Applied 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 , 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 ...... 3 ...... 3 Applications ...... 4 Differential Equations ...... 11 Discrete Mathematics and ...... 16 General Interest ...... 17 Geometry and ...... 18 ...... 19 Probability ...... 24 Index ...... 26 Ordering ...... 30

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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 ; on the other, in mind. In 1942, Leonid Kantorovich applied the newborn information transmission theory, combinatorics, finite machinery of to Monge’s problem, with , 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 of measure preserving maps, with appli- Whereas most books on 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 , , 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 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

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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 : 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 , has been applied with respect to a biology, and, more recently, 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- . 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 between game theory, but provides a basic introduction to all notions theory and . 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 thory, cryptography, and pseudorandom generators. University Lecture Series, Volume 55 2010; 114 pp.; softcover; ISBN: 978-0-8218-5192-0; List US$36; AMS members US$28.80; Order code: ULECT/55

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Classical and Quantum Computation A. Yu. Kitaev, California Institute of Technology, Pasadena, CA, and A. H. Shen and M. N. Vyalyi, Independent University of Moscow, Russia This book presents a concise introduction to an emerging and increasingly important topic, the theory of . The development of quantum computing exploded in 1994 with the discovery of its use in factoring large numbers—an extremely difficult and time-consuming problem when using a conventional computer. In less than 300 pages, the authors set forth a solid foundation to the theory, including results that have not appeared elsewhere and improvements on existing works. The book starts with the basics of classical , including NP-complete problems and the idea of complexity of an . Then the authors introduce general principles of quantum computing and pass to the study of main quantum computation algorithms: Grover’s algorithm, Shor’s factoring algorithm, and the Abelian hidden subgroup problem. In concluding sections, several related topics are discussed (parallel quantum computation, a quantum analog of NP-, and quantum error-correcting codes). This is a suitable textbook for a graduate course in quantum computing. Prerequisites are very modest and include , elements of theory and probability, and the notion of an algorithm (on a formal or an intuitive level). The book is complete with problems, solutions, and an appendix summarizing the necessary results from number theory. READERSHIP: Advanced undergraduates, graduate students, research mathematicians, physicists, and computer scientists inter- ested in and quantum theory. Graduate Studies in Mathematics, Volume 47 2002; 257 pp.; softcover; ISBN: 978-0-8218-3229-5; List US$40; AMS members US$32; Order code: GSM/47.S

Option Pricing and Portfolio Optimization Option Pricing and Portfolio Modern Methods of Financial Mathematics Optimization Ralf Korn and Elke Korn, University of Kaiserslautern, Germany Modern Methods of Financial Mathematics Ralf Korn Understanding and working with the current models of financial markets requires a sound knowl- Elke Korn edge of the mathematical tools and ideas from which they are built. Banks and financial houses all over the world recognize this and are avidly recruiting mathematicians, physicists, and other Graduate Studies in Mathematics Volume 31 scientists with these skills.

American Mathematical Society The mathematics involved in modern finance springs from the heart of probability and analysis: the Itô , stochastic control, differential equations, martingales, and so on. The authors give rigorous treatments of these topics, while always keeping the applications in mind. Thus, the way in which the mathematics is developed is governed by the way it will be used, rather than by the goal of optimal generality. Indeed, most of the purely mathematical topics are treated in extended “excursions” from the applications into the theory. Thus, with the main topic of financial modelling and optimization in view, the reader also obtains a self-contained and complete introduction to the underlying mathematics. This book is specifically designed as a graduate textbook. It could be used for the second part of a course in probability theory, as it includes an applied introduction to the basics of stochastic processes (martingales and Brownian motion) and . It would also be suitable for a course in continuous-time finance that assumes familiarity with stochastic processes. The prerequisites are basic probability theory and calculus. Some background in stochastic processes would be useful, but not essential.

Especially useful for students seeking a lively introduction to Itô calculus. —Short Book Reviews, International Statistical Institute

READERSHIP: Graduate level and research mathematicians, physicists, financial analysts, and actuarians interested in . Graduate Studies in Mathematics, Volume 31 2001; 253 pp.; hardcover; ISBN: 978-0-8218-2123-7; List US$43; AMS members US$34.40; Order code: GSM/31

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TEXTBOOK

TEXTBOOKS Introduction to PDEs FROM THE AMS Training Manual on Training Manual and Waves for the on Transport Transport and Fluids and Fluids Atmosphere and TEXTBOOK John C. Neu, University of

Ocean John C. Neu California, Berkeley, CA Andrew Majda, New York John Neu’s book presents the University-Courant Institute of basic ideas of fluid mechanics, Graduate Studies in Mathematics Mathematical Sciences, New York Volume 109 and of the transport of matter, in

The goals of these lecture notes, American Mathematical Society a clear and reader-friendly way. based on courses presented by the Then it proposes a collection of author at the Courant Institute of problems, starting with easy ones Mathematical Sciences, are to introduce mathematicians and gradually leading up to harder ones. Each problem to the fascinating and important area of atmosphere/ocean is solved with all the steps explained. In the course of science (AOS) and, conversely, to develop a mathematical solving these problems, many fundamental methods of viewpoint on basic topics in AOS of interest to the disci- analysis are introduced and explained. This is an ideal plinary AOS community, ranging from graduate students to book for use as a text, or for individual study. researchers. The lecture notes emphasize the serendipitous —Joseph B. Keller, Stanford University connections between and geophys- ical flows in the style of modern applied mathematics, I have learned a lot from John Neu over the past years, where rigorous as well as asymptotic, and his book reflects very well his sense of style and qualitative, and numerical modeling all interact to ease purpose. the understanding of physical phenomena. Reading these lecture notes does not require a previous course in fluid —Walter Craig, McMaster University, Hamilton, Ontario, dynamics, although a serious reader should supplement Canada and Fields Institute for Research in Mathematical these notes with material such as additional information on Sciences, Toronto, Ontario, Canada geophysical flows, as suggested in the preface. This book presents elementary models of transport in The book is intended for graduate students and researchers continuous media and a corresponding body of math- working in interdisciplinary areas between mathematics ematical technique. Physical topics include convection and atmosphere/ocean science. and diffusion as the simplest models of transport; local READERSHIP: Graduate students and researchers working conservation laws with sources as the general framework in partial differential equations and their applications to of continuum mechanics; ideal fluid as the simplest model atmosphere/ocean science (AOS); applied mathematicians. of a medium with mass; momentum and energy transport; Titles in this series are co-published with the Courant Institute of and finally, free surface waves, in particular, shallow water Mathematical Sciences at New York University. theory. Courant Lecture Notes, Volume 9 There is a strong emphasis on dimensional analysis and 2003; 234 pp.; softcover; ISBN: 978-0-8218-2954-7; List US$34; scaling. Some topics, such as physical similarity and simi- AMS members US$27.20; Order code: CLN/9 larity solutions, are traditional. In addition, there are reductions based on scaling, such as incompressible flow as a limit of compressible flow, and shallow water theory derived asymptotically from the full equations of free surface waves. More and deeper examples are presented as problems, including a series of problems that model a tsunami approaching the shore. The problems form an embedded subtext to the book. Each problem is followed by a detailed solution emphasizing process and craftsmanship. The problems express the practice of applied mathematics as the examination and re-examination of simple but essential ideas in many inter- related examples. READERSHIP: Graduate students and research math- ematicians interested in applications of PDE to physics, in particular, fluid dynamics. Graduate Studies in Mathematics, Volume 109 2010; 265 pp.; hardcover; ISBN: 978-0-8218-4083-2; List US$59; AMS members US$47.20; Order code: GSM/109

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Computational Introduction to the Complexity Theory Introduction to Mathematics of the Mathematics Finance Steven Rudich, Carnegie Mellon of Finance University, Pittsburgh, PA, and Avi R. J. Williams, University of Wigderson, Institute for Advanced R. J. Williams California, San Diego, La Jolla, CA Study, Princeton, NJ, Editors The modern subject of mathematical Graduate Studies Computational Complexity Theory in Mathematics Volume 72 finance has undergone considerable is the study of how much of a given development, both in theory and resource is required to perform the practice, since the seminal work of computations that interest us the Black and Scholes appeared a third most. Four decades of fruitful research have produced a of a century ago. This book is intended as an introduction rich and subtle theory of the relationship between different to some elements of the theory that will enable students resource measures and problems. At the core of the theory and researchers to go on to read more advanced texts and are some of the most alluring open problems in math- research papers. ematics. The book begins with the development of the basic ideas of This book presents three weeks of lectures from the hedging and pricing of European and American IAS/Park City Mathematics Institute Summer School on in the discrete (i.e., discrete time and discrete state) setting computational complexity. The first week gives a general of binomial tree models. Then a general discrete finite introduction to the field, including descriptions of the basic market model is introduced, and the fundamental theorems models, techniques, results and open problems. The second of asset pricing are proved in this setting. Tools from prob- week focuses on lower bounds in concrete models. The final ability such as conditional expectation, filtration, (super) week looks at randomness in computation, with discussions martingale, equivalent martingale measure, and martingale of different notions of pseudorandomness, interactive proof representation are all used first in this simple discrete systems and zero knowledge, and probabilistically checkable framework. This provides a bridge to the continuous (time proofs (PCPs). and state) setting, which requires the additional concepts READERSHIP: Graduate students and research mathema- of Brownian motion and stochastic calculus. The simplest ticians interested in computational complexity. model in the continuous setting is the famous Black-Scholes model, for which pricing and hedging of European and Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of American derivatives are developed. The book concludes the Mathematical Association of America (MAA) and the National with a description of the fundamental theorems for a Council of Teachers of Mathematics (NCTM) receive a 20% continuous market model that generalizes the simple Black- discount from list price. Scholes model in several directions. IAS/Park City Mathematics Series, Volume 10 READERSHIP: Graduate students interested in financial 2004; 389 pp.; hardcover; ISBN: 978-0-8218-2872-4; List US$72; AMS members US$57.60; Order code: PCMS/10 mathematics. Graduate Studies in Mathematics, Volume 72 2006; 150 pp.; hardcover; ISBN: 978-0-8218-3903-4; List US$39; AMS members US$31.20; Order code: GSM/72

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STUDENT MATHEMATICAL LIBRARY VOLUME 18 Cryptography: An Inverse Problems, Multi-Scale Introduction Analysis, and Effective Medium Cryptography: An V. V. Yaschenko, Moscow Center Theory Introduction for Continuous Mathematics Habib Ammari, Ecole Polytechnique, Palaiseau, France, V. V. Yaschenko Education, Russia, Editor and Hyeonbae Kang, Seoul National University, Korea, Editor Learning about cryptography Editors requires examining fundamental Contemporary Mathematics, Volume 408 issues about . 2006; 265 pp.; softcover; ISBN: 978-0-8218-3968-3; List US$69; AMS Questions abound, ranging from members US$55.20; Order code: CONM/408 “From whom are we protecting ourselves?” and “How can we measure levels of security?” Algebraic Coding Theory and to “What are our opponent’s capabilities?” and “What are their goals?” Answering these questions requires an understanding of basic cryptography. This book, written by A. Ashikhmin, Bell Labs, Lucent Technologies, Murray Russian cryptographers, explains those basics. Hill, NJ, and A. Barg, University of Maryland, College Chapters are independent and can be read in any order. Park, MD, Editors Co-published with the Center for Discrete Mathematics and The introduction gives a general description of all the main Theoretical Computer Science. notions of modern cryptography: a cipher, a key, security, an electronic digital signature, a cryptographic protocol, DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, Volume 68 etc. Other chapters delve more deeply into this material. The final chapter presents problems and selected solutions 2005; 177 pp.; hardcover; ISBN: 978-0-8218-3626-2; List US$83; AMS members US$66.40; Order code: DIMACS/68 from Russian “Cryptography Olympiads for High School Students”. This English translation of a Russian textbook is suitable Control and Nonlinearity for advanced high school students and undergraduates Jean-Michel Coron, Université de Paris-Sud, Orsay, studying information security. It is also appropriate for a France general mathematical audience interested in cryptography. This well written book by Jean-Michel Coron, READERSHIP: Undergraduates, graduate students, and one of the world['s] leading experts in the field, research mathematicians interested in cryptography; enables the reader to enter the difficult subject general mathematical audience. and to understand the most important methods Student Mathematical Library, Volume 18 used here. A book like this was urgently needed. 2002; 229 pp.; softcover; ISBN: 978-0-8218-2986-8; List US$43; AMS members US$34.40; Order code: STML/18 —Zentralblatt MATH Mathematical Surveys and Monographs, Volume 136 Discrete Methods in Epidemiology 2007; 426 pp.; hardcover; ISBN: 978-0-8218-3668-2; List US$99; James Abello, DIMACS, Piscataway, NJ, and AMS members US$79.20; Order code: SURV/136 ask.com Research, Piscataway, NJ, and Graham Cormode, DIMACS, Piscataway, NJ, and Bell Coding Theory and Quantum Laboratories, Murray Hill, NJ, Editors Co-published with the Center for Discrete Mathematics and Computing Theoretical Computer Science. David Evans and Jeffrey J. Holt, University of Virginia, DIMACS: Series in Discrete Mathematics and Theoretical Charlottesville, VA, Chris Jones, St. Mary’s College Computer Science, Volume 70 of California, Moraga, CA, and Karen Klintworth, 2006; 260 pp.; softcover; ISBN: 978-0-8218-4379-6; List US$89; AMS Brian Parshall, Olivier Pfister, and Harold N. Ward, members US$71.20; Order code: DIMACS/70.S University of Virginia, Charlottesville, VA, Editors Contemporary Mathematics, Volume 381 Gems in Experimental Mathematics 2005; 147 pp.; softcover; ISBN: 978-0-8218-3600-2; List US$51; AMS Tewodros Amdeberhan, Tulane University, New members US$40.80; Order code: CONM/381 Orleans, LA, Luis A. Medina, University of Puerto Rico, San Juan, PR, and Victor H. Moll, Tulane University, New Orleans, LA, Editors Contemporary Mathematics, Volume 517 2010; 413 pp.; softcover; ISBN: 978-0-8218-4869-2; List US$115; AMS members US$92; Order code: CONM/517

