Maths Catalogue 2009 by Cambridge University Press

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Additional new features: • Much-improved navigation via side bars that provide rapid overview of modules and guided browsing • Media libraries giving a snapshot of movies, each with descriptive labels • Facility to create movie playlists, which are invaluable in teaching • Higher-resolution graphics, with full- or part-screen viewing options Praise for the first edition: “Homsy and his colleagues have now provided us with a new and powerful teaching aid... This CD is an ambitious project, and, in my view, it has been accomplished with remarkable success ... I have no doubt that this CD-ROM should be regarded as a ‘set text’ for viscous fluid mechanics courses at the undergraduate or starting graduate levels.” –Journal of Fluid Mechanics “… a superb rendition of some of the most important concepts in fluid mechanics… This reviewer estimates the ration (educational value to cost) to be (almost) infinite… this reviewer highly recommends the CD to instructors as well as students… Multimedia Fluid Mechanics is an excellent study-companion… it is also a bargain.” – Applied Mechanics Review

G. M. Homsy, University of California, Santa Barbara; H. Aref, Virginia Polytechnic Institute and Technical University of Denmark; K. S, Breuer, Brown University; John W. M. Bush, Massachusetts Institute of Technology; Christophe Clanet, Ecole Polytechnique, Paris; Marc Fermigier, ESPCI, Paris; Simone Hochgreb, University of Cambridge; J. R. Koseff, Stanford University; B. R. Munson, Iowa State University; K. G. Powell, University of Michigan; David Quere, ESPCI and Ecole Polytechnique, Paris; J. J. Riley, University of Washington; C. R. Robertson, Stanford University; A. J. Smits, Princeton University; S. T. Thoroddsen, National University of Singapore; J. M. Wallace, University of Maryland.

MULTIMEDIA FLUID MECHANICS Second Edition • A perfect complement to any course in Fluid Mechanics • Now with four times more movies • Twice as many topics covered

Second Edition

Catherine Atkins Phone + 44 (0)1223 325566 / 325577 Fax + 44 (0)1223 325959 / 325151 Email ukcustserve@cambridge.org westeurope@cambridge.org intcustserve@cambridge.org Your telephone call may be monitored for training purposes. Account-holding booksellers can order online at www.cambridge.org/booksellers or at www.PubEasy.com

This completely new edition, now on DVD, has: • Twice the coverage, with new modules on turbulence, control volumes, interfacial phenomena, and similarity and scaling • Four times the number of fluids movies, now nearly 1,000 • Now more than 20 virtual labs and simulations – a threefold increase • Dozens of new interactive demonstrations and animations

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G. M. Homsy et al.

MULTIMEDIA FLUID MECHANICS

Booksellers

Allows students to: • Gain insight into and develop intuition about fluid flows • See the mathematical relationships brought to life through movies • Conduct simulations to show the effect of parameter variation.

Homsy et al.

MULTIMEDIA FLUID MECHANICS, Second Edition

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Customer Services

• Now more than 20 virtual labs and simulations– a threefold increase • Much-improved navigation • Now compatible with Windows XP and Mac OSX

Cover image courtesy of Hung Le and Parviz Moin, Center for Turbulence Research, Stanford University and NASA Cover design by Alice Soloway

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Mathematics 2009 www.cambridge.org/mathematics

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Contents Analysis and Probability 1 Discrete Mathematics and 2 Foundations 5 Algebra and Geometry Number Theory and Algebra 5 7 Scientific Computing Dynamical Systems, Mechanics 8 and Modelling Mathematics for Physics and Biology 11 Statistics, Applied Probability 12 and Finance Mathematical Finance 14 16 SIAM books Computer Science 19 General and Recreational 21 Maths New Series 21 Information on related journals Inside back cover

Highlights

Mathematics from Cambridge… Research that always adds up ➤ See page 1

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The ANZIAM Journal is published on behalf of the Australian Mathematical Society, and considers papers in any field of applied mathematics and related mathematical sciences. journals.cambridge.org/anz Journal of the Australian Mathematical Society is the oldest journal of the Society. The Journal covers all areas of pure mathematics and mathematical statistics. journals.cambridge.org/jaz

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This catalogue contains a selection of our most recent publishing in this area. Please visit our website for a full and searchable listing of all our titles in print and also an extensive range of news, features and resources. Our online ordering service is secure and easy to use.

