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Applied-Math-Catalog-Web.Pdf Applied mathematics was once only associated with the natural sciences and en- gineering, yet over the last 50 years it has blossomed to include many fascinat- ing subjects outside the physical sciences. Such areas include game theory, bio- mathematics and mathematical economy demonstrating mathematics' presence throughout everyday human activity. The AMS book publication program on applied and interdisciplinary mathematics strengthens the connections between mathematics and other disciplines, highlighting the areas where mathematics is most relevant. These publications help mathematicians understand how math- ematical ideas may benefit other sciences, while offering researchers outside of mathematics important tools to advance their profession. Table of Contents Algebra and Algebraic Geometry .............................................. 3 Analysis ........................................................................................... 3 Applications ................................................................................... 4 Differential Equations .................................................................. 11 Discrete Mathematics and Combinatorics .............................. 16 General Interest ............................................................................. 17 Geometry and Topology ............................................................. 18 Mathematical Physics ................................................................... 19 Probability ...................................................................................... 24 Index ................................................................................................ 26 Ordering Information .................................................................. 30 Order by Phone | 1-401-455-4000 or 1-800-321-4267 Algebra and Algebraic Geometry, Analysis Algebra and Algebraic Analysis Geometry Topics in Optimal Mathematical Topics in Optimal Transportation Surveys Algebraic Geometric and Monographs Volume 139 Algebraic Codes: Basic Notions Transportation Cédric Villani, École Normale Geometric Supérieure de Lyon, France , French- Codes: Michael Tsfasman Cédric Villani Cedric Villani’s book is a lucid Basic Russian Poncelet Laboratory (CNRS and Ind. Univ. Moscow), Graduate Studies and very readable documentation Notions in Mathematics Russia, and Institute for Volume 58 of the tremendous recent analytic Michael Tsfasman progress in “optimal mass Serge Vla˘dut¸ Information Transmission Dmitry Nogin Problems, Moscow, Russia, Serge transportation” theory and of its diverse and unexpected American Mathematical Society Vlaˇdut¸, Institut de Mathématiques de Luminy, France, and Institute applications in optimization, nonlinear PDE, geometry, for Information Transmission and mathematical physics. Problems, Moscow, Russia, and Dmitry Nogin, Institute —Lawrence C. Evans, University of California at Berkeley for Information Transmission Problems, Moscow, Russia The book is devoted to the theory of algebraic geometric In 1781, Gaspard Monge defined the problem of “optimal codes, a subject formed on the border of several domains transportation”, or the transferring of mass with the least of mathematics. On one side there are such classical areas possible amount of work, with applications to engineering as algebraic geometry and number theory; on the other, in mind. In 1942, Leonid Kantorovich applied the newborn information transmission theory, combinatorics, finite machinery of linear programming to Monge’s problem, with geometries, dense packings, etc. applications to economics in mind. In 1987, Yann Brenier used optimal transportation to prove a new projection The authors give a unique perspective on the subject. theorem on the set of measure preserving maps, with appli- Whereas most books on coding theory build up coding cations to fluid mechanics in mind. theory from within, starting from elementary concepts and almost always finishing without reaching a certain depth, Each of these contributions marked the beginning of a this book constantly looks for interpretations that connect whole mathematical theory, with many unexpected rami- coding theory to algebraic geometry and number theory. fications. Nowadays, the Monge-Kantorovich problem is used and studied by researchers from extremely diverse There are no prerequisites other than a standard algebra horizons, including probability theory, functional analysis, graduate course. The first two chapters of the book can serve isoperimetry, partial differential equations, and even meteor- as an introduction to coding theory and algebraic geometry ology. respectively. Special attention is given to the geometry of curves over finite fields in the third chapter. Finally, in the Originating from a graduate course, the present volume is last chapter the authors explain relations between all of at once an introduction to the field of optimal transporta- these: the theory of algebraic geometric codes. tion and a survey of the research on the topic over the last 15 years. The book is intended for graduate students and READERSHIP: Graduate students and research mathema- researchers, and it covers both theory and applications. ticians interested in algebraic geometry and coding theory. Readers are only assumed to be familiar with the basics of Mathematical Surveys and Monographs, Volume 139 measure theory and functional analysis. 