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Disease Evolution Mathematics of Information and Models, Concepts, and Analyses Coding Zhilan Feng, Purdue University, West Lafayette, IN, Te Sun Han and Kingo Kobayashi, The University of Ulf Dieckmann, International Institute for Applied Electro-Communications, Tokyo, Japan Systems Analysis, Laxenburg, Austria, and Simon Levin, This is a comprehensive, thoroughly written book Princeton University, NJ, Editors devoted to one of the most important applied topics in DIMACS: Series in Discrete Mathematics and Theoretical discrete mathematics. —Mathematical Reviews Computer Science, Volume 71 2006; 237 pp.; hardcover; ISBN: 978-0-8218-3753-5; List US$89; Translations of Mathematical Monographs, Volume 203 AMS members US$71.20; Order code: DIMACS/71 2002; 286 pp.; softcover; ISBN: 978-0-8218-4256-0; List US$104; AMS members US$83.20; Order code: MMONO/203.S Algebraic Methods in Cryptography Introduction to Mathematical Lothar Gerritzen, Ruhr-Universität Bochum, Germany, Dorian Goldfeld, Columbia University, New York, NY, Finance Martin Kreuzer and Gerhard Rosenberger, Universität David C. Heath, Cornell University, Ithaca, NY, and Dortmund, Germany, and Vladimir Shpilrain, The City Glen Swindle, Avista Energy, Houston, TX, Editors College of New York, NY, Editors Proceedings of Symposia in Applied Mathematics, Volume 57 Contemporary Mathematics, Volume 418 1999; 167 pp.; hardcover; ISBN: 978-0-8218-0751-4; List US$34; 2006; 178 pp.; softcover; ISBN: 978-0-8218-4037-5; List US$59; AMS AMS members US$27.20; Order code: PSAPM/57 members US$47.20; Order code: CONM/418 Geometric and Algorithmic Aspects Mathematical Studies on Human of Computer-Aided Design and Disease Dynamics Manufacturing Emerging Paradigms and Challenges Ravi Janardan, University of Minnesota, Minneapolis, Abba Gumel, Editor-in-Chief, University of Manitoba, MN, Michiel Smid, Carleton University, Ottawa, ON, Winnipeg, MB, Canada, Carlos Castillo-Chavez, Canada, and Debasish Dutta, University of Michigan, Arizona State University, Tempe, AZ, Ronald E. Ann Arbor, MI, Editors Mickens, Clark Atlanta University, GA, and Dominic Co-published with the Center for Discrete Mathematics and P. Clemence, North Carolina A&T State University, Theoretical Computer Science. Greensboro, NC, Editors DIMACS: Series in Discrete Mathematics and Theoretical Contemporary Mathematics, Volume 410 Computer Science, Volume 67 2006; 389 pp.; softcover; ISBN: 978-0-8218-3775-7; List US$99; AMS 2005; 360 pp.; hardcover; ISBN: 978-0-8218-3628-6; List US$104; members US$79.20; Order code: CONM/410 AMS members US$83.20; Order code: DIMACS/67

Modeling Paradigms and Analysis of Modeling and Simulation of Disease Transmission Models Biological Networks Abba B. Gumel, University of Manitoba, Winnipeg, MB, Reinhard C. Laubenbacher, Virginia Canada, and Suzanne Lenhart, University of Tennessee, Institute at Virginia Tech, Blacksburg, VA, Editor Knoxville, TN, Editors Proceedings of Symposia in Applied Mathematics, Volume 64 Co-published with the Center for Discrete Mathematics and 2007; 151 pp.; hardcover; ISBN: 978-0-8218-3964-5; List US$39; Theoretical Computer Science. AMS members US$31.20; Order code: PSAPM/64 DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, Volume 75 Data Depth: Robust Multivariate 2010; approximately 278 pp.; hardcover; ISBN: 978-0-8218-4384-0; List US$104; AMS members US$83.20; Order code: DIMACS/75 Analysis, and Applications Regina Y. Liu, Rutgers University, New Brunswick, NJ, Robert Serfling, University of Texas at Dallas, Richardson, TX, and Diane L. Souvaine, Tufts University, Medford, MA, Editors Co-published with the Center for Discrete Mathematics and Theoretical Computer Science. DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, Volume 72 2006; 246 pp.; hardcover; ISBN: 978-0-8218-3596-8; List US$89; AMS members US$71.20; Order code: DIMACS/72

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Recent Trends in Coding Theory and Recent Advances in Adaptive Its Applications Computation Wen-Ching Winnie Li, Pennsylvania State University, Z.-C. Shi and Z. Chen, Chinese Academy of Sciences, University Park, PA, Editor Beijing, China, T. Tang, Hong Kong Baptist University, Titles in this series are co-published with International Press, China, and D. Yu, Chinese Academy of Sciences, Beijing, Cambridge, MA. China, Editors AMS/IP Studies in Advanced Mathematics, Volume 41 Contemporary Mathematics, Volume 383 2007; 200 pp.; softcover; ISBN: 978-0-8218-4298-0; List US$59; AMS 2005; 386 pp.; softcover; ISBN: 978-0-8218-3662-0; List US$114; members US$47.20; Order code: AMSIP/41 AMS members US$91.20; Order code: CONM/383

Quantum Computation Advances in Information Recording A Grand Mathematical Challenge for the Paul H. Siegel, University of California, San Diego, Twenty-First Century and the Millennium La Jolla, CA, Emina Soljanin and Adriaan J. van , Bell Laboratories, Murray Hill, NJ, and Samuel J. Lomonaco, Jr., Editor Wijngaarden Bane Vasic´, University of Arizona, Tucson, AZ, Editors A very accessible invitation to some of the essential Co-published with the Center for Discrete Mathematics and aspects of quantum computation … The book is great Theoretical Computer Science. both for self-study and for a beginning course, and it is DIMACS: Series in Discrete Mathematics and Theoretical enjoyable reading. Computer Science, Volume 73 —Palle Jorgensen 2008; 165 pp.; hardcover; ISBN: 978-0-8218-3752-8; List US$79; AMS members US$63.20; Order code: DIMACS/73 Proceedings of Symposia in Applied Mathematics, Volume 58 2002; 358 pp.; hardcover; ISBN: 978-0-8218-2084-1; List US$76; New Perspectives in Mathematical AMS members US$60.80; Order code: PSAPM/58 Biology

STUDENT MATHEMATICAL LIBRARY VOLUME 11 An Introduction to Siv Sivaloganathan, University of Waterloo, ON, An Introduction to Canada, Editor Game-Theoretic Game-Theoretic Modelling Titles in this series are co-published with the Fields Institute for Second Edition Modelling Research in Mathematical Sciences (Toronto, Ontario, Canada). Michael Mesterton-Gibbons Second Edition Fields Institute Communications, Volume 57 2010; approximately 139 pp.; hardcover; ISBN: 978-0-8218-4845-6; Mike Mesterton-Gibbons, List US$79; AMS members US$63.20; Order code: FIC/57 Florida State University, Tallahassee, FL Prediction and Discovery The mathematics described [in the book] is fascinating and well Joseph Stephen Verducci, Ohio State University, worth studying … The examples are great, and the Columbus, OH, Xiaotong Shen, University of Minnesota, author has clearly put enormous effort into building Minneapolis, MN, and John Lafferty, Carnegie Mellon this collection … a perfect source of problems for a University, Pittsburgh, PA, Editors Moore method course … a valuable contribution to Contemporary Mathematics, Volume 443 the literature … Everyone interested in game theory or 2007; 226 pp.; softcover; ISBN: 978-0-8218-4195-2; List US$69; AMS mathematical modelling should take a look at it. members US$55.20; Order code: CONM/443 —MAA Online Topological Quantum Computation Student Mathematical Library, Volume 11 Zhenghan Wang, Microsoft, Santa Barbara, CA 2001; 368 pp.; softcover; ISBN: 978-0-8218-1929-6; List US$43; AMS A co-publication of the AMS and CBMS. members US$34.40; Order code: STML/11 CBMS Regional Conference Series in Mathematics, Number 112 and Mathematical 2010; 115 pp.; softcover; ISBN: 978-0-8218-4930-9; List US$34; AMS members US$27.20; All Individuals US$27.20; Order code: Programming CBMS/112 Panos M. Pardalos, University of Florida, Gainesville, FL, and Pierre Hansen, HEC Montréal, QC, Canada, Mathematics of Finance Editors George Yin, Wayne State University, Detroit, MI, and CRM Proceedings & Lecture Notes, Volume 45 Qing Zhang, University of Georgia, Athens, GA, Editors 2008; 234 pp.; softcover; ISBN: 978-0-8218-4352-9; List US$85; AMS Contemporary Mathematics, Volume 351 members US$68; Order code: CRMP/45 2004; 398 pp.; softcover; ISBN: 978-0-8218-3412-1; List US$104; AMS members US$83.20; Order code: CONM/351

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Differential Equations

Mathematical Surveys and Nonlocal Diffusion Problems Monographs Volume 165 Nonlocal Fuensanta Andreu-Vaillo, José M. Mazón, Universitat de València, Spain, Julio D. Rossi, Diffusion Universidad de Alicante, Spain, and , Universitat de València, Spain Problems J. Julián Toledo-Melero Nonlocal diffusion problems arise in a wide variety of applications, including biology, image Fuensanta Andreu-Vaillo José M. Mazón processing, particle systems, coagulation models, and mathematical finance. These types of prob- Julio D. Rossi J. Julián Toledo-Melero lems are also of great interest for their purely mathematical content. This book presents recent results on nonlocal evolution equations with different boundary condi- American Mathematical Society Real Sociedad Matemática Española tions, starting with the linear theory and moving to nonlinear cases, including two nonlocal models for the evolution of sandpiles. Both existence and uniqueness of solutions are considered, as well as their asymptotic behaviour. Moreover, the authors present results concerning limits of solutions of the nonlocal equations as a rescaling parameter tends to zero. With these limit procedures the most frequently used diffusion models are recovered: the heat equation, the p-Laplacian​ evolution equation, the porous media equation, the total variation flow, a convection-diffusion equation and the local models for the evolution of sandpiles due to Aronsson- Evans-Wu and Prigozhin. Readers are assumed to be familiar with the basic concepts and techniques of functional analysis and partial differential equations. The text is otherwise self-contained, with the exposition emphasizing an intuitive understanding and results given with full proofs. It is suitable for graduate students or researchers. The authors cover a subject that has received a great deal of attention in recent years. The book is intended as a reference tool for a general audience in analysis and PDEs, including mathematicians, engineers, physicists, biologists, and others interested in nonlocal diffusion problems. READERSHIP: Graduate students and research mathematicians interested in diffusion problems and nonlinear PDE. Mathematical Surveys and Monographs, Volume 165 2010; approximately 264 pp.; hardcover; ISBN: 978-0-8218-5230-9; List US$82; AMS members US$65.60; Order code: SURV/165