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Bulletin of the Australian Mathematical Society aims at quick publication of original research in all branches of mathematics, and is published on behalf of the Australian Mathematical Society. journals.cambridge.org/baz European Journal of Applied Mathematics focuses on those areas of applied mathematics inspired by real-world applications, at the same time fostering the development of theoretical methods with a broad range of applicability. journals.cambridge.org/ejm

eBooks from Cambridge University Press We offer an extensive catalogue of eBooks across all subject disciplines. These are made available through carefully selected third party vendors and our own eBookstore.

Glasgow Mathematical Journal publishes original research papers in any branch of pure and applied mathematics, and is published for the Glasgow Mathematical Journal Trust. journals.cambridge.org/gmj

The Review of Symbolic Logic is designed to cultivate and promote exciting new fields on the borders of logic, philosophy, mathematics and computer science. The Journal is published for the Association of Symbolic Logic (ASL). journals.cambridge.org/rsl

Acta Numerica is an annual collection of review articles including survey papers from leading researchers in numerical analysis and scientific computing. journals.cambridge.org/anu Journal of the Institute of Mathematics of Jussieu covers all domains in pure mathematics, including operator algebra, number theory, algebraic and Lie groups, differential and symplectic geometry, partial differential equations, Banach spaces, potential theory, mathematical physics, and probability. journals.cambridge.org/jmj

Combinatorics, Probability & Computing is devoted to the three areas of combinatorics, probability theory and theoretical computer science. journals.cambridge.org/cpc Probability in the Engineering and Informational Sciences primarily focuses on stochastic modelling in the physical and engineering sciences. journals.cambridge.org/pes

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Ergodic Theory and Dynamical Systems focuses on a rich variety of research areas which, although diverse, employ global dynamical methods as a common theme. journals.cambridge.org/ets

The Journal of K-Theory includes research on K-theory and its applications to algebra, geometry, analysis and topology., it is published for Independent Scholarly Online and Print Publishing (ISOPP). journals.cambridge.org/jkt

For more information and free sample papers visit journals.cambridge.org/maths

Also of interest • Journal of Fluid Mechanics journals.cambridge.org/flm • Mathematical Structures in Computer Science journals.cambridge.org/msc

• Journal of Fluid Mechanics Digital Archive journals.cambridge.org/jfm • Econometric Theory journals.cambridge.org/ect

Mathematical Proceedings of the Cambridge Philosophical Society is one of the few high-quality journals publishing original research papers that cover the whole range of pure and applied mathematics, theoretical physics and statistics. journals.cambridge.org/psp Compositio Mathematica aims to publish first-class mathematical research papers that traditionally focus on the mainstream of pure mathematics. The Journal is produced, marketed and distributed for the London Mathematical Society. journals.cambridge.org/com Proceedings of the Edinburgh Mathematical Society contains research papers on topics in a broad range of pure and applied mathematics, together with a number of topical book reviews. The Journal is published on behalf of The Edinburgh Mathematical Society. journals.cambridge.org/pem Proceedings of the Royal Society of Edinburgh: Section A Mathematics is the flagship journal of the Royal Society of Edinburgh and publishes papers of international standard across the whole spectrum of mathematics, although emphasis is placed on applied analysis and differential equations. journals.cambridge.org/prm

Analysis and Probability

Analysis and Probability Graduate Textbook

Lévy Processes and Stochastic Calculus Second edition David Applebaum University of Sheffield

of the Hilbert transform; 5. Relationship between the Hilbert transform and some common transforms; 6. The Hilbert transform of periodic functions; 7. Inequalities for the Hilbert transform; 8. Asymptotic behavior of the Hilbert transform; 9. Hilbert transforms of some special functions; 10. Hilbert transforms involving distributions; 11. The finite Hilbert transform; 12. Some singular integral equations; 13. Discrete Hilbert transforms; 14. Numerical evaluation of Hilbert transforms; References; Subject index; Author index.

A unique development of these two subjects contained in a single volume. New topics featured in this fully revised edition include regular variation and subexponential distributions, characterisation of Lévy processes with finite variation, multiple Wiener-Lévy integrals and chaos decomposition, and introductions to Malliavin calculus and stability theory for Lévy-driven SDEs.