2007; 338 pp.; hardcover; ISBN: 978-0-8218-4306-2; List US$89; READERSHIP: Graduate students and research mathema- AMS members US$71.20; Order code: SURV/139 ticians interested in probability theory, functional analysis, isoperimetry, partial differential equations, and meteor- ology. Graduate Studies in Mathematics, Volume 58 2003; 370 pp.; hardcover; ISBN: 978-0-8218-3312-4; List US$62; AMS members US$49.60; Order code: GSM/58 3 Order Online | www.ams.org/bookstore Applications TEXTBOOK TEXTBOOKS An Introductory FROM THE AMS Applications An Introductory Course on Course on Mathematical Mathematical Game A Primer on TEXTBOOK Game Theory Theory Pseudorandom Julio González-Díaz Ignacio García-Jurado Volume 55 Generators M. Gloria Fiestras-Janeiro Julio González-Díaz, A Primer on Universidade de Santiago de Oded Goldreich, Weizmann Graduate Studies Pseudorandom in Mathematics Compostela, Spain, Ignacio Generators Institute of Science, Rehovot, Israel Volume 115 García-Jurado, Universidad de Oded Goldreich American Mathematical Society A fresh look at the question Real Sociedad Matemática Española Coruña, Spain, and M. Gloria of randomness was taken in the Fiestras-Janeiro, Universidad de theory of computing: A distribu- Vigo, Spain tion is pseudorandom if it cannot Game theory provides a mathematical setting for analyzing be distinguished from the uniform competition and cooperation in interactive situations. The distribution by any efficient procedure. This paradigm, theory has been famously applied in economics, but is originally associating efficient procedures with polyno- relevant in many other sciences, such as political science, mial-time algorithms, has been applied with respect to a biology, and, more recently, computer science. This book variety of natural classes of distinguishing procedures. The presents an introductory and up-to-date course on game resulting theory of pseudorandomness is relevant to science theory addressed to mathematicians and economists, and at large and is closely related to central areas of computer to other scientists having a basic mathematical background. science, such as algorithmic design, complexity theory, and The book is self-contained, providing a formal descrip- cryptography. tion of the classic game-theoretic concepts together with This primer surveys the theory of pseudorandomness, rigorous proofs of the main results in the field. The theory starting with the general paradigm, and discussing various is illustrated through abundant examples, applications, and incarnations while emphasizing the case of general-purpose exercises. pseudorandom generators (withstanding any polyno- The style is distinctively concise, while offering motiva- mial-time distinguisher). Additional topics include the tions and interpretations of the theory to make the book “derandomization” of arbitrary probabilistic polynomial- accessible to a wide readership. The basic concepts and time algorithms, pseudorandom generators withstanding results of game theory are given a formal treatment, and the space-bounded distinguishers, and several natural notions mathematical tools necessary to develop them are carefully of special-purpose pseudorandom generators. presented. Cooperative games are explained in detail, with The primer assumes basic familiarity with the notion bargaining and TU-games being treated as part of a general of efficient algorithms and with elementary probability framework. The authors stress the relation between game theory, but provides a basic introduction to all notions theory and operations research. that are actually used. As a result, the primer is essentially READERSHIP: Advanced undergraduates and graduate self-contained, although the interested reader is at times students interested in game theory. referred to other sources for more detail. Graduate Studies in Mathematics, Volume 115 Advanced undergraduates and computer READERSHIP: 2010; 324 pp.; hardcover; ISBN: 978-0-8218-5151-7; List US$62; science majors, graduate students, and research mathema- AMS members US$49.60; Order code: GSM/115 ticians interested in complexity
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