A Geometric Approach to A Geometric Approach to Free Boundary Problems Free Boundary Luis Caffarelli, University of Texas, Austin, TX, and Sandro Salsa, Politecnico di Milano, Italy Problems Free boundary (or moving boundary or phase transition) problems surface in many areas of analysis, geometry, and applied mathematics. A typical example is the evolving interphase between a solid Luis Caffarelli Sandro Salsa and liquid phase: if we know the initial configuration well enough, we should be able to reconstruct its evolution, in particular, the evolution of the interphase. In this book we present a series of ideas,

Graduate Studies methods, and techniques for treating the most basic issues of such a problem. In particular, we in Mathematics

Volume 68 describe the very fundamental tools of geometry and that make this possible: proper- ties of harmonic and caloric measures in Lipschitz domains, a relation between parallel surfaces and elliptic equations, monotonicity formulas and rigidity, etc. We hope that the tools and ideas presented here will serve as a basis for the study of more complex phenomena and problems. READERSHIP: Graduate students and research mathematicians interested in partial differential equations. Graduate Studies in Mathematics, Volume 68 2005; 270 pp.; hardcover; ISBN: 978-0-8218-3784-9; List US$51; AMS members US$40.80; Order code: GSM/68

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Translations of Homogenization STUDENT MATHEMATICAL LIBRARY An Introduction to IAS PARK CITY MATHEMATICAL SUBSERIES MATHEMATICAL VOLUME 3 MONOGRAPHS Methods and Applications the Mathematical Volume 234 An Introduction Theory of Waves G. A. Chechkin, Moscow State to the Homogenization Mathematical Methods and University, Russia, and Narvik Theory of Waves Roger Knobel, University of Applications University College, Norway, Roger Knobel Texas-Pan American, Edinburg,

G. A. Chechkin A. L. Piatnitski, Lebedev Physical TX A. L. Piatnitski A. S. Shamaev Institute, Moscow, Russia, and Linear and nonlinear waves are a MATH N EM A A IC T ΤΡΗΤΟΣ ΜΗ I R Ω Τ Ι Σ Ι Ε C Ε E A

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A Narvik University College, Norway, ΑΓΕΩΜ HEMAT AT IC M A L F N ΤΡΗΤΟΣ ΜΗ O 8 Ω Τ Ι Σ Ι Ε U 8 central part of the theory of PDEs. S 8 A ND 1 O ED C I

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F OU 88 Institute for Advanced Study NDED 18 and A. S. Shamaev, Institute for This book begins with a description Problems in Mechanics, Moscow, of one-dimensional waves and their Russia, and Moscow State through computer-aided techniques. Next, University, Russia traveling waves are covered, such as solitary waves for the Homogenization is a collection of powerful techniques in Klein-Gordon and KdV equations. Finally, the author gives partial differential equations that are used to study differen- a lucid discussion of waves arising from conservation laws, tial operators with rapidly oscillating coefficients, boundary including shock and rarefaction waves. As an application, value problems with rapidly varying boundary conditions, interesting models of traffic flow are used to illustrate equations in perforated domains, equations with random conservation laws and wave phenomena. coefficients, and other objects of theoretical and practical This book is based on a course given by the author at the interest. IAS/Park City Mathematics Institute. It is suitable for inde- The book focuses on various aspects of homogenization pendent study by undergraduate students in mathematics, theory and related topics. It comprises classical results engineering, and science programs. and methods of homogenization theory, as well as modern READERSHIP: Advanced undergraduates, graduate subjects and techniques developed in the last decade. students, and research mathematicians interested in Special attention is paid to averaging of random parabolic nonlinear PDEs. equations with lower order terms, to homogenization of singular structures and measures, and to problems with Student Mathematical Library, Volume 3 rapidly alternating boundary conditions. 2000; 196 pp.; softcover; ISBN: 978-0-8218-2039-1; List US$25; AMS members US$20; Order code: STML/3 The book contains many exercises, which help the reader to better understand the material presented. All the main results are illustrated with a large number of examples, ranging from very simple to rather advanced. READERSHIP: Graduate students and research mathema- ticians interested in partial differential equations. Translations of Mathematical Monographs, Volume 234 2007; 234 pp.; hardcover; ISBN: 978-0-8218-3873-0; List US$89; AMS members US$71.20; Order code: MMONO/234

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TEXTBOOK TEXTBOOK

TEXTBOOKS TEXTBOOKS FROM THE AMS Differential Equations, FROM THE AMS Optimal Control of Optimal Control of Partial Mechanics, and Differential Equations Partial Differential Theory, Methods and Applications TEXTBOOK Computation TEXTBOOK Equations

Richard S. Palais, University of Fredi Tröltzsch Theory, Methods and California, Irvine, CA, and Robert Applications A. Palais, University of Utah, Salt Graduate Studies Fredi Tröltzsch, Technische Lake City, UT in Mathematics Volume 112 Universität Berlin, Germany

This book provides a concep- American Mathematical Society Translated by Jürgen Sprekels tual introduction to the theory of ordinary differential equations, Optimal is concerned concentrating on the initial value problem for equations with finding control functions that minimize cost func- of evolution and with applications to the calculus of varia- tions for systems described by differential equations. The tions and classical mechanics, along with a discussion of methods have found widespread applications in aeronau- and ecological models. It has a unified and tics, mechanical engineering, the life sciences, and many visual introduction to the theory of numerical methods and other disciplines. a novel approach to the analysis of errors and stability of This book focuses on optimal control problems where the various numerical solution algorithms based on carefully state equation is an elliptic or parabolic partial differen- chosen model problems. While the book would be suitable tial equation. Included are topics such as the existence of as a textbook for an undergraduate or elementary graduate optimal solutions, necessary optimality conditions and course in ordinary differential equations, the authors have adjoint equations, second-order sufficient conditions, and designed the text also to be useful for motivated students main principles of selected numerical techniques. It also wishing to learn the material on their own or desiring to contains a survey on the Karush-Kuhn-Tucker theory of supplement an ODE textbook being used in a course they nonlinear programming in Banach spaces. are taking with a text offering a more conceptual approach to the subject. The exposition begins with control problems with linear equations, quadratic cost functions and control constraints. READERSHIP: Undergraduate and graduate students To make the book self-contained, basic facts on weak interested in ordinary differential equations and numerical solutions of elliptic and parabolic equations are intro- methods. duced. Principles of functional analysis are introduced Student Mathematical Library, Volume 51 and explained as they are needed. Many simple examples 2009; 313 pp.; softcover; ISBN: 978-0-8218-2138-1; List US$51; AMS illustrate the theory and its hidden difficulties. This start members US$40.80; Order code: STML/51 to the book makes it fairly self-contained and suitable for advanced undergraduates or beginning graduate students. Advanced control problems for nonlinear partial differen- tial equations are also discussed. As prerequisites, results on boundedness and continuity of solutions to semilinear elliptic and parabolic equations are addressed. These topics are not yet readily available in books on PDEs, making the exposition also interesting for researchers. Alongside the main theme of the analysis of problems of optimal control, Tröltzsch also discusses numerical tech- niques. The exposition is confined to brief introductions into the basic ideas in order to give the reader an impres- sion of how the theory can be realized numerically. After reading this book, the reader will be familiar with the main principles of the of PDE-constrained optimization. READERSHIP: Graduate students and research mathema- ticians interested in optimal control theory and PDEs. Graduate Studies in Mathematics, Volume 112 2010; 399 pp.; hardcover; ISBN: 978-0-8218-4904-0; List US$69; AMS members US$55.20; Order code: GSM/112

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High-Dimensional Partial Differential Semilinear Schrödinger Equations Equations in Science and Engineering Thierry Cazenave, Université de Paris VI, Pierre et André Bandrauk, Université de Sherbrooke, QC, Marie Curie, France Canada, Michel C. Delfour, Université de Montréal, This book would be an excellent place to start for readers QC, Canada, and Claude Le Bris, École Nationale des interested in an introduction to these topics. There is an Ponts et Chaussés, Marne La Vallée, France, and INRIA extensive bibliography which nicely complements the Rocquencourt, Le Chesnay, France, Editors author’s discussions. Titles in this series are co-published with the Centre de Recherches Mathématiques. —Woodford W. Zachary for Mathematical Reviews CRM Proceedings & Lecture Notes, Volume 41 Titles in this series are co-published with the Courant Institute of 2007; 194 pp.; softcover; ISBN: 978-0-8218-3853-2; List US$79; AMS Mathematical Sciences at New York University. members US$63.20; Order code: CRMP/41 Courant Lecture Notes, Volume 10 2003; 323 pp.; softcover; ISBN: 978-0-8218-3399-5; List US$44; AMS Partial Differential Equations members US$35.20; Order code: CLN/10 L. Bers, F. John, and M. Schechter Lectures in Applied Mathematics, Volume 3 Partial Differential Equations and 1964; 343 pp.; softcover; ISBN: 978-0-8218-0049-2; List US$51; AMS Inverse Problems members US$40.80; Order code: LAM/3.1 Carlos Conca, Raúl Manásevich, Gunther Uhlmann, and Michael S. Vogelius, Editors Recent Advances in Nonlinear Contemporary Mathematics, Volume 362 Partial Differential Equations and 2004; 410 pp.; softcover; ISBN: 978-0-8218-3448-0; List US$104; Applications AMS members US$83.20; Order code: CONM/362 L. L. Bonilla, Universidad Carlos III de Madrid, Leganés, Spain, A. Carpio, Universidad Complutense de Madrid, Mathematical Analysis of Partial Spain, J. M. Vega, Universidad Politécnica de Madrid, Differential Equations Modeling Spain, and S. Venakides, Duke University, Durham, NC, Electrostatic MEMS Editors Pierpaolo Esposito, Università degli Studi Roma Tre, Proceedings of Symposia in Applied Mathematics, Volume 65 Rome, Italy, Nassif Ghoussoub, University of British 2007; 217 pp.; hardcover; ISBN: 978-0-8218-4211-9; List US$49; Columbia, Vancouver, BC, Canada, and Yujin Guo, AMS members US$39.20; Order code: PSAPM/65 University of Minnesota, Minneapolis, MN Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University. Courant Lecture Notes, Volume 20 2010; 318 pp.; softcover; ISBN: 978-0-8218-4957-6; List US$46.50; AMS members US$37.20; Order code: CLN/20

Hyperbolic Partial Differential Equations and Wave Phenomena Mitsuru Ikawa, Kyoto University, Japan Translations of Mathematical Monographs (Iwanami Series in Modern Mathematics), Volume 189 2000; 190 pp.; softcover; ISBN: 978-0-8218-1021-7; List US$39; AMS members US$31.20; Order code: MMONO/189

