In eleven chapters, Krantz’s book succeeds be found elsewhere in book form, unfolds systematically in three parts, in providing a reference work for “the work- starting from such preliminaries as the basic structures of quasi-metric ing engineer or scientist” encompassing spaces, the homogeneity property and measure theory. More advanced the essence of real analysis. True to the 2 topics are then covered, including Calderón-Zygmund decompositions, L idea of a handbook, there are good, but brief, explanations, well-cho- techniques, weighted norm inequalities, BMO, and Hardy spaces. The final sen examples, and only a few proofs. In addition to the book’s principal aim is to encourage a well-developed way of thinking about some math- audience, students preparing for exams at either the undergraduate or ematical and even physical problems, i.e., Newtonian and Riesz potentials, master’s level will find this a valuable resource.”—MAA REVIEWS fields and their derivatives, mean value and Harnack inequalities related to Hölder regularity, wavelet type analysis on non-Euclidean contexts, etc. This concise, well-written handbook provides a distillation of real variable theory with a particular focus on the subject’s significant applica- The book is suitable for self-study or as a classroom resource for graduate tions to differential equations and Fourier analysis. Ample examples students in analysis and PDEs. Real analysis and topology, some basics of and brief explanations—with very few proofs and little axiomatic ma- Fourier analysis and PDEs are requisite background for the reader. chinery—are used to highlight all the major results of real analysis, from 2007 / APPROX. 300 PP., 20 ILLUS. / HARDCOVER/$79.95 (TENT.) the basics of sequences and series to the more advanced concepts of ISBN_13 978-0-8176-4315-7 ISBN_10 0-8176-4315-X Taylor and Fourier series, Baire Category, and the Weierstrass Approxi- APPLIED AND NUMERICAL HARMONIC ANALYSIS mation Theorem. Replete with realistic, meaningful applications to differential equations, boundary-value problems, and Fourier analysis, this unique work is a practical, hands-on manual of real analysis that is ideal for applied Integration and Modern Analysis mathematicians, physicists, engineers, economists, and others who From Classical Real Variables to Distribution Theory wish to use the fruits of real analysis but who do not necessarily have John J. Benedetto, University of Maryland, College Park, MD; the time to appreciate all of the theory. Valuable as a comprehensive Wojciech Czaja, University of Maryland, College Park, MD and reference, a study guide for students, or a quick review, A Handbook of Uniwersytet Wroclawski, Wroclaw, Poland Real Variables will benefit a wide audience. 2004 / 201 PP., 30 ILLUS. / HARDCOVER / $54.95 The subject of real analysis is unified in this modern text by several central ISBN_13 978-0-8176-4329-4 concepts, in particular the notion of absolute continuity. Absolute conti- ISBN_10 0-8176-4329-X nuity, a major underlying idea in formulating and proving the Fundamen- tal Theorem of Calculus (FTC), the Lebesgue Dominated Convergence Theorem, and the Radon–Nikodym Theorem, is essential in dealing with problems of switching limits and of understanding the amazing inverse Köthe–Bochner Function Spaces relationship between integration and differentiation (FTC). Also, it leads Pei-Kee Lin, University of Memphis, Memphis, TN to fundamental notions and results in terms of weak convergence of “This book … gives in fact an exhaustive and very up-to-date account measures, a topic generally not treated in standard real variable texts. of several aspects of the general theory (isomorphic) and geometry The topics are examined in depth and in a way that is valuable not only of Banach spaces. This book is self-contained with an exhaustive list from a theoretical point of view, but in a way that presents a sophisticated of references at the end of each chapter. Apart from well thought-out array of tools with which to deal with a host of difficult practical problems. exercises at the end of each section, the `Notes and Remarks’ section at the end of each chapter contains several open questions with Key topics and features: additional comments and references. This book is worth having on • Historical remarks and perspective on the development of real variables the shelves of anyone interested in Banach space theory. I thoroughly • Covers all basic results in real variables, showing many possible enjoyed going through it.”—ZENTRALBLATT MATH generalizations and both standard and nonstandard examples 2004 / 370 PP. / HARDCOVER / $99.00 ISBN_13 978-0-8176-3521-3 • Expanded material on distribution theory and the Riesz Representation ISBN_10 0-8176-3521-1 Theorem to present a more unified theory of measure and integral • A careful treatment of symmetric perfect sets is used as a foundation for the introduction of fractals and analysis on them—a subject that has emerged in recent years • An extensive array of exercises, ranging from the routine to more challenging problems. 2007 / APPROX. 456 PP., 10 ILLUS./HARDCOVER/$64.95 (TENT.) ISBN_13 978-0-8176-4306-5 ISBN_10 0-8176-4306-0

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Mathematical Analysis Mathematical Analysis Linear and Metric Structures, Approximation and Discrete Continuity Processes Mariano Giaquinta, Scuola Normale Mariano Giaquinta, Scuole Normale Superiore, Pisa, Italy; Superiore, Pisa, Italy and Giuseppe Modica, Università degli Studi di Giuseppe Modica, Università degli Studi di Firenze, Italy Firenze, Italy These independent, fairly self-contained “This self-contained book aims to introduce the texts, under the general title Mathematical main ideas for studying approximation pro- Analysis, provide both a rigorous introduc- cesses, more generally discrete processes at tion to the modern subject and a unique graduate level. The use of computers induces examination of its historical evolution. This a growing need for studying discrete processes. third volume in the sequence encompasses linear and metric spaces, The exposition requires only a sound knowledge of calculus and the functions with detailed coverage at the graduate level. Divided into three parts, of one variable. A key feature this lively yet rigorous and systematic treatment the text opens with a presentation of linear and matrix structures, and is the historical accounts of ideas and methods of the subject. Ideas in math- then proceeds to the topology of metric spaces. Lastly, continuity in in- ematics develop in cultural, historical and economical contexts, thus the authors finite dimensions is discussed, along with Hilbert spaces and the theory made brief accounts of those aspects and used a large number of beautiful of compact operators; applications to geodesics and nonlinear ordinary illustrations.”—ZENTRALBLATT MATH differential equations are examined. This work embraces a broad range of topics in analysis at the graduate level, With its beautiful illustrations, numerous exercises, and comprehensive requiring only a sound knowledge of calculus and the functions of one variable. index, Mathematical Analysis: Linear and Metric Structures, Continuity A key feature of this lively yet rigorous and systematic exposition is the historical will be valuable as a text or reference for graduate students and researchers accounts of ideas and methods pertaining to the relevant topics. Most interesting in mathematics, physics, and engineering. and useful are the connections developed between analysis and other math- 2007 / 384 PP., 122 ILLUS. / HARDCOVER/$149.00 ematical disciplines, in this case, numerical analysis and probability theory. ISBN_13 978-0-8176-4374-4 ISBN_10 0-8176-4374-5 The text is divided into two parts: The first examines the systems of real and complex numbers and deals with the notion of sequences in this context. Af- ter the presentation of natural numbers as a subset of the reals, elements of combinatorics and a discussion of the mathematical notion of the infinite are Mathematical Analysis introduced. The second part is dedicated to discrete processes starting with a Functions of One Variable study of the processes of infinite summation both in the case of numerical series and of power series. The volume closes with introductory chapters on the study Mariano Giaquinta, Scuola Normale of discrete dynamical systems and discrete probability. Superiore, Pisa, Italy and Giuseppe Modica, Università degli Studi di Mathematical Analysis: Approximation and Discrete Processes is replete with Firenze, Italy beautiful illustrations, examples, exercises at the end of each chapter, and a comprehensive index to aid the reader. “Many teachers and students could benefit 2004 / 388 PP., 152 ILLUS. / HARDCOVER / $149.00 from thinking about its unique perspec- ISBN_13 978-0-8176-4313-3 tives.”—SIAM REVIEW ISBN_10 0-8176-4313-3 SOFTCOVER/$69.95 “Giaquinta … and Modica … present the ISBN_13 978-0-8176-4337-9 differential and integral calculus for real ISBN_10 0-8176-4337-0 functions of a single real variable from a sophisticated point of view. Their book is far better suited as a source of unique perspectives on the logical development of calculus ideas and their physical applications … [so that] it will better serve the experi- An Introduction to the Uncertainty enced calculus instructor seeking new approaches to familiar material Principle or the student who has already mastered the basic ideas and techniques of calculus but wishes to see it all again, ‘done right,’ . … Highly Hardy’s Theorem on Lie Groups recommended.”—CHOICE Sundaram Thangavelu, Indian Statistical Institute, Bangalore, India “This self-contained book introduces the main ideas and fundamental “This nicely written book by Thangavelu is concerned with extensions methods of mathematical analysis without losing sight of the context of Hardy’s theorem to settings that arise from noncommutative har- in which it was developed and the role played in science, particularly monic analysis .… Each chapter contains several applications to the in physics .… Each chapter has a short summary where the most im- heat equation in various settings and ends with an extensive presenta- portant facts discussed are collected. There is also a large number of tion of related topics, current research, detailed references to the litera- exercises inserted at various points into the text .… The book is meant ture, and lists of open problems. This makes the book an invaluable principally for students in mathematics, physics, engineering, and com- resource for graduate students and researchers in harmonic analysis puter science, but it can be used at technological and scientific faculties and applied mathematics.”—SIAM REVIEW by anyone who wants to approach these topics.”—ZENTRALBLATT MATH “Each chapter ends with useful notes and open problems. Everything is 2003/353 PP., 196 ILLUS./HARDCOVER/$89.95 written in sufficient detail to benefit specialized interested readers …”— ISBN_13 978-0-8176-4312-6 ISBN_10 0-8176-4312-5 MATHEMATICAL REVIEWS 2004 / 174 PP. / HARDCOVER / $69.95 ISBN_13 978-0-8176-4330-0 ISBN_10 0-8176-4330-3 PROGRESS IN MATHEMATICS, VOL. 217

32 Order By Phone: 1-800-777-4643 • Fax: 201-348-4505 • Or Online: www.birkhauser.com Analysis / Operator Theory

Basic Classes of Basic Real Analysis Linear Operators Houshang H. Sohrab, Towson University, Towson, MD Israel Gohberg, University of Tel Aviv, Israel; Seymour Goldberg, University of Mary- “Students who find Goffman’s ‘Real Functions’ (1953), Halmos’s land, College Park, MD; and ‘Measure Theory’ (1950), Hewitt and Stromberg’s ‘Real and Abstract Marinus A. Kaashoek, Vrije Universiteit Analysis’ (1965), Lang’s (1969) or Royden’s ‘Real Analysis’ (1963), de Boelelaan, The Netherlands or Rudin’s (1973) or Yosida’s ‘Functional Analysis’ (1965) to be too hard, or too easy, may find Sohrab’s presentation just right. Problems “With a name like Gohberg–Goldberg– and exercises abound; an appendix constructs the reals as the Cauchy Kaashoek, it has got to be good. But let (sequential) completion of the rationals; references are copious and me count the ways. If you are interested judiciously chosen; and a detailed index brings up the rear . … Recom- in learning the basic theories of Hilbert mended.”—CHOICE and Banach spaces together with the well- known operators that act on them, this book is for you. It is intended “This book is intended as a text for a one-year course for senior un- for advanced undergraduate and beginning graduate students in dergraduates or beginning graduate students, though it seems to the mathematics . … The volume is actually a second edition of `Basic Op- reviewer that it contains more than enough material for one year’s erator Theory’ by Gohberg and Goldberg . … Exercises and examples study . … The quality of the exposition is good: strong and complete have been added.... The text is well written, clear, and readable .… A versions of theorems are preferred, and the material is organized so student at the specified level will have no difficulty understanding the that all the proofs are of easily manageable length; motivational com- presentation.”—SIAM REVIEW ments are helpful, and there are plenty of illustrative examples. The reader is strongly encouraged to learn by doing: exercises are sprin- This book provides an introduction to functional analysis with an em- kled liberally throughout the text and each chapter ends with a set of phasis on the theory of linear operators and its application to differen- problems, about 650 in all, some of which are of considerable intrinsic tial equations, integral equations, infinite systems of linear equations, interest.”—MATHEMATICAL REVIEWS approximation theory, and numerical analysis. As a textbook designed for senior undergraduate and graduate students, it begins with the ge- “The book is a clear and well-structured introduction to real analysis ometry of Hilbert spaces and proceeds to the theory of linear opera- aimed at senior undergraduate and beginning graduate students .… The tors on these spaces including Banach spaces. Presented as a natural author managed to confine within a reasonable size book, all the basic continuation of linear algebra, the book provides a firm foundation in concepts in real analysis and also some developed topics … The text operator theory for students of mathematics, engineering, and other contains carefully worked out examples which contribute [motivation technical sciences. and help for understanding] the theory. There is also an excellent selec- 2003 / 423 PP. / SOFTCOVER / $89.95 tion of exercises within the text and problem sections at the end of each ISBN_13 978-3-7643-6930-9 chapter. In fact this textbook can serve as a source of examples and ISBN_10 3-7643-6930-2 exercises in real analysis . … This book can be highly recommended as a good reference on real analysis.”—ZENTRALBLATT MATH Solutions manual available upon adoption of the text. Complex Analysis 2003 / 559 PP. / HARDCOVER / $59.95 ISBN_13 978-0-8176-4211-2 in One Variable ISBN_10 0-8176-4211-0 Second Edition Raghavan Narasimhan, University of 2002 Ferran Sunyer i Balaguer Prize Winner Chicago, IL and Yves Nievergelt, Eastern Washington Automorphic Pseudodifferential University, Cheney, WA Analysis and Higher Level “The book introduces and makes use of concepts from many different areas of Weyl Calculi mathematics, especially ideas used in sev- André Unterberger, Université de Reims, France eral complex variables and differential geometry. There is also a short … introductory The primary subject of this monograph is the study of automorphic chapter dealing with several complex variables . … The exercises in distributions and the operators associated with such distributions un- Part 2 vary from basic to advanced, and provide good practice for der the Weyl rule of symbolic calculus. The concept of quantization the concepts and techniques of the subject . … The choice of topics pervades the whole book: an entirely new approach to composition covered gives an excellent introduction to modern complex analysis. formulas, in general, is needed, and the main lines of a new program The exposition is well written. All in all, this book is a welcome addition in this direction are indicated. This work will be of interest to researchers to the list of books presenting a first course in complex analysis.”—MATH- in pseudodifferential analysis and related fields. EMATICAL REVIEWS 2003 / 256 PP. / HARDCOVER / $114.00 ISBN_13 978-3-7643-6909-5 2000 / 400 PP., 15 ILLUS. / HARDCOVER / $69.95 ISBN_10 3-7643-6909-4 ISBN_13 978-0-8176-4164-1 PROGRESS IN MATHEMATICS, VOL. 209 ISBN_10 0-8176-4164-5

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Derivatives and Integrals of The Implicit Function Multivariable Functions Theorem Alberto Guzman, The City College of New York, CUNY, New York, NY History, Theory, and Applications “The book under review presents a systematic introduction to the cal- Steven G. Krantz, Washington Univer- culus of real functions of several variables … . The presentation of the sity, St. Louis, MO and Harold R. Parks, material is very clear throughout. Proofs are carefully worked out, theo- Oregon State University, Corvallis, OR rems are illustrated by examples, and exercises at the end of each sec- “The authors offer a useful and fascinating tion will help to master the calculus. The book is highly recommend- manuscript which should be of interest and able to students to build a foundation for further studies in analysis useful to graduate and postgraduate stu- and differential geometry.”—ZENTRALBLATT MATH dents, professional mathematicians, teach- “Guzman … offers a well-crafted treatment of this standard material, in- ers as well as researchers. Most of them tentionally more advanced than in the most widely used books … . With will be able to find all fundamental ideas in the field and simple and that emphasis on the theoretical aspects of the subject, the book will transparent proofs of all main implicit function theorems and theo- appeal … to students intending ultimately to pursue graduate work in rems closely related to these.”—ZENTRALBLATT MATH mathematics … Recommended.”—CHOICE “For the analyst who uses the Implicit Function Theorem or the instruc- 2003 / 319 PP., 44 ILLUS. / SOFTCOVER / $59.95 ISBN_13 978-0-8176-4274-7 tor who teaches elementary or more advanced variants of it, this book ISBN_10 0-8176-4274-9 is extremely useful .… The presentation is nice and fluent, and the book is accessible even to undergraduate students with a minimum of background in calculus.”—JOURNAL OF OPERATOR THEORY The implicit function theorem is part of the bedrock of mathematics analy- Continuous Functions of Vector sis and geometry. Finding its genesis in eighteenth century studies of real Variables analytic functions and mechanics, the implicit and inverse function theo- Alberto Guzman, The City College of New York, CUNY, New York, NY rems have now blossomed into powerful tools in the theories of partial differential equations, differential geometry, and geometric analysis. “The book is devoted to mathematical analysis in multi-dimensional The history of the implicit function theorem is a lively and complex story, spaces, including infinite-dimensional ones … One of the important and intimately bound up with the development of fundamental ideas in characteristics of the text is the topological approach … The language analysis and geometry. This entire development, together with mathemati- is very clear and sometimes very “fresh” if compared with classical cal examples and proofs, is recounted for the first time here. It is an exciting textbooks, so that it may better appeal to the reader. There are many tale, and it continues to evolve. exercises, and the book concludes with a chapter containing solu- 2002 / 174 PP. / HARDCOVER / $59.95 tions.”—MATHEMATICAL REVIEWS ISBN_13 978-0-8176-4285-3 “This is a textbook on calculus of several variables. It covers algebraic ISBN_10 0-8176-4285-4 and metric structure of the Euclidean space, convergence, basic properties of continuous functions and topology in normed spaces . … In my opinion, this topological approach is one of the advantages of the book under review. It is written very clearly and contains numerous examples Hilbert Space Operators and instructive pictures. Each section is endowed with a set of exercises, A Problem Solving Approach and the book is concluded with solutions to these exercises. This is a Carlos S. Kubrusly, Catholic University of Rio de Janeiro, Brazil nice and user-friendly textbook which can be recommended for a one- semester course in multivariable calculus.”—ZENTRALBLATT MATH “The author treats many new subjects of operator theory for graduate students and mathematicians, i.e., quasihyponormal operators, para- “The presentation is detailed and clear. The leisurely discursive style normal operators, proper contractions, quasireducible operators, a de- adopted by the author will be appreciated by beginners. The fact that tailed presentation of the Lomonosov theorem on nontrivial hyperinvari- the solution of each and every exercise can be found at the end of ant subspaces for compact operators, etc. This book will be of benefit the book considerably enhances its value and makes it suitable also to graduate students (in mathematics, physics, engineering, economics, for individual study. This book successfully bridges the gap between and statistics) and many mathematicians.”—ZENTRALBLATT MATH elementary calculus and such higher disciplines as real functions, general topology, and, in particular, functional analysis.”—PUBLICATIONES “Many totally new subjects are offered to the potential reader … . The MATHEMATICAE, DEBRECEN author has great teaching experience reflected by the skillful selection 2002 / 224 PP., 26 ILLUS. / SOFTCOVER / $44.95 of background material, the gradual statements of the problems, and ISBN_13 978-0-8176-4273-0 the detailed presentation of the solutions. The book is intended [for] an ISBN_10 0-8176-4273-0 audience mainly formed by various types of graduate students: in mathematics, statistics, physics and, perhaps, in engineering and economics. It can be useful even for working mathematicians, as a reference book in a broad sense … . ”—MATHEMATICAL REVIEWS 2003 / 149 PP., 10 ILLUS. / SOFTCOVER/$59.95 ISBN_13 978-0-8176-3242-7 ISBN_10 0-8176-3242-5

34 Order By Phone: 1-800-777-4643 • Fax: 201-348-4505 • Or Online: www.birkhauser.com Analysis / Operator Theory

An Introduction to A Primer of Real Multivariable Analysis Analytic Functions From Vector to Manifold Second Edition Harold R. Parks, Oregon State University, Piotr Mikusiński and Michael D. Taylor, both, University of Corvallis, OR and Central Florida, Orlando, Fl Steven G. Krantz, Washington University, St. Louis, MO “This is a self-contained textbook devoted to multivariable analysis based on non- “This is the second, improved edition of the standard geometrical methods. The book only existing monograph devoted to real- can be used either as a supplement to a analytic functions, whose theory is rightly course on single variable analysis or as a considered in the preface ‘the wellspring semester-long course introducing students to manifolds and differen- of mathematical analysis’. Organized in six tial forms.”—MATHEMATICAL REVIEWS 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 elemen- “The authors strongly motivate the abstract notions by a lot of intuitive tary to the most advanced aspects, it is useful for both beginners and examples and pictures. The exercises at the end of each section range advanced researchers.” —MATHEMATICAL REVIEWS from computational to theoretical. The book is highly recommended for undergraduate or graduate courses in multivariable analysis for “Bringing together results scattered in various journals or books and students in mathematics, physics, engineering, and economics.”—STU- presenting them in a clear and systematic manner, the book is of in- DIA UNIVERSITATIS BABES-BOLYAI, SERIES MATHEMATICA terest first of all for analysts, but also for applied mathematicians and researchers in real algebraic geometry.” —ACTA APPLICANDAE MATHEMATICAE The subject of multivariable analysis is of interest to pure and applied 2002 / 224 PP., 5 ILLUS. / HARDCOVER / $69.95 mathematicians, physicists, electrical, mechanical and system engi- ISBN_13 978-0-8176-4264-8 neers, mathematical economists, biologists and statisticians. ISBN_10 0-8176-4264-1 BIRKHÄUSER ADVANCED TEXTS Core topics in multivariable analysis that are basic for senior undergraduates and graduate studies in differential geometry and for analysis in N dimensions and on manifolds are covered in this introductory text. Aside from mathematical maturity, prerequisites are a one-semester under- A Distributional graduate course in advanced calculus or analysis, and linear algebra. 2001 / 312 PP., 50 ILLUS. / HARDCOVER / $69.95 Approach to ISBN_13 978-0-8176-4234-1 ISBN_10 0-8176-4234-X Asymptotics Theory and Applications Second Edition Elements of Operator Theory Ricardo Estrada, Universidad de Costa Rica, San José, Costa Rica and Carlos S. Kubrusly, Catholic University of Rio de Janeiro, Brazil Ram P. Kanwal, Pennsylvania State “This is a rigorous, logically well-organized textbook presenting basic University, State College, PA principles and elementary theory of operators. It is written with great “The authors of this remarkable book are care, gradually increasing in complexity. The forte features of the book among the very few that have faced up are the teaching style, illuminating explanation of numerous delicate to the challenge of explaining what an asymptotic expansion is, and points, detailed presentation of topics. Hence, the book can be warmly of systematizing the handling of asymptotic series. The idea of using recommended to a first work for the study of operator theory … it is an distributions is an original one, and we recommend that you read the admirable work for a modern introduction in operator theory.”—ZENTRAL- book … [it] should be on your bookshelf if you are at all interested BLATT MATH in knowing what an asymptotic series is.”—THE BULLETIN OF MATHEMATICS “The author endeavors to present the concepts and ideas as an alterna- BOOKS (review of the first edition) tive to the computational approach, trying to avoid long calculations by “The book is a valuable one, one that many applied mathemati- stressing the mathematical thoughts behind the statements . … many cians may want to buy. The authors are undeniably experts in their problems [are] stated throughout the book, very often accompanied field … most of the material has appeared in no other book.”—SIAM RE- by hints.”—MATHEMATICAL REVIEWS VIEW (review of the first edition) 2001 / 544 PP. / HARDCOVER / $69.95 ISBN_13 978-0-8176-4174-0 2002 / 480 PP., 3 ILLUS. / HARDCOVER / $79.95 ISBN_10 0-8176-4174-2 ISBN_13 978-0-8176-4142-9 ISBN_10 0-8176-4142-4 BIRKHÄUSER ADVANCED TEXTS

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State Spaces of Operator Algebras Real Analysis Basic Theory, Orientations, and C*-products Emmanuele DiBenedetto, Vanderbilt University, Nashville, TN Erik M. Alfsen, University of Oslo, Norway and “The book serves as a solid building block for research in analysis, PDEs, Frederic W. Shultz, Wellesley College, Wellesley, MA the calculus of variations, probability theory and approximation theory; it provides an excellent foundation of real analysis.”—ZENTRALBLATT MATH “A useful introduction to an elegant aspect of the theory of operator algebras which has close links to mathematical physics, as well as be- “This is a very good book. It begins with the standard material, but ing of interest in its own right.”—MATHEMATICAL REVIEWS also includes chapters dealing with distributions and weak derivatives, 2001 / 368 PP. / HARDCOVER / $69.95 special topics, and Sobolev spaces … The Lebesgue integral is done ISBN_13 978-0-8176-3890-0 in Rn and compared to the integral of Riemann … abstract measure ISBN_10 0-8176-3890-3 theory and the Radon-Nikodým theorem are also treated … the author MATHEMATICS: THEORY & APPLICATIONS 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 Geometry of State Spaces of “Each chapter is completed by a set of exercises and problems that add new features and shed new light on the results from the main text. Operator Algebras Bringing together, in a relatively small number of pages, important and Erik M. Alfsen, University of Oslo, Norway and difficult results in real analysis that are of current use in application to Frederic W. Shultz, Wellesley College, Wellesley, MA PDEs, Fourier and harmonic analysis, and approximation, this valu- “The two books together provide a predominantly self -contained pre- able book is of great interest to researchers working in these areas, sentation of the geometric theory of operator algebra state spaces, but it can be used for advanced graduate courses in real analysis as culminating in the classification theorem of Alfsen, Hanche-Olsen and well.”—STUDIA UNIVERSITATIS BABES-BOLYAI, SERIES MATHEMATICA Shultz. Until now much of this material has been accessible only in The focus of this modern graduate text in real analysis is to prepare the the original papers, which makes the two volumes a welcome addi- potential researcher to a rigorous “way of thinking” in applied mathe- tion to the literature . … The result is a clear and comprehensive ac- matics and partial differential equations. The book will provide excellent count . … the book describes a beautiful solution to a problem dating foundations and serve as a solid building block for research in analysis, back to the foundations of the subject.”—MATHEMATICAL REVIEWS PDEs, the calculus of variations, probability, and approximation theory. 2003 / 488 PP. / HARDCOVER / $79.95 All the core topics of the subject are covered, from a basic introduction ISBN_13 978-0-8176-4319-5 to functional analysis, to measure theory, integration and weak differen- ISBN_10 0-8176-4319-2 MATHEMATICS: THEORY & APPLICATIONS tiation of functions, and in a presentation that is hands-on, with little or no unnecessary abstractions. 2002 / 512 PP. / HARDCOVER / $79.95 ISBN_13 978-0-8176-4231-0 ISBN_10 0-8176-4231-5 Gian-Carlo Rota on BIRKHÄUSER ADVANCED TEXTS Analysis and Probability Selected Papers and Commentaries Jean Dhombres, EHESS, Paris, France; Handbook of Complex Variables Joseph P.S. Kung, University of North Texas, Denton, TX; and Steven G. Krantz, Washington University, St. Louis, MO Norton Starr, Amherst College, Amherst, MA “This modern book can be warmly recommended to mathematicians “What makes this collection extraordinarily enjoyable to read are the com- as well as to users of applied texts in complex analysis; in particular mentaries that guide the reader between the gallery of results and are it will be useful to students preparing for an examination in the sub- full of stories about Rota and of reflections about his mathematical style, ject.”—MATHEMATICAL REVIEWS about how he was led to areas and insights, about what he saw in them “Creating a ‘handbook’ such as this is an interesting concept, and to and what he thought they could do for other areas.”—MATHEMATICAL REVIEWS this reviewer’s knowledge this is the only one of its type in complex “This mixture of reprinted papers and articles about Rota tell the story analysis … This book may well be timely and useful to the readers it is of his mathematical journey . … Apart from the opportunity to trace intended for: working scientists, students, and engineers … The topics Rota’s mathematical development through his papers, the book offers contained are quite broad … It is noteworthy that a glossary is included eighteen articles on Rota’s work. These range from reminiscences and that provides the reader with a useful guide to terminology and basic biographical details, to articles explaining the background to specific concepts. Other valuable features are: (1) a discussion of the available papers.”—THE MATHEMATICAL GAZETTE computer packages that can do some complex analysis such as Maple ® “Rota’s work contains many fresh ideas stimulating further research. If and Mathematica , (2) a pictorial catalog of conformal well-known a PhD student asks for a book that might serve as a starting point to maps, and (3) tables of Laplace transforms.”—SIAM REVIEW his/her research, the present volume is an excellent choice. Experts in 1999 / 352 PP., 102 ILLUS. / HARDCOVER / $79.95 ISBN_13 978-0-8176-4231-0 analysis and probability can also find continual values in seeing Rota’s ISBN_10 0-8176-4231-5 writings in a single volume.”—ACTA SCIENTIARIUM MATHEMATICARUM 2003 / 416 PP., 6 ILLUS. / HARDCOVER / $114.00 ISBN_13 978-0-8176-4275-4 ISBN_10 0-8176-4275-7 CONTEMPORARY MATHEMATICIANS