Encyclopedia of Mathematics and its Applications, 124

Contents: Preface to second edition; Preface to first edition; Overview; Notation; 1. Lévy processes; 2. Martingales, stopping times and random measures; 3. Markov processes, semigroups and generators; 4. Stochastic integration; 5. Exponential martingales; 6. Stochastic differential equations; References; Index of notation; Subject index.

University of Wisconsin, Eau Claire

Cambridge Studies in Advanced Mathematics, 116

2009 228 x 152 mm 490pp 130 exercises 55 worked examples 978-0-521-73865-1 Paperback £35.00 www.cambridge.org/9780521738651

2-Volume Set

Hilbert Transforms Frederick W. King University of Wisconsin, Eau Claire

Written in a style that suits a wide audience (including physical sciences), this book will become the reference of choice on the Hilbert transform, whatever the subject background of the reader. It explains all the common Hilbert transforms, mathematical techniques for evaluating them, and has detailed discussions of their application.

2009 234 x 156 mm 896pp 15 tables 350 exercises 80 figures 978-0-521-88762-5 Hardback £80.00 www.cambridge.org/9780521887625

Hilbert Transforms Volume 2 Frederick W. King Contents: Preface; List of symbols; List of abbreviations; Volume II: 15. Hilbert transforms in En; 16. Some further extensions of the classical Hilbert transform; 17. Linear systems and causality; 18. The Hilbert transform of waveforms and signal processing; 19. Kramers–Kronig relations; 20. Dispersion relations for some linear optical properties; 21. Dispersion relations for magneto-optical and natural optical activity; 22. Dispersion relations for nonlinear optical properties; 23. Some further applications of Hilbert transforms; Appendix 1. Table of selected Hilbert transforms; Appendix 2. Atlas of selected Hilbert transform pairs; References; Subject index; Author index. Encyclopedia of Mathematics and its Applications, 125

2009 234 x 156 mm 698pp 145 exercises 50 figures 978-0-521-51720-1 Hardback £75.00 www.cambridge.org/9780521517201

Forthcoming

Multidimensional Stochastic Processes as Rough Paths

Encyclopedia of Mathematics and its Applications

Theory and Applications Peter Friz

2009 234 x 156 mm 1440pp 500 exercises 130 figures 978-0-521-51723-2 Set £140.00 www.cambridge.org/9780521517232

University of Cambridge

Hilbert Transforms Volume 1 Frederick W. King University of Wisconsin, Eau Claire

Contents: Preface; List of symbols; List of abbreviations; Volume I: 1. Introduction; 2. Review of some background mathematics; 3. Derivation of the Hilbert transform relations; 4. Some basic properties

and Nicolas Victoir J.P. Morgan, New York

An appealing introduction to Lyons’ important theory and its applications. Based on successful courses at the graduate level, it presents the finitedimensional story and emphasizes the underlying geometry and algebra. This viewpoint keeps the book as accessible as possible and is particularly powerful

when discussing applications to stochastic processes. 2009 228 x 152 mm 450pp 978-0-521-87607-0 Hardback c. £40.00 www.cambridge.org/9780521876070

Trends in Stochastic Analysis Edited by Jochen Blath Technische Universität Berlin

Peter Mörters University of Bath

and Michael Scheutzow Technische Universität Berlin

Presenting important trends in the field of stochastic analysis, this collection of thirteen articles provides an overview of recent developments and new results. Leading experts discuss a wide range of topics, ranging from an alternative setup of rigorous probability to sampling of conditioned diffusions, from Feynmann formulas to genetic inference. London Mathematical Society Lecture Note Series, 353

2009 228 x 152 mm 396pp 9 tones 2 tables 30 worked examples 25 figures 978-0-521-71821-9 Paperback £38.00 www.cambridge.org/9780521718219

Representation Theorems in Hardy Spaces Javad Mashreghi Université Laval, Québec

Gives a complete description of representation theorems with direct proofs for both classes of Hardy spaces. Clear and concise, it features over 300 exercises and is ideal for advanced undergraduate and graduate students taking courses in Advanced Complex Analysis, Function Theory or Theory of Hardy Spaces. Contents: Preface; 1. Fourier series; 2. Abel–Poisson means; 3. Harmonic functions in the unit disc; 4. Logarithmic convexity; 5. Analytic functions in the unit disc; 6. Norm inequalities for the conjugate function; 7. Blaschke products and their applications; 8. Interpolating linear operators; 9. The Fourier transform; 10. Poisson integrals; 11. Harmonic functions in the upper half plane; 12. The Plancherel transform; 13. Analytic functions in the upper half plane; 14. The Hilbert transform on R; A. Topics from real analysis; B. A panoramic view of the representation theorems; Bibliography; Index. London Mathematical Society Student Texts, 74