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Lectures on Elliptic and Parabolic Tools for PDE Equations in Hölder Spaces Pseudodifferential Operators, N. V. Krylov, University of Minnesota, Minneapolis, MN Paradifferential Operators, and Layer Graduate Studies in Mathematics, Volume 12 Potentials 1996; 164 pp.; hardcover; ISBN: 978-0-8218-0569-5; List US$34; Michael E. Taylor, University of North Carolina, Chapel AMS members US$27.20; Order code: GSM/12 Hill, NC Mathematical Surveys and Monographs, Volume 81 Fine Regularity of Solutions of 2000; 257 pp.; softcover; ISBN: 978-0-8218-4378-9; List US$62; AMS Elliptic Partial Differential Equations members US$49.60; Order code: SURV/81.S Jan Maly´, Charles University, Prague, Czech Republic, and William P. Ziemer, Indiana University, Bloomington and Numerical Mathematical Surveys and Monographs, Volume 51 Analysis 1997; 291 pp.; hardcover; ISBN: 978-0-8218-0335-6; List US$87; P. Winternitz, Université de Montréal, QC, Canada, AMS members US$69.60; Order code: SURV/51 D. Gomez-Ullate, Universitat Politècnica de Catalunya, Barcelona, Spain, A. Iserles, , Nonlinear Dispersive Equations UK, D. Levi, Università degli Studi Roma, Italy, Existence and Stability of Solitary and P. J. Olver, University of Minnesota, Minneapolis, MN, Periodic Travelling Wave Solutions R. Quispel, La Trobe University, Victoria, Australia, and P. Tempesta, Scuola Internazionale Superiore di Studi Jaime Angulo Pava, IME-USP, São Paulo, Brazil Avanzati (SISSA), Trieste, Italy, Editors Mathematical Surveys and Monographs, Volume 156 Titles in this series are co-published with the Centre de Recherches 2009; 256 pp.; hardcover; ISBN: 978-0-8218-4897-5; List US$79; Mathématiques. AMS members US$63.20; Order code: SURV/156 CRM Proceedings & Lecture Notes, Volume 39 2005; 298 pp.; softcover; ISBN: 978-0-8218-3565-4; List US$104; Nonlinear Wave Equations AMS members US$83.20; Order code: CRMP/39 Walter A. Strauss, Brown University, Providence, RI Wigner Measure and Semiclassical CBMS Regional Conference Series in Mathematics, Number 73 1990; 91 pp.; softcover; ISBN: 978-0-8218-0725-5; List US$22; Limits of Nonlinear Schrödinger AMS members US$17.60; All Individuals US$17.60; Order code: Equations CBMS/73 Ping Zhang, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, People’s Hyperbolic Problems: Theory, Republic of China Numerics and Applications Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University. Eitan Tadmor, University of Maryland, College Park, Courant Lecture Notes, Volume 17 MD, Jian-Guo Liu, Duke University, Durham, NC, and University of Maryland, College Park, MD, and 2008; 197 pp.; softcover; ISBN: 978-0-8218-4701-5; List US$30; AMS members US$24; Order code: CLN/17 Athanasios E. Tzavaras, University of Maryland, College Park, MD, and University of Crete, Heraklion, Greece, Editors To order individual parts/volumes or the complete set, please specify the relevant order code. Proceedings of Symposia in Applied Mathematics, Volume 67 Part 1: 2009; 333 pp.; hardcover; ISBN: 978-0-8218-4729-9; Order code: PSAPM/67.1 Part 2: 2009; 999 pp.; hardcover; ISBN: 978-0-8218-4730-5; Order code: PSAPM/67.2 Set: 2009; 1332 pp.; hardcover; ISBN: 978-0-8218-4728-2; List US$223; AMS members US$178.40; Order code: PSAPM/67

15 Order Online | www.ams.org/bookstore Discrete Mathematics and Combinatorics

rithms, operations research, economics, or analysis of Discrete Mathematics and algorithms. Combinatorics Donald E. Knuth is one of the most prominent figures of modern computer science. His works in The Art of Volume 10 Stable Marriage are classic. He is also renowned and Its Relation for his development of TEX and METAFONT. In 1996, C CRM Knuth won the prestigious Kyoto Prize, considered to be R to Other PROCEEDINGS & the nearest equivalent to a Nobel Prize in computer science. M LECTURE NOTES Combinatorial Centre de Recherches Mathématiques Université de Montréal Problems READERSHIP: Advanced undergraduates, graduate Stable Marriage and students and researchers interested in mathematical Its Relation to Other An Introduction to the Combinatorial Problems patterns. An Introduction to the Mathematical Analysis Titles in this series are co-published with the Centre de Recherches Mathematical Analysis of Mathématiques. Algorithms of Algorithms Donald E. Knuth CRM Proceedings & Lecture Notes, Volume 10

THEMAT A IC M A L N ΤΡΗΤΟΣ ΜΗ Ω Τ Ι Σ Ι Ε A S , Stanford O C Donald E. Knuth I

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FO 8 U 88 1997; 74 pp.; softcover; ISBN: 978-0-8218-0603-6; List US$22; AMS NDED 1 University, CA members US$17.60; Order code: CRMP/10 “This is a very stimulating book!” “This is a very stimulating book!” Public-Key —N. G. de Bruijn Proceedings of Symposia in —N. G. de Bruijn A PPLIED M ATHEMATICS Cryptography Volume 62 “This short book will provide extremely enjoyable reading Paul Garrett, University of “This short book will provide extremely enjoyable reading Public-Key to anyoneto anyone with with an interestan interest in in discrete discrete mathematics mathematics and and Minnesota, Minneapolis, MN, Cryptography algorithmalgorithm design.” design.” and Daniel Lieman, Fidelity —Mathematical Reviews Paul Garrett Investments, Merrimack, NH, —Mathematical Reviews Daniel Lieman Editors Editors “This book is an excellent (and enjoyable) means of Proceedings of Symposia in Applied

“This book is an excellent (and enjoyable) means of sketching THEMAT A IC M A L N ΤΡΗΤΟΣ ΜΗ Ε S

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M Y Mathematics, Volume 62 sketching a large area of computer science for specialists A FO 8 U 88 a large area of computer science for specialists in other NDED 1 fields:in It otherrequires fields: little It previous requires knowledge,little previous but knowledge,expects of the but 2005; 183 pp.; hardcover; ISBN: 978-0- expects of the reader a degree of mathematical facility 8218-3365-0; List US$41; AMS members US$32.80; Order code: reader a degree of mathematical facility and a willingness to PSAPM/62 participate.and a It willingness is really neither to participate. a survey nor It is an really introduction; neither a rather,survey it is a paradigm, nor an introduction; a fairly complete rather, treatment it is a paradigm, of a single a fairly complete treatment of a single example used as a Trends in example used as a synopsis of a larger subject.” Proceedings of Symposia in synopsis of a larger subject.” A PPLIED M ATHEMATICS Optimization —SIGACT News Volume 61 —SIGACT News Serkan Hos¸ten, San Fransciso Trends in State University, San Francisco, “Anyone would enjoy reading this book. If one had to Optimization CA, Jon Lee, IBM, T.J. Watson learn French first, it would be worth the effort!” “Anyone would enjoy reading this book. If one had to Serkan Hosten¸ Center, Yorktown Heights, NY, and learn French first, it would be worth the effort!” Jon Lee —Computing Reviews Rekha R. Thomas Rekha R. Thomas, University of Editors —Computing Reviews Washington, Seattle, WA, Editors

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A Proceedings of Symposia in Applied FO 8 U 88 NDED 1 The above citations are taken from reviews of the initial Mathematics, Volume 61 French version of this text—a series of seven expository 2004; 140 pp.; hardcover; ISBN: 978-0- lectures that were given at the University of Montreal in 8218-3584-5; List US$41; AMS members US$32.80; Order code: PSAPM/61 November of 1975. The book uses the appealing theory of stable marriage to introduce and illustrate a variety of important concepts and techniques of computer science and mathematics: data structures, control structures, combinatorics, probability, analysis, algebra, and especially the . The presentation is elementary, and the topics are inter- esting to nonspecialists. The theory is quite beautiful and developing rapidly. Exercises with answers, an annotated bibliography, and research problems are included. The text would be appropriate as supplementary reading for undergraduate research seminars or courses in algorithmic analysis and for graduate courses in combinatorial algo-

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General Interest

Modelling in Healthcare The Complex Systems Modelling Group (CSMG), The IRMACS Center, Simon Fraser University, Burnaby, BC, Canada How many patients will require admission to my hospital in two days? How widespread will influenza be in my community in two weeks? What will the changing demographics of our community do to affect demand for medical services in our region in two years? These and similar questions are the province of Modelling in Healthcare. This new volume, presented by the Complex Systems Modelling Group at Simon Fraser University in Canada, uses plain language, sophisticated mathematics and vivid examples to guide and instruct. Sage advice on the benefits and limitations of the modeling process and model predictions is generously distributed so that the reader comes away with an understanding not only of the process but also on the practical uses (and misuses!) of models. Perhaps the most important aspect of this book is that the content and the logic are readily understandable by modelers, administrators and clinicians alike. This volume will surely serve as their common and thus preferred reference for modeling in healthcare for many years. —Timothy G. Buchman, Ph.D., M.D., FACS, FCCM

Modelling in Healthcare adds much-needed breadth to the curriculum, giving readers the introduction to simulation methods, network analysis, game theory, and other essential modeling techniques that are rarely touched upon by traditional texts. —Ben Klemens, Ph.D.

Mathematical and statistical modeling has tremendous potential for helping improve the quality and efficiency of health care delivery and as a tool for decision making by health care professionals. This book provides many relevant and successful applications of modeling in health care and can serve as an important resource and guide for those working in this exciting new field. —Reinhard Laubenbacher, Ph.D.

READERSHIP: Anyone interested in mathematics and healthcare. 2010; 218 pp.; hardcover; ISBN: 978-0-8218-4969-9; List US$69; AMS members US$55.20; All Individuals US$59; Order code: MBK/74

TEXTBOOK

TEXTBOOKS Mathematical World • Volume 13 A Gentle Introduction to Game Theory FROM THE AMS Saul Stahl, University of Kansas, Lawrence, KS

TEXTBOOK A Gentle The mathematical theory of games was first developed as a model for situations of conflict, Introduction to whether actual or recreational. It gained widespread recognition when it was applied to the GAME theoretical study of economics by von Neumann and Morgenstern in Theory of Games and THEORY Economic Behavior in the 1940s. The later bestowal in 1994 of the Nobel Prize in economics on Nash underscores the important role this theory has played in the intellectual life of the Saul Stahl twentieth century. This volume is based on courses given by the author at the University of Kansas. The exposition is “gentle” because it requires only some knowledge of coordinate geometry; linear program- American Mathematical Society ming is not used. It is “mathematical” because it is more concerned with the mathematical solution of games than with their applications. Existing textbooks on the topic tend to focus either on the applications or on the mathematics at a level that makes the works inaccessible to most non-mathematicians. This book nicely fits in between these two alternatives. It discusses examples and completely solves them with tools that require no more than high school algebra. In this text, proofs are provided for both von Neumann’s Minimax Theorem and the existence of the Nash Equilibrium 2 ​​2 in the × case. Readers will gain both a sense of the range of applications and a better understanding of the theoretical framework of these two deep mathematical concepts. READERSHIP: Undergraduates in any area, interested in game theory. Mathematical World, Volume 13 1999; 176 pp.; softcover; ISBN: 978-0-8218-1339-3; List US$28; AMS members US$22.40; Order code: MAWRLD/13 17 Order Online | www.ams.org/bookstore Geometry and Topology

TEXTBOOK

TEXTBOOKS Portraits of FROM THE AMS Geometry and Topology the Earth

TEXTBOOK TEXTBOOK A Mathematician TEXTBOOKS Computational Looks at Maps FROM THE AMS Topology Timothy G. Feeman, TEXTBOOK An Introduction Villanova University, PA Herbert Edelsbrunner, Duke Maps are exciting, visual tools University, Durham, NC, and that we encounter on a daily Geomagic, Research Triangle basis: from street maps to maps Park, NC, and John L. Harer, of the world accompanying Duke University, Durham, NC news stories to geologic maps depicting the underground Combining concepts from structure of the earth. This book explores the mathematical topology and algorithms, this ideas involved in creating and analyzing maps, a topic that book delivers what its title is rarely discussed in undergraduate courses. It is the first promises: an introduction to the modern book to present the famous problem of mapping field of . Starting with motivating the earth in a style that is highly readable and math- problems in both mathematics and computer science and ematically accessible to most students. Feeman’s writing is building up from classic topics in geometric and algebraic inviting to the novice, yet also interesting to readers with topology, the third part of the text advances to persistent more mathematical experience. Through the visual context homology. This point of view is critically important in of maps and mapmaking, students will see how contempo- turning a mostly theoretical field of mathematics into one rary mathematics can help them to understand and explain that is relevant to a multitude of disciplines in the sciences the world. and engineering. Students will explore: The main approach is the discovery of topology through algorithms. The book is ideal for teaching a graduate or • the shape of the earth advanced undergraduate course in computational topology, as it develops all the background of both the mathematical • the determination of latitude and longitude and algorithmic aspects of the subject from first principles. • elementary spherical geometry Thus the text could serve equally well in a course taught in a mathematics department or computer science department. • the uses and computation of scale factors • the design of optimal routes for air or sea navigation READERSHIP: Graduate students and research mathema- ticians interested in topology, algorithms, and applications • Gaussian curvature to science and engineering. • why one can’t make a perfect flat map of the earth 2010; 241 pp.; hardcover; ISBN: 978-0-8218-4925-5; List US$59; AMS members US$47.20; Order code: MBK/69 • how to evaluate maps critically and analytically • how to design atlas maps using both hand-drawn tech- niques and computer This book would make an excellent text for a basic under- graduate mathematics or geography course and would be especially appealing to the teacher who is interested in exciting visual applications in the classroom. It would also serve nicely as supplementary reading for a course in calculus, linear algebra, or . Prerequisites include a strong grasp of and basic calculus. READERSHIP: Undergraduates and graduate students studying mathematics and geography; general mathematical audience.