36 Order By Phone: 1-800-777-4643 • Fax: 201-348-4505 • Or Online: www.birkhauser.com Probability / Statistics / Numerical Methods

Point Process Theory A First Course in and Applications Statistics for Signal Marked Point and Piecewise Analysis Deterministic Processes Wojbor A. WoyczyŃski, Case Western Martin Jacobsen, University of Reserve University, Cleveland, OH Copenhagen, Denmark This essentially self-contained, deliberately This text examines the basic theory of compact, and user-friendly textbook is marked point processes, developing ran- designed for a first, one-semester course in domly over time, and shows how this the- statistical signal analysis for a broad audi- ory may be used to treat piecewise deter- ence of students in engineering and the ministic stochastic processes in continuous physical sciences. The emphasis throughout time. It details point processes that generate only finitely many points is on fundamental concepts and relationships in the statistical theory in finite time intervals, resulting, in particular, in piecewise deterministic of stationary random signals, explained in a concise, yet fairly rigorous processes with “few jumps.” presentation. The second part of the book shows how the theory developed earlier Topics and Features: is used to analyze various models in statistics and applied probability • Fourier series and transforms are developed from scratch, empha- with examples from survival analysis, branching processes, risk theory, sizing the time-domain vs. frequency-domain duality. finance, queueing theory, and sports (soccer). • Basic concepts of probability theory, laws of large numbers, the Graduate students, postdocs, and researchers in the above-mentioned stability of fluctuations law, and statistical parametric inference areas will find this text an excellent resource, requiring only a solid foun- procedures are presented. dation in probability and measure theory as well as basic knowledge of stochastic processes and martingales. • Introduction of the fundamental concept of a stationary random 2005 / 350 PP. / HARDCOVER / $59.95 signal and its autocorrelation structure. ISBN_13 978-0-8176-4215-0 • Many diverse examples as well as end-of-chapter problems and ISBN_10 0-8176-4215-3 PROBABILITY AND ITS APPLICATIONS 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, Introduction to Probability with computer, and biomedical engineering, as well as the physical sciences. Statistical Applications The work is also an excellent resource of educational and training mate- Geza Schay, University of Massachusetts, Boston, MA rial for scientists and engineers working in research laboratories. 2006/ 206 PP., 65 ILLUS. / SOFTCOVER / $39.95 Introduction to Probability with Statistical Applications targets non-math- ISBN_13 978-0-8176-4398-0 ematics students, undergraduates and graduates, who do not need an ISBN_10 0-8176-4398-2 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. Statistics and Analysis of Shapes Key features: Hamid Krim, North Carolina State University, Raleigh, NC; • Clear definitions, simplified notation and techniques of statisti- Anthony Yezzi, Jr., Georgia Institute of Technology, Atlanta, GA (Eds.) cal analysis, combined with well-chosen examples and exercises, The subject of pattern analysis and recognition pervades many aspects motivate the exposition of our daily lives, including user authentication in banking, object re- • Theory and applications carefully balanced trieval from databases in the consumer sector, and the omnipresent surveillance and security measures around sensitive areas. Shape • Topics include random phenomena–discrete and continuous ran- analysis, a fundamental building block in many approaches to these dom variables–expectations and variance, and common probability applications, is also used in statistics, biomedical applications (Magnetic distributions such as the binomial, Poisson, and normal Resonance Imaging), and many other related disciplines. • Combinatorial principles involve all four arithmetic operations; With contributions from some of the leading experts and pioneers in emphasis on tree diagrams the field, this self-contained, unified volume is the first comprehensive • References to more advanced concepts throughout the book, but treatment of theory, methods, and algorithms, available in a single re- may be safely skipped, depending on the reader. For students in source, without the typical quagmire of vast information scattered over a variety of disciplines, including computer science, engineering, a wide body of literature. Developments are discussed from a rapidly natural and social sciences. increasing number of research papers in diverse fields, including the 2007 / APPROX. 300 PP., 10 ILLUS. / SOFTCOVER / $49.95 (TENT.) mathematical and physical sciences, engineering, and medicine. ISBN_13 978-0-8176-4497-0 2006 / 395 PP., 143 ILLUS. / HARDCOVER / $79.95 ISBN_10 0-8176-4497-0 ISBN_13 978-0-8176-4376-8 ISBN_10 0-8176-4376-1 MODELING AND SIMULATION IN SCIENCE, ENGINEERING AND TECHNOLOGY

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Lagrangian Probability Invariant Probabilities Distributions of Markov-Feller Prem C. Consul, University of Calgary, Operators Alberta, Canada and Felix Famoye, Central Michigan University, and Their Supports Mount Pleasant, MI Radu Zaharopol, Mathematical Reviews, Foreword by Samuel Kotz, George Ann Arbor Washington University, Washington, DC “The book is essentially self-contained and Lagrangian expansions can be used to ob- very well written, in a reader-friendly style. tain numerous very useful probability mod- The work is addressed to researchers in- els, which have been applied to real-life terested in Markov-Feller operators and re- situations, including branching processes, lated topics, but it should also be useful to queuing processes, stochastic processes, environmental toxicology, dif- people in several fields, for instance, Markov processes, ergodic theory, fusion of information, ecology, strikes in industries, sales of new prod- and dynamical systems, to name a few.”—MATHEMATICAL REVIEWS ucts, and the amount of production for optimum profits. This book is a This book details invariant probabilities for a large class of discrete-time comprehensive, systematic treatment of the two classes of Lagrangian homogeneous Markov processes known as Feller processes. These probability distributions along with some of their sub-families, proper- Feller processes appear in the study of iterated function systems with ties, and applications to a variety of fields. probabilities, convolution operators, and certain time series. The book Containing exercises in many chapters, the book may be used in gradu- obtains “formulas” for the supports of various types of invariant prob- ate courses and seminars on distribution theory and Lagrangian distri- ability measures and then uses these “formulas” to study properties butions, or as a reference text. The variety of applications presented of the processes themselves. Rather than deal with the processes, the will be useful to a broad audience of applied scientists, researchers, book focuses on the transition probabilities and the operators associ- and students in environmental statistics, reliability, sales management, ated to these processes. epidemiology, operations research, and the optimization of profits in In the work, special effort is made to attract newcomers to the theory of manufacturing and marketing. Markov processes, in general, and to the topics covered, in particular. Most 2005 / 390 PP. / HARDCOVER / $79.95 of the results are new and deal with areas of intense research interest. ISBN_13 978-0-8176-4365-2 2005 / 120 PP. / SOFTCOVER / $39.95 ISBN_10 0-8176-4365-6 ISBN_13 978-3-7643-7134-0 ISBN_10 3-7643-7134-X FRONTIERS IN MATHEMATICS Resampling Methods A Practical Guide to Data Analysis Real and Stochastic Analysis Third Edition New Perspectives Phillip Good, Information Research, M. M. Rao, University of California, Riverside, CA (Ed.) Huntington Beach, CA The interplay between functional and stochastic analysis has wide im- “The author has packaged an excellent and plications for problems in partial differential equations, noncommuta- modern set of topics around the develop- tive or “free” probability, and Riemannian geometry. Written by active ment and use of quantitative models . … If researchers, each of the six independent chapters in this volume is you need to learn about resampling, this devoted to a particular application of functional analytic methods in sto- book would be a good place to start.”—TECH- chastic analysis, ranging from work in hypoelliptic operators to quantum NOMETRICS (review of second edition) field theory. Every chapter contains substantial new results as well as a clear, unified account of the existing theory; relevant references and This thoroughly revised and expanded third edition is a practical guide numerous open problems are also included. to data analysis using the bootstrap, cross-validation, and permutation 2004 / 405 PP. / HARDCOVER / $139.00 tests. Only requiring minimal mathematics beyond algebra, it provides ISBN_13 978-0-8176-4332-4 a table-free introduction to data analysis utilizing numerous exercises, ISBN_10 0-8176-4332-X practical data sets, and freely available statistical shareware. TRENDS IN MATHEMATICS New to the third edition are additional program listings and screen shots of C++, CART, Blossom, Box Sampler (an Excel add-in), R, Resa- mpling Stats, SAS macros, S-Plus or Stata, which accompany each resampling procedure. A glossary and solutions to selected exercises have also been added. With its accessible style and intuitive topic development, the book is an excellent text or self-study resource for students, industrial statisticians, statistical consultants, and research professionals in science, engineering, and technology. 2005 / 280 PP., 40 ILLUS. / HARDCOVER / $79.95 ISBN_13 978-0-8176-4386-7 ISBN_10 0-8176-4386-9

38 Order By Phone: 1-800-777-4643 • Fax: 201-348-4505 • Or Online: www.birkhauser.com Probability / Statistics / Numerical Methods

Handbook of A Natural Introduction to Computational and Probability Theory Numerical Methods Ronald Meester, Vrije Universiteit Amsterdam, The Netherlands “The book [is] an excellent new introductory text on probability. The clas- in Finance sical way of teaching probability is based on measure theory. In this Svetlozar T. Rachev, University of book discrete and continuous probability are studied with mathematical California, Santa Barbara (Ed.) precision, within the realm of Riemann integration and not using no- This volume presents current research and tions from measure theory … . Numerous topics are discussed, such as: survey articles focusing on various numerical random walks, weak laws of large numbers, infinitely many repetitions, methods in finance. Key topics covered in- strong laws of large numbers, branching processes, weak convergence clude: methodological issues, i.e., genetic al- and [the] central limit theorem. The theory is illustrated with many origi- gorithms or programming, neural networks, nal and surprising examples and problems.”—ZENTRALBLATT MATH Monte-Carlo methods, finite difference methods, stochastic portfolio op- “Most textbooks designed for a one-year course in mathematical sta- timization, as well as the application of other computational and numeri- tistics cover probability in the first few chapters as preparation for the cal methods in finance and risk management. The book is designed for statistics to come. This book in some ways resembles the first part of the academic community and will also serve professional investors. such textbooks: it’s all probability, no statistics. But it does the probability 2004 / 466 PP., 15 ILLUS. / HARDCOVER / $79.95 more fully than usual, spending lots of time on motivation, explanation, ISBN_13 978-0-8176-3219-9 and rigorous development of the mathematics … . The exposition is usu- ISBN_10 0-8176-3219-0 ally 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 2004 / 191 PP. / SOFTCOVER / $34.95 ISBN_13 978-3-7643-2188-8 Analysis of Variance for Random ISBN_10 3-7643-2188-1 Models Volume I: Balanced Data Volume II: Unbalanced Data Theory and Applications of Hardeo Sahai, Universidad del Caribe, Bayamon, PR and Long-Range Dependence Mario M. Ojeda, University of Veracruz, Mexico Murad Taqqu, Boston University, Boston, MA; “This book is accessible to readers with only a modest mathematical Paul Doukhan, Université de Cergy-Pointoise, France; and and statistical background. The work will appeal to a broad audience George Oppenheim, Université de Paris Sud, Orsay, France (Eds.) of students, researchers, and practitioners in the mathematical, life, “The present volume contains 28 surveys of the field, treating and social, and engineering sciences. It may be used as a textbook in up- merging both theory and applications, giving a global picture of the per-level undergraduate and graduate courses, or as a reference for field.”—QUARTERLY OF APPLIED MATHEMATICS readers interested in the use of random effects models for data analy- Each self-contained chapter in this work begins with introductory back- sis.”—ZENTRALBLATT MATH ground material, and the book covers a wide range of topics: fractional Analysis of variance (ANOVA) models have become widely used tools Brownian motion, models, inequalities and limit theorems, periodic and play a fundamental role in much of the application of statistics to- long-range dependence, parametric, semiparametric, and non-para- day. In particular, ANOVA models involving random effects have found metric estimation, long-memory stochastic volatility models, robust es- widespread application to experimental design in a variety of fields re- timation, and prediction for long-range dependence sequences. There quiring measurements of variance, including agriculture, biology, animal is a thorough introduction to multifractals and a special section on breeding, applied genetics, econometrics, quality control, medicine, en- mathematical techniques. gineering, and social sciences. 2003 / 750 PP., 72 ILLUS. / HARDCOVER / $95.00 This two-volume work is a comprehensive presentation of different ISBN_13 978-0-8176-4168-9 ISBN_10 0-8176-4168-8 methods and techniques for point estimation, interval estimation, and tests of hypotheses for linear models involving random effects. Volume I examines models having balanced data (orthogonal models); Volume II studies models with unbalanced data (non-orthogonal models). Volume I: Balanced Data 2004 / 504 PP., 9 ILLUS. / HARDCOVER / $89.95 ISBN_13 978-0-8176-3230-4 ISBN_10 0-8176-3230-1 Volume II: Unbalanced Data 2005 / 480 PP., 14 ILLUS. / HARDCOVER / $89.95 ISBN_13 978-0-8176-3229-8 ISBN_10 0-8176-3229-8

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Empirical Process Techniques for A Probability Path Dependent Data Sidney I. Resnick, Cornell University, Ithaca, NY Herold Dehling, University of Bochum, Germany; “This book is different from the classical textbooks on probability theory Thomas Mikosch, University of Copenhagen, Denmark; and in that it treats the measure theoretic background not as a prerequisite Michael Sørensen, University of Copenhagen, Denmark but as an integral part of probability theory. The result is that the reader gets a thorough and well-structured framework needed to understand This book contains accessible surveys by several leading experts in the the deeper concepts of current day advanced probability as it is used field. The first part is a thorough and comprehensive introduction to the in statistics, engineering, biology and finance … The pace of the book existing theory of empirical process techniques for dependent data, start- is quick and disciplined. Yet there are ample examples sprinkled over ing from the classical contributions of Billingsley and including present- the entire book and each chapter finishes with a wealthy section of day research. The remaining parts of the book give an overview of the inspiring problems.”—PUBLICATIONS OF THE INT’L STATISTICAL INSTITUTE most recent applications in various fields related to empirical processes such as spectral analysis of time series, the bootstrap for stationary se- “A very nice introductory measure-theoretic probability textbook … quences, extreme-value theory, and the empirical process for mixing de- The emphasis [is] on developing a broad, deeper understanding pendent observations, including the case of strong dependence. of basic probability theory, the needs of students kept specifically in mind … Students will appreciate its clear, concise, and focused presentation This book is an ideal introductory text that will serve as a reference or re- of the material.”—JASA source for classroom use in the areas of statistics, time-series analysis, extreme-value theory, point process theory, and applied probability theory. “This book is a rather comfortable probability path leading from funda- 2002 / 400 PP., 2 ILLUS. / HARDCOVER / $84.95 mental notions of measure theory and probability theory to martingale ISBN_13 978-0-8176-4201-3 theory, since fundamental concepts and basic theorems are always ISBN_10 0-8176-4201-3 illustrated by important examples and results of additional theoretical value.”—STATISTICS & DECISION Solutions manual is available upon adoption of the text. Lévy Processes 1998 / 472 PP., 10 ILLUS. / HARDCOVER / $64.95 ISBN_13 978-0-8176-4055-2 Theory and Applications ISBN_10 0-8176-4055-X Ole E. Barndorff-Nielsen, University of Aarhus, Denmark; Thomas Mikosch, University of Copenhagen, Denmark; and Sidney I. Resnick, Cornell University, Ithaca, NY (Eds.) Stochastic Calculus “This volume presents a useful summary of some of the recent scientific Applications in Science and developments concerning Lévy processes. Both introductory and more Engineering advanced articles are included. The interested researcher will get a good overview of ‘where the action is’ whereas students will find numerous Mircea Grigoriu, Cornell University, interesting research topics to work on … I am convinced that the text will Ithaca, NY contribute further to making stochastic models based on general Lévy “When familiar at least with the basics of processes even more popular. I, therefore, take pleasure in recommend- measure theoretic probability, one may ing this volume to all interested readers.”—ISI SHORT BOOK REVIEWS use this book to get a feel for the type of 2001 / 432 PP., 32 ILLUS. / HARDCOVER / $95.00 problems one tackles with the given meth- ISBN_13 978-0-8176-4167-2 ISBN_10 0-8176-4167-X ods and the type of results one can expect and then proceed to more detailed expositions … the book is an impressive achieve- ment.”—MATHEMATICAL REVIEWS Adventures in “The large number of examples … as well as the good survey on ad- Stochastic Processes vanced mathematical techniques make the textbook very valuable for people working in mathematics with a view towards applications … The Sidney I. Resnick, Cornell University, applications range from climate dynamics over material sciences and Ithaca, NY mechanics to pattern formation, physics and finance. The presentation is “Resnik has succeeded to write a very fine text- very successful in providing a sound mathematical background without book which will become popular among stu- getting lost in too much technical detail . … At the end of each chapter a dents as well as among professors preparing list of instructive exercises is provided . … Altogether this textbook has all an introductory course on stochastic processes.” the necessary prerequisites for boosting the interdisciplinary collabora- —INTERNATIONALE MATHEMATISCHE NACHRICHTEN tion between applied scientists and probabilists.” —ZENTRALBLATT MATH 2002 / 792 PP., 177 ILLUS. / HARDCOVER / $79.95 “Definitely the best textbook for a second ISBN_13 978-0-8176-4242-6 course in probability now available. Written ISBN_10 0-8176-4242-0 with excruciating lucidity, and with an excellent choice of exercises.”—GIAN-CARLO ROTA, THE BULLETIN OF MATHEMATICS BOOKS “A splendid book to bring home the value and importance of stochastic processes. Highly recommended.”—CHOICE Solutions manual is available upon adoption of the text. 1994 / 640 PP. / HARDCOVER / $69.95 ISBN_13 978-0-8176-3591-6 ISBN_10 0-8176-3591-2

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The Laplace Distribution Modern Differential Geometry in and Generalizations Gauge Theories A Revisit with Applications to Communications, Volume I: Maxwell Fields Economics, Engineering, and Finance Anastasios Mallios, University of Athens Panepistimioupolis, Athens, Greece Samuel Kotz, The George Washington University, Washington, DC; Differential geometry, in the classical sense, is developed through the Tomasz Kozubowski, University of Nevada, Reno, NV; and theory of smooth manifolds. In the early 1990s, the author of this work Krzystof Podgórski, Indiana University-Purdue University, Indianapolis, IN initiated a new kind of differential geometry in which all the machinery “ A useful source of information for research in applied and theoretical of classical differential geometry can be explained without any notion of statistics. No doubt, this volume will become a necessary part of any smoothness. This was achieved via sheaf theory (geometry) and sheaf mathematical and statistical library as well as of a number of technical cohomology (analysis). libraries.”—MATHEMATICAL REVIEWS This two-volume work systematically applies the author’s sheaf-theo- “This book will be useful for those who are interested in tractable models retic approach to such physical theories as gauge theory. Both volumes which allow one to go beyond the normal distribution.”—ISI SHORT BOOK REVIEWS contain a wealth of detailed and rigorous computations, and will appeal to mathematicians and physicists as well as advanced undergraduate “This book is devoted to presenting properties, generalizations and ap- and graduate students studying applications of differential geometry to plications of the Laplace distribution … This distribution is a natural and physical theories. sometimes superior alternative to the normal distribution … The rich set 2005 / 450 PP. / SOFTCOVER / $119.00 of exercises is an integral part of the discussion.”—ZENTRALBLATT MATH ISBN_13 978-0-8176-4378-2 2001/ 349 PP., 37 ILLUS. / HARDCOVER / $84.95 ISBN_10 0-8176-4378-8 ISBN_13 978-0-8176-4166-5 ISBN_10 0-8176-4166-1 Volume 2: Yang-Mills Fields Continuing his point of view started in Volume I, the author extends the Mathematical Finance application of his sheaf-theoretic approach to Yang-Mills fields in gen- and Probability eral. Important topics covered include cohomological classification of Yang-Mills fields, the geometry of Yang-Mills A-connections and moduli A Discrete Introduction space of a vector sheaf, and Einstein’s equation in a vacuum. Pablo Koch Medina, Swiss Re, Zürich, 2007/APPROX. 304 PP./SOFTCOVER/$119.00(TENT.) Switzerland and ISBN_13 978-0-8176-4379-9 Sandro Merino, UBS, Zürich, Switzerland ISBN_10 0-8176-4379-6 “The style of presentation will appeal to anyone who is seeking an elementary but rigor- Set of Volume 1 and Volume 2 ous introduction to the pricing of derivative 2007/$199.00(TENT.) ISBN_13 978-0-8176-4476-5 securities. The book is written carefully and ISBN_10 0-8176-4476-8 is very readable.” —MATHEMATICAL REVIEWS “The book offers a self-contained elementary but rigorous and very clear introduction to the pricing of derivative instruments in discrete time . … For the interested reader who has not been exposed to modern Extremum Problems for probability theory before, the book provides an excellent starting point Eigenvalues of Elliptic Operators for studying the theory of derivative pricing. In particular, for a rigorous Antoine Henrot, Université Henri Poincaré, Vandoeuvre-les-Nancy, France course on derivative pricing in an economics department or at a business school this introduction seems to be well-suited.”—ZENTRALBLATT MATH Problems linking the shape of a domain or the coefficients of an el- 2003 / 340 PP. / SOFTCOVER / $63.95 liptic operator to the sequence of its eigenvalues are among the most ISBN_13 978-3-7643-6921-7 fascinating of mathematical analysis. In this book, we focus on extremal ISBN_10 3-7643-6921-3 problems. For instance, we look for a domain which minimizes or maxi- mizes a given eigenvalue of the Laplace operator with various boundary conditions and various geometric constraints. We also consider the case Continuum Thermomechanics of functions of eigenvalues. We investigate similar questions for other elliptic operators, such as the Schrödinger operator, non-homogeneous Alfredo Bermúdez de Castro, University of Santiago de Compostela, Spain membranes, or the bi-Laplacian, and we look at optimal composites and The general goal of this book is to deduce rigorously, from the first prin- optimal insulation problems in terms of eigenvalues. Providing also a self- ciples, the partial differential equations governing the thermodynamic contained presentation of classical isoperimetric inequalities for eigenval- processes undergone by continuum media under forces and heat. Solids ues and 30 open problems, this book will be useful for pure and applied and fluids are considered in a unified framework. Reacting mixtures of mathematicians, particularly those interested in partial differential equa- fluids are also included for which general notions of thermodynamics tions, the calculus of variations, differential geometry, or spectral theory. are recalled, such as the Gibbs equilibrium theory. Linear approximate 2006 / 202 PP., 16 ILLUS. / SOFTCOVER / $49.95 models are mathematically obtained by calculating the derivatives of the ISBN_13 978-3-7643-7705-2 ISBN_10 3-7643-7705-4 constitutive response functions. FRONTIERS IN MATHEMATICS 2005/ 209 PP. / HARDCOVER / $79.95 ISBN_13 978-3-7643-7265-1 ISBN_10 3-7643-7265-6 PROGRESS IN MATHEMATICAL PHYSICS, VOL. 43

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Determining Spectra Einstein, 1905-2005 in Quantum Theory Poincaré Seminar 2005 Michael Demuth, Technische Thibault Damour, IHÉS, Bures-sur-Yvette, France; Universität Clausthal, Germany and Olivier Darrigol, Université Denis Diderot, Paris, France; Maddaly Krishna, Institute of Bertrand Duplantier, CEA-Saclay, Gif-sur-Yvette, France; Mathematical Sciences, Chennai, India Vincent Rivasseau, Université Paris XI, Orsay, France (Eds.) “In my opinion, the basic idea of the mono- This volume is devoted to Einstein’s 1905 papers and their legacy. After graph is to help graduate students working a presentation of Einstein’s epistemological approach to physics, and on spectral theory and beginning research- the genesis of special relativity, a centenary perspective is offered. The ers in the field to build a toolkit. The book geometry of relativistic spacetime is explained in detail. Single photon definitely has more than enough material experiments are presented, as a spectacular realization of Einstein’s for this purpose, some of which is quite ad- light quanta hypothesis. A previously unpublished lecture by Einstein, vanced, and it is very up to date. In conclusion, I believe that this book which presents an illuminating point of view on statistical physics in will prove extremely useful for its target audience (advanced graduate 1910, at the dawn of quantum mechanics, is reproduced. The volume students with an interest in this area). Moreover, it will also very much ends with an essay on the historical, physical and mathematical aspects feel at home on the bookshelf of an expert.”—MATHEMATICAL REVIEWS of Brownian motion. 2006/ 293 PP., 48 ILLUS. / HARDCOVER / $99.00 The spectral theory of Schrödinger operators, in particular those with ISBN_13 978-3-7643-7435-8 random potentials, continues to be a very active field of research. This ISBN_10 3-7643-7435-7 work focuses on various known criteria in the spectral theory of selfad- PROGRESS IN MATHEMATICAL PHYSICS, VOL. 47 joint operators in order to identify the spectrum and its components a la Lebesgue decomposition. The book provides an exposition of criteria that are especially useful in The Quantum Hall Effect determining the spectra of deterministic and random Schrödinger operators occurring in quantum theory, by systematically using measures Poincaré Seminar 2004 and their transforms (Fourier, Borel, wavelet) as a unifying theme. Cov- Benoît Douçot, CNRS and Universités Paris VI/VII, France; erage also includes a treatment of applications to show point spectrum Bertrand Duplantier, CEA-Saclay, France; and continuous spectrum in some models of random operators. Vincent Pasquier, CEA-Saclay, France; Vincent Rivasseau, Université 2005/219 PP./HARDCOVER/$119.00 Parix XI, France (Eds.) ISBN_13 978-0-8176-4366-9 ISBN_10 0-8176-4366-4 This volume is devoted to the Quantum Hall effect. After a historical PROGRESS IN MATHEMATICAL PHYSICS and general presentation by Nobel prize winner Klaus von Klitzing, dis- coverer of this effect, the volume proceeds with reviews on the mathematics and physics of both the integer and fractional case. It includes up to date presentations of the tunneling and metrology experiments Conformal and Potential Analysis related to the quantum Hall effect. It will serve the community of physi- in Hele-Shaw Cells cists and mathematicians at the professional or graduate student level. 2005 / 197 PP. / HARDCOVER / $89.95 Björn Gustafsson, Royal Institute of Technology, Stockholm, Sweden; ISBN_13 978-3-7643-7300-9 Alexander Vasil’ev, University of Bergen, Norway ISBN_10 3-7643-7300-8 PROGRESS IN MATHEMATICAL PHYSICS, VOL. 45 This monograph aims at giving a presentation of recent and new ideas that arise from the problems of planar fluid dynamics and which are interesting from the point of view of geometric function theory and potential theory. In particular, this book is concerned with geometric Slow Rarefied Flows problems for Hele-Shaw flows. Also Hele-Shaw flows on parameter spaces (e.g., the Teichmüller space) are treated and connections with Theory and Application to Micro-Electro - string theory are revealed. Ultimately, the interaction between several Mechanical Systems branches of complex and potential analysis, and planar fluid mechanics Carlo Cercignani, Politecnico di Milano, Italy is discussed. For most parts of this book the background provided by The book presents the mathematical tools used to deal with problems graduate courses in real and complex analysis, in particular, the theory related to slow rarefied flows, with particular attention to basic concepts of conformal mappings and in fluid mechanics is assumed. There are and problems which arise in the study of micro- and nanomachines. some historical remarks concerning the people that have contributed to The mathematical theory of slow flows is presented in a practically the topic. The book is as self-contained as possible. complete fashion and provides a rigorous justification for the use of the 2006 / 231 PP. / HARDCOVER / $89.95 ISBN_13 978-3-7643-7703-8 linearized Boltzmann equation, which avoids costly simulations based ISBN_10 3-7643-7703-8 on Monte Carlo methods. The book surveys the theorems on validity ADVANCES IN MATHEMATICAL FLUID MECHANICS, vol. 44 and existence, with particular concern for flows close to equilibria, and discusses recent applications of rarefied lubrication theory to micro- electro-mechanical systems (MEMS). It gives a general acquaintance of modern developments of rarefied gas dynamics in various regimes with particular attention to low speed microscale gas dynamics. 2006/ 166 PP. / HARDCOVER / $74.95 ISBN_13 978-3-7643-7534-8 ISBN_10 3-7643-7534-5 PROGRESS IN MATHEMATICAL PHYSICS, VOL. 41

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Homogenization of Partial Continuum Differential Equations Mechanics using Vladimir A. Marchenko, and Mathematica® Evgueni Ya. Khruslov, B.Verkin, both; Institute for Low Temperature Physics and Engineering, Kharkov, Ukraine Fundamentals, Applications, and Scientific Computing The present monograph is a comprehensive study of homogenized problems, based on the asymptotic analysis of boundary value problems as Antonio Romano, University of Napoli, Italy; the characteristic scales of the microstructure decrease to zero. The work Renato Lancellotta, Politechnico di Torino, focuses on the construction of nonstandard models: non-local models, Italy; and Addolorata Marasco, multicomponent models, and models with memory. Along with com- University of Napoli, Italy plete proofs of all main results, numerous examples of typical structures This book examines mathematical tools, of microinhomogeneous media with their corresponding homogenized principles, and fundamental applications of models are provided. Graduate students, applied mathematicians, physi- continuum mechanics, providing a solid basis for a deeper study of more cists, and engineers will benefit from this monograph, which may be challenging problems in elasticity, fluid mechanics, plasticity, piezoelec- used in the classroom or as a comprehensive reference text. tricity, ferroelectricity, magneto-fluid mechanics, and state changes. An 2006/ 398 PP., 28 ILLUS. / HARDCOVER / $139.00 accompanying CD-ROM with Mathematica®-based exercises, examples, ISBN_13 978-0-8176-4351-5 and programs allows readers to quickly solve complex, time-consuming ISBN_10 0-8176-4351-6 PROGRESS IN MATHEMATICAL PHYSICS, VOL. 46 problems related to the application areas covered. The work is suitable for advanced undergraduates, graduate students, and researchers in applied mathematics, mathematical physics, and engineering. 2005 / 350 PP., 40 ILLUS. / HARDCOVER WITH CD-ROM / $79.95 Molecular Gas Dynamics ISBN_13 978-0-8176-3240-3 ISBN_10 0-8176-3240-9 Theory, Techniques, and Applications MODELING AND SIMULATION IN SCIENCE, ENGINEERING AND TECHNOLOGY

Yoshio Sone, University of Kyoto, Japan This self-contained book is an up-to-date description of the basic theory of molecular gas dynamics and its various applications. The progress in the Vortices in the field over the last thirty years has greatly enhanced the original theory and has stimulated interesting and critical gas dynamic phenomena and prob- Magnetic Ginzburg - lems. ‘Molecular Gas Dynamics’, unique in the literature, presents working Landau Model knowledge, theory, techniques, and typical phenomena in rarefied gases Etienne Sandier, Université Paris-12 for theoretical development and application. Basic theory is developed in a Val-de-Marne, Créteil, France; systematic way and presented in a form easily applied for practical use. Sylvia Serfaty, Courant Institute of 2007/658 PP., 179 ILLUS./HARDCOVER/$119.00 Mathematical Sciences, New York, NY ISBN_13 978-0-8176-4345-4 ISBN_10 0-8176-4345-1 With the discovery of type-II superconductivity MODELING AND SIMULATION IN SCIENCE, ENGINEERING AND TECHNOLOGY by Abrikosov, the prediction of vortex lattices, and their experimental observation, quan- Also by Sone: tized vortices have become a central object of study in superconductivity, superfluidity, and Bose-Einstein condensa- Kinetic Theory and Fluid Dynamics tion. This book presents the mathematics of superconducting vortices in the framework of the acclaimed two-dimensional Ginzburg-Landau model, “This book gives an impressive overview of the formidable amount of with or without magnetic field, and in the limit of a large Ginzburg-Landau work done by the author … [It] is very detailed, and very carefully writ- parameter, kappa. ten, aimed at a great generality of results and physical situations … In- The book also provides a list of open problems and a guide to the increasingly teresting physical phenomena and engineering applications are pre- diverse mathematical literature on Ginzburg-Landau related topics. It will ben- sented throughout … supported by numerical analysis and sometimes efit both pure and applied mathematicians, physicists, and graduate students even by experimental demonstration. All of that makes the book ap- having either an introductory or an advanced knowledge of the subject. pealing in various fields, including applied mathematics, physics, and engineering, especially at the level of graduate students and young 2007/ 294 PP., 13 ILLUS. / HARDCOVER / $119.00 ISBN_13 978-0-8176-4316-4 researchers.”—EUROPEAN JOURNAL OF MECHANICS, B/FLUIDS ISBN_10 0-8176-4316-8 “This book will be a useful and lasting reference point for kinetic PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS, VOL. 70 boundary layers in the continuum limit. It isn’t reading for the faint at heart—the technical skill and fearlessness of lengthy expansions of the author are visible. Yet this is a collection of a lifetime of research, conveniently collected in one place.”—MATHEMATICAL REVIEWS 2002 / 368 PP., 44 ILLUS. / HARDCOVER / $69.95 ISBN_13 978-0-8176-4284-6 ISBN_10 0-8176-4284-6 MODELING AND SIMULATION IN SCIENCE, ENGINEERING AND TECHNOLOGY

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Conformal Groups in Geometry Classical Mechanics and Spin Structures Emmanuele DiBenedetto, Vanderbilt University, Nashville, TN Pierre Angles, Université Paul Sabatier, Toulouse, France Classical mechanics is one of those special occurrences in science where interdisciplinary contributions have come together in a perfect Conformal groups play a key role in geometry and spin structures. This book blend, providing a most elegant and penetrating example of “modeling” provides a self-contained overview of this important area of mathematical in science. Following Lagrangrian principles, the author employs mathe- physics, beginning with its origins in the works of Cartan and Chevalley and matics not only as a “unifying” language, but also to exemplify its role as progressing to recent research in spinors and conformal geometry. a catalyst behind new concepts and discoveries, such as the d’Alembert Key topics: principle, complex systems dynamics, and Hamiltonian mechanics. • The first chapter focuses on the basic material on Clifford algebras Today, these same dynamics are now being focused to address other and spinor spaces, along with the necessary mathematical tools interdisciplinary areas of research in fields such as biology and chemistry. • The second chapter examines conformal spin geometry, starting Offering a rigorous mathematical treatment of the subject and requiring with an elementary study of the classical conformal group in Euclid- of the reader only a solid background in introductory physics, multivari- ean space; it then treats covering groups of the conformal group able calculus, and linear algebra, Classical Mechanics can serve as a text and includes a section on the complex group for advanced undergraduates and graduate students in mathematics, physics, engineering, and the natural sciences, as well as an excellent • Conformal flat geometry and “conformal spinor groups” are intro- reference for applied mathematicians and mathematical physicists. duced, and the text proceeds through a systematic development of 2007 / APPROX. 350 PP., 50 ILLUS. / HARDCOVER / $59.95 manifolds endowed with conformal spin-structure and the theory ISBN_13 978-0-8176-4526-7 of conformal connections ISBN_10 0-8176-4526-8 • Chapter III covers conformal symplectic geometry and includes a discussion of conformal symplectic flat geometry and the covering groups of the real conformal symplectic group Planar Ising Correlations and the • The final chapter provides a detailed treatment of conformal pseudo-unitary spin structures, with emphasis on projective quadrics and Deformation Analysis of Scaling pseudo-Hermitian spaces and their associated Clifford algebras John Palmer, University of Arizona, Tucson, AZ 2007 / APPROX. 320 PP., 40 ILLUS. / HARDCOVER / $89.95 (TENT.) This book is principally devoted to an analysis showing that the scal- ISBN_13 978-0-8176-3512-1 ing functions are tau functions associated with monodromy-preserving ISBN_10 0-8176-3512-2 PROGRESS IN MATHEMATICAL PHYSICS, vol. 50 deformations of the Dirac equation. While charting a fairly direct route to this analysis via new results of Palmer and others, as well as previous research of the Kyoto School --- Sato, Miwa, and Jimbo -- -are the primary focus of this book, other interesting mathematical insights oc- Integrable Systems in Celestial cur all along the way. For example, the Ising model has been a source of rich mathematics from Szego limit theorems to Wick type theorems Mechanics for infinite spin groups. Diarmuid Ó’Mathúna, Dublin Institute for Advanced Studies, Dublin, Ireland Also, some aspects of the solution of the Ising model are elegantly expressed in terms of Pfaffian and determinant bundles over infinite This work focuses on the two integrable systems of relevance to ce- dimensional Grassmannians. These constructs generalize the more lestial mechanics, both of which date back to the 18th century. Under familiar objects in finite dimensional algebraic geometry and have ap- discussion are the Kepler (two-body) problem and the Euler (two-fixed peared only recently in the mathematics literature. center) problem, the latter being the more complex and more instruc- Exploring the Ising model as a microcosm of the confluence of interest- tive, as it exhibits a richer and more varied solution structure. Further, ing ideas in mathematics and physics, this work will appeal to graduate because of the interesting investigations by the 20th century math- students, mathematicians, and physicists interested in the mathematics ematical physicist J.P. Vinti, the Euler problem is now recognized as of statistical mechanics and quantum field theory. being intimately linked to the Vinti (earth-satellite) problem; in short, 2007 / approx. 375 pp., 30 ILLUS. / HARDCOVER / $69.95 (tent.) the Euler problem and the earth-satellite problem are in a dual comple- ISBN_13 978-0-8176-4248-8 mentary relation. The present work shows that the solutions to all of ISBN_10 0-8176-4248-X these integrable problems can be put in a form that admits the general PROGRESS IN MATHEMATICAL PHYSICS, vol. 49 representation of the orbits and follows a definite shared pattern. A key feature of this treatment involves a full analysis of the planar Euler problem (yielding an exact solution form in terms of Jacobian elliptic functions) via a clear generalization of the form of the solution in the Kepler case (expressed in terms of trigonometric functions). In con- trasting the issues involved in the Kepler-Euler problems, the author raises current issues in analysis and astronomy, placing these classical problems in a modern context, with original insights that have not yet appeared in book form. 2007 / APPROX. 240 PP. / HARDCOVER / $89.95 (TENT.) ISBN_13 978-0-8176-4096-5 ISBN_10 0-8176-4096-7 PROGRESS IN MATHEMATICAL PHYSICS, VOL. 51

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Mathematical Physics / Physics

Hemodynamical Flows Quantum Decoherence Modeling, Analysis and Simulation Poincaré Seminar 2005 Giovanni P. Galdi and Anne M. Robertson, University of Pittsburgh, PA; Bertrand Duplantier, CEA Saclay, Gif-sur-Yvette, France; Rolf Rannacher, Universität Heidelberg, Germany; Jean-Michel Raimond, ENS Paris, France; Stefan Turek, Universität Dortmund, Germany Vincent Rivasseau, Université Paris XI, France (Eds.) This book surveys results on physical and mathematical modeling as This volume is devoted to Quantum Decoherence. A broad perspective well as the numerical simulation of hemodynamical flows, i.e., of fluid on the subject is provided by the contributions of W. H. Zurek, H. D. and structural mechanical processes occurring in the human blood cir- Zeh and E. Joos, together with clean up-to-date presentations of the cuit. The topics treated are continuum mechanical description, choice of actual experiments on decoherence both in the mesoscopic systems suitable liquid and wall models, mathematical analysis of coupled mod- of atomic physics, by J.M. Raimond and S. Haroche, and in the “quan- els, numerical methods for flow simulation, parameter identification and tronic” or condensed matter context, by D. Esteve et al. Further, the model calibration, fluid-solid interaction, mathematical analysis of piping question of quantum codes and error corrections is discussed in the systems, particle transport in channels and pipes, artificial boundary con- contribution of J. Kempe. ditions, and many more. Hemodynamics is an area of active research, 2007 / 200 PP. / HARDCOVER / $89.95 and this book provides an entry into the field for graduate students and ISBN_13 978-3-7643-7807-3 researchers. It has grown out of a series of lectures given by the authors ISBN_10 3-7643-7807-7 PROGRESS IN MATHEMATICAL PHYSICS, VOL. 48 at the Oberwolfach Research Institute in November, 2005. 2007 / APPROX. 400 PP. / SOFTCOVER / $49.95 (TENT.) ISBN_13 978-3-7643-7805-9 ISBN_10 3-7643-7805-0 OBERWOLFACH SEMINARS, VOL. 35 Physical Applications of Homogeneous Balls Yaakov Friedman, Jerusalem College of Technology, Israel Quaternions, Clifford Algebras With the assistance of Tzvi Scarr, Jerusalem College of Technology, Israel and Relativistic Physics “This fine book provides a highly original approach to theoretical phys- Patrick R. Girard, INSA Lyon, France ics, its contents reflecting the author’s and his collaborators’ copious contributions to many branches of mathematics and physics over the The use of Clifford algebras in mathematical physics and engineering past years.”—ZENTRALBLATT MATH has grown rapidly in recent years. Whereas other developments have privileged a geometric approach, the author uses an algebraic approach One of the mathematical challenges of modern physics lies in the which can be introduced as a tensor product of quaternion algebras development of new tools to efficiently describe different branches and provides a unified calculus for much of physics. The book proposes of physics within one mathematical framework. This text introduces a pedagogical introduction to this new calculus, based on quaternions, precisely such a broad mathematical model, one that gives a clear with applications mainly in special relativity, classical electromagnetism geometric expression of the symmetry of physical laws and is entirely and general relativity. The volume is intended for students, researchers determined by that symmetry. and instructors in physics, applied mathematics and engineering inter- The first three chapters discuss the occurrence of bounded symmetric ested in this new quaternionic Clifford calulus. domains (BSDs) or homogeneous balls and their algebraic structure in 2007 / APPROX. 200 PP. / SOFTCOVER / $49.95 (TENT.) physics. The book further provides a discussion of how to obtain a triple ISBN_13 978-3-7643-7790-8 algebraic structure associated to an arbitrary BSD; the relation between ISBN_10 3-7643-7790-6 the geometry of the domain and the algebraic structure is explored as well. The last chapter contains a classification of BSDs revealing the connection between the classical and exceptional domains. Handbook of Normal Frames 2005 / 280 PP., 77 ILLUS. / HARDCOVER / $79.95 ISBN_13 978-0-8176-3339-4 and Coordinates ISBN_10 0-8176-3339-1 PROGRESS IN MATHEMATICAL PHYSICS, VOL. 40 Bozhidar Z. Iliev, Institute for Nuclear Research and Nuclear Energy, Sofia, Bulgaria The main subject of the book is an up-to-date and in-depth survey of the theory of normal frames and coordinates in differential geometry. The book can be used as a reference manual, a review of the existing results and an introduction to some new ideas and developments. 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 full, in some cases new, proofs. All classical results are expanded and generalized in various directions. Theorems of existence, uniqueness and, possibly, holonomicity of the normal frames and coordinates are proved; mostly, the proofs are constructive and some of their parts can be used independently for other tasks. 2006/441 PP./HARDCOVER/$125.00 ISBN_13 978-3-7643-7618-5 ISBN_10 3-7643-7618-X PROGRESS IN MATHEMATICAL PHYSICS, VOL. 42

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Rigorous Quantum Field Theory Advances in Analysis and A Festschrift for Jacques Bros Geometry Anne Boutet de Monvel, Université Paris VII, France; New Developments using Clifford Algebras Detlev Buchholz, Universität Göttingen, Germany; Tao Qian, University of Macau, Macau; Thomas Hempfling, Basel, Switzerland; Daniel Iagolnitzer, CEA/Saclay, Gif-sur-Yvette, France; Alan McIntosh, Australian National University, Canberra, Australia; and Ugo Moschella, Università dell’Insubria, Como, Italy (Eds.) Frank Sommen, Ghent University, Belgium (Eds.) Jacques Bros has greatly advanced our present understanding of rigorous The study of systems of special partial differential operators arising quantum field theory through numerous fundamental contributions. The naturally from the use of Clifford algebra as a calculus tool lies at the impact of his work is also visible in several articles in this book. Quantum heart of Clifford analysis. The focus is on the study of Dirac operators fields are considered as genuine mathematical objects, whose various and related ones, together with applications in mathematics, physics, properties and relevant physical interpretations have to be studied in a and engineering. well-defined mathematical framework. Key topics: Analytic structures of QFT, renormalization group methods, gauge QFT, stability properties and The three parts of this book reflect the analytic and geometric aspects extension of the axiomatic framework, QFT on models of curved spacet- of Clifford analysis and its applications: Part A deals with differential op- imes, QFT on noncommutative Minkowski spacetime. erators and operator theory; Part B focuses on global analysis and dif- Contributors: D. Bahns, M. Bertola, R. Brunetti, D. Buchholz, A. Connes, ferential geometry; Part C presents applications to artificial intelligence, F. Corbetta, S. Doplicher, M. Dubois-Violette, M. Dütsch, H. Epstein, number theory, numerical analysis, and physics. C.J. Fewster, K. Fredenhagan, C. Gérard, D. Iagolnitzer, C.D. Jäkel, C. Kopper, 2004 / 392 PP. / HARDCOVER / $129.00 G. Lechner, G. Morchio, U. Moschella, J. Mund, H. Narnhofer, G. Piacitelli, ISBN_13 978-3-7643-6661-2 ISBN_10 3-7643-6661-3 K.-H. Rehren, P.L. Ribeiro, V. Rivasseau, J.E. Roberts, B. Schroer, Trends in Mathematics O. Steinmann, F. Strochhi, G.A. Viano, F. Vignes-Tourneret 2007 / 326 PP. / HARDCOVER / $99.00 ISBN_13 978-3-7643-7433-4 ISBN_10 3-7643-7433-0 Mathematical PROGRESS IN MATHEMATICS, VOL. 251 Theory of Diffraction Arnold Sommerfeld Analysis of Dirac Systems and Translated by Raymond J. Nagem, Boston University, Boston, MA; Computational Algebra Mario Zampolli, NATO SACLANT Undersea Fabrizio Colombo and Irene Sabadini, both, Politecnico di Milano, Research Centre, La Spezia, Italy; and Milano, Italy; Guido Sandri, Boston University, Boston, MA Franciscus Sommen, Ghent University, Belgium; and “This is a very nice book for those interested Daniele C. Struppa, George Mason University, Fairfax, VA in the theory of diffraction since it pres- “Altogether the book is a pioneering, and quite successful, attempt ents, for the first time in English, the strik- to apply computational and algebraic techniques to several branches ingly original work of Sommerfeld—which marks a milestone in optical of hypercomplex analysis … The book provides a very different way theory—enriched with historical background and technical details. The to look at some important questions which arise when one tries to interest of this book is not only historical but also technical as it presents develop multi-dimensional theories.”—MATHEMATICAL REVIEWS a surprisingly rich and complex mix of pure and applied mathemat- The subject of Clifford algebras has become an increasingly rich area of ics.”—MATHEMATICAL REVIEWS research with a significant number of important applications not only to Arnold Sommerfeld’s Mathematische Theorie der Diffraction marks a mathematical physics, but also to numerical analysis, harmonic analy- milestone in optical theory, full of insights that are still relevant today. In sis, and computer science. a stunning tour de force, Sommerfeld derives the first mathematically rigorous solution of an optical diffraction problem. Indeed, his diffrac- This work is devoted to the analysis of systems of linear partial differen- tion analysis is a surprisingly rich and complex mix of pure and applied tial equations with constant coefficients, focusing attention on null solu- mathematics, and his often-cited diffraction solution is presented only tions of Dirac systems. In addition to their usual significance in physics, as an application of a much more general set of mathematical results. such solutions are important mathematically as an extension of the The body of Sommerfeld’s work is devoted to the systematic devel- function theory of several complex variables. The term computational opment of a method for deriving solutions of the wave equation on in the title emphasizes two main features of the book, namely, the heu- Riemann surfaces, a fascinating but perhaps under-appreciated topic in ristic use of computers to discover results in some particular cases, and mathematical physics. the application of Gröbner bases as a primary theoretical tool. This complete translation, reflecting substantial scholarship, is the first Analysis of Dirac Systems and Computational Algebra may be used publication in English of Sommerfeld’s original work. The extensive by graduate students and researchers interested in (hyper)complex notes by the translators are rich in historical background and further analysis, Clifford analysis, systems of partial differential equations with provide technical details for the reader. constant coefficients, and mathematical physics. 2004 / 157 PP., 38 ILLUS. / HARDCOVER / $59.95 2004 / 332 PP., 6 ILLUS. / HARDCOVER / $89.95 ISBN_13 978-0-8176-3604-3 ISBN_13 978-0-8176-4255-6 ISBN_10 0-8176-3604-8 ISBN_10 0-8176-4255-2 PROGRESS IN MATHEMATICAL PHYSICS, VOL. 35 PROGRESS IN MATHEMATICAL PHYSICS, VOL. 39

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Geometric Phases in Lectures on Clifford Classical and (Geometric) Algebras Quantum Mechanics and Applications Dariusz CHRUśCIŃśKI Andrzej Rafał Abłamowicz, Tennessee Jamiołkowski, both, Nicholas Copernicus Technological University, Cookeville, TN and University, Torun, Poland Garret Sobczyk, Universidad de las Americas, Puebla, Mexico (Eds.) “The book forms a compact, yet comprehensive, introduction to the mathematical “This book is recommended reading for be- physics of this young field .… Its large bibli- ginning graduate students and other new- ography should serve as a quick reference comers in this field. The authors of each to the relevant literature. Mathematical ap- chapter are world leading experts in their pendices have been thoughtfully provided for students. Suggested ref- fields and the chapters are well written and organized. In spite of the intro- erences for further reading and illustrative exercises listed at the end of ductory level of each chapter, many references are given which will help each chapter are useful to gain a better understanding of the respec- the interested reader go deeper into the subject of interest. Moreover, an tive topic . … All in all, this is a good textbook ushering the graduate appendix written by the editors gives a summary of the existing Clifford student through the wonderland of geometric phase and whetting up algebra software for symbolic computations.”—MATHEMATICAL REVIEWS the appetite for further exploration.” —CURRENT SCIENCE “This text contains a set of lectures presented by P. Lounesto, Introduc- “This new textbook examines one of the most interesting findings of tion to Clifford Algebras; I. Porteous, Mathematical Structure of Clifford the last several decades–the physical importance of the topological Algebras; J. Ryan, Clifford Analysis; W.E. Baylis, Applications of Clifford and geometrical phases in classical and quantum mechanics . … The Algebras in Physics; J.M. Selig, Clifford Algebras in Engineering; T. Bran- number of research publications on this topic has grown at such a son, Clifford Bundles and Clifford Algebras; and an appendix by R. pace that, for non-experts, it has become difficult to follow the numer- Ablamowicz and G. Sobczyk describing software for solving different ous theoretical ideas and experimental proposals that have been pre- kinds of problems involving computations with Clifford algebras. Each sented . … What distinguishes the present book...is that it treats both one of the lectures is a jewel and will be appreciated [by] newcomers the quantum and classical geometric phases from a unified (fibre bun- wanting an introduction to a rapidly developing field as well [as] by dle connection) point of view at an advanced textbook level . … Every practitioners, [who] for pleasure certainly will enjoy reading the texts of chapter contains illustrative problems and an annotated list of refer- those well-known experts . …”—ZENTRALBLATT MATH ences for further reading . … The book is well written and…the choice 2004 / 221 PP., 25 ILLUS. / SOFTCOVER / $29.95 of topics presented and their mathematical description and physical ISBN_13 978-0-8176-3257-1 explanation are well balanced and appropriate. The book is aimed ISBN_10 0-8176-3257-3 mainly at graduate students in mathematics and theoretical physics. It would, however, also be useful to (young and mature) researchers in different fields of theoretical physics and chemistry who want Multiscale Methods to familiarize themselves with modern differential geometry methods and techniques, and to mathematicians who wish to learn about a in Quantum class of applications of the above methods in classical and quantum theory.”—JOURNAL OF GEOMETRY AND SYMMETRY IN PHYSICS Mechanics 2004 / 332 PP., 20 ILLUS. / HARDCOVER / $89.95 Theory and Experiment ISBN_13 978-0-8176-4282-2 ISBN_10 0-8176-4282-X Philippe Blanchard, University of PROGRESS IN MATHEMATICAL PHYSICS, VOL. 36 Bielefeld, Germany and Gianfausto Dell’antonio, Universita di Roma Clifford Algebras In the last few years, multiscale methods have lead to spectacular progress in our Applications to Mathematics, Physics, and understanding of complex physical systems Engineering and have stimulated the development of very refined mathematical tech- Rafał Abłamowicz, Tennessee Technological University, Cookeville, TN (Ed.) niques. At the same time on the experimental side, equally spectacular progress has been made in developing experimental machinery and The invited papers in this volume provide a detailed examination of Clif- techniques to test the foundations of quantum mechanics. In view of ford algebras and their significance to geometry, analysis, physics, and this progress, this volume is very timely; it is the first text totally devoted engineering. While the papers require that the reader possess a solid to multiscale methods as applied to various areas of physics and to the knowledge of appropriate background material, they lead to the most relative developments in mathematics. current research topics. With its wide range of topics, well-established contributors, and excellent references and index, this book will appeal The book is aimed at mathematical physicists, theoretical physicists, to graduate students and researchers. applied mathematicians, and experimental physicists working in such areas as decoherence, quantum information, and quantum optics. Main Contents: 2004 / 400 PP. / HARDCOVER / $139.00 Part I–Clifford Analysis / Part II–Geometry / Part III–Mathematical Struc- ISBN_13 978-0-8176-3256-4 ISBN_10 0-8176-3256-5 tures / Part IV–Physics / Part V–Applications in Engineering / Index TRENDS IN MATHEMATICS 2004 / 626 PP., 44 ILLUS. / HARDCOVER / $89.95 ISBN_13 978-0-8176-3525-1 ISBN_10 0-8176-3525-4 PROGRESS IN MATHEMATICAL PHYSICS, VOL. 34

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Foundations of Topics in Quantum Classical Mechanics Electrodynamics Floyd Williams, University of Massachu- setts, Amherst, MA Charge, Flux, and Metric “ A number of interesting and classical ap- Friedrich W. Hehl, University of Cologne, plications (some involving detailed compu- Germany and University of Missouri, tations) are included. Most of the book is Columbia, MO; and Yuri N. Obukhov, dedicated to covering the traditional mate- University of Cologne, Germany and Moscow rial but there are also some innovations, State University, Russia both in the choice of topics and in the way “[The authors] … have stressed the phe- they are presented . … overall, I shall say nomena underlying the axioms chosen that this is a very good text that is welcome and the operational interpretation of the quantities introduced. In this, both from the conceptual and the operational points of view. The theo- they have clearly succeeded.” —MATHEMATICAL REVIEWS retical physics community should also find here a good source on the subject.”—MATHEMATICAL REVIEWS “Throughout this book, the rationalized MKS system of units is used, making analysis more intelligible, and there are many diagrams which This monograph introduces the basic elements of quantum mechanics are of great help in understanding the text. Each part of the book is for a readership of mathematical researchers and graduate students followed by a copious list of references.... Also, in appropriate places whose background in physics might be rather modest. The self-con- there are indications how computer algebra (REDUCE/EXCALC) can tained exposition offers substantial foundational material: for example, be used . … The printing and appearance of the book are excellent … It a discussion of Planck and Schrödinger quantization, de Broglie’s wave- can be warmly recommended.” —ZENTRALBLATT MATH length, Heisenberg’s uncertainty principle, group representations and selection rules, Pauli’s spin functions, and an introduction to multielec- This text presents a fresh, original exposition of the foundations of tron atoms. Topics include Feynman path integrals, quantum statisti- classical electrodynamics in the tradition of the so-called metric-free cal partition functions, and high and low temperature asymptotics of approach. The fundamental structure of classical electrodynamics is quantum fields over negatively curved space-time. described in the form of six axioms: (1) electric charge conservation, 2003 / 416 PP., 20 ILLUS. / HARDCOVER / $79.95 (2) existence of the Lorentz force, (3) magnetic flux conservation, (4) ISBN_13 978-0-8176-4311-9 localization of electromagnetic energy-momentum, (5) existence of an ISBN_10 0-8176-4311-7 electromagnetic spacetime relation, and (6) splitting of the electric cur- PROGRESS IN MATHEMATICAL PHYSICS, VOL. 27 rent into material and external pieces. Coverage unfolds systematically at a level suitable for graduate students and researchers in mathematics, physics, and electrical engineering. 3-D Spinors, Spin-Weighted 2003 / 424 PP. / HARDCOVER / $79.95 ISBN_13 978-0-8176-4222-8 Functions and Their Applications ISBN_10 0-8176-4222-6 PROGRESS IN MATHEMATICAL PHYSICS, VOL. 33 Gerardo F. Torres del Castillo, Universidad Autonoma de Puebla, Puebla, Mexico “In summary … the book gathers much of what can be done with 3- D spinors in an easy-to-read, self-contained form designed for appli- Small Viscosity and Boundary cations that will supplement many available spinor treatments. The Layer Methods book … should be appealing to graduate students and researchers in relativity and mathematical physics.”—MATHEMATICAL REVIEWS Theory, Stability Analysis, and Applications This unique introductory treatment of three-dimensional spinors avoids Guy Métivier, Université de Bordeaux 1, France the customary Clifford algebra approach; instead, spinors are developed This book is an introduction to the stability analysis of noncharacteristic here in a language analogous to the spinor formalism used in relativ- boundary layers, emphasizing selected topics and developing math- istic spacetime. A wide range of topics is covered, including conformal ematical tools relevant to the study of multidimensional problems. rescalings, connections with torsion, and Cartan’s structural equations Boundary layers are present in problems from physics, engineering, in spinor form. mechanics, and fluid mechanics, typically appearing for problems with 2003 / 246 PP., 10 ILLUS. / HARDCOVER / $84.95 small diffusion. Boundary layers also occur in free boundary value prob- ISBN_13 978-0-8176-3249-6 lems, particularly in the analysis of shock waves. ISBN_10 0-8176-3249-2 PROGRESS IN MATHEMATICAL PHYSICS, VOL. 32 This monograph is for researchers, practitioners, and graduate students in applied mathematics, mathematical physics, and engineering and will be a useful supplement for the study of mathematical models in the applied sciences. 2004 / 194 PP. / HARDCOVER / $69.95 ISBN_13 978-0-8176-3390-5 ISBN_10 0-8176-3390-1 MODELING AND SIMULATION IN SCIENCE, ENGINEERING AND TECHNOLOGY