Mathematical World, Volume 18 2002; 123 pp.; softcover; ISBN: 978-0-8218-3255-4; List US$28; AMS members US$22.40; Order code: MAWRLD/18

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13 A Brief Mathematical Physics OLIVER BÜHLER Introduction to Dirichlet Branes Classical, Statistical, A Brief and Quantum and Mirror Introduction to Classical, Mechanics Symmetry Statistical, Oliver Bühler, New York Paul S. Aspinwall, Duke and University, Courant Institute, University, Durham, NC, NY Tom Bridgeland, , United Kingdom, This book provides a rapid Alastair Craw, University of overview of the basic methods Glasgow, United Kingdom, and concepts in mechanics for Michael R. Douglas, beginning Ph.D. students and Stony Brook University, NY, advanced undergraduates in applied mathematics or related Mark Gross, University of fields. It is based on a graduate course given in 2006–07 at California, San Diego, La Jolla, CA, Anton Kapustin, the Courant Institute of Mathematical Sciences. Among California Institute of Technology, Pasadena, CA, other topics, the book introduces Newton’s law, action principles, Hamilton-Jacobi theory, geometric wave theory, Gregory W. Moore, Rutgers University, Piscataway, analytical and numerical statistical mechanics, discrete NJ, Graeme Segal and Balázs Szendro˝i, University of and continuous quantum mechanics, and quantum path- Oxford, United Kingdom, and P.M.H. Wilson, University integral methods. of Cambridge, United Kingdom A natural sequel to the first Clay monograph on Mirror The focus is on fundamental mathematical methods that Symmetry, it presents the new ideas coming out of the provide connections between seemingly unrelated subjects. interactions of and algebraic geometry in a An example is Hamilton-Jacobi theory, which appears in coherent logical context. We hope it will allow students the , in Fermat’s principle of classical and researchers who are familiar with the language of one mechanics, and in the geometric theory of dispersive wave- of the two fields to gain acquaintance with the language of trains. The material is developed in a of simple the other. examples and the book can be used in a one-semester class on classical, statistical, and quantum mechanics. Some The book first introduces the notion of Dirichlet brane familiarity with differential equations is required but other- in the context of topological quantum field theories, and wise the book is self-contained. In particular, no previous then reviews the basics of string theory. After showing knowledge of physics is assumed. how notions of branes arose in string theory, it turns to an introduction to the algebraic geometry, sheaf theory, READERSHIP: Advanced undergraduates, graduate and homological algebra needed to define and work with students and research mathematicians interested in derived categories. The physical existence conditions for mechanics, mathematical physics, and applied probability. branes are then discussed and compared in the context of Titles in this series are co-published with the Courant Institute of mirror symmetry, culminating in Bridgeland’s definition of Mathematical Sciences at New York University. stability structures, and its applications to the McKay corre- Courant Lecture Notes, Volume 13 spondence and quantum geometry. The book continues 2006; 153 pp.; softcover; ISBN: 978-0-8218-4232-4; List US$29; AMS with detailed treatments of the Strominger–Yau–Zaslow members US$23.20; Order code: CLN/13 conjecture, Calabi–Yau metrics and homological mirror symmetry, and discusses more recent physical develop- ments. One difficulty in understanding all aspects of this work is that it requires being able to speak two different languages, the language of string theory and the language of algebraic geometry. The 2002 Clay School on Geometry and String Theory set out to bridge this gap, and this monograph builds on the expository lectures given there to provide an up-to-date discussion including subsequent developments. READERSHIP: Graduate students and research mathema- ticians interested in mathematical aspects of , in particular string theory and mirror symmetry. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA). Clay Mathematics Monographs, Volume 4 2009; 681 pp.; hardcover; ISBN: 978-0-8218-3848-8; List US$109; AMS members US$87.20; Order code: CMIM/4

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19 Quantum Fields An Introduction to and Strings: A Course Quantum Fields and STEPHEN CHILDRESS Theoretical Fluid for Mathematicians Strings: A Course for Mechanics Mathematicians An Introduction to Theoretical Stephen Childress, New York Pierre Deligne, Institute for Fluid Mechanics University, Courant Institute of Advanced Study, Princeton, NJ, Mathematical Sciences, NY Pavel Etingof, Massachusetts

Pierre Deligne David Kazhdan Institute of Technology, Cambridge, This book gives an overview of Pavel Etingof John W. Morgan Daniel S. Freed David R. Morrison Lisa C. Jeffrey Edward Witten Editors MA, Daniel S. Freed, University THEMAT A IC classical topics in fluid dynamics, M A L N ΤΡΗΤΟΣ ΜΗ Ω Τ Ι Σ Ι Ε A S

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A Institute for Advanced Study F OU 88 focusing on the kinematics and NDED 18 of Texas, Austin, TX, Lisa C. dynamics of incompressible inviscid Jeffrey, University of Toronto, and Newtonian viscous fluids, but also including some ON, Canada, David Kazhdan, Harvard University, material on compressible flow. The topics are chosen Cambridge, MA, John W. Morgan, Columbia University, to illustrate the mathematical methods of classical fluid New York, NY, David R. Morrison, Duke University, dynamics. The book is intended to prepare the reader for Durham, NC, and Edward Witten, Institute for more advanced topics of current research interest. Advanced Study, Princeton, NJ, Editors READERSHIP: Graduate students and research mathema- Ideas from quantum field theory and string theory have had ticians interested in fluid mechanics. considerable impact on mathematics over the past 20 years. Advances in many different areas have been inspired by Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University. insights from physics. Courant Lecture Notes, Volume 19 In 1996–97 the Institute for Advanced Study (Princeton, NJ) 2009; 201 pp.; softcover; ISBN: 978-0-8218-4888-3; List US$31; AMS organized a special year-long program designed to teach members US$24.80; Order code: CLN/19 mathematicians the basic physical ideas which underlie the mathematical applications. The purpose is eloquently stated in a letter written by Robert MacPherson: “The goal is to create and convey an understanding, in terms congenial to mathematicians, of some fundamental notions of physics … [and to] develop the sort of intuition common among physi- cists for those who are used to thought processes stemming from geometry and algebra.” These volumes are a written record of the program. They contain notes from several long and many short courses covering various aspects of quantum field theory and perturbative string theory. The courses were given by leading physicists and the notes were written either by the speakers or by mathematicians who participated in the program. The book also includes problems and solutions worked out by the editors and other leading participants. Interspersed are mathematical texts with background mate- rial and commentary on some topics covered in the lectures. These two volumes present the first truly comprehensive introduction to this field aimed at a mathematics audience. They offer a unique opportunity for mathematicians and mathematical physicists to learn about the beautiful and difficult subjects of quantum field theory and string theory. READERSHIP: Graduate students and research mathema- ticians working in various related to quantum field theory. To order individual parts/volumes or the complete set, please specify the relevant order code. Volume 1: 1999; 723 pp.; softcover; ISBN: 978-0-8218-2012-4; List US$32; AMS members US$25.60; Order code: QFT/1.S Volume 2: 1999; 777 pp.; softcover; ISBN: 978-0-8218-2013-1; List US$32; AMS members US$25.60; Order code: QFT/2.S Set: 1999; 1501 pp.; softcover; ISBN: 978-0-8218-2014-8; List US$58; AMS members US$46.40; Order code: QFT/1/2.S

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Lectures on Quantum Mechanics for Mathematics Students L. D. Faddeev, Steklov Mathematical Institute, St. Petersburg, Russia, and O. A. Yakubovskiı˘, St. Petersburg University, Russia with an appendix by Leon Takhtajan This book is based on notes from the course developed and taught for more than 30 years at the Department of Mathematics of Leningrad University. The goal of the course was to present the basics of quantum mechanics and its mathematical content to students in mathematics. This book differs from the majority of other textbooks on the subject in that much more attention is paid to general principles of quantum mechanics. In particular, the authors describe in detail the relation between classical and quantum mechanics. When selecting particular topics, the authors emphasize those that are related to interesting mathematical theories. In particular, the book contains a discussion of problems related to group and to scattering theory. This book is rather elementary and concise, and it does not require prerequisites beyond the standard undergraduate math- ematical curriculum. It is aimed at giving a mathematically oriented student the opportunity to grasp the main points of quantum theory in a mathematical framework. READERSHIP: Undergraduate and graduate students interested in learning the basics of quantum mechanics. Student Mathematical Library, Volume 47 2009; 234 pp.; softcover; ISBN: 978-0-8218-4699-5; List US$39; AMS members US$31.20; Order code: STML/47

TEXTBOOK

TEXTBOOKS FROM THE AMS Quantum Mechanics for Mathematicians Quantum Mechanics for Leon A. Takhtajan, Stony Brook University, NY TEXTBOOKMathematicians This book provides a comprehensive treatment of quantum mechanics from a mathematics

Leon A. Takhtajan perspective and is accessible to mathematicians starting with second-year graduate students. In addition to traditional topics, like classical mechanics, mathematical foundations of quantum mechanics, quantization, and the Schrödinger equation, this book gives a mathematical treatment

Graduate Studies in Mathematics of systems of identical particles with spin, and it introduces the reader to functional methods in Volume 95 quantum mechanics. This includes the Feynman path integral approach to quantum mechanics, American Mathematical Society integration in functional spaces, the relation between Feynman and Wiener integrals, Gaussian integration and regularized determinants of differential operators, fermion systems and integration over anticommuting (Grassmann) variables, and localization in loop spaces, and supersymmetric derivation of the Atiyah-Singer formula for the index of the Dirac operator. Prior to this book, mathemati- cians could find these topics only in physics textbooks and in specialized literature. This book is written in a concise style with careful attention to precise mathematics formulation of methods and results. Numerous problems, from routine to advanced, help the reader to master the subject. In addition to providing a funda- mental knowledge of quantum mechanics, this book could also serve as a bridge for studying more advanced topics in quantum physics, among them quantum field theory. Prerequisites include standard first-year graduate courses covering linear and , topology and geometry, and real and . READERSHIP: Graduate students and research mathematicians interested in mathematical aspects of quantum mechanics. Graduate Studies in Mathematics, Volume 95 2008; 387 pp.; hardcover; ISBN: 978-0-8218-4630-8; List US$69; AMS members US$55.20; Order code: GSM/95

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Mathematical Snowbird Lectures on String Mathematical Methods in Quantum Mechanics Methods in Quantum Geometry With Applications to Schrödinger Operators Mechanics Katrin Becker and Melanie Becker, Texas A&M

Gerald Teschl With Applications to University, College Station, TX, Aaron Bertram, Schrödinger Operators University of Utah, Salt Lake City, UT, Paul S. Green, University of Maryland, College Park, MD, and