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Poincaré Seminar 2003 The Evolution Bose–Einstein Condensation–Entropy Problem in Jean Dalibard, Paris, France; Bertrand Duplantier, CEA-Saclay, France; General Relativity Vincent Rivasseau, Polytechnique, Paris, France (Eds.) Sergiu Klainerman, Princeton University, Princeton, NJ and The Poincaré Seminar is held twice a year at the Institute Henri Poincaré Francesco Nicolò, University of Rome, in Paris. The goal of this seminar is to provide up-to-date information “Tor Vergata”, Rome, Italy about general topics of great interest in physics. Both theoretical and experimental results are covered, with some historical background. Par- “The book … gives a new proof of the cen- ticular care is devoted to the pedagogical nature of the presentation. tral part of the theorem of Christodoulou and S. Klainerman, ‘The global nonlinear This volume contains the lectures of the third and fourth Poincaré Sem- stability of the Minkowski space’ … The inar, both held in 2003. The third lecture is devoted to Bose–Einstein authors prove, working in terms of double null foliations, a nonlin- Condensation: it covers the physics of superfluid liquid helium as well ear stability, or global existence for small data, result for exterior do- as the recently discovered atomic Bose–Einstein condensates. Major mains.”—MATHEMATICAL REVIEWS experimental results are presented, together with relevant theoretical approaches and remaining open questions. The fourth lecture covers “ … Important results in this book are presented in a more ‘digestible’ entropy, giving a comprehensive account of the history and various form [than] in the preceding book [‘The global nonlinear stability of the realizations of this concept, from thermodynamics to black holes. Minkowski space’] and thus scientists and graduate students working 2004 / 264 PP. / HARDCOVER / $139.00 in relativity are recommended to read at least the introduction and the ISBN_13 978-3-7643-7106-7 conclusions.”—APPLICATIONS OF MATHEMATICS ISBN_10 3-7643-7106-4 SOFTCOVER / $69.95 “ … This important monograph, presenting the detailed proof of an impor- ISBN_13 978-3-7643-7116-6 tant result in general relativity, is of great interest to researchers and gradu- ISBN_10 3-7643-7116-1 ate students in mathematics, mathematical physics, and physics in the area PROGRESS IN MATHEMATICAL PHYSICS, VOL. 38 of general relativity.”—STUDIA UNIVERSITATIS BABES-BOLYAI, SERIES MATHEMATICA 2002 / 400 PP., 20 ILLUS. / HARDCOVER / $89.95 ISBN_13 978-0-8176-4254-9 ISBN_10 0-8176-4254-4 Poincaré Seminar 2002 PROGRESS IN MATHEMATICAL PHYSICS, VOL. 25 Vacuum Energy, Renormalization Bertrand Duplantier, CEA, Saclay, France and Vincent Rivasseau, Université Paris XI, Orsay, France (Eds.) Symmetry in This volume contains the lectures of the 2002 Poincaré Seminars. The Mechanics main topic of the first seminar was the vacuum energy, in particular the Casimir effect and the nature of the cosmological constant. The sec- A Gentle, Modern Introduction ond seminar concentrated on renormalization, giving a comprehensive Stephanie Frank Singer, Haverford account of its mathematical structure and applications to high-energy College, Haverford, PA physics, statistical mechanics, and classical mechanics. “This is a very interesting book. Those edu- 2003 / 340 PP. / HARDCOVER / $92.00 cated in traditional mechanics will acquire ISBN_13 978-3-7643-0579-6 ISBN_10 3-7643-0579-7 [from reading it] knowledge of modern SOFTCOVER / $49.95 mathematics hidden beyond traditional ISBN_13 978-3-7643-0527-7 concepts in the realm of celestial mechan- ISBN_3-7643-0527-4 ics, [and] … pure mathematicians will un- PROGRESS IN MATHEMATICAL PHYSICS, VOL. 30 derstand how their discipline enters into practical problems. The author shows how fundamental concepts of symplectic geometry implicitly occur in mechanics … the mathematical presentation is ingenious and subtle. There are a lot of exercises for the reader and the solutions of most of them are given in a separate chapter. I can highly recommend this book to undergraduate and PhD students … it is ideally suited for teaching a course on the subject.”—MATHEMATICAL REVIEWS “’Symmetry in Mechanics’ is directed to students at the undergraduate level and beyond, and offers a lovely presentation of the subject … Singer uses this example [of the two-body problem] from classical physics throughout the book as a vehicle for explaining the concepts of differential geometry and for illustrating their use … These ideas and techniques will allow the reader to understand advanced texts and research literature in which considerably more difficult problems are treated and solved by identical or related methods. 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 / 208 PP., 30 ILLUS. / SOFTCOVER / $37.95 ISBN_13 978-0-8176-4145-0 ISBN_10 0-8176-4145-9

50 Order By Phone: 1-800-777-4643 • Fax: 201-348-4505 • Or Online: www.birkhauser.com Mathematical Physics / Physics

An Introduction to Dirac Mathematical Operators on Manifolds Methods in Physics Jan Cnops, Gent Polytechnic, Gent, Belgium Distributions, Hilbert Space Operators, and “The text should be accessible for senior undergraduate and gradu- Variational Methods ate students. It requires very little previous knowledge of the domains Philippe Blanchard, University of Bielefeld, Germany and covered. More advanced readers could perhaps appreciate the new Erwin Bruening, University of Durban-Westville, South Africa approach to the theory as well as some new results on boundary value “This text is a translated, considerably revised and extended version of theory.” —MATHEMATICAL REVIEWS the book Distributionen und Hilbertraumoperatoren: Mathematische “This book gives an introduction to Dirac operators on manifolds for Methoden der Physik . … The book is written in a very nice and under- readers with little knowledge in differential geometry and analy- standable form and addresses mainly students with interest in the inter- sis . … Compared to other books treating similar subjects...the present action between physics and mathematics.”—Mathematica Bohemica book is considerably more elementary and is mostly restricted to results “[This] English version has been considerably revised and extended that can easily be obtained out of the definitions.”—ZENTRALBLATT MATH in order to improve the usefulness for students of physics and math- 2002 / 208 PP. / HARDCOVER / $64.95 ISBN_13 978-0-8176-4298-3 ematics alike. For instance, proofs are now more detailed. Many added ISBN_10 0-8176-4298-6 examples illustrate abstract mathematical concepts. Exercises were PROGRESS IN MATHEMATICAL PHYSICS, VOL. 24 included to improve the skill of beginners. Some of these exercises hint to physical problems arising either in quantum mechanics or field theory . … Notably, there is one chapter at the end, dealing exclusively with physics applications, the density functional theory of atoms and Singularity Theory molecules due to Hohenberg, Kohn, and Sham. In my view this is a nice and Gravitational way to illustrate the calculus of variations . … the book is self-contained, the only prerequisites being a solid background in analysis and linear Lensing algebra.” —ZENTRALBLATT MATH Arlie O. Petters, Duke University, 2002 / 496 PP., 20 ILLUS. / HARDCOVER / $79.95 Durham, NC; ISBN_13 978-0-8176-4228-0 Harold Levine, Brandeis University, ISBN_10 0-8176-4228-5 PROGRESS IN MATHEMATICAL PHYSICS, VOL. 26 Waltham, MA; and Joachim Wambsganss, Universitat Potsdam, Potsdam, Germany “A well-developed monograph on gravita- Computer Algebra tional lensing both from the observational Recipes for and mathematical point of view … a good source for several types of singularity theories … index and bibliography are very well done.”— Mathematical Physics ZENTRALBLATT MATH Richard H. Enns, Simon Fraser University, “The time is ripe for a comprehensive volume explaining gravita- Burnaby, BC, Canada tional lensing to mathematicians and reviewing relevant singularity “This book is a self-contained guide to the theory for astrophysicists. This is such a book. [It … is accessible and Maple CAS which draws its examples from attractive, … ranging widely through the history, physics and mathe- mathematical physics. The format of the book matics to paint a full picture of this … theory. This most attractively pre- is very pleasant for the reader. The book con- sented book summarizes current mathematical methods in the field sists of short examples, each about 1-3 pages, and sets the stage for further exciting developments … A collaboration which describe the problem studied and then between a mathematical physicist, a mathematician, and a physicist, it provide a recipe to solve it. Each example begins with a humorous or witty has something for everybody.”—MATHEMATICAL REVIEWS citation from the writers of the past -- a good method to stimulate the read- This monograph, unique in the literature, is the first to develop a mather.This book is best suited for physicists but also mathematicians would find ematical theory of gravitational lensing.. The theory applies to any finite this text very useful.”—ZENTRALBLATT MATH number of deflector planes and highlights the distinctions between The more than two hundred novel and innovative computer algebra work- single and multiple plane lensing. sheets or “recipes” in this book enable readers in engineering, physics, and Mathematical topics discussed: • Morse Theory, • Whitney Sin- mathematics to easily and rapidly solve and explore most problems they gularity Theory, • Thom Catastrophe Theory, • Mather Stability Theory, encounter in their mathematical physics studies. While the aim of this text is • Arnold Singularity Theory, • and the Euler Characteristic via Projectiv- to illustrate applications, a brief synopsis of the fundamentals for each topic ized Rotation Numbers. is presented, the topics being organized to correlate with those found in traditional mathematical physics texts. These tools are applied to the study of stable lens systems, local and global geometry of caustics, caustic metamorphoses, multiple lens im- The recipes are presented in the form of stories and anecdotes, a peda- ages, lensed image magnification, magnification cross sections, and gogical approach that makes a mathematically challenging subject easier lensing by singular and nonsingular deflectors. and more fun to learn. Every chapter contains supplementary recipes and 2001 / 640 PP., 184 ILLUS. / HARDCOVER / $84.95 solutions on a CD-ROM. This is a self-contained and standalone text using ISBN_13 978-0-8176-3668-5 MAPLE that may be used in the classroom, for self-study, as a reference, or ISBN_10 0-8176-3668-4 as a text for an online course. PROGRESS IN MATHEMATICAL PHYSICS, VOL. 21 2005 / 392 PP., 106 ILLUS. / SOFTCOVER WITH CD-ROM / $69.95 ISBN_13 978-0-8176-3223-6 ISBN_10 0-8176-3223-9

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Computer Algebra Nonlinear Physics Recipes for Classical with MATHEMATICA® Mechanics for Scientists Richard Enns, Simon Fraser University, and Engineers Burnaby, BC, Canada and Richard Enns, Simon Fraser University, George McGuire, University College of the Burnaby, Canada and Fraser Valley, Abbotsford, BC, Canada George C. McGuire, University College of “[The authors’] purpose is not simply to re- the Fraser Valley, Abbotsford, Canada hash … classical topics, but rather to show how a computer algebra system (CAS) “This book is a revision of an earlier work may be used as a pedagogical tool to carry that looked at nonlinear physics using MAPLE® software. As with that out both standard numerical computations and complicated symbolic work, Enns and McGuire incorporate theory, experiment, and numeri- manipulations in the context of classical mechanics . … Other interest- cal applications in a thorough introduction to a wide range of nonlin- ing features of the book include the use of a relevant quotation at ear topics. Also included is a CD-ROM with the needed MATHEMATI- the beginning of each section and the creation of story problems to CA® files. The book assumes no familiarity with nonlinear physics or introduce and illustrate virtually every topic, making the book more MATHEMATICA® … The authors do an extraordinary job of integrating application and theory. They provide applications from a variety of readable and accessible to students.”—CHOICE disciplines throughout the sections that introduce the theory and that “It can be a very useful complementary tool to classical lectures in the look at methods of analysis and consider the various approaches to field of classical mechanics. addressing nonlinear problems. It is not an exaggeration to say that Using this text as a unique basis for a course in classical mechanics is this book considers all areas of interest in nonlinear analysis with solid possible … ”—MATHEMATICAL REVIEWS introductions. (This reviewer, having taught the basics of nonlinear physics over the last 15 years, wishes he had had this book as a tutor.) “This is a textbook discussing the use of computer algebra for com- Added to this are 33 experimental activities using MATHEMATICA® putations in elementary classical mechanics. It is based on the system that demonstrate concepts and applied examples.”—CHOICE Maple 8; no prior knowledge of it is required . … The book gives a solid 2001 / 712 PP., 282 ILLUS. / HARDCOVER WITH CD-ROM / $79.95 introduction into the basic use of Maple . … The book should serve ISBN_13 978-0-8176-4223-5 well as an exercise or lab book accompanying a standard course on ISBN_10 0-8176-4223-4 elementary classical mechanics.” —ZENTRALBLATT MATH 2003 / 280 PP., 100 ILLUS. / SOFTCOVER WITH CD-ROM / $59.95 ISBN_13 978-0-8176-4291-4 Also available ISBN_10 0-8176-4291-9 CO-PUBLISHED WITH SPRINGER Nonlinear Physics with MAPLE® for Scientists and Engineers Electrodynamics Second Edition Richard Enns, Simon Fraser University, Burnaby, Canada and A Modern Geometric Approach George C. McGuire, University College of the Fraser Valley, Abbotsford, William E. Baylis, University of Windsor, Canada Canada “[The book] has a nice blend of mathematical physics, fundamentals “Correctly balances a good treatment of nonlinear, but also noncha- of electromagnetic theory and practical applications … It is extremely otic, behavior of systems with some of the exciting findings about cha- well written and contains numerous exercises and problems to help otic dynamics…One of the book’s strengths is the divers selection of the reader gain familiarity with new concepts. Throughout … the au- examples from mechanical, chemical, electronic, fluid and man other thor emphasizes the conceptual framework of electromagnetism so systems…Another strength of the book is the diversity of approaches that the reader does not get lost in details. Such a style is very valuable that the student is encourages to take…the authors have chosen well in a physics textbook … The book simultaneously teaches the reader the trio of text, MAPLE-bases software, and the lab manual gives the electromagnetic theory and more advanced mathematical concepts in newcomer to nonlinear physics quite an effective set of tools…this a very concrete physical context … Essentially self-contained … it will test simultaneously serves as an excellent, structured introduction to serve as an excellent textbook for graduate level physics courses on MAPLE V…Basic ideas are explained clearly and illustrated with many electromagnetic theory and mathematical physics. It is also a good examples.”— Physics Today (on the first edition) reference book for researchers in applied mathematics, theoretical “An…excellent book…the authors have been able to cover an extraor- physics and electrical engineering.”—CURRENT SCIENCE dinary range of topics and hopefully excite a wide audience to inves- Solutions manual is available upon adoption of the text. tigate nonlinear phenomena…accessible to advanced undergradu- 2001 / 400 PP., 43 ILLUS. / HARDCOVER / $59.95 ates and yet challenging enough for graduate student and working ISBN_13 978-0-8176-4025-5 scientists….The reader is guided through it all with sound advice and ISBN_10 0-8176-4025-8 humor….I hope that many will adopt the text.”— American Journal of PROGRESS IN MATHEMATICAL PHYSICS, VOL. 17 Physics (on the first edition) 2000 / 676 PP., 282 ILLUS. / HARDCOVER WITH CD-ROM / $79.95 ISBN_13 978-0-8176-4119-1 ISBN_10 0-8176-4119-X

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Variational Methods Free Energy and in Shape Optimization Self-Interacting Problems Particles Dorin Bucur, Université de Metz, France and Takashi Suzuki, Osaka University, Japan Giuseppe Buttazzo, Università di Pisa, Italy “This book is introductory in the sense of The study of shape optimization problems in- being accessible to students not only of volves a wide area of academic research and mathematics, but also of the physical and applications to the real world. In this work, the engineering sciences once they have such problems are treated from the classical mastered the introductory mathemati- and modern perspectives and target a broad cal courses. …Overall, the presentation audience of graduate students in pure and is quite detailed regarding the needs of applied mathematics, as well as engineers requiring a solid mathemati- the practitioner with many examples to engineering, earth sciences, cal basis for the solution of practical problems. Driven by several good etc. (among others elasticity, vibrations, heat transfer, fluid flow; also examples and illustrations, the book requires only standard knowledge of eigenvalue problems), and special but important items not so often the calculus of variations, differential equations, and functional analysis. covered in other texts, e.g., how to cope with the specific difficulties arising in polar coordinates. Both numerous exercises and codes in Key topics: Ansys, Fortran, Mathematica® and MATLAB direct the reader towards • Presents foundational introduction to shape optimization theory experimentation of his own.”— Monatshefte fur Mathematik • Studies some classical problems: the isoperimetric problem and the This book examines a nonlinear system of parabolic partial differential Newton problem involving the best aerodynamical shape, optimi- equations (PDEs) arising in mathematical biology and statistical me- zation problems over classes of convex domains chanics. In the context of biology, the system typically describes the • Treats optimal control problems under a general scheme, giving chemotactic feature of cellular slime molds. One way of deriving these a topological framework, a survey of G-convergence, problems equations is via the random motion of a particle in a cellular automa- governed by ODE ton. In statistical mechanics, the system is associated with the motion of the mean field of self-interacting particles under gravitational force. • Examines shape optimization problems with Dirichlet and Neumann condition on the free boundary, the existence of clas- Physically, such a system is related to Langevin, Fokker–Planck, Liouville sical solutions. and gradient flow equations. Mathematically, the mechanism can be re- 2005 / 350 PP., 10 ILLUS. / HARDCOVER / $69.95 ferred to as a quantized blowup. This book describes the whole picture, ISBN_13 978-0-8176-4359-1 i.e., the mathematical and physical principles: derivation of a series of equa- ISBN_10 0-8176-4359-1 tions, biological modeling based on biased random walks, the study of PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS, equilibrium states via the variational structure derived from the free energy, vol. 65 and the quantized blowup mechanism based on several PDE techniques. Free Energy and Self-Interacting Particles is suitable for researchers and graduate students of mathematics and applied mathematics who Vortices in Bose- are interested in nonlinear PDEs in stochastic processes, cellular au- Einstein Condensates tomata, variational methods, and their applications to natural sciences. It is also suitable for researchers in other fields such as physics, chem- Amandine Aftalion, CNRS, Laboratoire istry, biology, and engineering. Jacques-Louis Lions, Paris, France 2005 / 366 PP., 7 ILLUS. / HARDCOVER / $129.00 One of the key issues related to superfluid- ISBN_13 978-0-8176-4302-7 ISBN_10 0-8176-4302-8 ity is the existence of vortices. In very recent PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS, experiments on Bose-Einstein condensates, VOL. 62 vortices have been observed by rotating the trap holding the atoms. In contrast to a classical fluid for which the equilibrium velocity 2001 Ferran Sunyer i Balaguer Prize Winner corresponds to solid body rotation, a quantum fluid such as a Bose–Einstein conden- Perturbation Methods and sate can rotate only through the nucleation of quantized vortices. Semilinear Elliptic Problems on RN This monograph is dedicated to the mathematical modelling of these Antonio Ambrosetti, SISSA, Trieste; phenomena. The mathematical tools employed are energy estimates, Andrea Malchiodi, SISSA, Trieste Gamma convergence, and homogenization techniques. The mathematical analysis is made in the framework of the Gross–Pitaevskii This book has been awarded the Ferran Sunyer i Balaguer 2005 prize. The energy. Results are presented and open problems related to recent aim of this monograph is to discuss several elliptic problems on Rn with two experiments are explained. main features: they are variational and perturbative in nature, and standard tools of nonlinear analysis based on compactness arguments cannot be The work can serve as a reference for mathematical researchers and used in general. For these problems, a more specific approach that takes theoretical physicists interested in superfluidity and quantum conden- advantage of such a perturbative setting seems to be the most appropriate. sates, and can also complement a graduate seminar in elliptic PDEs or The first part of the book is devoted to these abstract tools, which provide a modelling of physical experiments. unified frame for several applications, often considered different in nature. 2006 / 203 PP., 18 ILLUS. / HARDCOVER / $99.00 2006 / 183 PP. / HARDCOVER / $59.95 ISBN_13 978-0-8176-4392-8 ISBN_13 978-3-7643-7321-4 ISBN_10 0-8176-4392-3 ISBN_10 3-7643-7321-0 PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS, VOL. 67 PROGRESS IN MATHEMATICS, VOL. 240

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An Analytical Approach Fuchsian Reduction Self-Dual Gauge Field Vortices Lasers, Cosmology, Combustion, and Geometry Gabriella Tarantello, Università di Roma “Tor Vergata”, Roma, Italy Satyanad Kichenassamy, Universite de Reims Champagne-Ardenne, Reims, France In modern theoretical physics, gauge field theories are of great- im portance since they keep internal symmetries and account for phe- Fuchsian Reduction is a method for explicitly representing solutions of nomena such as spontaneous symmetry breaking, the quantum Hall nonlinear PDEs near singularities. The technique has multiple applica- effect, charge fractionalization, superconductivity and supergravity. This tions in soliton theory, Einstein’s equations and cosmology, stellar mod- monograph discusses specific examples of self-dual gauge field struc- els, laser collapse, conformal geometry and combustion. Developed in tures, including the Chern--Simons model, the abelian--Higgs model, the 1990s for semilinear wave equations, Fuchsian Reduction research and Yang--Mills gauge field theory. The author builds a foundation for has grown in response to those problems in pure and applied math- gauge theory and self-dual vortices by introducing the basic mathe- ematics, where numerical computations fail. The exposition unfolds sys- matical language of gauge theory and formulating examples of Chern- tematically in four parts, with theory and applications nicely interwoven. Simons-Higgs theories (in both abelian and non-abelian settings). The methods used in various applications examined in Part III may serve Thereafter, the Electroweak theory and self-gravitating Electroweak as prototypes for future new applications. Background results in weighted strings are examined. The final chapters treat elliptic problems involving Sobolev and Holder spaces as well as Nash--Moser implicit function the- Chern—Simmons models, concentration-compactness principles, and orem are provided. Most chapters contain a problem section and notes Maxwell—Chern—Simons vortices. Many open questions still remain in with references to the literature. This volume can be used as a text in the field and are examined in this work in connection with Liouville-type graduate courses in PDEs and/or Algebra or as a resource for researchers equations and systems. The goal of this text is to form an understand- working with applications to Fuchsian Reduction. ing of self-dual solutions arising in a variety of physical contexts and 2007 / APPROX. 305 PP. / HARDCOVER / $149.00 (TENT.) thus is ideal for graduate students and researchers interested in partial ISBN_13 978-0-8176-4352-2 differential equations and mathematical physics. ISBN_10 0-8176-4352-4 PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS 2007 / 334 PP. / HARDCOVER / $79.95 (TENT.) ISBN_13 978-0-8176-4310-2 ISBN_10 0-8176-4310-9 PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS Spectral Theory of Infinite-Volume Hyperbolic Surfaces An Invitation to Variational David Borthwick, Emory University, Atlanta, GA Methods in Differential Equations This book is a self-contained monograph on spectral theory for noncompact Riemann surfaces, focused on the infinite-volume case. A hy- David G. Costa, University of Nevada, Las Vegas, NV perbolic surface of infinite volume provides for a qualitatively different This textbook introduces variational methods and their applications to context from either the compact or finite-volume cases, a context in differential equations to graduate students and researchers interested which spectral theory of the Laplacian operator emerges as scattering in differential equations and nonlinear analysis. theory. Scattering theory, in particular the theory of resonances, is of great interest in physics, geometry, and analytic number theory. The topics covered include: By focusing on the scattering theory of hyperbolic surfaces, this work • Minimizations provides a compelling introductory example which will be accessible to • Deformations results a broad audience. The book opens with an introduction to the geom- • The mountain-pass and saddle-point theorems etry of hyperbolic surfaces. Then a thorough development of the spectral theory of a geometrically finite hyperbolic surface of infinite volume • Critical points under constraints is given, which serves also as an attractive introduction to geometric • Issues of compactness The straightforward and systematic scattering theory and the theory of resonances. presentation includes many exercises and examples to motivate The final sections of the recent developments, for which no thorough the study of variational methods. expository account exists, include resonance counting (illustrating tech- 2007 / APPROX. 160 PP., 5 ILLUS. / HARDCOVER / $49.95 (TENT.) niques developed for potential and obstacle scattering), analysis of the ISBN_13 978-0-8176-4535-9 ISBN_10 0-8176-4535-7 Selberg zeta function, the Poisson formula relating the resonance set to BIRKHAUSER ADVANCED TEXTS the length spectrum, and the proof that the resonance set determines a surface up to finitely many possibilities. 2007 / APPROX. 240 PP., 10 ILLUS. / HARDCOVER / $59.95 (TENT.) ISBN_13 978-0-8176-4524-3 ISBN_10 0-8176-4524-1 PROGRESS IN MATHEMATICS, VOL. 282

54 Order By Phone: 1-800-777-4643 • Fax: 201-348-4505 • Or Online: www.birkhauser.com Differential Equations / Dynamical Systems

Surface Evolution Equations Phase Space Analysis of Partial A Level Set Approach Differential Equations Yoshikazu Giga, University of Tokyo, Japan Antonio Bove, Università di Bologna, Italy; Ferruccio Colombini, Università di Pisa, Italy; This book presents a self-contained introduction to the analytic foun- Daniele Del Santo, Università di Trieste, Italy (Eds.) dation of a level set approach for various surface evolution equations including curvature flow equations. These equations are important in This collection of original articles and surveys treats linear and nonlin- many applications, such as material sciences, image processing and ear aspects of the theory of partial differential equations. Phase space differential geometry. The goal is to introduce a generalized notion of analysis methods, also known as microlocal analysis, have yielded strik- solutions allowing singularities, and to solve the initial-value problem ing results over the past years and have become one of the main tools globally-in-time in a generalized sense. Various equivalent definitions of investigation. Equally important is their role in many applications to of solutions are studied. Several new results on equivalence are also physics, for example, in quantum and spectral theory. presented. Moreover, structures of level set equations are studied in 2007 / 330 PP. / HARDCOVER / $139.00 detail. Further, a rather complete introduction to the theory of viscosity ISBN_13 978-0-8176-4511-3 solutions is contained, which is a key tool for the level set approach. ISBN_10 0-8176-4511-X PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS, VOL. 69 2006 / 264 PP. / HARDCOVER / $119.00 ISBN_13 978-3-7643-2430-8 ISBN_10 3-7643-2430-9 MONOGRAPHS IN MATHEMATICS, VOL. 99 Linear Partial Differential Equations for Scientists and Engineers Introduction to Mathematical Fourth Edition Tyn Myint-U, Manhattan College, New York, NY; Systems Theory Lokenath Debnath, University of Texas Pan-American, Edinburgh, TX Linear Systems, Identification and Control This significantly expanded fourth edition is designed as an introduction Christiaan Heij, Erasmus University Rotterdam, The Netherlands; to the theory and applications of linear PDEs. The authors provide fun- André C.M. Ran, Vrije Universiteit Amsterdam, The Netherlands; damental concepts, underlying principles, a wide range of applications, F. van Schagen, Vrije Universiteit Amsterdam, The Netherlands and various methods of solutions to PDEs. The purpose of this book is to provide an introduction to the theory In addition to essential standard material on the subject, the book of linear systems and control for students in business mathematics, contains new material that is not usually covered in similar texts and econometrics, computer science, and engineering. The subjects treated reference books, including conservation laws, the spherical wave equa- are for one the central topics from deterministic linear system theory, tion, the cylindrical wave equation, higher-dimensional boundary-value i.e. controllability, observability, realization theory, stability and stabiliza- problems, the finite element method, fractional partial differential equation by feedback, LQ-optimal control theory. Kalman filtering and LQC- tions, and nonlinear partial differential equations with applications. control of stochastic systems are also discussed. Finally, attention is paid to modelling, e.g. time series analysis and model specification, Linear Partial Differential Equations for Scientists and Engineers, Fourth along with model validation. All topics in the book are supported by Edition will primarily serve as a textbook for the first two courses in exercises requiring the use of Matlab, which illustrate and enhance the PDEs, or in a course on advanced engineering mathematics. main concepts and techniques in the text. 2007 4th ed. / 800 PP., 79 ILLUS. / HARDCOVER / $89.95 ISBN_13 978-0-8176-4393-5 2007 / APPROX. 176 PP. / HARDCOVER With CD-ROM / $49.95 ISBN_10 0-8176-4393-1 ISBN_13 978-3-7643-7548-5 ISBN_10 3-7643-7548-5

Dynamical Systems with Nonlinear Partial Differential Applications Using Mathematica® Equations with Applications Stephen Lynch, Manchester Metropolitan University, Manchester, UK Tomás Roubicek, Charles University, Praha, Czech Republic Dynamical Systems with Applications Using Mathematica® provides an intro- ® This book primarily concerns quasilinear and semilinear elliptic and duction to the theory of dynamical systems with the aid of the Mathematica parabolic partial differential equations, inequalities, and systems. The computer algebra package. The book has a very hands-on approach and takes exposition leads general theory as fast as possible towards the analysis the reader from basic theory to recently published research material. Emphasized of concrete equations, which have specific applications in continuum throughout are numerous applications to biology, chemical kinetics, economics, (thermo-) mechanics of solids and fluids, electrically (semi-) conduc- electronics, epidemiology, nonlinear optics, mechanics, population dynamics, tive media, modelling of biological systems, or in mechanical engineer- and neural networks. Exercises are included at the end of every chapter. ing. Selected parts are rather an introduction into the subject while The book is intended for senior undergraduate and graduate students some others form an advanced textbook. The intended audience is as well as working scientists in applied mathematics, the natural sci- graduate and PhD students and researchers in the theory of partial ences, and engineering. The material is also accessible to readers with a differential equations or in mathematical modelling of distributed general mathematical background. Many chapters of the book are es- parameter systems. pecially useful as reference material for senior undergraduate indepen- 2005 / 405 PP. / HARDCOVER / $139.00 dent project work. Working Mathematica® notebooks will be available at: ISBN_13 978-3-7643-7293-4 http://library.wolfram.com/infocenter/Books/AppliedMathematics/. ISBN_10 3-7643-7293-1 2007 / APPROX. 550 PP., 350 ILLUS. / SOFTCOVER / $59.95 (TENT.) INTERNATIONAL SERIES OF NUMERICAL MATHEMATICS, VOL. 153 ISBN_13 978-0-8176-4482-6 ISBN_10 0-8176-4482-2

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Dynamical Systems Nonlinear Partial with Applications Differential using MAPLE Equations for Scientists Second Edition and Engineers Stephen Lynch, Manchester Metropolitan Second Edition University, Manchester, UK Lokenath Debnath, University of Texas “The text treats a remarkable spectrum of Pan American, Edinburg, TX topics … and has a little for everyone. It can serve as an introduction to many of the “Nonlinear partial differential equations is an topics of dynamical systems, and will help old and vast area of research. There is a big even the most jaded reader, such as this and well-developed theory as well as a huge reviewer, enjoy some of the interactive aspects of studying dynamics variety of applications. It seems to be impossible to embrace this subject in a single monograph. The book of Lokenath using Maple®.”—U.K. NONLINEAR NEWS (1st Edition) Debnath is a quite successful attempt. It is a second edition of the book, “The book will be useful for all kinds of dynamical systems considerably extended and revised. The author is trying to balance the deep courses . … [It] shows the power of using a computer algebra program and rigorous theory and a variety of approaches and often seminal ex- to study dynamical systems, and, by giving so many worked exam- amples. To examples, he gives the leading, more than just an illustrative, ples, provides ample opportunity for experiments . … [It] is well written role.... The book could serve as a good selection of choices for a kernel of and a pleasure to read, which is helped by its attention to historical a graduate or even undergraduate module in Applied Mathematics or En- background.”— Mathematical Reviews (1st Edition) gineering Sciences. For more fundamental courses the book is also useful, since it contains a lot of motivations and well elaborated exercises.... Overall, 2006 2nd ed / APPROX. 500 PP., 350 ILLUS. / SOFTCOVER / $59.95 (TENT.) it is a useful book for teaching, a rich source of examples, and I am happy to ISBN_13 978-0-8176-4389-8 have it on a shelf of my library.”–UK Nonlinear News (Review of Second Edition) ISBN_10 0-8176-4389-3 “An exceptionally complete overview. 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 Dynamical Systems with point … This reviewer feels that it is a very hard act to follow, and recommends Applications using MATLAB® it strongly. [This book] is a jewel.”—APPLIED MECHANICS REVIEW (Review of First Edition) This expanded and revised second edition offers a comprehensive and system- Stephen Lynch, Manchester Metropolitan University, Manchester, UK atic treatment of linear and nonlinear partial differential equations and their varied “As a basic principle, these examples are investigated with MATLAB and applications. This new edition contains updated modern examples and appli- over 60 programs are listed throughout the book. The source code of cations from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear these programs can be downloaded from the web as well. No advanced dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propaga- techniques or prerequisites from e.g., functional analysis are needed to tion. Also included are revised exercises, updated references, and several revised, understand the book and beyond mathematicians, the text is also read- nonlinear real-world models, covering traffic flow, flood waves, chromatographic able for applied scientists and engineers.”—ZENTRALBLATT MATH models, sediment transport in rivers, glacier flow, and roll waves. 2005 2nd ed/ 760 PP., 77 ILLUS. / HARDCOVER / $79.95 An introduction to dynamical systems theory, this text covers both ISBN_13 978-0-8176-4323-2 discrete and continuous dynamical systems using ordinary differential ISBN_10 0-8176-4323-0 equations. A tutorial guide to MATLAB® is provided, and the author employs hands-on examples and the MATLAB® graphical interface to guide readers through the theory. The SIMULINK® accessory to MATLAB® is used to simulate real-world dynamical systems as well. Gradient Flows 2004 / 458 PP., 330 ILLUS. / SOFTCOVER / $59.95 In Metric Spaces and in the Space of Probability Measures ISBN_13 978-0-8176-4321-8 ISBN_10 0-8176-4321-4 Luigi Ambrosio and Nicola Gigli, both, Scuola Normale Superiore, Roma, Italy; Giuseppe Savaré, Università di Pavia, Italy This book is devoted to a theory of gradient flows in spaces that are not Adaptive Finite Element Methods necessarily endowed with a natural linear or differentiable structure. It consists of two parts, the first one concerning gradient flows in metric for Differential Equations spaces, and the second one devoted to gradient flows in the Wasserstein Wolfgang Bangerth, The University of Texas at Austin, TX and space of probability measures on a separable Hilbert space. Rolf Rannacher, University of Heidelberg, Germany The two parts have some connections, due to the fact that the Was- “Most graduate students in engineering and physical sciences should be serstein space of probability measures provides an important model to able to handle the material without excessive difficulty. The presentation which the ”metric’’ theory applies; however, the book is conceived in is very much a tutorial approach promoting a hands-on experience, rein- such a way that the two parts can be read independently, the first one by forced with practical exercises at the end of each chapter, aimed towards the reader more interested in nonsmooth analysis and analysis in metric practitioners . … [The] present book provides a gentler introduction for the spaces, and the second one by the reader more oriented to the applica- beginning graduate student or nonspecialist practitioner.”— SIAM REVIEW tions in partial differential equations, measure theory, and probability. 2003 / 207 PP. / SOFTCOVER / $29.95 2005 / 333 PP. / SOFTCOVER / $59.95 ISBN_13 978-3-7643-7009-1 ISBN_13 978-3-7643-2428-5 ISBN_10 3-7643-7009-2 ISBN_10 3-7643-2428-7 LECTURES IN MATHEMATICS. ETH ZÜRICH LECTURES IN MATHEMATICS. ETH ZÜRICH

56 Order By Phone: 1-800-777-4643 • Fax: 201-348-4505 • Or Online: www.birkhauser.com Differential Equations / Dynamical Systems

Nonlinear Stability Nonlinear Evolution Equations of Finite Volume and Related Topics Methods for Dedicated to Philippe Bénilan Wolfgang Arendt, Universität Ulm, Germany; Hyperbolic Haim Brézis, Université Pierre et Marie Curie, Paris, France; and Conservation Laws Michel Pierre, Université de Rennes I, France (Eds.) and Well-Balanced Philippe Bénilan was a most original and charismatic mathematician who had a deep and decisive impact on the theory of Nonlinear Evolu- Schemes for Sources tion Equations. This present volume is dedicated to him and contains François Bouchut, CNRS & Ecole research papers written by highly distinguished mathematicians. They Normale Supérieure, Paris, France are all related to Bénilan’s work and reflect the present state of this most active field. The contributions cover a wide range of nonlinear “This is a very interesting and useful book which provides a systematic and linear equations. Special topics include: Hamilton-Jacobi equations, presentation of the theory of finite volume methods and numerical the porous medium equation, reaction diffusion systems, integro-differ- simulations for hyperbolic systems of conservation laws. The author ential equations and visco-elasticity, maximal regularity for elliptic and provides a unified approach and notation to the study of nonlinear parabolic equations, and the Ornstein Uhlenbeck operator. Also in this stability of finite volume methods for hyperbolic systems of conserva- special volume, the legendary work of Bénilan-Brézis on Thomas-Fermi tion laws as the accent is put on the development of tools and design Theory is published for the first time. of schemes. The exposition of the book is very clear. It will be a very 2004 / 807 PP. / HARDCOVER / $99.00 useful tool for the researchers in this field as well as for engineers.”— ISBN_13 978-3-7643-7107-4 ZENTRALBLATT MATH ISBN_10 3-7643-7107-2 This book is devoted to finite volume methods for hyperbolic systems of conservation laws. The emphasis is on the development of tools and design of schemes for which one can rigorously prove nonlinear stability properties. Sufficient conditions for a scheme to preserve an invari- Semiconcave ant domain or to satisfy discrete entropy inequalities are systematically Functions, Hamilton- exposed, with analysis of suitable CFL conditions. Jacobi Equations, The monograph intends to be a useful guide for the engineer or researcher who needs very practical advice on how to obtain such de- and Optimal Control sired stability properties. The notion of approximate Riemann solver Piermarco Cannarsa and and the relaxation method, which are adapted to this aim, are espe- Carlo Sinestrari, Università di Roma “Tor cially explained. In particular, practical formulas are provided in a new Vergata”, Roma, Italy variant of the HLLC solver for the gas dynamics system, taking care of contact discontinuities, entropy conditions, and including vacuum. “The main purpose of this book is to provide a systematic study of the notion of In the second half of the book, nonconservative schemes handling semiconcave functions, as well as a pre- source terms are analyzed in the same spirit. Recent developments on sentation of mathematical fields in which well-balanced schemes that are able to capture steady states are also this notion plays a fundamental role . … One of the most attractive explained within a general framework that includes analysis of consis- features of this book is the interplay between several fields of math- tency and order of accuracy. ematical analysis . … Despite the many topics addressed in the book, 2004 / 134 PP. / SOFTCOVER / $49.95 the required mathematical background for reading it is limited. ISBN_13 978-3-7643-6665-0 ISBN_10 3-7643-6665-6 The book will be very useful to experts in nonsmooth analysis, non- FRONTIERS IN MATHEMATICS linear control theory and PDEs, in particular, as well as by advanced graduate students in this field. They will appreciate the many detailed examples, the clear proofs and the elegant style of presentation, the fairly comprehensive and up-to-date bibliography and the very perti- Optimal Stopping and Free nent historical and bibliographical comments at the end of each chap- Boundary Problems ter.”—MATHEMATICAL REVIEWS Goran Peskir, University of Aarhus, Denmark and 2004/312 PP./HARDCOVER/$135.00 ISBN_13 978-0-8176-4084-2 Albert Shiryaev, Steklov Institute of Mathematics, Moscow, Russia ISBN_10 0-8176-4084-3 SOFTCOVER / $59.95 This monograph examines concrete problems of general interest from ISBN_13 978-0-8176-4336-2 probability, mathematical statistics, and mathematical finance, which ISBN_10 0-8176-4336-2 can be reformulated as problems of optimal stopping of stochastic PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS, processes and solved by reduction to free-boundary problems of real VOL. 58 analysis (Stefan problems). Credits and historical comments are given at the end of each chapter, and references give suggestions for further reading and study in the field. 2005 / 150 PP. / SOFTCOVER / $59.95 ISBN_13 978-3-7643-2419-3 ISBN_10 3-7643-2419-8 LECTURES IN MATHEMATICS.ETH ZÜRICH

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A Stability Technique Regularity Theory for Mean for Evolution Partial Curvature Flow Differential Equations Klaus Ecker, Freie Universität Berlin, Berlin, Germany A Dynamical Systems “The central theme [in this book] is the regularity theory for mean cur- Approach vature flow leading to a clear simplified proof of Brakke‘s main regularity theorem for this special case . … [The] author gives a detailed Victor A. Galaktionov, University of account of techniques for the study of singularities and expresses the Bath, Bath, UK and underlying ideas almost entirely in the language of differential ge- Juan L. Vázquez, Universidad Autonoma ometry and partial differential equations . … This is a very nice book. de Madrid, Spain The presentations are very clear and direct. Graduate students and “The authors are famous experts in the field researchers in differential geometry and partial differential equations of PDEs and blow-up techniques. In this will benefit from this work.“—MATHEMATICAL REVIEWS book they present a stability theorem, the so-called S-theorem, and “For the last 20 years, the computational and theoretical study and ap- show, with several examples, how it may be applied to a wide range of plication of generalized motion by mean curvature and more general stability problems for evolution equations. The book [is] aimed primar- curvature flows have had enormous impact in diverse areas of pure and ily aimed at advanced graduate students.”—MATHEMATICAL REVIEWS applied mathematics. Klaus Ecker’s new book provides an attractive, This work is a blend of delicate analysis and broad application that intro- elegant, and largely self-contained introduction to the study of classical duces a state-of-the-art method for the study of the asymptotic behav- mean curvature flow, developing some fundamental ideas from mini- ior of solutions to evolution partial differential equations. The underlying mal surface theory … all with the aim of proving a version of Brakke’s theory hinges on a new stability result, formulated in the abstract setting regularity theorem and estimating the size of the ‘singular set.’ In order of infinite-dimensional dynamical systems, which states that under cer- to limit technicalities, the discussion is basically limited to classical flows tain hypotheses, the omega-limit set of a perturbed dynamical system up until a first singularity develops. This makes the book very readable is stable under arbitrary asymptotically small perturbations. The Stability and suitable for students and applied mathematicians who want to gain Theorem is examined in detail in the first chapter, followed by a review more insight into the subtleties of the subject.”—SIAM REVIEW of basic results and methods—many original to the authors—for the 2004 / 165 PP., 16 ILLUS. / HARDCOVER / $139.00 solution of nonlinear diffusion equations. Further chapters provide a ISBN_13 978-0-8176-3243-4 ISBN_10 0-8176-3243-3 self-contained analysis of specific equations, with carefully-constructed SOFTCOVER / $59.95 theorems, proofs, and references. ISBN_13 978-0-8176-3781-1 2004 / 377 PP., 10 ILLUS. / HARDCOVER / $99.00 ISBN_10 0-8176-3781-8 ISBN_13 978-0-8176-4146-7 PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS, ISBN_10 0-8176-4146-7 VOL. 57 PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS, VOL. 56

2001 Ferran Sunyer i Balaguer Prize Winner Flow Lines and Algebraic Invariants The Symmetry Perspective in Contact Form Geometry Abbas Bahri, Rutgers University, Piscataway, NJ From Equilibrium to Chaos in Phase Space and Physical Space “The approach of the author … has led him throughout the years to the introduction of several new concepts, such as true and false critical Martin Golubitsky, University of Houston, TX and points at infinity and cones associated to such points, as well as the Ian Stewart, University of Warwick, Coventry, UK introduction of novel algebraic tools, and to the discovery of several in- “This book was awarded the Ferran Sunyier i Balaguer Prize for 2001, teresting phenomena. The monograph under review gives an account and I am sure that it will be a very useful resource not only for researchers of all that. It discusses with a passionate style a number of results, also in this area but also for those who want to obtain the benefits of using this providing suggestions for further research.”—MATHEMATICAL REVIEWS approach in applications.” —BULLETIN OF THE AMS (Review of hardcover edition) “This text features a careful treatment of flow lines and algebraic in- “The title gives the program of this nice book: the world seen from the variants in contact form geometry, a vast area of research connect- symmetry point of view. In the past years we have seen a great number of ed to symplectic field theory, pseudo-holomorphic curves, and Gro- papers explaining experiments and other observations in science using bi- mov-Witten invariants (contact cohomology) … Fully detailed, explicit furcation and dynamical systems theory in the context of symmetry break- proofs and a number of suggestions for further research are provided ing. The authors of this book have shaped this development . … The theo- throughout.”—L’ENSEIGNEMENT MATHÉMATIQUE ry which is presented … is illustrated by many diagrams and figures . … Of 2003 / 219 PP., 50 ILLUS. / HARDCOVER / $89.95 course in this book the authors cannot give complete proofs of all relevant ISBN_13 978-0-8176-4318-8 ISBN_10 0-8176-4318-4 statements. But this reflects the spirit of the book, which is to provide ex- PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS, periments, describe examples and give (some) explanations of a part of VOL. 53 modern mathematics following one central theme: symmetry . … [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 2003 / 325 PP. / SOFTCOVER / $54.95 ISBN_13 978-3-7643-2171-0 ISBN_10 3-7643-2171-7

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The Nonlinear Limit-Point / 2003 Ferran Sunyer I Balaguer Prize Winner Limit-Circle Problem Miroslav Bartušek, Masaryk University, Brno, Czech Republic; Parabolic Quasilinear Zuzana Došlá, Masaryk University, Brno, Czech Republic; and John R. Graef, University of Tennessee, Chattanooga, TN Equations “This is the first monograph which includes nonlinear differential equa- Minimizing Linear tions. Apart from dealing with nonlinear problems, a substantial part Growth Functionals is devoted to an overview on the linear case, with an extensive list Fuensanta Andreu-Vaillo, Universidad of references for further reading … Conditions for continuability of all de Valencia, Burjassot, Spain; solutions are given, as well as necessary conditions and sufficient con- Vicent Caselles, Universidad Pompeu ditions for limit-circle type. Also, boundedness and (non)oscillation of Fabra, Barcelona, Spain; and solutions are investigated.” —ZENTRALBLATT MATH José M. Mazon, Universidad de Valencia, First posed by Hermann Weyl in 1910, the limit–point/limit–circle prob- Burjassot, Spain lem has inspired, over the last century, several new developments in “This book is well written … [and] should be of interest to anyone study- the asymptotic analysis of nonlinear differential equations. This mono- ing image reconstruction and to anyone in PDEs trying to see what kinds graph traces the evolution of this problem from its inception to its mod- of modern applications abound for the subject.” —MATHEMATICAL REVIEWS ern-day extensions to the study of deficiency indices and analogous properties for nonlinear equations. “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 The book discusses the problem in the linear case, as Weyl originally emphasis on the applications related to image restoration and nonlin- stated it, and then proceeds to a generalization for nonlinear higher- ear filters . … The book is written with great care, paying also a lot of at- order equations. The authors distill the classical theorems for second tention to the bibliographical and historical notes. It is a recommended and higher-order linear equations, and carefully map the progression to reading for all researchers interested in this field.”—ZENTRALBLATT MATH nonlinear limit–point results. The relationship between the limit–point/ 2004 / 340 PP. / HARDCOVER / $129.00 limit–circle properties and the boundedness, oscillation, and conver- ISBN_13 978-3-7643-6619-3 gence of solutions is explored, and in the final chapter, the connection ISBN_10 3-7643-6619-2 between limit–point/limit–circle problems and spectral theory is ex- PROGRESS IN MATHEMATICS, VOL. 223 amined in detail. With over 120 references, many open problems, and illustrative examples, this work will be valuable to graduate students and researchers in differential equations, functional analysis, operator theory, and related fields. Variational Problems in 2004 / 164 PP. / SOFTCOVER / $69.95 Riemannian Geometry ISBN_13 978-0-8176-3562-6 ISBN_10 0-8176-3562-9 Bubbles, Scans and Geometric Flows Paul Baird, Université de Bretagne Occidentale, Brest, France; Ahmad El Soufi, Université de Tours, France; and Ali Fardoun and Rachid Regbaoui, both, Université de Bretagne Kolmogorov Equations for Occidentale, Brest, France (Eds.) Stochastic PDEs This book collects invited contributions by specialists in the domain of Giuseppe Da Prato, Centre de Recerca Matemàtica, Barcelona, Spain elliptic partial differential equations and geometric flows. The articles The subject of this book is stochastic partial differential equations, in provide a balance between introductory surveys and the most recent particular, reaction-diffusion equations, Burgers and Navier-Stokes research, with a unique perspective on singular phenomena. Notions equations, and the corresponding Kolmogorov equations. Several re- such as scans and the study of the evolution by curvature of networks sults were proved by the author and his collaborators and appear in of curves are completely new and lead the reader to the frontiers of book form for the first time. the domain. The book will be of interest to postgraduate students and researchers in the fields of elliptic and parabolic partial differential equa- Presenting the basic elements of the theory in a simple and compact tions that arise from variational problems, as well as researchers in way, the book covers a one-year course directed to graduate students related fields such as particle physics and optimization. in mathematics or physics. The only prerequisites are basic probability 2004 / 148 PP. / HARDCOVER / $129.00 (including finite dimensional stochastic differential equations), basic ISBN_13 978-3-7643-2432-2 functional analysis, and some elements of the theory of partial differ- ISBN_10 3-7643-2432-5 ential equations. PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS, VOL. 59 2004 / 182 PP. / SOFTCOVER / $49.95 ISBN_13 978-3-7643-7216-3 ISBN_10 3-7643-7216-8 ADVANCED COURSES IN MATHEMATICS–CRM BARCELONA

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Advances in Spatial Patterns Dynamic Equations Higher Order Models in on Time Scales Physics and Mechanics L.A. Peletier, Leiden University, Martin Bohner, University of Missouri- The Netherlands and Rolla, MO and Allan Peterson, University W.C. Troy, University of Pittsburgh, Pittsburgh, PA of Nebraska, Lincoln, NE (Eds.) “The book is on the one hand written for From a review of Dynamic Equations mathematicians and mathematical physi- on Time Scales: cists, who want to learn about this fascinating “The monograph under review comes at subject, and on the other hand also acces- an excellent time in the rapid development sible to graduate students. One finds a large of dynamic equations on time scales. Both amount of exercises and open problems that authors are authorities in this field of study and they have produced can serve as a starting point for further research … The authors have pro- an excellent introduction to it. Much of the material is accessible to duced a well-written book, which gives a good picture of what is known upper-level undergraduate mathematics majors, and yet, the results about the canonical equation.”—QUANTUM INFORMATION AND COMPUTATION and the techniques are pertinent to active researchers in the area.” “The book is very well written in a very clear and readable style, which —MATHEMATICAL REVIEWS makes it accessible to a nonspecialist or graduate student. There are a The subject of dynamic equations on time scales continues to be a rapidly large number of exercises … as well as a good number of open prob- growing area of research. Behind the main motivation for the subject lies lems. There are also a large number of numerically computed graphs the key concept that dynamic equations on time scales is a way of unify- of branching curves and bifurcation curves throughout the book, which ing and extending continuous and discrete analysis. This work goes be- provide insights into the mathematically formulated results. The book yond an earlier introductory text Dynamic Equations on Time Scales: An is a valuable contribution to the literature, for both the specialist and Introduction with Applications (ISBN 0-8176-4225-0) and is designed the nonspecialist reader.”—MATHEMATICAL REVIEWS for a second course in dynamic equations at the graduate level. It will 2001 / 360 PP., 289 ILLUS. / HARDCOVER / $89.95 also be valuable to pure and applied mathematicians in the field. ISBN_13 978-0-8176-4110-8 ISBN_10 0-8176-4110-6 2003 / 360 PP. / HARDCOVER / $79.95 PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS, VOL. 45 ISBN_13 978-0-8176-4293-8 ISBN_10 0-8176-4293-5

Energy Methods for Free Stability of Time-Delay Systems Keqin Gu, Southern Illinois University at Edwardsville, Edwardsville, IL; Boundary Problems Vladimir L. Kharitonov, CINVESTAV-IPN, Mexico; and Applications to Nonlinear PDEs and Fluid Jie Chen, University of California, Riverside, CA Mechanics “This book is written by famous scientists in the area of time-delay sys- S. N. Antontsev, University of Beira Interior, Covilha, Portugal; tems. It presents a systematic treatment of the theory of such systems J. I. Díaz, Universidad Complutense de Madrid, Spain; and and their stability. It is devoted to the study of the stability of time-delay S. Shamarev, University of Oviedo, Spain systems, an area long pursued by mathematicians, physical and life scientists, engineers, and economists . … The book is well written and “The book contains some new unpublished results. It will appeal to contains a number of examples.”— ZENTRALBLATT MATH researchers in partial differential equations, nonlinear analysis, and continuum mechanics.”—ZENTRALBLATT MATH “The last 10-15 years have witnessed a renewed interest in time-delay control systems because of new problems, new models, and new “Very important and useful monograph … The book is addressed to techniques. This book has many useful features that complement the pure or applied mathematicians at universities and in industry and prior literature . … The reader can find useful information about soft- also to graduate level students. All results are presented in a systemat- ware implementation and computational complexity . … The authors ic and self-contained manner, precise proofs being usually sufficiently are experts in the field, and they relate their own experience. The book detailed. The topic makes the book appealing for any specialist inter- can be useful to engineers, applied mathematicians, and graduate ested in applications of energy methods for free boundary problems in students.”—IEEE CONTROL SYSTEMS MAGAZINE nonlinear PDEs and fluid mechanics.”—MATHEMATICAL REVIEWS 2003 / 353 PP., 16 ILLUS. / HARDCOVER / $79.95 2001 / 344 PP., 16 ILLUS. / HARDCOVER / $89.95 ISBN_13 978-0-8176-4212-9 ISBN_13 978-0-8176-4123-8 ISBN_10 0-8176-4212-9 ISBN_10 0-8176-4123-8 CONTROL ENGINEERING PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS, VOL. 48

60 Order By Phone: 1-800-777-4643 • Fax: 201-348-4505 • Or Online: www.birkhauser.com Applied Mathematics

Elementary Functions Generalized Collocations Methods Algorithms and Implementation Solutions to Nonlinear Problems Using Second Edition Mathematica® Jean-Michel Muller, CNRS-Laboratoire Nicola Bellomo, Bertrand Lods, Roberto Revelli, LIP, Lyon, France Luca Ridolfi, all Politecnico di Torino, Italy “In summary, this book seems like an es- Analysis of nonlinear models and problems is crucial in the application sential reference for the expert. More impor- of mathematics to real-world problems. This book approaches this im- tantly, this is an interesting book for the curi- portant topic by focusing on collocation methods for solving nonlinear ous. In this case, you’ll probably learn many evolution equations and applying them to a variety of mathematical interesting things from this book. If you teach problems, such as wave motion models, hydrodynamic models of ve- numerical analysis or approximation theory, hicular traffic flow, convection-diffusion models, reaction-diffusion mod- then this book will give you some good examples to discuss in class. els, and population dynamics models. There a few classic books on algorithms for computing elementary Generalized Collocation Methods is written for graduate students, ap- functions . … These books focused on software implementation using plied scientists, and engineers with an interest in modeling real-world polynomial approximations. Perhaps Muller’s book is destined to be- systems by differential or operator equations. It may be used as a text- come a new classic in this subject, but only time will tell . … Muller’s book book in graduate courses on modeling and nonlinear differential equa- contains few theorems and even fewer proofs. It does contain many nu- tions, or as a self-study resource for applied scientists and engineers merical examples, complete with Maple code . … In summary, this book with an interest in problem-solving techniques for nonlinear problems. seems like an essential reference for the experts (which I’m not). More 2007 / APPROX. 200 PP., 61 ILLUS. / HARDCOVER / $74.95 (TENT.) importantly, this is an interesting book for the curious (which I am). In ISBN_13 978-0-8176-4525-0 ISBN_10 0-8176-4525-X this case, you’ll probably learn many interesting things from this book. MODELING AND SIMULATION IN SCIENCE, ENGINEERING AND TECHNOLOGY If you teach numerical analysis or approximation theory, then this book will give you some good examples to discuss in class.”—MAA Reviews New to the second edition: Advances in Mathematical Finance • Number of revisions and additions, which incorporate numerous Robert J. Elliott, University of Calgary, Calgary, AB, Canada; new results obtained during the last few years. Michael C. Fu, University of Maryland, College Park, MD; • New algorithms invented since 1997—such as Matula’s bipartite Robert A. Jarrow, Cornell University, Ithaca, NY; method, another table-based method due to Ercegovac, Lang, Ju-Yi J. Yen, Vanderbilt University, Nashville, TN (Eds.) Tisserand, and Muller—as well as a new chapter on multiple-precision arithmetic have been added. This self-contained volume brings together a collection of chapters by some of the most distinguished researchers and practitioners in the 2005 / 266 PP. / HARDCOVER / $59.95 ISBN_13 978-0-8176-4372-0 field of mathematical finance and financial engineering. Presenting ISBN_10 0-8176-4372-9 state-of-the-art developments in theory and practice, the book has real- world applications to fixed-income and credit risk models, CDO pricing, tax rebates, tax arbitrage, and tax equilibrium. The book will be a valuable resource for graduate students, researchers, and practitioners in A Graph-Theoretic Approach to mathematical finance and financial engineering. Enterprise Network Dynamics Contributors include: H. Albrecher, D. Brody, P. Carr, E. Eberlein, Horst Bunke, University of Bern, Switzerland; R.J. Elliott, M. Fu, H. Geman, A. Hirsa, L. Hughston, R. Jarrow, X. Jin, W. Kluge, Peter J. Dickinson and Miro Kraetzl, both Defense Science and S.A. Ladoucette, A. Macrina, F. Milne, M. Musiela, P. Protter, W. Schoutens, Technology Organization, Adelaide, SA, Australia; E. Seneta, K. Shimbo, R. Sircar, J. van der Hoek, M. Yor, T. Zariphopoulou. Walter D. Wallis, Southern Illinois University, Carbondale, IL 2007 / APPROX. 310 PP., 50 ILLUS. / HARDCOVER / $79.95 (TENT.) ISBN_13 978-0-8176-4544-1 Networks have become nearly ubiquitous and increasingly complex, and ISBN_10 0-8176-4544-1 their support of modern enterprise environments has become fundamen- APPLIED AND NUMERICAL HARMONIC ANALYSIS tal. 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-the-art applications of graph theory in analysis of dynamic communication networks, dynamic databasing, and knowledge management. 2007 / 222 PP., 110 ILLUS. / HARDCOVER / $69.95 ISBN_13 978-0-8176-4485-7 ISBN_10 0-8176-4485-7 PROGRESS IN COMPUTER SCIENCE AND APPLIED LOGIC, VOL. 24