Graduate Studies Gerald Teschl, University of in Mathematics Benjamin McKay, University College, Cork, Ireland, Volume 99 Vienna, Austria Editors American Mathematical Society Quantum mechanics and the theory Contemporary Mathematics, Volume 401 of operators on Hilbert space have 2006; 104 pp.; softcover; ISBN: 978-0-8218-3663-7; List US$39; AMS been deeply linked since their begin- members US$31.20; Order code: CONM/401 nings in the early twentieth century. States of a quantum system correspond to certain elements of the configuration Quantum Graphs and Their space and observables correspond to certain operators on the space. This book is a brief, but self-contained, introduc- Applications tion to the mathematical methods of quantum mechanics, Gregory Berkolaiko, Texas A&M University, College with a view towards applications to Schrödinger operators. Station, TX, Robert Carlson, University of Colorado, Part 1 of the book is a concise introduction to the spectral Colorado Springs, CO, and Stephen A. Fulling and theory of unbounded operators. Only those topics that will Peter Kuchment, Texas A&M University, College Station, be needed for later applications are covered. The spectral TX, Editors theorem is a central topic in this approach and is introduced Contemporary Mathematics, Volume 415 at an early stage. Part 2 starts with the free Schrödinger 2006; 307 pp.; softcover; ISBN: 978-0-8218-3765-8; List US$89; AMS equation and computes the free resolvent and time evolu- members US$71.20; Order code: CONM/415 tion. Position, momentum, and angular momentum are discussed via algebraic methods. Various mathematical Universality and Renormalization methods are developed, which are then used to compute the spectrum of the hydrogen atom. Further topics include the From Stochastic Evolution to nondegeneracy of the ground state, spectra of atoms, and Renormalization of Quantum Fields scattering theory. Ilia Binder, University of Toronto, ON, Canada, and This book serves as a self-contained introduction to spectral Dirk Kreimer, Institut des Hautes Études Scientifiques, theory of unbounded operators in Hilbert space with full Bures-sur-Yvette, France, Editors proofs and minimal prerequisites: Only a solid knowledge Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada). of advanced calculus and a one-semester introduction to complex analysis are required. In particular, no functional Fields Institute Communications, Volume 50 analysis and no Lebesgue integration theory are assumed. 2007; 404 pp.; hardcover; ISBN: 978-0-8218-4273-7; List US$119; It develops the mathematical tools necessary to prove some AMS members US$95.20; Order code: FIC/50 key results in nonrelativistic quantum mechanics. Mathematical Methods in Quantum Mechanics is intended Spectral and Scattering Theory for for beginning graduate students in both mathematics and Quantum Magnetic Systems physics and provides a solid foundation for reading more Philippe Briet, Université Sud Toulon-Var, Marseille, advanced books and current research literature. It is well Cedex, France, François Germinet, Université Cergy- suited for self-study and includes numerous exercises (many Pontoise, France, and Georgi Raikov, Pontificia with hints). Universidad Catolica de Chile, Santiago, Chile, Editors READERSHIP: Graduate students and research mathema- Contemporary Mathematics, Volume 500 ticians interested in mathematical physics and quantum 2009; 186 pp.; softcover; ISBN: 978-0-8218-4744-2; List US$69; AMS mechanics. members US$55.20; Order code: CONM/500 Graduate Studies in Mathematics, Volume 99 2009; 305 pp.; hardcover; ISBN: 978-0-8218-4660-5; List US$59; AMS members US$47.20; Order code: GSM/99

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Clay Mathematics Proceedings Volume 3 CONTEMPORARY Strings and Geometry MATHEMATICS Moving Interface Problems Strings 4 6 6 and Moving Interface Problems and Applications in Fluid Geometry Michael Douglas, Rutgers University, and Applications in Fluid Dynamics Michael Douglas Jerome Gauntlett Piscataway, NJ, , Dynamics Jerome Gauntlett Boo Cheong Khoo Mark Gross Zhilin Li Editors Ping Lin University of London, England, and Mark Editors

THEMAT A IC M A , National University L N ΤΡΗΤΟΣ ΜΗ Boo Cheong Khoo Ω Τ Ι Σ Ι Ε A S

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FO 8 U 88 NDED 1 Gross, University of California San Diego, American Mathematical Society Clay Mathematics Institute American Mathematical Society of Singapore, Singapore, Zhilin Li, North La Jolla, CA, Editors Carolina State University, Raleigh, NC, and Clay Mathematics Proceedings, Volume 3 Ping Lin, University of Dundee, United 2004; 376 pp.; softcover; ISBN: 978-0-8218-3715-3; List US$72; AMS Kingdom, Editors members US$57.60; Order code: CMIP/3 Contemporary Mathematics, Volume 466 2008; 190 pp.; softcover; ISBN: 978-0-8218-4267-6; List US$59; AMS The Principle of the members US$47.20; Order code: CONM/466 The Principle of the Fermionic Projector Fermionic Translations of MATHEMATICAL Far-from-Equilibrium Projector Felix Finster, Universität Regensburg, MONOGRAPHS Felix Finster Germany Volume 209 Dynamics Titles in this series are co-published with Far-from- International Press, Cambridge, MA. Equilibrium Yasumasa Nishiura, Hokkaido University, Dynamics Sapporo, Japan AMS/IP Studies in Advanced Mathematics, Volume 35 Yasumasa Nishiura

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FO 8 U 88 2006; 302 pp.; hardcover; ISBN: 978-0-8218-3974-4; List US$65; NDED 1 (Iwanami Series in Modern Mathematics), AMS members US$52; Order code: AMSIP/35 Volume 209 2002; 311 pp.; softcover; ISBN: 978-0-8218-2625-6; List US$69; AMS CONTEMPORARY Adventures in members US$55.20; Order code: MMONO/209 MATHEMATICS 4 4 7 Adventures in Mathematical Physics Mathematical FIELDS INSTITUTE Topics in Kinetic Theory Physics François Germinet, Université de Cergy- COMMUNICATIONS François Germinet THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES Peter D. Hislop Editors Pontoise, France, and Peter D. Hislop, Topics in Thierry Passot, CNRS, Nice, France, University of Kentucky, Lexington, KY, Kinetic Theory Catherine Sulem, University of Toronto,

American Mathematical Society Thierry Passot Catherine Sulem Editors Pierre-Louis Sulem ON, Canada, and Pierre-Louis Sulem, Editors

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A Observatoire de la Cote d’Azur, Nice, FO 8 U 88 Contemporary Mathematics, Volume 447 NDED 1 American Mathematical Society 2007; 256 pp.; softcover; ISBN: 978-0-8218-4241-6; List US$79; AMS France, Editors members US$63.20; Order code: CONM/447 Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada). Fields Institute Communications, Volume 46 2005; 312 pp.; hardcover; ISBN: 978-0-8218-3723-8; List US$114; AMS members US$91.20; Order code: FIC/46

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Probability

Filtering and Prediction: A Primer B. Fristedt, N. Jain, and N. Krylov, University of Minnesota, Minneapolis, MN Filtering and prediction is about observing moving objects when the observations are corrupted by random errors. The main focus is then on filtering out the errors and extracting from the observa- tions the most precise information about the object, which itself may or may not be moving in a somewhat random fashion. Next comes the prediction step where, using information about the past behavior of the object, one tries to predict its future path. The first three chapters of the book deal with discrete probability spaces, random variables, condi- tioning, Markov chains, and filtering of discrete Markov chains. The next three chapters deal with the more sophisticated notions of conditioning in nondiscrete situations, filtering of continuous- space Markov chains, and of Wiener process. Filtering and prediction of stationary is discussed in the last two chapters. The authors believe that they have succeeded in presenting necessary ideas in an elementary manner without sacrificing the rigor too much. Such rigorous treatment is lacking at this level in the litera- ture. In the past few years the material in the book was offered as a one-semester undergraduate/beginning graduate course at the University of Minnesota. Some of the many problems suggested in the text were used in homework assignments. READERSHIP: Undergraduate and graduate students interested in filtering and prediction for random processes. Student Mathematical Library, Volume 38 2007; 252 pp.; softcover; ISBN: 978-0-8218-4333-8; List US$39; AMS members US$31.20; Order code: STML/38

Volume 8 Lectures on the Mathematics of Finance

C CRM R MONOGRAPH Ioannis Karatzas, Columbia University, New York, NY M SERIES In this text, the author discusses the main aspects of mathematical finance. These include arbitrage, Centre de Recherches Mathématiques Université de Montréal hedging and pricing of contingent claims, portfolio optimization, incomplete and/or constrained Lectures on the Mathematics of markets, equilibrium, and transaction costs. The book outlines advances made possible during the Finance last fifteen years due to the methodologies of stochastic analysis and control. Readers are presented Ioannis Karatzas with current research, and open problems are suggested.

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F OU 88 NDED 18 to graduate students in mathematics. Familiarity is assumed with stochastic analysis and parabolic partial differential equations. The text makes significant use of students’ mathematical skills, but always in connection with interesting applied problems. READERSHIP: Graduate students in mathematics, statistics, physics, and engineering who want to learn about the Mathematics of Finance. Titles in this series are co-published with the Centre de Recherches Mathématiques. CRM Monograph Series, Volume 8 1997; 148 pp.; softcover; ISBN: 978-0-8218-0909-9; List US$45; AMS members US$36; Order code: CRMM/8.S

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FIELDS INSTITUTE Lectures on Monte Lectures in MONOGRAPHS Carlo Methods Parts 1 and 2 THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES Neal Madras, York University, Yu. N. Linkov​ Lectures on Monte Toronto, ON, Canada Translations of Mathematical Monographs, Volume 229 Carlo Methods Monte Carlo methods form an 2005; 321 pp.; hardcover; ISBN: 978-0-8218-3732-0; List US$105; Neal Madras experimental branch of math- AMS members US$84; Order code: MMONO/229 ematics that employs simulations

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F O 88 Information Theory and Stochastics U 8 NDED 1 American Mathematical Society tors. These methods are often used for Multiscale Nonlinear Systems when others fail, since they are much less sensitive to the “curse of dimensionality”, which Andrew J. Majda and Rafail V. Abramov, Courant plagues deterministic methods in problems with a large Institute of Mathematical Sciences, New York University, number of variables. Monte Carlo methods are used in NY, and Marcus J. Grote, University of Basel, many fields: mathematics, statistics, physics, chemistry, Switzerland finance, computer science, and biology, for instance. CRM Monograph Series, Volume 25 This book is an introduction to Monte Carlo methods 2005; 133 pp.; hardcover; ISBN: 978-0-8218-3843-3; List US$41; for anyone who would like to use these methods to study AMS members US$32.80; Order code: CRMM/25 various kinds of mathematical models that arise in diverse areas of application. The book is based on lectures in a Financial Markets graduate course given by the author. It examines theo- Stochastic Analysis and the Pricing of retical properties of Monte Carlo methods as well as practical issues concerning their computer implementation Securities and statistical analysis. The only formal prerequisite is an A. V. Melnikov​ , Steklov Institute of Mathematics, undergraduate course in probability. Moscow, Russia The book is intended to be accessible to students from a Translations of Mathematical Monographs, Volume 184 wide range of scientific backgrounds. Rather than being a 1999; 133 pp.; hardcover; ISBN: 978-0-8218-1082-8; List US$74; detailed treatise, it covers the key topics of Monte Carlo AMS members US$59.20; Order code: MMONO/184 methods to the depth necessary for a researcher to design, implement, and analyze a full Monte Carlo study of a math- ematical or scientific problem. The ideas are illustrated with diverse running examples. There are exercises sprinkled throughout the text. The topics covered include computer generation of random variables, techniques and examples for variance reduction of Monte Carlo estimates, Markov chain Monte Carlo, and statistical analysis of Monte Carlo output. READERSHIP: Advanced undergraduates, graduate students, research mathematicians, statisticians, physicists, chemists, engineers, and computer scientists interested in numerical analysis, probability theory, and stochastic processes. Titles in this series are co-published with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada). Fields Institute Monographs, Volume 16 2002; 103 pp.; hardcover; ISBN: 978-0-8218-2978-3; List US$34; AMS members US$27.20; Order code: FIM/16