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A Software-Defined Modeling of Biological Materials GPS and Francesco Mollica, Universita di Ferrara, Italy; Luigi Preziosi, Politecnico di Torino, Torino, Italy; Galileo Receiver Kumbakonam R. Rajagopal, University of Texas A&M, College A Single-Frequency Approach Station, TX (Eds.) Kai Borre, and Soren Holdt Jensen, In modeling and subsequent mathematical treatment, many biomechan- both Aalborg University, Aalborg, Denmark; ical problems related to different parts of the human body share very Dennis M. Akos, University of Colorado, similar basic ideas; however, because the applications examined are very Boulder, CO; Nicolaj Bertelsen, Klarup, different, the relevant literature is widely spread across journals with dif- Denmark; Peter Rinder, Aalborg, Denmark fering styles and often mutually nonintersecting communities of readers, e.g., engineers, biologists, and medical doctors. This book and companion DVD provide hands-on exploration of new technologies This volume addresses this situation to a certain degree by collecting sev- in the rapidly growing field of satellite navigation receivers. One of the eral survey papers by actively working specialists, dealing with some of the unique features of the work is the interactive approach used, giving most important problems—both theoretical and practical— in biomechan- readers the ability to construct their own Global Navigation Systems ics. This unique collection brings to the forefront the central role played by (GNSS) receivers. A complete GPS software receiver implemented us- modeling in general, and the modeling of mechanical considerations that ing MATLAB code as well as GPS and GIOVE-A signal recordsóavailable have an effect in the biology, chemistry, and physics of living matter. on the companion cross-platform DVD—allows readers to change vari- 2007 / APPROX. 400 PP., 100 ILLUS. / HARDCOVER / $89.95 (TENT.) ISBN_13 978-0-8176-4410-9 ous parameters and immediately see their effects. ISBN_10 0-8176-4410-5 The book is aimed at applied mathematicians, electrical engineers, MODELING AND SIMULATION IN SCIENCE, ENGINEERING AND TECHNOLOGY geodesists, and graduate students. It may be used as a textbook in various GPS technology and signal processing courses, or as a self- study reference for anyone working with satellite navigation receivers. Supplementary course material for instructors is available at Representation and Control of http://gps.aau.dk/softgps. Infinite-Dimensional Systems 2006 / 200 PP., 98 ILLUS. / SOFTCOVER With DVD / $79.95 Second Edition ISBN_13 978-0-8176-4390-4 ISBN_10 0-8176-4390-7 Alain Bensoussan, University of Texas at Dallas, Richardson, TX; APPLIED AND NUMERICAL HARMONIC ANALYSIS Giuseppe Da Prato, Scuola Normale Superiore, Pisa, Italy; Michel C. Delfour, Université de Montréal, Canada; Sanjoy K. Mitter, Massachusetts Institute of Technology, Cambridge, MA Atmospheric and Space Flight Reviews of the previous edition: Dynamics “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 ® Modeling and Simulation with MATLAB and very recently have found a satisfactory solution . … Many readers will Simulink® appreciate the concise exposition… Ashish Tewari, Indian Institute of Technology, Kanpur, India

Modern aerospace vehicles, such as the space shuttle, other launch ve- This unified, revised second edition of a two-volume set is a self-con- hicles, and long-range ballistic missiles, do not discriminate between at- tained account of quadratic cost optimal control for a large class of mospheric and space flight. Most texts on flight dynamics, however, make infinite-dimensional systemsóa topic with a wide range of challenging this artificial distinction and therefore do not simultaneously cover aircraft applications. The work is a key reference for anyone working with these and spacecraft. Bridging this gap in the literature, Atmospheric and Space applications, which arise from new phenomenal studies or technologi- Flight Dynamics is a unified presentation, demonstrating that the two dis- cal developments, and more stringent design requirements. It will be ciplines have actually evolved from the same set of physical principles. useful for mathematicians, researchers, graduate students, and engi- Key features include: numerical examples and simulations that uti- neers interested in the field of control. lize MATLAB® and Simulink®; realistic and instructive simulations that 2007 2nd ed., XXVIII/580 PP., 5 ILLUS./HARCOVER/$89.95 ISBN_13 978-0-8176-4461-1 are usually not found in books on the same topic; and examples that ISBN_10 0-8176-4461-X allow readers to easily build their own simulations for aircraft, missiles, SYSTEMS & CONTROL: FOUNDATIONS & APPLICATIONS launch vehicles, reentry vehicles, and spacecraft. Primarily useful as a textbook for advanced undergraduate and beginning graduate-level students, the work is also an excellent reference or self-study guide for researchers and practitioners in aerospace engineering, aviation, mechanical engineering, dynamics, astrodynamics, aeronautics, and astronautics. 2006 / APPROX. 576 PP., 207 ILLUS. / HARDCOVER / $89.95 ISBN_13 978-0-8176-4437-6 ISBN_10 0-8176-4437-7 MODELING AND SIMULATION IN SCIENCE, ENGINEERING AND TECHNOLOGY

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Transport Phenomena and Contemporary Cryptology Kinetic Theory Dario Catalano, Ecole Normale Supérieure, Paris, France; Ronald Cramer, CWI, Amsterdam, The Netherlands; Applications to Gases, Semiconductors, Ivan Damgard, University of Aarhus, Denmark; Photons, and Biological Systems Giovanni Di Crescenzo, Telcorida Technologies, Inc., Morristown, NJ; Carlo Cercignani, Politecnico Milano, Italy; David Pointcheval, Ecole Normale Supérieure, Paris, France; Ester Gabetta, University of Pavia, Italy (Eds.) Tsuyoshi Takagi, Future University-Hakodate, Hokkaiodo, Japan The study of kinetic equations related to gases, semiconductors, pho- The aim of this text is to treat selected topics of the subject of contempo- tons, and other systems has developed rapidly in recent years because rary cryptology, structured in five quite independent but related themes: of its role as a mathematical tool in many applications in areas such efficient distributed computation modulo a shared secret, multiparty as engineering, meteorology, biology, chemistry, materials science, and computation, foundations of modern cryptography, provable security for pharmacy. Written by leading specialists in their respective fields, this public key schemes and efficient and secure public-key cryptosystems. book presents various examples of these applications, with an empha- This book is intended for graduates and postgraduates in mathematics sis on both mathematical properties and their physical meaning. and computer science, researchers, and professionals in cryptology. Transport Phenomena and Kinetic Theory is an excellent self-study ref- 2005I / 237 PP. / SOFTCOVER / $44.95 erence for graduate students, researchers, and professionals working in ISBN_13 978-3-7643-7294-1 ISBN_10 3-7643-7294-X pure and applied mathematics, mathematical physics, and engineer- ADVANCED COURSES IN MATHEMATICS–CRM BARCELONA ing. It may also be used in a course or seminar on selected topics in transport phenomena or applications of the Boltzmann equation to many-particle transport. 2007/272 PP., 26 ILLUS./HARDCOVER/$79.95 Optimal Stopping and ISBN_13 978-0-8176-4489-5 ISBN_10 0-8176-4489-X Free-Boundary Problems MODELING AND SIMULATION IN SCIENCE, ENGINEERING AND TECHNOLOGY Goran Peskir, The University of Manchester, UK; Albert Shiryaev, Steklov Mathematical Institute, Moscow, Russia New Material and Original Features of the Second Edition: Advances in Discrete Tomography • Part I on finite dimensional controlled dynamical systems contains and its Applications new material: an expanded chapter on the control of linear systems Gabor T. Herman, City University of New York, NY; including a glimpse into H-infiinity theory and dissipative systems, Attila Kuba, University of Szeged, Hungary (Eds.) and a new chapter on linear quadratic two-person zero-sum differential games. Advances in Discrete Tomography and its Applications is a unified presentation of new methods, algorithms, and select applications that • A unique chapter on semigroup theory and interpolation of linear are the foundations of multidimensional image construction and recon- operators brings together advanced concepts and techniques that struction. The self-contained survey chapters, written by leading math- are usually treated independently. ematicians, engineers, and computer scientists, present cutting-edge • The material on delay systems and structural operators is not avail- research and results in the field. able elsewhere in book form. Three main areas are covered: theoretical results, algorithms, and practical The book aims at disclosing a fascinating connection between optimal applications. Following an historical and introductory overview of the field, stopping problems in probability and free-boundary problems in analysis the book explores the various mathematical and computational prob- using minimal tools and focusing on key examples. The general theory lems of discrete tomography with an emphasis on new applications. of optimal stopping is exposed at the level of basic principles in both dis- 2007 / APPROX. 455 PP., 125 ILLUS. / HARDCOVER / $99.00 crete and continuous time covering martingale and Markovian methods. ISBN_13 978-0-8176-3614-2 Methods of solution explained range from classic ones (such as change ISBN_10 0-8176-3614-5 of time, change of space, change of measure) to more recent ones (such APPLIED AND NUMERICAL HARMONIC ANALYSIS as local time-space calculus and nonlinear integral equations). A detailed chapter on stochastic processes is included making the material more Also by G. T. Herman & A. Kuba accessible to a wider cross-disciplinary audience. The book may be viewed as an ideal compendium for an interested reader Discrete Tomography who wishes to master stochastic calculus via fundamental examples. Areas of application where examples are worked out in full detail include financial Foundations, Algorithms, and Applications mathematics, financial engineering, mathematical statistics. 1999/ 479 PP., 155 ILLUS. / HARDCOVER / $99.00 2006 / 500 PP. / HARDCOVER / $59.95 ISBN_13 978-0-8176-4101-6 ISBN_13 978-3-7643-2419-3 ISBN_10 0-8176-4101-7 ISBN_10 3-7643-2419-8 APPLIED AND NUMERICAL HARMONIC ANALYSIS LECTURES IN MATHEMATICS. ETH ZURICH

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Mathematical Fourier Analysis and Convexity Modeling of Luca Brandolini, Università di Bergamo, Italy; Leonardo Colzani, Università di Milano-Bicocca, Italy; Complex Biological Alex Iosevich, University of Missouri-Columbia, Columbia, MO; Systems Giancarlo Travaglini, Università di Milano-Bicocca, Italy (Eds.) This book presents both a broad overview of Fourier analysis and convex- A Kinetic Theory Approach ity, as well as an intricate look at applications in some specific settings; it Abdelghani Bellouquid, University will be useful to graduate students and researchers in harmonic analysis, Cadi Ayad, Ecole Nationale des Sciences convex geometry, functional analysis, number theory, computer science, Appliquées, Safi, Morocco; and combinatorial analysis. A wide audience will benefit from the careful Marcello Delitala, Politecnico di Torino, demonstration of how Fourier analysis is used to distill the essence of Italy many mathematical problems in a natural and elegant way. This book describes the evolution of several socio-biological systems Contributors: J. Beck, C. Berenstein, W.W.L. Chen, B. Green, H. Groemer, using mathematical kinetic theory. Specifically, it deals with modeling A. Koldobsky, M. Kolountzakis, A. Magyar, A.N. Podkorytov, B. Rubin, and simulations of biological systems—comprised of large populations D. Ryabogin, T. Tao, G. Travaglini, A. Zvavitch. of interacting cells—whose dynamics follow the rules of mechanics as 2004 / 280 PP.,32 ILLUS. / HARDCOVER / $84.95 well as rules governed by their own ability to organize movement and ISBN_13 978-0-8176-3263-2 biological functions. The authors propose a new biological model for ISBN_10 0-8176-3263-8 APPLIED AND NUMERICAL HARMONIC ANALYSIS the analysis of competition between cells of an aggressive host and cells of a corresponding immune system. The book will be a valuable resource for applied mathematicians as well as researchers in the field of biological sciences. It may be used for advanced Introduction to graduate courses and seminars in biological systems modeling with applications to collective social behavior, immunology, and epidemiology. Computational Biology 2006 / 188 PP., 47 ILLUS. / HARDCOVER / $79.95 An Evolutionary Approach ISBN_13 978-0-8176-4395-9 Thomas Wiehe, Freie Universität Berlin, ISBN_10 0-8176-4395-8 MODELING AND SIMULATION IN SCIENCE, ENGINEERING AND TECHNOLOGY Germany; Bernhard Haubold, University of Applied Sciences Weihenstephan, Freising, Germany Neural Networks and Sea Time Analysis of molecular sequence data is the Series main subject of this introduction to computational biology. There are two closely Reconstruction and Extreme-Event Analysis connected aspects to biological sequences: (i) their relative position in Brunello Tirozzi, Stefano Pittalis, Antonello Bruschi, the space of all other sequences, and (ii) their movement through this Sara Morucci, Enrico Ferraro, all University of Rome sequence space in evolutionary time. Accordingly, the first part of the “La Sapienza,” Rome, Italy; book deals with classical methods of sequence analysis: pairwise align- Silvia Puca, European Meteorological Satellite Org., Rome, Italy; ment, exact string matching, multiple alignment, and hidden Markov Stefano Corsini, Agenzia per la Protezione dell’Ambiente e per i Servizi models. In the second part evolutionary time takes center stage and Tecnici, Rome, Italy phylogenetic reconstruction, the analysis of sequence variation, and the Increasingly, neural networks are used and implemented in a wide dynamics of genes in populations are explained in detail. In addition, range of fields and have become useful tools in probabilistic analysis the book contains a computer programs with a graphical user interface and prediction theory. This book—unique in the literature—studies the that allows the reader to experiment with a number of key concepts application of neural networks to the analysis of time series of sea data, developed by the authors. namely significant wave heights and sea levels. The particular problem This textbook is intended for student enrolled in courses in computa- examined as a starting point is the reconstruction of missing data, a tional biology or bioinformatics as well as for molecular biologist, math- general problem that appears in many cases of data analysis. ematicians, and computer scientists. This careful blend of theory and applications is an excellent introduction 2006 / 250 PP. / HARDCOVER WITH CD-ROM/$49.95 ISBN_13 978-3-7643-6700-8 to the use of artificial neural networks, which may encourage readers ISBN_10 3-7643-6700-8 to try analogous approaches in other important application areas. Re- searchers, practitioners, and advanced graduate students in neural networks, hydraulic and marine engineering, prediction theory, and data analysis will benefit from the results and novel ideas presented in this useful resource. 2006 / 179 PP., 64 ILLUS. / HARDCOVER / $89.95 ISBN_13 978-0-8176-4347-8 ISBN_10 0-8176-4347-8 MODELING AND SIMULATION IN SCIENCE, ENGINEERING AND TECHNOLOGY

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Fundamentals of Harmonic Analysis Multibody Dynamics and Applications Theory and Applications In Honor of J.J. Benedetto Farid Amirouche, University of Illinois, Christopher Heil, Georgia Institute of Chicago, IL Technology, Atlanta, GA (Ed.) “The book is well-written with good organi- John J. Benedetto has had a profound influ- zation. It has good quality graphics. It clearly ence not only on the direction of harmonic represents a considerable effort by the au- analysis and its applications, but also on thor to present a state-of-the-art exposition. the entire community of people involved The book should be of interest and use to in the field. This self-contained volume in practitioners and researches as well as to honor of John covers a wide range of top- students. It brings together methodologies from various fields into a sin- ics in harmonic analysis and related areas, including weighted-norm gle volume. Purchase by libraries is recommended.”—ZENTRALBLATT MATH inequalities, frame theory, wavelet theory, time-frequency analysis, and sampling theory. The invited chapters pay tribute to John’s many “This textbook offers a comprehensive exposition of contemporary achievements and express an appreciation for both the mathematical multibody dynamics elaborated by an expert in and an experienced and personal inspiration he has given to so many students, coauthors, teacher of the field. There are five features that distinguish this publica- and colleagues. tion: comprehensivity, orientation towards computer implementation, utilization of matrix algebra, teaching-by-examples methodology, and Although the scope of the book is broad, chapters are clustered by embedding in the author’s own research accomplishments.... [T]his is topic to provide authoritative expositions that will be of lasting interest. an excellent textbook for undergraduate, graduate, and doctoral stu- The original papers collected here are written by prominent, well-re- dents of mechanical engineering, industrial physics and robotics; it spected researchers and professionals in the field of harmonic analy- may also be recommended as a reference text for researchers in these sis. Harmonic Analysis and Applications is an excellent reference for areas.”—Mathematical Reviews graduate students, researchers, and professionals in pure and applied mathematics, engineering, and physics. Because of its versatility in analyzing a broad range of applications, multibody dynamics has grown in the past two decades to be an impor- Contributors: A. Aldroubi, L. Baggett, G. Benke, C. Cabrelli, P.G. Casazza, tant tool for designing, prototyping, and simulating complex articulated O. Christensen, W. Czaja, M. Fickus, J.-P. Gabardo, K. Gröchenig, K. Guo, mechanical systems. This textbook brings together diverse concepts E. Hayashi, C. Heil, H.P. Heinig, J.A. Hogan, E. Kovačević, D. Labate, of dynamics, combining the efforts of many researchers in the field of J.D. Lakey, D. Larson, M.T. Leon, S. Li, W.-Q Lim, A. Lindner, U. Molter, mechanics. Bridging the gap between dynamics and engineering ap- A.M. Powell, B. Rom, E. Schulz, T. Sorrells, D. Speegle, K.F. Taylor, J. Tremain, plications such as microrobotics, virtual reality simulation of interactive D. Walnut, G. Weiss, E. Wilson, G. Zimmermann mechanical systems, nanomechanics, flexible biosystems, crash simu- 2006 / 374 PP.,13 ILLUS. / HARDCOVER / $89.95 lation, and biomechanics, the book puts into perspective the impor- ISBN_13 978-0-8176-3778-1 ISBN_10 0-8176-3778-8 tance of modeling in the dynamic simulation and solution of problems APPLIED AND NUMERICAL HARMONIC ANALYSIS in these fields. Junior/senior undergraduates and first-year graduate engineering students taking a course in dynamics, physics, control, robotics, or biomechanics will find this a useful book with a strong computer orientation Applied Laplace Transforms towards the subject. The work may also be used as a self-study resource and z-Transforms for Scientists or research reference for practitioners in the above-mentioned fields. 2005 / 720 PP., 215 ILLUS. / HARDCOVER / $129.00 and Engineers ISBN_13 978-0-8176-4236-5 ISBN_10 0-8176-4236-6 A Computational Approach Using a Mathematica® Package Urs 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 This book presents the theory and applications of Laplace and z-transforms together with a Mathematica® package developed by the author. The package substantially enhances the built-in Laplace and z-transforms facilities of Mathematica®. The emphasis of the work is on the computational and applied side, particularly in the fields of control engineering, electrical engineering, and mechanics (heat conduction, diffusion, vibrations). Many worked-out examples from engineering and sciences illustrate the applicability of the theory and the usage of the package. 2004 / 500 PP. / HARDCOVER WITH CD-ROM / $89.95 ISBN_13 978-3-7643-2427-8 ISBN_10 3-7643-2427-9

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An Introduction to Cellular Automaton Continuous-Time Modeling of Biological Stochastic Processes Pattern Formation Theory, Models, and Characterization, Applications to Finance, Applications, and Analysis Biology, and Medicine Andreas Deutsch, Dresden University of Vincenzo Capasso and Technology, Dresden, Germany and David Bakstein, Miriam Research Centre for Sabine Dormann University of Industrial and Applied Mathematics, Milan, Italy, Osnabrück, Germany both Univeristy of Miami, FL. With a Foreword by Philip K. Maini, Cen- “This is an introductory text on continuous tre for Mathematical Biology, Oxford, UK time stochastic processes and their applications to finance and biology. “This book focuses on [the] application of so-called lattice-gas cellular au- The book will be useful for applied mathematicians who are not proba- tomaton models to the field of biological pattern formation.... In the book, bilists to get a quick flavour of the techniques of stochastic calculus, the authors describe an interesting number of applications of the method in and for professional probabilists to get a quick flavour of the applica- the field of biological pattern formation. The examples include tumor devel- tions.”—ZENTRALBLATT MATH opment, population growth, swarming behavior, and cell sorting.... The book “This book provides a mathematical overview of the theory of continu- is a good starting point for scientists and students [who] would like to move ous-time stochastic processes, with emphasis on stochastic differential into the field of studying effects of spatial pattern formation in biology. The equations (SDEs). Applications in finance and population modelling introductory chapters are fun reading.... The introduction to the lattice-gas are also briefly reviewed . … The primary audience for this book will method is thorough and sound, and the array of applications of the method be mathematicians (both pure and applied) active in other areas who to systems of biological pattern formation is impressive and inspiring.... I par- require an introduction to stochastic theory. Scientists already working ticularly like the format of suggesting potential further projects at the end of in the applications of SDEs will also benefit from this mathematically each chapter, which shows that the field is only starting and many research rigorous reference text. The core of the text on Ito calculus...would be questions still have to be explored.”—Mathematical Biosciences suitable supplementary reading for graduate or advanced undergrad- While there are various books treating cellular automaton modeling, this in- uate students of stochastic theory . … The style of the text … is concise terdisciplinary work is the first one covering biological applications. The book and rigorous . … Each chapter concludes with a set of exercises inviting is aimed at researchers, practitioners, and students in applied mathematics, readers to prove supplementary results and review particular aspects mathematical biology, computational physics, bioengineering, and computer of the theory . … In summary, I have found this to be a useful reference science interested in a cellular automaton approach to biological modeling. text, and would recommend it to those wishing to delve in to the math- 2005 / 334 PP., 131 ILLUS. / HARDCOVER / $89.95 ematical theory of stochastic processes.”—UK Nonlinear News ISBN_13 978-0-8176-4281-5 2004 / 343 PP., 13 ILLUS. / HARDCOVER / $79.95 ISBN_10 0-8176-4281-1 ISBN_13 978-0-8176-3234-2 MODELING AND SIMULATION IN SCIENCE, ENGINEERING AND TECHNOLOGY ISBN_10 0-8176-3234-4 MODELING AND SIMULATION IN SCIENCE, ENGINEERING AND TECHNOLOGY Time–Frequency and Time–Scale An Introduction to Frames and Methods Riesz Bases Adaptive Decompositions, Uncertainty Principles, Ole Christensen, Technical University of Denmark, Lyngby, Denmark and Sampling Jeffrey A. Hogan, University of Arkansas, Fayetteville, AR and “The book is well written, the proofs are clear and not too terse, and Joseph D. Lakey, New Mexico State University, Las Cruces, NM the work is well suited for use as a textbook. The author has made many contributions to the theory of frames and Riesz bases, and the “[This book] covers an enormous range in time-frequency analysis and book benefits from his scope and perspective.”—ZENTRALBLATT MATH time-scale analysis.... [It] is about methods and ideas. The main goal is to motivate, discuss, and describe important results and new develop- “The book is a well-written and detailed course into the theory of bases ments in time-frequency and time-scale analysis and frames in Hilbert spaces. The composition is very clear, and the proofs are well achieved … . In the basic chapters, a large number of …The resulting book is like a gigantic mosaic. Each facet describes an carefully chosen examples and exercises are included. That first part interesting result. While neighboring facets are not necessarily related can be used in a graduate course. The material of the later chapters in any formal way, the entire mosaic, when viewed from a distance, is more in the line of current research … . I recommend this book to displays a coherent and magnificent picture, the picture of time-fre- graduate students and researchers working in pure and applied math- quency and time-scale analysis. “—Bulletin of the AMS ematics. It will appeal to an audience interested in the theory behind “[The] book under review is written from a relatively novel perspective: its goal many signal processing tools stimulating further research.”—ZAA is to carefully and deeply study the similarities and differences between time- 2002 / 464 PP., 16 ILLUS. / HARDCOVER / $69.95 frequency and time-scale methods. Thus, one may view the present book ISBN_13 978-0-8176-4295-2 ISBN_10 0-8176-4295-1 as a continuation of the famous textbook of Ingrid Daubechies [Ten Lectures APPLIED AND NUMERICAL HARMONIC ANALYSIS on Wavelets] … In my opinion, the two books nicely complement each other and both are a ‘must have’ for everyone who is interested in a deeper understanding of time-frequency and time-scale methods.”—Zentralblatt MATH 2005 / 390 PP., 22 ILLUS. / HARDCOVER / $74.95 ISBN_13 978-0-8176-4276-1 ISBN_10 0-8176-4276-5 APPLIED AND NUMERICAL HARMONIC ANALYSIS

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Multiscale Potential Approximation Theory Theory From Taylor Polynomials to With Applications to Geoscience Wavelets Ole Christensen and Willi Freeden and Volker Michel, Khadija Laghrida Christensen, both, University of Kaiserslautern, Kaiserslautern, Technical University of Denmark, Lyngby, Germany Denmark “The book is devoted to well-posed and ill- “Approximation methods and wavelets posed boundary value problems arising in geo- have found many important applications science, elasticity, gravimetry and other areas, in signal processing. This well-written text- including satellite problems. New mathemati- book provides an elementary introduc- cal methods and fast computational schemes tion to approximation theory. The authors based on harmonic analysis and wavelet transforms are developed. The concentrate on the presentation of main ideas and demonstrate the book may be used for graduate-level courses in geomathematics, applied great influence of classical approximation theory on modern applied mathematics, and geophysics. It is also an up-to-date reference text for geomathematics. This book, with many illustrative examples, is easy to scientists, applied mathematicians, and engineers.”—ZENTRALBLATT MATH read…[and] will be very useful for anyone interested in approximation This self-contained text/reference provides a basic foundation for prac- theory and wavelets.”—ZENTRALBLATT MATH titioners, researchers, and students interested in any of the diverse ar- Key topics and features: eas of multiscale (geo)potential theory. • Description of wavelets in words rather than mathematical symbols Presented are multiscale approaches for numerous geoscientific problems, including geoidal determination, magnetic field reconstruction, • Elementary introduction to approximation using polynomials (Weier- deformation analysis, and density variation modelling. strass’ and Taylor’s theorems) 2004 / 509 PP., 127 ILLUS. / HARDCOVER / $89.95 • Introduction to infinite series, with emphasis on approximation-theo- ISBN_13 978-0-8176-4105-4 ISBN_10 0-8176-4105-X retic aspects APPLIED AND NUMERICAL HARMONIC ANALYSIS • Introduction to Fourier analysis • Discussion of the role of wavelets in digital signal processing and data compression, such as the FBI’s use of wavelets to store fingerprints Analytical Methods • Exercises that may be used in undergraduate and graduate courses on in Anisotropic infinite series and Fourier series. 2004 / 156 PP., 40 ILLUS. / SOFTCOVER / $34.95 Elasticity ISBN_13 978-0-8176-3600-5 ISBN_10 0-8176-3600-5 With Symbolic Computational APPLIED AND NUMERICAL HARMONIC ANALYSIS Tools Omri Rand, Technion–Israel Institute of Technology, Haifa, Israel and Vladimir Y. Rovenski, University of Haifa, Israel Computational Methods for Linear “The book is intended to be a self-contained Integral Equations reference for the topic and aimed at practic- Prem Kythe and Pratap Puri, both, University of New Orleans ing engineers who put the analytical approaches for anisotropic elas- “The monograph is devoted to numerical methods for solving one- ticity problems to practical use. Graduate, postgraduate and doctoral dimensional linear integral equations. Fredholm and Volterra integral students of mechanical engineering could benefit from using the book equations of first and second kinds are considered. The authors pay as well. This well-written book is a reader-friendly and well organized more attention to computational aspects of solving integral equations. handbook in the field of anisotropic elasticity. It can be highly recom- A lot of numerical examples and results of computations by computers mended for experts in Mechanics of Solids, engineers, and for graduate, are presented.”—MATHEMATICAL REVIEWS ZENTRALBLATT MATH postgraduate and doctoral students.”— 2002 / 528 PP., 12 ILLUS. / HARDCOVER / $109.00 This comprehensive textbook/reference focuses on the mathematical ISBN_13 978-0-8176-4192-4 ISBN_10 0-8176-4192-0 techniques and solution methodologies required to establish the foundations of anisotropic elasticity, and provides the theoretical background for composite material analysis. Specific attention is devoted to the potential of modern symbolic computational tools to support highly complex analytical solutions and their contribution to the rigor, analytical uniformity, and exactness of the derivation. The work will appeal to a broad audience working in mathematical modeling, including graduate students, applied mathematicians, numerical analysts, scientists, and engineers. Included is a CD-ROM with the symbolic codes (MAPLE; Versions 8 and 9) for the solutions presented, which may be activated to create numerous additional examples containing detailed expressions and graphics. 2005 / 451 PP., 167 ILLUS. / SOFTCOVER WITH CD-ROM / $79.95 ISBN_13 978-0-8176-4272-3 ISBN_10 0-8176-4272-2