25 Order Online | www.ams.org/bookstore Index by Title and Author Index by Title and Author

a Carlos �������������������9 Douglas, Goldfeld, Dorian �����9 An Introduction to Michael R. ��� 19, 23 Theoretical Fluid Abello, James �����������8 Cazenave, Goldreich, Oded �����4 Mechanics ���������� 20 Thierry ���������������14 Dutta, Debasish �������9 Abramov, Rafail V. �25 Gomez-Ullate, D. �15 An Introductory Chechkin, G. A. �����12 Advances in E González-Díaz, Course on Information Chen, Z. ���������������10 Julio ���������������������4 Mathematical Edelsbrunner, Recording �����������10 Game Theory �������� 4 Childress, Herbert �������������18 Green, Paul S. �������22 Adventures in Stephen �������������20 Inverse Problems, Esposito, Gross, Mark ���� 19, 23 Mathematical Multi-Scale Classical and Pierpaolo �����������14 Physics �����������������23 Grote, Marcus J. ���25 Analysis, and Quantum Etingof, Pavel ��������20 Effective Medium Algebraic Coding Computation �������5 Group Theory Theory ���������������� 8 Theory and Evans, David �����������8 and Numerical Clemence, Information Analysis �������������15 Iserles, A. �������������� 15 Theory �����������������8 Dominic P. �����������9 F Gumel, Abba B. �������9 Coding Theory Algebraic Geometric Faddeev, L. D. �������21 J and Quantum Guo, Yujin �������������14 Codes: Basic Jain, N. ���������������� 24 Notions �����������������3 Computing �����������8 Far-from-Equilibrium Dynamics �����������23 H Janardan, Ravi �������� 9 Algebraic Methods in The Complex Systems Cryptography �������9 Modelling Group Feeman, Han, Te Sun �����������9 Jeffrey, Lisa C. ������ 20 (CSMG) �����������17 Timothy G. �������18 Amdeberhan, Hansen, Pierre �������10 John, F. ���������������� 14 Feng, Zhilan �����������9 Tewodros �������������8 Computational Harer, John L. �������18 Jones, Chris ������������ 8 Complexity Fiestras-Janeiro, M. Ammari, Habib �������8 Theory �����������������7 Heath, David C. �������9 Gloria �������������������4 K Andreu-Vaillo, High-Dimensional Computational Filtering and Kang, Hyeonbae ���� 8 Fuensanta �����������11 Partial �������������18 Prediction: A Equations in Kapustin, Anton ���� 19 Ashikhmin, A. ���������8 Primer ���������������24 Conca, Carlos �������14 Science and Karatzas, Aspinwall, Paul S. ���19 Financial Markets ��25 Engineering �������14 Control and Ioannis �������������� 24 Nonlinearity ���������8 Fine Regularity of Hislop, Peter D. �����23 Kazhdan, David ���� 20 B Solutions of Elliptic Cormode, Graham ���8 Holt, Jeffrey J. ���������8 Bandrauk, André ���14 Partial Differential Khoo, Coron, Equations �����������15 Homogenization �����12 Boo Cheong ������ 23 Barg, A. �������������������8 Jean-Michel ���������8 Finster, Felix ���������23 Hos¸ ten, Serkan �����16 Kitaev, A. Yu. ���������� 5 Becker, Katrin �������22 Craw, Alastair ���������19 Becker, Freed, Daniel S. �����20 Hyperbolic Partial Klintworth, Karen �� 8 Cryptography: An Differential Melanie �������������22 Fristedt, B. �������������24 Knobel, Roger ������ 12 Introduction ���������8 Equations and Wave Berkolaiko, Fulling, Phenomena ���������14 Knuth, Donald E �� 16 Gregory �������������22 D Stephen A. ���������22 Hyperbolic Problems: Kobayashi, Kingo ���� 9 Bers, L. �����������������14 Data Depth: Robust Theory, Numerics Multivariate G Korn, Elke �������������� 5 Bertram, and Applications �15 Analysis, García-Jurado, Korn, Ralf �������������� 5 Aaron �����������������22 Computational Ignacio �����������������4 I Binder, Ilia �������������22 Geometry and Kreimer, Dirk �������� 22 Applications ���������9 Garrett, Paul ���������16 Ikawa, Mitsuru �������14 Bonilla, L. L. ���������14 Kreuzer, Martin ������ 9 Gauntlett, Information Theory Data Mining and Krylov, N. ������ 15, 24 Bridgeland, Tom ���19 Mathematical Jerome ���������������23 and Stochastics for Multiscale Kuchment, A Brief Introduction Programming �����10 Gems in Experimental Nonlinear Peter ���������������� 22 to Classical, Delfour, Michel C. �14 Mathematics ���������8 Statistical, Systems ���������������25 A Gentle Introduction and Quantum Deligne, Pierre �������20 An Introduction to L to Game Theory ���17 Mechanics �����������19 Dieckmann, Ulf �������9 Game-Theoretic Lafferty, John �������� 10 Geometric and Modelling �����������10 Briet, Philippe �������22 Laubenbacher, Differential Equations, Algorithmic Aspects Introduction to Reinhard C. �������� 9 Bühler, Oliver �������19 Mechanics, and of Computer- Computation �����13 Mathematical Aided Design and Le Bris, Claude ���� 14 Finance ���������������9 Dirichlet Branes Manufacturing �����9 C Lectures on Elliptic and Mirror An Introduction to Caffarelli, Luis �������11 A Geometric Approach and Parabolic Symmetry �����������19 the Mathematical to Free Boundary Equations in Hölder Carlson, Robert �����22 Theory of Waves ���12 Discrete Methods in Problems �������������11 Spaces ���������������� 15 Carpio, A. �������������14 Epidemiology ���������8 Introduction to the Germinet, Lectures in Mathematics of Castillo-Chavez, François ������ 22, 23 Mathematical Disease Evolution �����9 Finance ���������������7 Statistics ������������ 25 Gerritzen, Lothar �����9 Introduction to PDEs Lectures on the Ghoussoub, and Waves for the Mathematics of Nassif �����������������14 Atmosphere and Finance ������������ 24 Ocean �������������������6

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Lectures on Monte Modeling and Prediction and Sivaloganathan, U Carlo Methods ����� 25 Simulation of Discovery ������������� 10 Siv ��������������������� 10 Uhlmann, Biological Lectures on Quantum A Primer on Smid, Michiel ����������� 9 Gunther ������������� 14 Networks ��������������� 9 Mechanics for Pseudorandom Snowbird Lectures on Universality and Mathematics Modelling in Generators ������������� 4 String Geometry � 22 Renormalization � 22 Students ������������� 21 Healthcare ���������� 17 The Principle of Soljanin, Emina ����� 10 Lee, Jon ����������������� 16 Moll, Victor H. ������� 8 the Fermionic V Projector ������������� 23 Souvaine, Diane L. ��� 9 Lenhart, Suzanne ����� 9 Moore, Gregory W. 19 van Wijngaarden, Public-Key Spectral and Scattering Adriaan J. ����������� 10 Levi, D. ����������������� 15 Morgan, John W. ��� 20 Cryptography ������� 16 Theory for Quantum Vasic´, Bane ������������� 10 Levin, Simon ����������� 9 Morrison, David R. 20 Magnetic Systems � 22 Vega, J. M. ������������� 14 Li, Wen-Ching Moving Interface q Stable Marriage and Winnie ��������������� 10 Problems and Quantum Its Relation to Other Venakides, S. ���������� 14 Applications in Fluid Computation ������� 10 Combinatorial Li, Zhilin ��������������� 23 Verducci, Joseph Dynamics ����������� 23 Problems ������������� 16 Quantum Fields and Stephen ��������������� 10 Lieman, Daniel ������� 16 Strings: A Course for Stahl, Saul �������������� 17 Villani, Cédric ���������� 3 Lin, Ping ��������������� 23 N Mathematicians ��� 20 Strauss, Walter A. ��� 15 Neu, John C. ����������� 6 Vlaˇdut¸, Serge ����������� 3 Lin kov, Yu. N. ������� 25 Quantum Graphs ​ Strings and New Perspectives in and Their Vogelius, Liu, Jian-Guo ��������� 15 Geometry ������������� 23 Mathematical Applications ������� 22 Michael S. ����������� 14 Liu, Regina Y. ����������� 9 Biology ��������������� 10 Sulem, Catherine ��� 23 Quantum Vyalyi, M. N. ����������� 5 Lomonaco, Nishiura, Yasumasa � 23 Mechanics for Sulem, Samuel J., Jr. ������� 10 Mathematicians ��� 21 Pierre-Louis ������� 23 Nogin, Dmitry ��������� 3 w Quispel, R. ������������� 15 Swindle, Glen ����������� 9 Wang, Zhenghan ��� 10 M Nonlinear Dispersive Equations ����������� 15 Szendro˝i, Balázs ����� 19 Ward, Harold N. ����� 8 Madras, Neal ��������� 25 R Nonlinear Wave Wigderson, Avi ��������� 7 Majda, Andrew ���6, 25 Raikov, Georgi ������� 22 Equations ����������� 15 T Wigner Measure Mally ´, Jan ��������������� 15 Recent Advances Tadmor, Eitan ������� 15 Nonlocal Diffusion and Semiclassical in Adaptive Manásevich, Raúl ��� 14 Problems ������������� 11 Takhtajan, Limits of Nonlinear Computation ������� 10 Leon A. ������������� 21 Schrödinger Mathematical Recent Advances in Equations ����������� 15 Analysis of Partial O Tang, T. ����������������� 10 Nonlinear Partial Differential Olver, P. J. ������������� 15 Williams, R. J. ��������� 7 Differential Taylor, Equations Modeling Optimal Control of Equations and Michael E. ��������� 15 Wilson, P.M.H. ������� 19 Electrostatic Partial Differential Applications ������� 14 MEMS ���������������� 14 Tempesta, P. ����������� 15 Winternitz, P. ��������� 15 Equations ����������� 13 Recent Trends in Mathematical Methods Teschl, Gerald ��������� 22 Witten, Edward ����� 20 Option Pricing Coding Theory and in Quantum and Portfolio Its Applications ��� 10 Thomas, Rekha R. � 16 Mechanics ����������� 22 Optimization ��������� 5 y Rosenberger, Toledo-Melero, J. Mathematical Studies Yakubovskiı˘, O. A. � 21 Gerhard ��������������� 9 Julián ����������������� 11 on Human Disease p Yaschenko, V. V. ������� 8 Dynamics ������������� 9 Rossi, Julio D. ������� 11 Tools for PDE ��������� 15 Palais, Richard S. ��� 13 Yin, George ����������� 10 Mathematics Rudich, Steven ��������� 7 Topics in Kinetic Palais, Robert A. ����� 13 of Finance ����������� 10 Theory ����������������� 23 Yu, D. �������������������� 10 Pardalos, Mathematics of S Topics in Optimal Panos M. ����������� 10 Information and Salsa, Sandro ��������� 11 Transportation ����� 3 z Coding ����������������� 9 Parshall, Brian ����������� 8 Zhang, Ping ����������� 15 Schechter, M. ��������� 14 Topological Quantum Mazón, José M. ����� 11 Partial Differential Computation ������� 10 Zhang, Qing ����������� 10 Segal, Graeme ��������� 19 Equations ����������� 14 McKay, Benjamin ��� 22 Training Manual Ziemer, William P ��� 15 Semilinear Schrödinger Partial Differential on Transport and Medina, Luis A. ������� 8 Equations ����������� 14 Equations and Fluids ������������������� 6 Mel nikov, A. V. ����� 25 Inverse Problems � 14 Serfling, Robert ������� 9 ​ Trends in Mesterton-Gibbons, Passot, Thierry ������� 23 Shamaev, A. S. ������� 12 Optimization ������� 16 Mike ������������������� 10 Pava, Shen, A. H. ������������� 5 Tröltzsch, Fredi ����� 13 Mickens, Jaime Angulo ����� 15 Shen, Xiaotong ������� 10 Tsfasman, Michael ��� 3 Ronald E. ������������� 9 Pfister, Olivier ����������� 8 Shi, Z.-C. ��������������� 10 Tzavaras, Modeling Paradigms Piatnitski, A. L. ������� 12 Athanasios E. ����� 15 and Analysis of Shpilrain, Vladimir ��� 9 Disease Transmission Portraits of Siegel, Paul H. ������� 10 Models ������������������� 9 the Earth ������������� 18