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The Evolution of Methods of Applied Applied Harmonic Mathematics with a Analysis MATLAB Overview Models of the Real World Jon H. Davis, Queen’s University, Kingston, Ontario, Canada Elena Prestini, Università di Roma “Tor Vergata,” Rome, Italy “Overall, this textbook has an attractive format with lots of figures, programs, and for- “Can be thoroughly recommended to any mulas, and it presents, in a very traditional reader who is curious about the physical way, a body of material that is fundamen- world and the intellectual underpinnings tal in applied mathematics, science, and that have lead to our expanding under- engineering. It would make an excellent standing of our physical environment and textbook for courses focused around Fourier analysis and applications to our halting steps to control it. Everyone who uses instruments that to differential equations.”—SIAM Review are based on harmonic analysis will benefit from the clear verbal descriptions that are supplied.”—R. BRACEWELL, STANFORD UNIVERSITY “The aim of this book is to provide an introduction to a number of methods of applied mathematics, especially those arising from Fourier “Prestini … traces the development of harmonic analysis from its ori- analysis. Classical problems of [a] mathematical physics nature are gins to applications of the present. She begins with a biography of discussed throughout the book. Those problems represent the pretext Fourier and a brief description of the mathematics behind Fourier se- or the basis for the elaboration of mathematical models. The book ries, then turns to an overview of the many areas of science that have presents numerical schemes and analytical results as well.... This book benefited from Fourier’s results. The last seven chapters could be seen is excellent material for students of applied mathematics and engi- as a brief history of technology as Prestini takes readers from the early neers, covering the theory of Fourier analysis with interesting applica- days of telegraphy, radio, and the telephone, through human under- tions and numerical examples in MATLAB.”—ZENTRALBLATT MATH standing of sound and optics to more modern technologies such as X-ray crystallography, MRI, and radio astronomy—all filtered through Solutions manual available upon adoption of the text. the lens of harmonic analysis. A good read for anyone interested in 2004 / 721 PP., 300 ILLUS. / HARDCOVER / $79.95 applied mathematics . … Highly recommended. Upper-division under- ISBN_13 978-0-8176-4331-7 ISBN_10 0-8176-4331-1 CHOICE graduates through faculty.”— APPLIED AND NUMERICAL HARMONIC ANALYSIS “It is evident that a great deal of effort has been spent in the preparation of this book. The author has diligently worked to create a cogent, sensibly organized exposition. The text is supplemented with dozens of interesting pictures and graphs. The author certainly deserves to Sampling, Wavelets, be commended for writing in English, which (as she mentions in the and Tomography preface) is not her native tongue.”—MAA REVIEWS John Benedetto, University of Maryland, 2003 / 320 PP., 169 ILLUS. / SOFTCOVER / $59.95 ISBN_13 978-0-8176-4125-2 College Park, MD and Ahmed Zayed, ISBN_10 0-8176-4125-4 DePaul University, Chicago, IL (Eds.) APPLIED AND NUMERICAL HARMONIC ANALYSIS “The book places emphasis on all three themes it considers. It presents applications with a broad perspective . … The book, Modern Sampling Theory containing contributions of some of the renowned scientists in the field, is interesting Mathematics and Applications and informative, and presents an insightful John J. Benedetto, University of Maryland, College Park, MD and approach towards wavelets, sampling theo- Paulo J.S.G. Ferreira, Universidade de Aveiro, Aveiro, Portugal (Eds.) ry, and tomography. To conclude, the book is of immense value to the mathematically inclined researcher whose work centers around the ap- “The introduction (Chapter 1) gives an excellent overview of the his- plication of sampling theory.”—JOURNAL OF THE INDIAN INSTITUTE OF SCIENCE tory and development of sampling theory. It shows that the WSK sampling theory has roots in many classical areas of mathematics, such Sampling, wavelets, and tomography are three active areas of con- as harmonic analysis, number theory, and interpolation theory . … The temporary mathematics sharing common roots that lie at the heart introduction then proceeds to show how sampling theory is connected of harmonic and Fourier analysis. The advent of new techniques in to more recent topics in mathematical analysis, such as wavelets, Ga- mathematical analysis has strengthened their interdependence and led bor systems, density theorems, frames, and sampling in locally com- to some new and interesting results. pact abelian groups.”—MATHEMATICAL REVIEWS Aimed at mathematicians, scientists, and engineers working in signal “Engineers and mathematicians working in wavelets, signal process- and image processing and medical imaging, the work is designed to ing, and harmonic analysis, as well as scientists and engineers working be accessible to an audience with diverse mathematical backgrounds. on applications as varied as medical imaging and synthetic aperture Although the volume reflects the contributions of renowned mathema- radar, will find the book to be a modern and authoritative guide to ticians and engineers, each chapter has an expository introduction writ- sampling theory.“—PUBLICATIONES MATHEMATICAE ten for the non-specialist. 2001 / 440 PP., 30 ILLUS. / HARDCOVER / $89.95 2004 / 344 PP., 50 ILLUS. / HARDCOVER / $74.95 ISBN_13 978-0-8176-4023-1 ISBN_13 978-0-8176-4304-1 ISBN_10 0-8176-4023-1 ISBN_10 0-8176-4304-4 APPLIED AND NUMERICAL HARMONIC ANALYSIS APPLIED AND NUMERICAL HARMONIC ANALYSIS

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Wavelets and Signal An Introduction to Processing Linear and Lokenath Debnath, University of Texas Pan Nonlinear Finite American, Edinburg, TX (Ed.) “The Editor of this volume has performed a Element Analysis commendable job of compiling a set of ar- A Computational Approach ticles, a majority of which can be branded Prem K. Kythe and Dongming Wei, as excellent, into a single volume, which in- both, University of New Orleans, LA cludes state-of-the-art theoretical results as well as some applications. The book will be “This is an introductory textbook on finite useful for researchers as well as practicing element analysis and practice aimed at professionals, not only because of its contents, but also because of the students with diverse backgrounds from fact that it provides directions for future developments.”—Journal of the engineering, technology, physics, geophysics and applied mathemat- Indian Institute of Science ics. The book provides accessibility to all students, with a minimum of 2003 / 435 PP., 108 ILLUS. / HARDCOVER / $79.95 mathematical analysis . … The last chapter is dedicated to computer ® ISBN_13 978-0-8176-4235-8 programs in Mathematica , Ansys, Mathlab and Fortran. There are six ISBN_10 0-8176-4235-8 appendices, 87 examples and 148 exercises. The book ends with a APPLIED AND NUMERICAL HARMONIC ANALYSIS bibliography and a detailed subject index.”—MATHEMATICAL REVIEWS “This book is introductory in the sense of being accessible to students not only of mathematics, but also of the physical and the engineer- Wavelet Transforms and ing sciences once they have mastered the introductory mathematical courses . … Overall, the presentation is quite detailed regarding the Time-Frequency Signal Analysis needs of the practitioner with many examples to engineering, earth Lokenath Debnath, University of Texas Pan American, Edinburg, TX (Ed.) sciences, etc. (among others elasticity, vibrations, heat transfer, fluid flow; also eigenvalue problems), and special but important items not “This book is a great collection of recent material of recent investiga- so often covered in other texts, e.g., how to cope with the specific tion on wavelet and time-frequency analysis that is not covered in the difficulties arising in polar coordinates. Both numerous exercises and literature . … The book is an important source for all readers interested codes in Ansys, Fortran, Mathematica® and MATLAB direct the reader in a broad perspective. In particular, a wide variety of applications towards experimentation of his own.”—Monatshefte fur Mathematik are presented that are important for interdisciplinary collaborative research.”—ZAA Supporting material and selected solutions to problems are 2001 / 456 PP., 86 ILLUS. / HARDCOVER / $79.95 available at the authors’ websites. ISBN_13 978-0-8176-4104-7 2004 / 445 PP., 152 ILLUS. / HARDCOVER / $79.95 ISBN_10 0-8176-4104-1 ISBN_13 978-0-8176-4308-9 APPLIED AND NUMERICAL HARMONIC ANALYSIS ISBN_10 0-8176-4308-7 http://www.math.uno.edu/fac/pkythe.html http://www.math.uno.edu/fac/dwei.html Wavelet Transforms and Their Applications Advances in Multifield Theories of Lokenath Debnath, University of Texas Pan American, Edinburg, TX Continua with Substructure “It contains a wealth of information that should make it useful in sig- Gianfranco Capriz, Università di Pisa, Italy and nal processing and perhaps some other areas of engineering … I like Paolo M. Mariano, Università di Roma La Sapienza, Italy (Eds.) the book as a possible text for a beginning graduate course in, say, mathematical methods in engineering. It covers a number of topics The current use of complex materials in nanotechnology and industrial that are quite useful but are rarely covered in mainstream mathemat- engineering has led to a number of intricate problems in mechanics, ics courses … a lot of the proofs are short and computational, which and the macroscopic behavior of such materials often depends critically is necessary in such a book that covers a large number of topics … [It] on their substructures. This work, written by leading mathematicians would serve as a good text, provided that the aim of the course is to and engineers, features a broad range of topics that offer both experi- present a variety of transforms useful in signal processing, as well as mental results and clear, detailed answers to fundamental questions the wavelet transforms.”—MATHEMATICAL REVIEWS about the general formulation of multifield theories within the context 2001 / 584 PP., 69 ILLUS. / HARDCOVER / $89.95 of modeling material substructures. Applied mathematicians, mechani- ISBN_13 978-0-8176-4204-4 cal and structural engineers, material scientists, graduate students, and ISBN_10 0-8176-4204-8 researchers in the above areas will benefit from the work and may find suggestions for further research in its rich collection of open problems. Contributors: D. Bernardini, G. Capriz, C. M. Casciola, H. Cendra, E. De Angelis, Y. Grabovsky, P. M. Mariano, J. Marsden, I. Müller, O. B. Naimark, G. P. Parry, T. J. Pence, R. Piva, T. S. Ratiu, R. Segev, M. Silhavy. 2003 / 280 PP., 45 ILLUS. / HARDCOVER / $89.95 ISBN_13 978-0-8176-4324-9 ISBN_10 0-8176-4324-9 MODELING AND SIMULATION IN SCIENCE, ENGINEERING AND TECHNOLOGY

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Transforms and The Mathematics of Fast Algorithms for Internet Congestion Signal Analysis and Control Representations Rayadurgam Srikant, University of Illinois, Urbana, IL Guoan Bi, Nanyang Technical University, Singapore and “This first book on the mathematics of con- Yonghong Zeng, gestion control [is] very useful for both stu- The University of Hong Kong, Hong Kong dents and researchers, but also for system engineers developing new Internet protocols. “This is perhaps the best text on transforms This is an elementary book for graduate stu- for signal processing since Nussbaumer’s dents that uses a rich pallet of mathematical Fast Fourier Transform and Convolution tools: convex optimization and control theory (Lyapunov stability and Ny- Algorithms (Springer, 1982) and Elliott and Rao’s, Fast Transforms: quist criteria and stochastic processes). The tools are summarized well in Algorithms, Analyses, Applications (Academic Press, 1982). Its nine appendices which makes the book self-contained and easy to read. The chapters encompass almost all the knowledge needed to apply signal book is very well written and will undoubtedly remain a major reference processing transforms successfully in practice. on the topic for years to come.”—MATHEMATICAL REVIEWS Chapter 8 is unique, in the sense that ‘to the best of my knowledge’ “This well-written book presents an overview of the mathematics be- this material has never appeared in a book before. The chapter deals hind internet congestion control. Focusing on the well-established TCP with integer transforms, which might be thought of as derived from protocol, it starts with a gentle introduction on TCP and the packet/ac- the DCT and discrete sine transforms; these are gaining in popularity knowledgement structure of the internet, before proceeding to conges- in various transform coding schemes for both video and audio . … In tion and the principles of congestion control . … Overall, this book pres- conclusion, this book is a highly practical and very welcome addition ents in an easy to understand way the principles of internet congestion to the collection of texts on signal processing techniques and applica- control with a focus on the mathematical concepts behind them. The tions.”—ANALOG DIALOGUE book concludes with a useful index and a rich source of bibliographical 2004 / 422 PP., 92 ILLUS. / HARDCOVER / $79.95 references.”—ZENTRALBLATT MATH ISBN_13 978-0-8176-4279-2 ISBN_10 0-8176-4279-X 2004 / 164 PP., 19 ILLUS. / HARDCOVER / $54.95 APPLIED AND NUMERICAL HARMONIC ANALYSIS ISBN_13 978-0-8176-3227-4 ISBN_10 0-8176-3227-1 SYSTEMS & CONTROL: FOUNDATIONS & APPLICATIONS Modeling and Computational Methods for Kinetic Equations Graphs Pierre Degond, Université Paul Sabatier, Toulouse, France; and Networks Lorenzo Pareschi, Università di Ferrara, Italy; and Giovanni Russo, Università di Catania, Italy (Eds.) Transfinite and Nonstandard Armen H. Zemanian, State University of In recent years kinetic theory has developed in many areas of the physi- New York at Stony Brook, Stony Brook, NY cal sciences and engineering, and has extended the borders of its traditional fields of application. This monograph is a self-contained presen- “The book presents almost everything that tation of such recently developed aspects of kinetic theory, as well as a has been achieved so far in the relatively comprehensive account of the fundamentals of the theory. new field of transfinite graphs and electrical networks. The book must be appreci- Emphasizing modeling techniques and numerical methods, the book pro- ated especially because new results in the vides a unified treatment of kinetic equations not found in more focused field of transfinite graphs are also included. works. Specific applications presented include plasma kinetic models, Therefore, I find this book a welcome addi- traffic flow models, granular media models, and coagulation-fragmenta- tion to the literature.”—ZENTRALBLATT MATH tion problems. The work may be used for self-study, as a reference text, or in graduate-level courses in kinetic theory and its applications. This self-contained book examines results on transfinite graphs and 2004 / 356 PP., 65 ILLUS. / HARDCOVER / $79.95 networks achieved through continued research effort over the past ISBN_13 978-0-8176-3254-0 several years. These new results, covering the mathematical theory of ISBN_10 0-8176-3254-9 electrical circuits, are different from those presented in two previously MODELING AND SIMULATION IN SCIENCE, ENGINEERING AND TECHNOLOGY published books by the author, Transfiniteness for Graphs, Electrical Networks, and Random Walks and Pristine Transfinite Graphs and Per- missive Electrical Networks. Specific topics covered include connectedness ideas, distance ideas, and nontransitivity of connectedness. The book will appeal to a diverse readership, including graduate students, electrical engineers, mathematicians, and physicists working on infinite electrical networks. Moreover, the growing and presently substantial number of mathematicians working in nonstandard analysis may well be attracted by the novel application of the analysis employed in the work. 2004 / 204 PP., 44 ILLUS. / SOFTCOVER / $84.95 ISBN_13 978-0-8176-4292-1 ISBN_10 0-8176-4292-7

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Advances in Gabor Analysis A Stochastic Control Framework Hans G. Feichtinger, University of Vienna, Austria and for Real Options in Strategic Thomas Strohmer, University of California, Davis, CA (Eds.) “The authors have put their effort into writing articles with the neces- Valuation sary background to make their presentations attractive and including Alexander Vollert, Universitat Karlsruhe (TH), Karlsruhe, Germany a complete set of references. Good introductions and detailed ex- “The book is written in a quite self-contained manner, and gives a nice positions of ideas are given in all the presentations. These features survey of the results on the subject, old and new. Many graphics are make this book an invaluable tool for researchers interested in signal provided along with theoretical illustrations to help explain the mate- analysis. The research community will benefit greatly from this publica- rials throughout the book. Numerical analysis as well as simulation tion.”—MATHEMATICAL REVIEWS are also provided in Chapter 6, which is particularly useful for both “Written by leading experts in the field, the volume appeals, by its inter- academic researchers and real world practitioners. Various examples disciplinary character, to a large audience, both novices, and experts, are provided in the book in order to show the potential of the new theoretically inclined researchers and practitioners as well. It brilliantly framework . … Could also be used as a reference book or as a source illustrates how application areas and pure and applied mathematics of problems for stochastic controlists.”—MATHEMATICAL REVIEWS can work together with profit for all.”—STUDIA UNIVERSITATIS BABES-BOLYAI, SE- “This book is devoted to developing both a stochastic control frame- RIES MATHEMATICA work that is capable of dealing with complex real option interactions 2003 / 376 PP., 22 ILLUS. / HARDCOVER / $79.95 and a graphical decomposition method for real option models which ISBN_13 978-0-8176-4239-6 can be transformed into numerical or analytical solution procedures.” — ISBN_10 0-8176-4239-0 APPLIED AND NUMERICAL HARMONIC ANALYSIS ZENTRALBLATT MATH 2003 / 288 PP., 77 ILLUS. / HARDCOVER / $89.95 ISBN_13 978-0-8176-4258-7 Also available by Feichtinger and Strohmer: ISBN_10 0-8176-4258-7 Gabor Analysis and Algorithms Theory and Applications Foundations of Time- 1998 / 512 PP., 29 ILLUS. / HARDCOVER / $89.95 ISBN_13 978-0-8176-3959-4 Frequency Analysis ISBN_10 0-8176-3959-4 Karlheinz Gröchenig, University of APPLIED AND NUMERICAL HARMONIC ANALYSIS Vienna, Austria “This book is written by one of the leading experts in Gabor analysis and deserves Computational considerable interest. It gives a unified approach to most of the modern theory for Financial Mathematics time-frequency analysis from a mathema- using Mathematica® tician’s point of view, with new proofs of many recent results.”—ZENTRALBLATT MATH Optimal Trading in Stocks and Options “’Foundations of Time-Frequency Analysis’ provides a clear and thorough exposition of some of the fundamental Srdjan Stojanovic, University of results in the theory and gives some important perspectives on a rapidly Cincinnati, OH growing field … An important feature of the book is complete, detailed “Stojanovic offers an excellent, user-friendly proofs of all claims and extensive motivation of topics … The author has presentation of advanced mathematical chosen topics that illuminate a path toward some of the most inter- techniques and Mathematica® program- esting and challenging research areas in mathematical time-frequency ming for solving problems in finance and analysis. A graduate student or researcher seeking research problems in trading. He demonstrates the value of probability, mathematical statis- this area can come to no better source . … The book is definitely suitable tics, calculus of variations, and optimal control of stochastic, ordinary for a graduate-level course in mathematical time-frequency analysis. and partial differential equations to the study of market analysis. Solu- It assumes a background in real analysis, Fourier analysis and Hilbert tions are computed symbolically, numerically, or by means of Monte- spaces. It is also suitable for self-study, as the exposition is superb.”— Carlo simulations . … A very useful and valuable book for researchers, MATHEMATICAL REVIEWS students, professionals, and individual investors.”—Choice 2000 / 365 PP., 15 ILLUS. / HARDCOVER / $69.95 ISBN_13 978-0-8176-4022-4 “It is an innovative approach and is very useful for students and prac- ISBN_10 0-8176-4022-3 titioners in finance to learn how to use mathematics for investment APPLIED AND NUMERICAL HARMONIC ANALYSIS analysis.”—Mathematical Reviews “This book is a state-of-the-art introduction to the mathematics of computational finance. The author reviews and extends several- re cent breakthroughs and also provides new material, which is highly recommended. The novel use of Mathematica® enhances the learning experience by letting the reader focus on the essential ideas. I thoroughly recommend this book to both students and practitioners.” — Peter Carr, Courant Institute, New York University 2002 / 520 PP., 50 ILLUS. / HARDCOVER WITH CD-ROM / $69.95 ISBN_13 978-0-8176-4197-9 ISBN_10 0-8176-4197-1 CO-PUBLISHED WITH TELOS

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Wavelets through a An Introduction to Looking Glass Wavelet Analysis The World of the Spectrum David F. Walnut, George Mason University, Fairfax, VA Ola Bratteli, University of Oslo, Norway and Palle Jorgensen, University of Iowa, “[This text] is carefully prepared, well-orga- Iowa City, IA nized, and covers a large part of the central theory … [there are] chapters on biorthog- “Mere words cannot adequately describe onal wavelets and wavelet packets, topics all the great features of the book … which which are rare in wavelet books. Both are has something for everyone of all math- important, and this feature is an extra argu- ematical persuasions . … This book has ment in favour of [this] book … [The] mate- quite a different perspective from the other rial is accessible [even] to less advanced monographs on wavelets … mainly because it emphasizes the Fourier readers.”—ZENTRALBLATT MATH domain as the proper “window” or “looking glass” from which one can most easily study wavelet theory . … Whatever his or her level of exper- “This book can be recommended to everyone, especially to students tise with the subject, a reader of this book will never be bored . … Each looking for a detailed introduction to the subject.”—MATHEMATICAL REVIEWS chapter begins with an introductory section accessible to the layper- “D. Walnut’s lovely book aims at the upper undergraduate level, and son, often containing some historical background, and often extremely so it includes relatively more preliminary material … than is typically entertaining . … This is a fun book, full of exciting new results, written the case in a graduate text . … The applications to image compres- by two world-renowned experts in the field, which makes connections sion are wonderful, and the best I have seen in books at this level. I between a variety of important areas in pure and applied mathemat- also found the analysis of the best choice of basis and wavelet packet ics.”—SIAM REVIEW especially attractive. The later chapters include MATLAB codes. Highly “This is a quite unusual wavelet book, with a fresh view on the subject. recommended!”—BULLETIN OF THE AMS While the vast majority of wavelet books concentrate on multiresolu- “This textbook is an introduction to the mathematical theory of wave- tion analysis and its applications, this book treats the topic from an let analysis at the level of advanced calculus. Some applications are operator theoretic point of view, with a focus on techniques having a described, but the main purpose of the book is to develop—using only geometric or spectral theoretic flavor. In fact, while parts of the book tools from a first course in advanced calculus—a solid foundation in could be used in a wavelet course, other parts would be suitable in a wavelet theory. It succeeds admirably . … There are exercises at the course directed towards operator theory.”—ZENTRALBLATT MATH end of each section, 170 in all . … To cover the whole book would “The authors take a fresh look at the subject and develop a new intu- require a year. An excellent one-semester course could be based on a ition for many topics . … There are connections with many other areas selection of chapters from Parts II, III, and V.”—SIAM REVIEW of mathematics and physics not usually associated with wavelet theo- 2003 / 449 PP., 66 ILLUS. / HARDCOVER / $69.95 ry … The end of each chapter has a large selection of problems in which ISBN_13 978-0-8176-3962-4 ISBN_10 0-8176-3962-4 — MATHE- much of the standard theory can be worked out by the reader.” APPLIED AND NUMERICAL HARMONIC ANALYSIS MATICAL REVIEWS 2002 / 424 PP., 122 ILLUS. / HARDCOVER / $59.95 ISBN_13 978-0-8176-4280-8 ISBN_10 0-8176-4280-3 APPLIED AND NUMERICAL HARMONIC ANALYSIS Perturbation Methods for Differential Equations Bhimsen K. Shivamoggi, University of Central Florida, Orlando, FL Wavelets Made Easy “The book is concerned for the most part with singular perturbation phe- Yves Nievergelt, Eastern Washington University, Cheney, WA nomena for ordinary and partial differential equations. Instead of presenting general theory, the author shows how various perturbation tech- “Explains in a nice way the nature and computation of mathemati- niques work in concrete examples … Applications are quite numerous cal wavelets, which provide a framework and methods for the analy- and include fluid dynamics, solid mechanics, and plasma physics … On sis and synthesis of signals, images, and other arrays of data … the whole, a great variety of examples coming from real applications A useful text for engineers, financiers, scientists, and students.” makes the book a very nice source for courses on perturbation meth- —JOURNAL OF INFORMATION AND OPTIMIZATION SCIENCES ods. A number of exercises together with appendices covering some “Giving practice first and theory later, the author avoids discouraging mathematical topics used in the text help a lot in making it practically readers whose main subject is not mathematics. The book is written in self-contained.”—MATHEMATICAL REVIEWS a very comprehensible and lively style [and] is essentially self-contained “This book is focused on perturbation methods mainly applied to solve since many of the facts employed from analysis, linear algebra and both ordinary and partial differential equations … One of the unusual fea- functional analysis are stated and partially proved in the book.”—ZAA tures of the treatment is motivated by the author’s notes devoted to a mix 2001 / 320 PP., 53 ILLUS. / HARDCOVER / $49.95 ISBN_13 978-0-8176-4061-3 of students in applied mathematics, physics, and engineering. Therefore, ISBN_10 0-8176-4061-4 it is intended to serve as a textbook for undergraduate students of the previously mentioned branches of science. The book can serve also as an example of how an asymptotic analysis may easily move between various disciplines … Since the book covers a great deal of material, it is recommended to students and researchers already familiar with solid and fluid mechanics, as well as with plasma physics.”—APPLIED MECHANICS REVIEW 2002 / 368 PP., 62 ILLUS. / HARDCOVER / $59.95 ISBN_13 978-0-8176-4189-4 ISBN_10 0-8176-4189-0

72 Order By Phone: 1-800-777-4643 • Fax: 201-348-4505 • Or Online: www.birkhauser.com Modern birkhäuser classics

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.

Number Theory Volume III André Weil, (deceased) Contributors: A. Lascoux; S. Lichtenbaum; G. Lusztig; Z. Mebkhout; A. Ogus; A. Parshin; M. Raynaud; G.B. Shabat; An approach through history from Hammurapi to Legendre L. Szpiro; R. Thomason; A. Treibich; T.F. Trobaugh; J.-L.Verdier; 2007/376 PP., 18 ILLUS./SOFTCOVER/$39.95 V.A. Voevodsky; and Y.G. Zarhin ISBN_13 978-0-8176-4565-6 2007/496 PP./SOFTCOVER/$39.95 ISBN_10 0-8176-4565-9 ISBN_13 978-0-8176-4568-7 MODERN BIRKHAUSER CLASSICS ISBN_10 0-8176-4568-3 MODERN BIRKHAUSER CLASSICS Notions of Convexity Lars Hormander Metric Structures for 2007/414 PP./SOFTCOVER/$39.95 ISBN_13 978-0-8176-4584-7 Riemannian and ISBN_10 0-8176-4584-5 MODERN BIRKHAUSER CLASSICS Non-Riemannian Spaces Mikhail Gromov, Institut des Hautes Etudes Scientifiques, Bures-sur-Yvette, France Appendices by Mikhail Katz, Université de Montpellier, France; The Grothendieck Festschrifts Pierre Pansu A Collection of Articles Written in Honor of Translated by Sean M. Bates, Columbia University, New York, NY the 60th Birthday of Alexander Grothendieck 2007/586 PP., 100 ILLUS./SOFTCOVER/$39.95 Pierre Cartier Institut des Hautes Éludes Scientifiques, ISBN_13 978-0-8176-4582-3 Bures-sur-Yuette, France; ISBN_10 0-8176-4582-9 MODERN BIRKHAUSER CLASSICS Luc Illusie, Université de Paris-Sud, Orsay, France; Nicholas M. Katz, Princeton University, Princeton, NJ; GÉrard Laumon, Université de Paris-Sud, Orsay, France; Yuri I. Manin, Max-Planck Institut für Mathematik, Bonn, Germany; Tata Lectures on Theta Kenneth A. Ribet, University of California, Berkeley, CA (Eds.) David Mumford, Brown University, Providence, ri Volume I Volume I Contributors: A. Altman; M. M. Artin; V. Balaji; A. Beauville; Contributors: C. Musili, M. Nori, E. Previato, and M. Stillman A.A. Beilinson; P. Berthelot; J.-M. Bismut; S. Bloch; L. Breen; J.-L. Brylinski; J. Dieudonné; H. Gillet; A.B. Goncharov; K. Kato; 2007/236 PP./SOFTCOVER/$39.95 ISBN_13 978-0-8176-4572-4 S. Kleiman; W. Messing; V.V. Schechtman; C.S. Seshadri; C. Soulé; ISBN_10 0-8176-4572-1 J. Tate; M. Van Den Bergh; and A.N. Varchenko MODERN BIRKHAUSER CLASSICS 2007/498 PP./SOFTCOVER/$39.95 ISBN_13 978-0-8176-4566-3 ISBN_10 0-8176-4566-7 Volume II MODERN BIRKHAUSER CLASSICS Jacobian Theta Functions and Differential Equations Volume II Contributors: C. Musili, M. Nori, E. Previato, M. Stillman and H. Umemura Contributors: P. Cartier; C. Contou-Carrére; P. Deligne; 2007/272 PP./SOFTCOVER/$39.95 T. Ekedahl; G. Faltings; J.-m> Fontaine; H. Hamm; Y. Ihara; ISBN_13 978-0-8176-4569-4 ISBN_10 0-8176-4569-1 L. Illusie; M. Kashiwara; V.A. Kolyvagin; R. Langlands; LÉ. D.T.; MODERN BIRKHAUSER CLASSICS D. Shelstad; and A. Voros 2007/564 PP./SOFTCOVER/$39.95 ISBN_13 978-0-8176-4567-0 Volume III ISBN_10 0-8176-4567-5 MODERN BIRKHAUSER CLASSICS Contributors: Madhav Nori and Peter Norman 2007/202 PP./SOFTCOVER/$39.95 ISBN_13 978-0-8176-4570-0 ISBN_10 0-8176-4570-5 MODERN BIRKHAUSER CLASSICS

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Italian Mathematics The History of Between the Two World Wars Approximation Theory Angelo Guerraggio, Università Bocconi, From Euler to Bernstein Milano, Italy and Karl-Georg Steffens, Johann Wolfgang Pietro Nastasi, Università Palermo, Italy Goethe-Universität Frankfurt, Germany “What the book conveys is the richness of “The discussion of mathematical results Italian mathematics throughout the period and ideas constitutes the main part of the and, despite being expert in none of these book—always accompanied by moving fields, the authors captured my imagination stories, marked by devotion to science, by and made me want to know more of such humanity, and often by the cruelty of the mathematical ideas … immensely enjoyable political turbulence of Russian history. Un- for all that.”—MAA REVIEWS doubtedly, the author has succeeded in catching the spirit both of the This book describes Italian mathematics in the period between the Russian atmosphere of that time and of the depth and richness of the two World Wars, tracing its development through an analysis of both human relationships of the people involved.”—MATHEMATICAL REVIEWS interior and external influences. Italian mathematics during that period was shaped by a colorful array of strong personalities who concentrated This book traces the history of approximation theory from Leonhard their efforts on a select number of fields and won international recogni- Euler‘s cartographic investigations at the end of the 18th century to tion and respect in an incredibly short time. the early 20th century work of Sergei Bernstein defining a new branch of function theory. The main focus is on the St. Petersburg Mathemati- 2005 / 300 PP., 51 ILLUS. / HARDCOVER / $119.00 ISBN_13 978-3-7643-6555-4 cal School and its interaction with mathematicians in Goettingen. The ISBN_10 3-7643-6555-2 author presents a mathematical analysis of the subject together with a SCIENCE NETWORKS–HISTORICAL STUDIES, VOL. 29 discussion of the philosophical underpinnings of the differences in approach of the various schools of thought. There is an exciting exposition in which history, philosophy, and mathematics are integrated. While demonstrating excellent technical control of the underlying mathemat- Gnomes in the Fog ics, the work is focused on the essential results for the development The Reception of Brouwer’s Intuitionism of the theory. in the 1920s Biographical data about some sixty eminent mathematicians and an Dennis E. Hesseling, Den Haag, The Netherlands excellent index round out the work. Historians as well as students interested in the history of mathematics will find this book useful. “L.E.J. Brouwer is best known to many mathematicians for his seminal 2005 / 220 PP., 12 ILLUS. / SOFTCOVER / $79.95 contributions to topology. He is also the founder of mathematical intu- ISBN_13 978-0-8176-4353-9 itionism, and a key player in the debate on foundations of mathematics ISBN_10 0-8176-4353-2 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 The Legacy of Mario Pieri in enjoy this book. Mathematicians (especially logicians) may find some surprises in the first chapter, on Brouwer’s predecessors; philosophers Arithmetic and Geometry and science study scholars should especially appreciate the final chap- Elena A. Marchisotto, California State University, Northridge, CA and ter on the cultural context of the debate . … One of the many treasures James T. Smith, San Francisco State University, San Francisco, CA to be discovered in reading this book is the rich collection of original Mario Pieri (1860-1913) left a strong impact on many areas of 20th quotes in the many languages in which the debate took place, along century mathematics. A prominent disciple of two Italian schools at with the author’s translations.”—MAA ONLINE the University of Turin, namely that of Segre (algebraic geometry) and 2003 / 447 PP. / HARDCOVER / $139.00 Peano (logic), Pieri’s own research influenced many 20th century ISBN_13 978-3-7643-6536-3 mathematicians in such fields as algebraic and differential geometry, ISBN_10 3-7643-6536-6 SCIENCE NETWORKS. HISTORICAL STUDIES, VOL. 28 inversive geometry, number theory, and logic. The Legacy of Mario Pieri in Arithmetic and Geometry is the first of two volumes that together will provide a broad picture of Pieri’s work. In this volume, English translations are given for two of Pieri’s most important results: his postulates for arithmetic, which Peano judged superior to his own, and his foundation of elementary geometry on the basis of point and sphere, which Alfred Tarski used as a basis for his own system. Ad- ditionally, his papers are examined in relation to the research of others, notably Peano and Tarski. This beautifully written, thorough treatment of Pieri’s work will serve historians of mathematics as well as logicians, geometers, and number theorists. 2007 / 420 PP. / HARDCOVER / $99.00 (TENT.) ISBN_13 978-0-8176-3210-6 ISBN_10 0-8176-3210-7

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The Universe of General Relativity History of Banach Spaces and Jean Eisenstaedt, Observatoire de Paris, France; Linear Operations A.J. Kox, Universiteit van Amsterdam, The Netherlands (Eds.) Albrecht Pietsch, Friedrich-Schiller-University, Jena, Germany This volume from the Einstein Series is based largely on papers presented at the Sixth International Conference on the History of General Written by a distinguished specialist in functional analysis, this book Relativity, held in Amsterdam. These contributions from notable experts presents a comprehensive treatment of the history of Banach spaces offer both new and historical insights on gravitation, general relativity, and (abstract bounded) linear operators. While other historical texts on cosmology, unified field theory, and the history of science. the subject focus on developments before 1950, this one is mainly devoted to the second half of the 20th century. Topics discussed include the prehistory of special relativity, early attempts at a relativistic theory of gravitation, the beginnings of general Banach space theory is presented as a part of a broad mathematics relativity, the problem of motion in the context of relativity, conservation context, using tools from such areas as set theory, topology, algebra, laws, the axiomatization of relativity, classical and contemporary cos- combinatorics, probability theory, logic, etc. Equal emphasis is given to mology, gravitation and electromagnetism, quantum gravity, and relativ- both spaces and operators. Numerous examples and counterexamples ity as seen through the eyes of the public and renowned relativists. elucidate the scope of the underlying concepts. As a stimulus for further research, the text also contains many problems which have not been 2005 / APPROX. 383 PP., 17 ILLUS. / HARDCOVER / $99.00 ISBN_13 978-0-8176-4380-5 previously solved. ISBN_10 0-8176-4380-X 2007/APPROX. 880 PP. 82 ILLUS./HARDCOVER/$129.00 (TENT.) EINSTEIN STUDIES, VOL. 11 ISBN_978-0-8176-4367-6 ISBN_0-8176-4367-2

103 Trigonometry Mathematical Problems Olympiad Treasures From the Training of the USA Titu Andreescu, University of Texas, IMO Team Dallas, TX and Bogdan Enescu, B.P. Has- Titu Andreescu, University of Texas, deu National College, Buzau, Romania Dallas, TX and Zuming Feng, Phillips Exeter Academy, Exeter, NH “I took great pleasure in reading ’Math- ematical Olympiad Treasures,’ by Titu An- 103 Trigonometry Problems contains dreescu and Bogdan Enescu. This book is highly-selected problems and solutions the fruit of the prodigious activity of two used in the training and testing of the well-known creators of mathematics prob- USA International Mathematical Olympiad lems in various mathematical journals . … (IMO) team. Though many problems may initially appear impenetrable to the novice, most can be solved using only elementary high school ’Treasures’ is organized in six chapters. The mathematics techniques. This book’s presentation of problems evolves first three deal with problems from algebra, geometry and trigonometry, through gradual progression in difficulty to build and strengthen students’ number theory and combinatorics. Chapters 4, 5 and 6 give the solu- mathematical skills and techniques. It provides an in-depth enrichment tions to problems presented in the first three chapters. In all the chap- of problem-solving tactics and strategies, along with practical test-taking ters, the reader can find numerous challenging problems. All featured techniques, to better prepare students for possible participation in vari- solutions are interesting, given in increasing level of difficulty; some of ous mathematical competitions. them are real gems that will give great satisfaction to any math lover at- tempting to solve the problems—or even extend them. I believe strongly Topics covered include: trigonometric formulas and identities, their that ’Mathematical Olympiad Treasures’ will reveal the beauty of math- applications in the geometry of the triangle, trigonometric equations ematics to all students, teachers and all math lovers.”—MAA ONLINE and inequalities, and substitutions involving trigonometric functions. Mathematical Olympiad Treasures aims at building a bridge between Advanced high school students, undergraduates, and mathematics ordinary high school exercises and more sophisticated, intricate and teachers engaged in competition training will gain both skills and strate- abstract concepts and problems in undergraduate mathematics. The gies from this cogent problem-solving resource. book contains a stimulating collection of problems in the subjects of 2005 / 214 PP., 79 ILLUS. / SOFTCOVER / $49.95 algebra, geometry and trigonometry, number theory and combinator- ISBN_13 978-0-8176-4334-8 ISBN_10 0-8176-4334-6 ics. While it may be considered a sequel to Mathematical Olympiad Challenges, the focus of Treasures is on engaging a wider audience of undergraduates to think creatively in applying techniques and strategies to problems in the real world.’ 2004 / 238 PP., 99 ILLUS. / SOFTCOVER / $29.95 ISBN_13 978-0-8176-4305-8 ISBN_10 0-8176-4305-2

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Mathematical Olympiad Challenges The Math Problems Notebook Forthcoming Second Edition Valentin Boju, MontrealTech, Institute de Technologie de Montreal, Titu Andreescu, The University of Texas at Dallas, Richardson, TX; Quebec, Canada; Razvan Gelca, Texas Tech University, Lubbock, TX Louis Funar, CNRS, Université de Grenoble I, Institut Fourier, France Reviews of first edition: The Math Problems Notebook is a collection of non-trivial, unconven- tional problems requiring deep insight and imagination nostalgic of those “The authors are experienced problem solvers and coaches of math- discussed at the Sunday Math Circles. These Circles were comprised ematics teams. This expertise shows through and the result is a vol- of college students who had a common passion for mathematics, and ume that would be a welcome addition to any mathematician’s book- became a place for disseminating beautiful mathematics at an elemen- shelf.”—MAA ONLINE tary level. Following in the tradition of these math circles, the authors “This [book] is … much more than just another collection of interesting, hope to inspire further enjoyment of mathematics with their collection challenging problems, but is instead organized specifically for learning. of problems. The book expertly weaves together related problems, so that insights The problems cover many topics, including number theory, algebra, com- gradually become techniques, tricks slowly become methods, and meth- binatorics, geometry and analysis, of varying levels of difficulty; beginning ods eventually evolve into mastery . … The book is aimed at motivated with simple exercises and following with more difficult problems, chal- high school and beginning college students and instructors. It can be used lenging enough even for the experienced problem solver. The introduc- as a text for advanced problem-solving courses, for self-study, or as a re- tory problems focus on the basic methods and tools while the advanced source for teachers and students training for mathematical competitions, problems aim to develop problem solving techniques, intuition and to and for teacher professional development, seminars, and workshops. promote further research in the area. Undergraduates and teachers of I strongly recommend this book for anyone interested in creative prob- advanced mathematics, as will as the casual mathematician will mutually lem-solving in mathematics . … It has already taken up a prized posi- enjoy The Math Problems Notebook. tion in my personal library, and is bound to provide me with many 2007 / APPROX. 290 PP., 21 ILLUS. / SOFTCOVER / $39.95 (TENT.) hours of intellectual pleasure.”—THE MATHEMATICAL GAZETTE ISBN_13 978-0-8176-4546-5 ISBN_10 0-8176-4546-2 This significantly revised and expanded second edition ofMathematical Olympiad Challenges is a rich collection of problems put together by two experienced and well-known professors and coaches of the U.S. In- ternational Mathematical Olympiad Team. Hundreds of beautiful, chal- Exploring, Investigating and lenging, and instructive problems from algebra, geometry, trigonometry, combinatorics, and number theory from numerous mathematical com- Discovering in Mathematics petitions and journals have been selected and updated. The problems Vasile Berinde, University Baia Mare, Romania are clustered by topic into self-contained sections with solutions pro- “In the spirit of George Polya’s classic treatise `How to Solve It: A New vided throughout is on creative solutions to open-ended problems. Aspect of Mathematical Method,’ this book is Vasile Berinde’s attempt to 2007 / APPROX. 320 PP. / SOFTCOVER / $29.95 (TENT.) “algorithmetize” the creative process involved in problem-solving.... The ISBN_13 978-0-8176-4528-1 ISBN_10 0-8176-4528-4 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 2004 / 246 PP. / SOFTCOVER / $49.95 ISBN_13 978-3-7643-7019-0 ISBN_10 3-7643-7019-X

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Fibonacci Numbers Math Into LaTeX N. Vorobiev Third Edition Translated by Mircea Martin, Baker George Grätzer, University of Manitoba, Winnipeg, Canada University, Baldwin City, KS From reviews of a previous edition: “Quite the special topic, the Fibonacci num- “Writing a sufficiently long math text (lecture notes, monographs) by a bers nevertheless enjoy enormous popu- non-expert TeX writer … requires the use of a well-documented pack- larity, perhaps due to their connection with age. Grätzer’s book is a solution.”—EMS NEWSLETTER the golden mean. Vorobiev’s book, now translated, presents a solid overview, per- “Grätzer’s book can be recommended both as a very good introduc- fectly pitched to undergraduates … . Rec- tory text for beginners as well as a handy up-to-date LaTeX reference ommended; upper-division undergradu- for experienced users.”—REPORTS ON MATHEMATICAL PHYSICS ates and up.”—CHOICE “This book is truly unique in its focus on getting started fast yet keeping “This is a wonderful book with a huge amount of information on Fibonac- it simple. It is indispensable for the beginner and a handy reference for ci numbers. First published in the 1950s for high school students enrolled the experienced user.”—BULLETIN OF THE MATHEMATICAL ASSOCIATION OF INDIA in a mathematical circle at the Leningrad State University, the book only This third edition features a section devoted to book publishing and assumes knowledge of high school mathematics, but the reader will need typesetting, as well as an introduction to web development from LaTeX. the sophistication of a good upper-level mathematics major. The warmth It presents a detailed discussion of all aspects of LaTeX and the AMS and enthusiasm of the late author comes through Mircea Martin’s English packages and includes a formula gallery, sample files, and templates. translation . … This book would be useful to any mathematician with a Also included are useful appendices containing symbol tables and cov- desire to know more about the Fibonacci numbers. A student could use it ering special topics, such as the use of PostScript fonts and where to for a reading project on the Fibonacci numbers . … Overall, I enjoyed the find TeXware. book and highly recommend it.”—MAA ONLINE 2000 / 616 PP., 79 ILLUS. / SOFTCOVER / $49.95 2002 / 176 PP. / SOFTCOVER / $42.95 ISBN_13 978-0-8176-4131-3 ISBN_13 978-3-7643-6135-8 ISBN_10 0-8176-4131-9 ISBN_10 3-7643-6135-2 CO-PUBLISHED WITH SPRINGER

First Steps in LaTeX Trigonometry George Grätzer, University of Manitoba, Winnipeg, Canada I.M. Gelfand, Rutgers University, Piscataway, NJ and “The author lays a clear structure to guide the newcomer through the Mark Saul, Bronxville Schools, Bronxville, NY process of preparing a text with LaTeX . … Besides the comprehensive index at the end of the book, there is a useful Quick Finder at the be- “Cover[s] all of the basic topics that a ginning of the book; the reader can hardly get lost. The book fulfills the high school or beginning university stu- claim of the title . … [It] may also serve the more experienced TeXie as dent should be expected to know … There a reference.”—ZENTRALBLATT MATH are … . some nice touches; for example, a nice informal discussion showing that the “The book is very well organized, contains many practical examples sine of an angle in a right triangle does and, undoubtedly, will become an indispensable tool for a novice who not depend on whether the sides are mea- is in a hurry to write his first LaTeX paper.”— REVUE D’ANALYSE NUMÉRIQUE ET sured in inches or centimeters … ”—CHOICE DE THÉORIE DE L’APPROXIMATION “Covers all the basics of the subject through beautiful illustrations and “Fortunately, there are some excellent books for learning LaTeX. Grätzer’s examples . … Throughout, the treatment stimulates the reader to think book is one of these superb books. Readers who work through this book of mathematics as a unified subject.” —L’ENSEIGNEMENT MATHÉMATIQUE are likely to reuse it frequently as a reference while writing papers with mathematical content.”—JOURNAL OF MATHEMATICAL PSYCHOLOGY “As a teacher I enjoyed this book enormously and I will doubtless bor- 1999 / 136 PP., 10 ILLUS. / SOFTCOVER / $29.95 row many of the plums to spice up my lessons . … [For] that ideal stu- ISBN_13 978-0-8176-4132-0 dent who is to be prepared to be challenged to think what the subject ISBN_10 0-8176-4132-7 is really about, and has the patience to excavate the basic ideas for all CO-PUBLISHED WITH SPRINGER they are worth before jumping on to the next chapter, it should prove to be a godsend.”—THE MATHEMATICAL GAZETTE “The authors tried to explain the results of trigonometry as simply as possible . … The exercises include a few problems of each routine type. Most of the problems exhibit a new aspect of the technique or object under discussion. One of the goals of this book is to prepare students for a course in calculus. We recommend it for teachers and students.”— PUBLICATIONES MATHEMATICAE 2001 / 240 PP., 185 ILLUS. / SOFTCOVER / $22.95 ISBN_13 978-0-8176-3914-3 ISBN_10 0-8176-3914-4 GELFAND SCHOOL OUTREACH PROGRAM

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Algebra Writing the History I.M. Gelfand, Rutgers University, Piscataway, NJ and of Mathematics A. Shen, Institute of Problems of Information Transmission, Moscow, Russia Its Historical Development Joseph W. Dauben, City University of “The idea behind teaching is to expect students to learn why things are New York, New York, NY and true, rather than have them memorize ways of solving a few problems, Christoph J. Scriba, University of as most of our books have done. [This] same philosophy lies behind the Hamburg, Germany current text by Gelfand and Shen. There are specific ‘practical’ problems but there is much more development of the ideas … [The authors] have “This book, a historiographical one, is very shown how to write a serious yet lively look at algebra.”—THE AMERICAN useful as a reference . … The book is unique. MATHEMATICS MONTHLY It should be in all libraries that support grad- “Were `Algebra’ to be used solely for supplementary reading, it could uate level history and philosophy of science be wholeheartedly recommended to any high school student of any and mathematics. Other libraries should consider purchasing it. Indi- teacher … In fact, given the long tradition of mistreating algebra as viduals familiar with the subject may wish to own it. Beginners should a disjointed collection of techniques in the schools, there should be start with histories.”—MATHEMATICAL REVIEWS some urgency in making this book compulsory reading for anyone “It is really a valuable monograph which should be studied by every interested in learning mathematics.”—THE MATHEMATICAL INTELLIGENCER historian of mathematics.” —ZENTRALBLATT MATH 1995 / 160 PP., 27 ILLUS. / SOFTCOVER / $22.95 ISBN_13 978-0-8176-3677-7 “How good is the book? Well, quite good … The main content of the ISBN_10 0-8176-3677-3 other half is a collection of brief biographies of many significant histori- GELFAND SCHOOL OUTREACH PROGRAM ans of mathematics. I am very glad to have these! … Meanwhile, most history fanatics will want to have access to this book . … The upshot is that this is a book that should be in any library that tries to have a A Mathematician complete set of historical source material.”—MAA ONLINE “This historiographic monograph is a great step forward, both in re- Grappling With His storing this image and in detailing how histories of mathematics have been written . … The value of this book is further enhanced by a glos- Century sary of foreign terms and an extensive index. Anyone who is interested Laurent Schwartz (deceased) in the history of mathematics will enjoy and use this work . … Highly Translated by Lila Schneps recommended.”—CHOICE 2002 / 708 PP. / SOFTCOVER / $109.00 “The chapters of Laurent Schwartz’s auto- ISBN_13 978-3-7643-6167-9 biography are … filled with rich descriptions ISBN_10 3-7643-6167-0 of events and the ‘players.’ His development 2002/708 PP./HARDCOVER/$153.00 as a mathematician and active member of ISBN_13 978-3-7643-6166-2 ISBN_10 3-7643-6166-2 the international mathematical community SCIENCE NETWORKS–HISTORICAL STUDIES, VOL. 27 was a fascinating journey, aptly conveyed with a writing style that really gives the reader the feel of a fellow traveler.”—MAA ONLINE (on the english edition) On the English Edition: “Laurent Schwartz is a strategist of ideas, within mathematics and without. He is a great communicator who has drawn huge audiences and conveyed to them the fragrance of research, or the joy of teaching, or the value of freedom. His is a mind whose company is never dull. He belongs to the great libertarian tradition of France. And his book has the very French characteristic of giving serious consideration to the life of the intellect. No man’s life can be encompassed in one telling, yet the spirit of the man and his times are well caught in his autobiography.”—NOTICES OF THE AMS (On the French Edition) 2001 / 472 PP. / SOFTCOVER / $52.95 ISBN_13 978-3-7643-6052-8 ISBN_10 3-7643-6052-6

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Advances in Annales Henri Applied Clifford Poincaré Algebras A Journal of Theoretical and Managing Editor: j. keller, Universidad Mathematical Physics Nacional Autonoma de Mexico Chief Editor: V. Rivasseau, Print ISSN: 0188-7009 Université d Orsay, France Electronic ISSN: 1661-4909 Print ISSN 1424-0637 2007, Vol. 17 (4 issues) Electronic ISSN 1424-0661 2007, Vol. 8 (8 issues)

Aequationes Annals of Mathematicae Combinatorics Honorary Editor-in-Chief: J. ACZÉL, Managing Editor: W.Y.C. Chen, University of Waterloo, ON, Canada Nankai University, Tianjin, China and Los Alamos National Laboratory, Los Editor-in-Chief: L. Reich, Universität Graz, Alamos, NM Austria Print ISSN 0218-0006 Managing Editor: D. Gronau, Electronic ISSN 0219-3094 Universität Graz, Austria 2007, Vol. 11 (4 issues) Associate Managing Editor: C.T. NG, University of Waterloo, ON, Canada Print ISSN 0001-9054 Electronic ISSN 1420-8903 2007, Vols. 73-74 (3 issues per volume) Archiv der Mathematik algebra Managing Editor: E.-U. GEKELER, Universität des Saarlandes, Saarbrücken, universalis Germany Honorary Editors-in-Chief: Print ISSN 0003-889X B. JÓNSSON, Vanderbilt University, Electronic ISSN 1420-8938 Nashville, TN and N. MENDELSOHN, 2007: Vols. 88-89 (6 issues per volume) University of Manitoba, Winnipeg, MB, Canada Editor-in-Chief: G. Grätzer, University of Manitoba, Winnipeg, MB, Canada

Executive Editors: C.R. Platt and R.W. Quackenbush, both, University Complex Analysis of Manitoba, Winnipeg, MB, Canada Print ISSN 0002-5240 and Operator Electronic ISSN 1420-8911 2007, Vols. 57-58 (4 issues per volume) Theory Managing Editor: D. alpay, Ben Gurion University of the Negev, Be’er-Sheva, Israel Print ISSN: 1661-8254 Electronic ISSN: 1661-8262 2007: Vols. 1 (4 issues per volume)

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computational Journal of Fixed complexity Point Theory and Editor-in-Chief: J. von zur Gathen, Applications Universität Paderborn, Germany Editor-in Chief: a. granas, Université Associate Editors: S. ARORA, Princeton de Montreal, Montreal University, Princeton, NJ; P. BÜRGISSER, (Quebec) Canada Universität Paderborn, Germany; Print ISSN: 1661-7738 O. GOLDREICH, The Weizmann Institute, Electronic ISSN: 1661-7746 Rehovot, Israel 2007, Vol. 1 (2 issues) Print ISSN 1016-3328 Electronic ISSN 1420-8954 2007, Vol. 16 (4 issues)

Geometric and Journal of Fourier Functional Analysis and Analysis (GAFA) Applications (JFAA) Managing Editor: V. Milman, Tel Aviv Editor-in-Chief: H.G. Feichtinger, University, Israel University of Vienna, Austria Print ISSN 1016-443X Founding Editor-in-Chief: J.J. BENEDETTO, Electronic ISSN 1420-8970 University of Maryland, College Park, MD 2007, Vol. 17 (6 issues) Print ISSN 1069-5869 Electronic ISSN 1531-5851 2007, Vol. 13 (6 issues)

Integral Equations Journal of Geometry and Operator Theory Managing Editor: H.-J. Kroll, Technical Editors-in-Chief: I. Gohberg, Tel Aviv University of Munich, Germany University, Israel and Print ISSN 0047-2468 S.M. VERDUYN LUNEL, Leiden University, Electronic ISSN 1420-8997 2007, Vols. 88-90 (2 issues per volume) The Netherlands Print ISSN 0378-620X Electronic ISSN 1420-8989 2007, Vols. 57-59 (4 issues per volume)

Journal of Journal of Evolution Equations Mathematical Fluid Editors-in Chief: W. Arendt, Universität Ulm, Germany and R. Nagel, Universität Mechanics (JMFM) Tübingen, Germany Editors-in-Chief: G.P. Galdi (Managing editor), University of Print ISSN 1424-3199 Electronic ISSN 1424-3202 Pittsburgh, PA; J.G. HEYWOOD, 2007, Vol. 7 (4 issues) University of British Columbia, Vancou- ver, BC, Canada; and R. RANNACHER, Universität Heidelberg, Germany Print ISSN 1422-6928 Electronic ISSN 1422-6952 2007, Vol. 9 (6 issues)

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Logica Universalis Nexus Network Editor-in-Chief: JEAN-YVES BEZIAU, Journal Swiss National Science Foundation, Switzerland Architecture and Math- Print ISSN: 1661-8297 ematics Electronic ISSN: 1661-8300 Editor-in-Chief: kim williams 2007, Vol. 1 (2 issues) Print ISSN: 1590-5896 Electronic ISSN: 1522-4600 2007, Vol. 9 (2 issues)

Mathematics in Nonlinear Differential Computer Equations and Science Applications Editors-in-Chief: Dongming Zeng (NoDEA) (Managing editor), Beihang University, Managing Editor: Beijing, China; I. Capuzzo dolcetta (Chairman), ZHIMING ZENG, Beihang University, Università degli Studi di Roma “La Sapi- Beijing, China enza,” Rome, Italy Print ISSN: 1661-8270 Print ISSN 1021-9722 Electronic ISSN: 1661-8289 Electronic ISSN 1420-9004 2007, Vol. 1 (4 issues) 2007, Vol. 14 (6 issues)

Mediterranean Journal of Physics in Mathematics Perspective Editors-in-Chief: J.S. Rigden, American Editor-in-Chief: F. ALTOMARE, Università Institute of Physics, College Park, MD; and degli Studi di Bari, Italy R.H. Stuewer, University of Minnesota, Print ISSN: 1660-5446 Minneapolis, MN Electronic ISSN: 1660-5454 2007, Vol. 7 (4 issues) Print ISSN 1422-6944 Electronic ISSN 1422-6960 2007, Vol. 9 (4 issues)

Milan Journal of Mathematics Positivity Managing Editor: B. RUF, Università degli An International Math- Studi di Milano, Italy ematics Journal Print ISSN: 1424-9286 Devoted to the Theory and Electronic ISSN: 1424-9294 Applications 2007, Vol. 75 (1 issue) of Positivity Editor-in-Chief: charalambos d. aliprantis, Purdue University, West Lafayette, IN Print ISSN: 1385-1292 Electronic ISSN: 1572-9281 2007, Vol. 11 (4 issues)

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Results in Zeitschrift für Mathematics Angewandte H. Wefelscheid, Universitat Duisburg- Mathematik und Essen, Germany Print ISSN 1422-6383 Physik (ZAMP) 2007, Vols. 51-52 (4 issues per volume) Journal of Applied Math- ematics and Physics Managing Editor: K. Nipp, ETH Zentrum, Zürich, Switzerland Print ISSN 0044-2275 Electronic ISSN 1420-9039 2007, Vol. 58 (6 issues)

Selecta Mathematica, New Series Editor-in-Chief: I.M. Gelfand, Rutgers University, Piscataway, NJ Managing Editor: A. Cohen, Rutgers University, Piscataway, NJ Print ISSN 1022-1824 Electronic ISSN 1420-9020 2007, Vol. 13 (4 issues)

Transformation Groups Editor-in-Chief: E.B. Vinberg, Moscow State University, Russia M. Brion, Institut Fourier, Saint-Martin d’HËres 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 2007, Vol. 12 (4 issues)

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