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Computational Topology: An Contemporary Mathematics CRM Monograph Series 8. Volumes 1-7 were co-published Introduction ����������������������18 (CONM) (CRMM) with the Association for Computer Modelling in Healthcare ���������������17 Machinery (ACM), and Volume This series of high-quality, refereed This series includes monographs 36 was co-published with the Quantum Fields and Strings: proceedings written by recognized developed from lectures given National Council of Teachers of A Course for experts in their fields maintains at the Centre de Recherches Mathematics (NCTM). (ISSN Mathematicians �����������������20 high scientific standards. Volumes Mathématiques located at the 1052-1798) Hardcover; reprints in draw from worldwide conferences Université de Montréal. This softcover. AMS/IP Studies in Advanced and symposia sponsored by the series is co-published by the AMS Mathematics (AMSIP) American Mathematical Society and the Centre de Recherches VOL. TITLE PAGE and other organizations. (ISSN Mathématiques. (ISSN 1065-8599) 75 Modeling Paradigms This series, jointly published by 0271-4132) Softcover. Hardcover. and Analysis of Disease the AMS and International Press, Transmission Models ���������� 9 includes monographs, lecture VOL. TITLE PAGE VOL. TITLE PAGE notes, collections, and confer- 517 Gems in Experimental 25 Information Theory and 73 Advances in Information ence proceedings on current Mathematics ������������������������ 8 Stochastics for Multiscale Recording ����������������������������10 topics of importance in advanced 500 Spectral and Scattering Nonlinear Systems ������������25 72 Data Depth: Robust mathematics. Harvard University Theory for Quantum 8 Lectures on the Multivariate Analysis, Professor of Mathematics Shing- Magnetic Systems ��������������22 Mathematics of Finance ��24 Computational Geometry Tung Yau is Editor-in-Chief for the and Applications ������������������ 9 466 Moving Interface Problems series. (ISSN 1089-3288) Hardcover CRM Proceedings & Lecture 71 Disease Evolution: Models, and softcover. and Applications in Fluid Dynamics ����������������������������23 Notes (CRMP) Concepts, and Data VOL. TITLE PAGE Analyses �������������������������������� 9 447 Adventures in Mathematical This series encompasses confer- 41 Recent Trends in Coding Physics ��������������������������������23 70 Discrete Methods in ence proceedings and lecture Epidemiology ������������������������ 8 Theory and Its 443 Prediction and Discovery 10 notes from important research Applications ������������������������10 conferences held at the Centre 68 Algebraic Coding Theory 418 Algebraic Methods in and Information Theory ���� 8 35 The Principle of the Cryptography ���������������������� 9 de Recherches Mathématiques at Fermionic Projector ����������23 the Université de Montréal. This 67 Geometric and Algorithmic 415 Quantum Graphs and Their series is co-published by the AMS Aspects of Computer-Aided CBMS Regional Conference Applications ������������������������22 and the Centre de Recherches Design and Series in Mathematics (CBMS) 410 Mathematical Studies on Mathématiques. (ISSN 1065-8580) Manufacturing ��������������������� 9 Human Disease Dynamics: Softcover. Each monograph offers a written Emerging Paradigms and Fields Institute VOL. TITLE PAGE account of lectures given by the Challenges ���������������������������� 9 Communications (FIC) author as principal speaker at a 408 Inverse Problems, Multi- 45 Data Mining and regional conference sponsored Scale Analysis, and Effective Mathematical This series features proceed- by the Conference Board of Medium Theory ������������������ 8 Programming ����������������������10 ings and lecture notes from the the Mathematical Sciences and 41 High-Dimensional Partial activities at the Fields Institute supported by the National Science 401 Snowbird Lectures on String for Research in Mathematical Geometry ����������������������������22 Differential Equations Foundation. The material in these in Science and Sciences in Toronto, Ontario, lectures is accessible to nonspecial- 383 Recent Advances in Engineering ������������������������14 Canada. The publications evolve ists. All individuals receive the Adaptive Computation ����10 from each year’s main program. individual member price. (ISSN 39 Group Theory and Interdisciplinary titles emerge 381 Coding Theory and Numerical Analysis ����������15 0160-7642) Softcover. Quantum Computing �������� 8 from programs and workshops 10 Stable Marriage and that discuss applications of the NO. TITLE PAGE 362 Partial Differential Its Relation to Other mathematical sciences in science, Equations and Inverse 112 Topological Quantum Combinatorial Problems: engineering, industry, and business. Problems ������������������������������14 Computation ����������������������10 An Introduction to the (ISSN 1069-5265) Hardcover. 73 Nonlinear Wave 351 Mathematics of Finance ��11 Mathematical Analysis of VOL. TITLE PAGE Equations ����������������������������15 Algorithms ��������������������������16 Courant Lecture Notes (CLN) 57 New Perspectives in Mathematical Biology ������10 Clay Mathematics This important series, co-published DIMACS: Series in Discrete Monographs (CMIM) by the AMS and the Courant Mathematics and Theoretical 50 Universality and Computer Science (DIMACS) Renormalization: From Each volume in the CMIM series Institute of Mathematical Sciences at New York University, offers Stochastic Evolution provides a state-of-the-art exposi- This series includes conference and cutting-edge research in math- to Renormalization of tion by leading mathematicians of workshop proceedings and volumes ematics and theoretical computer Quantum Fields �����������������22 an active area of current research. on education in discrete math- science. NYU faculty and visitors 46 Topics in Kinetic This series is co-published by the ematics and theoretical computer have written most of the volumes, Theory ��������������������������������23 Clay Mathematics Institute and the science. Volumes are derived from which are primarily based on AMS. (ISSN 1539-6061) Hardcover; programs at Rutgers University’s graduate courses and minicourses Fields Institute Monographs reprints in softcover. Center for Discrete Mathematics offered at the Institute. (ISSN 1529- and Theoretical Computer Science (FIM) VOL. TITLE PAGE 9031) Softcover. and also sponsored by Princeton This series features high-quality 4 Dirichlet Branes and Mirror VOL. TITLE PAGE University, AT&T Labs–Research, research monographs gener- Symmetry ����������������������������19 20 Mathematical Analysis Alcatel-Lucent Bell Laboratories, ated from the activities at the Cancer Institute of New Jersey Clay Mathematics Proceedings of Partial Differential Fields Institute for Research in Equations Modeling (CINJ), NEC Laboratories America, Mathematical Sciences in Toronto, (CMIP) Electrostatic MEMS ����������14 and Telcordia Technologies. Ontario, Canada. The publica- Each volume in this series is 19 An Introduction to Research at DIMACS includes tions evolve from each year’s derived from lectures given at the Theoretical Fluid discrete and computational geom- main program. (ISSN 1069-5273) annual Clay Mathematics Institute Mechanics ��������������������������20 etry, discrete optimization, data Hardcover. structures and algorithms, compu- summer schools or other CMI 17 Wigner Measure and VOL. TITLE PAGE tational intractability, massive conferences. The volumes offer Semiclassical Limits of data sets, networks, , 16 Lectures on Monte Carlo clear, accessible introductions to Nonlinear Schrödinger combinatorics, computational Methods ������������������������������25 areas of current research. This Equations ����������������������������15 series is co-published by the Clay number theory and cryptology, Mathematics Institute and the 13 A Brief Introduction to discrete probability, recursive func- AMS. (ISSN 1534-6455) Softcover. Classical, Statistical, and tion theory and , Quantum Mechanics ��������19 Boolean functions, computational VOL. TITLE PAGE 10 Semilinear Schrödinger and mathematical biology, and 3 Strings and Geometry ������23 Equations ����������������������������14 computational algebra. Titles in this 9 Introduction to PDEs and series are co-published with the Waves for the Atmosphere Center for Discrete Mathematics and Ocean ���������������������������� 6 and Theoretical Computer Science beginning with Volume

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Graduate Studies in Lectures in Applied Proceedings of Symposia in Translations of Mathematical Mathematics (GSM) Mathematics (LAM) Applied Mathematics (PSAPM) Monographs (MMONO) The volumes in this series are The volumes contain lectures given The symposia in applied math- This series contains works of specifically designed as graduate at summer seminars in applied ematics have been held under advanced mathematical research studies texts, but are also suitable mathematics sponsored by the the auspices of the American and exposition translated primarily for recommended and/or supple- American Mathematical Society Mathematical Society and other from Japanese and Russian. (ISSN mental course reading. With appeal and Society for Industrial and organizations since 1967. In 0065-9282) Hardcover; reprints to both students and professors, Applied Mathematics on various this series, Volume 21 and most in softcover. Now included as a these texts make ideal independent topics in applied mathematics. subsequent volumes consist of subseries to this series are original study resources. The breadth No further volumes will be the proceedings of short courses works translated from publisher and depth of the series’ coverage published in this series, however sponsored by the AMS and Iwanami Shoten (Tokyo). Volumes make it an ideal acquisition for all back volumes are available. (ISSN held at the time of the January in the Iwanami Series in Modern academic libraries that support 0075-8485) Hardcover; reprints in meetings. Symposia that were Mathematics are in softcover. mathematics programs. (ISSN softcover. sponsored jointly by the AMS VOL. TITLE PAGE 1065-7338) Hardcover. and the Society for Industrial and VOL. TITLE PAGE Applied Mathematics (SIAM) 234 Homogenization: Methods VOL. TITLE PAGE 3.1 Partial Differential have been published in the series and Applications ����������������12 115 An Introductory Equations ����������������������������14 SIAM-AMS Proceedings. (Volumes 229 Lectures in Mathematical Course on Mathematical 1-14: LC 50-1183) (ISSN 0160- Statistics: Parts 1 and 2 ����25 Game Theory ���������������������� 4 Mathematical Surveys and 7634) Hardcover; most reprints in 209 Far-from-Equilibrium 112 Optimal Control of Partial Monographs (SURV) softcover. Dynamics ����������������������������23 Differential Equations: This series of high-level mono- VOL. TITLE PAGE 203 Mathematics of Information Theory, Methods and graphs is designed to meet the and Coding ��������������������������� 9 Applications ������������������������13 67 Hyperbolic Problems: need for careful expositions in Theory, Numerics and 189 Hyperbolic Partial 109 Training Manual on research fields of current interest. Applications ������������������������15 Differential Equations and Transport and Fluids ���������� 6 Each volume gives a survey of the 65 Recent Advances in Wave Phenomena ��������������14 99 Mathematical Methods in subject, along with a brief intro- Nonlinear Partial 184 Financial Markets: Quantum Mechanics: With duction to recent developments Differential Equations and Stochastic Analysis and Applications to Schrödinger and unsolved problems. (ISSN Applications ������������������������14 the Pricing of Derivative Operators ����������������������������22 0076-5376) Hardcover; reprints in 64 Modeling and Simulation of Securities ����������������������������25 95 Quantum Mechanics for softcover. Biological Networks ������������ 9 Mathematicians �����������������21 VOL. TITLE PAGE 62 Public-Key University Lecture Series 72 Introduction to the 165 Nonlocal Diffusion Cryptography ��������������������16 (ULECT) Mathematics of Finance ���� 7 Problems ������������������������������11 61 Trends in Optimization ����16 Each book in this series focuses on 68 A Geometric Approach 156 Nonlinear Dispersive 58 Quantum Computation: an important and rapidly devel- to Free Boundary Equations: Existence and A Grand Mathematical oping topic, and is designed to give Problems ������������������������������11 Stability of Solitary and Challenge for the Twenty- readers the most current informa- 58 Topics in Optimal Periodic Travelling Wave First Century and the tion on the subject area. Some Transportation �������������������� 3 Solutions ������������������������������15 Millennium ������������������������10 books in the series originated from 47 Classical and Quantum 139 Algebraic Geometric Codes: important lecture series given by 57 Introduction to Computation ������������������������ 5 Basic Notions ����������������������� 3 outstanding mathematicians world- Mathematical Finance �������� 9 31 Option Pricing and Portfolio 136 Control and Nonlinearity �� 8 wide. (ISSN 1047-3998) Softcover. Optimization: Modern 81 Tools for PDE: Student Mathematical Library VOL. TITLE PAGE Methods of Financial Pseudodifferential (STML) 55 A Primer on Pseudorandom Mathematics ������������������������ 5 Operators, Paradifferential Generators ���������������������������� 4 12 Lectures on Elliptic and Operators, and Layer The AMS undergraduate series, the Parabolic Equations in Potentials ����������������������������15 Student Mathematical Library, is for books that will spark students’ Hölder Spaces ��������������������15 51 Fine Regularity of Solutions interests in modern mathematics of Elliptic Partial Differential and increase their appreciation IAS/Park City Mathematics Equations ����������������������������15 Series (PCMS) for research. Books published Mathematical World in the series emphasize original This series comprises lecture notes, topics and approaches. The step graduate texts, and educational (MAWRLD) from mathematical coursework to material arising out of the activities This accessible series brings the mathematical research is one of of the Park City Geometry Institute beauty and wonder of mathematics the most important developments in Park City, Utah. The Institute to the advanced high school in a mathematician’s career. To convenes mathematicians from student, the mathematics teacher, make the transition successfully, all sectors in month-long summer the scientist or engineer, and the the student must be motivated and programs. Each Institute features lay reader with a strong interest in interested in doing mathematics approximately five lecture series mathematics. Mathematical World rather than merely learning it. They given by prominent mathemati- features well-written, challenging are suitable for honors courses, cians. (ISSN 1079-5634) Hardcover. expository works that illustrate upper-division seminars, reading courses, or self-study. (ISSN 1520- VOL. TITLE PAGE the fascination and usefulness of mathematics. (ISSN 1055-9426) 9121) Softcover. 10 Computational Complexity Softcover. Theory ���������������������������������� 7 VOL. TITLE PAGE VOL. TITLE PAGE 51 Differential Equations, 18 Portraits of the Earth: A Mechanics, and Mathematician Looks at Computation ����������������������13 Maps ������������������������������������18 47 Lectures on Quantum 13 A Gentle Introduction to Mechanics for Mathematics Game Theory ��������������������17 Students ������������������������������21 38 Filtering and Prediction: A Primer ����������������������������������24 18 Cryptography: An Introduction ������������������������ 8 11 An Introduction to Game- Theoretic Modelling: Second Edition ������������������10 3 An Introduction to the Mathematical Theory of Waves ����������������������������������12

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