2009 228 x 152 mm 384pp 16 tones 2 tables 335 exercises 45 figures 978-0-521-51768-3 Hardback £60.00 978-0-521-73201-7 Paperback £23.99 www.cambridge.org/9780521517683

eBooks available at www.cambridge.org/online

Analysis and Probability / Discrete Mathematics and Foundations Groups and Analysis The Legacy of Hermann Weyl Edited by Katrin Tent Universität Bielefeld, Germany

The work of Hermann Weyl has had a lasting influence on areas of mathematics such as topological groups, Lie groups and representation theory, harmonic analysis, and on the foundations of mathematics itself. In this volume leading experts outline the connections between Weyl’s theorems and up-to-date results in many contemporary topics. London Mathematical Society Lecture Note Series, 354

2008 228 x 152 mm 354pp 3 tables 7 worked examples 2 figures 978-0-521-71788-5 Paperback £38.00 www.cambridge.org/9780521717885

Textbook

A Guide to Complex Variables Steven G. Krantz American Institute of Mathematics, Palo Alto

A quick and easy-to-use introduction to the key topics in complex variables, providing a solid grounding in this fundamental area. Its lively exposition, and wealth of figures and examples make this book a useful companion to more daunting texts. A valuable resource for mathematicians and nonmathematicians alike. Dolciani Mathematical Expositions, 32

2008 228 x 152 mm 200pp 978-0-88385-338-2 Hardback £25.99 www.cambridge.org/9780883853382

Analysis in Positive Characteristic Anatoly N. Kochubei

MAA Book

Calculus Deconstructed A Second Course in First-Year Calculus Zbigniew H. Nitecki Tufts University, Massachusetts

A thorough and mathematically rigorous exposition of single-variable calculus for readers with some previous experience of calculus techniques. This book can be used as a textbook for an undergraduate course on calculus or as a reference for self-study. Contents: Preface; Contents; 1. Precalculus; 2. Sequences and their limits; 3. Continuity; 4. Differentiation; 5. Integration; 6. Power series; A. Methods of proof; B. Answers to selected problems; Bibliography; Index. Mathematical Association of America Textbooks

2009 247 x 170 mm 540pp 978-0-88385-756-4 Hardback c. £50.00 www.cambridge.org/9780883857564

Dynamics of Linear Operators Frédéric Bayart

Cambridge Tracts in Mathematics, 178

2009 228 x 152 mm 220pp 978-0-521-50977-0 Hardback £40.00 www.cambridge.org/9780521509770

2006 252 x 225 mm 682pp 700 line figures 978-0-521-86744-3 Hardback £29.99 www.cambridge.org/9780521867443

Discrete Mathematics and Foundations Graduate Textbook

Université de Clermont-Ferrand II (Université Blaise Pascal), France

Combinatorics: The Rota Way

and Étienne Matheron

Joseph P. S. Kung

Université d’Artois, France

University of North Texas

The first book to assemble the wide body of theory which has rapidly developed on the dynamics of linear operators. Written for researchers in operator theory, but also accessible to anyone with a reasonable background in functional analysis at the graduate level.

Gian-Carlo Rota and Catherine H. Yan

Cambridge Tracts in Mathematics, 179

2009 228 x 152 mm 350pp 105 exercises 25 worked examples 978-0-521-51496-5 Hardback c. £43.00 Publication June 2009 www.cambridge.org/9780521514965

National Academy of Sciences of Ukraine

Devoted to counterparts of classical structures of mathematical analysis in analysis over local fields of positive characteristic, this is one of the first books to treat positive characteristic phenomena from an analytic viewpoint. The author’s development of the work begun by Carlitz provides a foundation for studying various special functions.

functions; 16. Pi is irrational; 17. Planetary motion; 18. The logarithm and exponential functions; 19. Integration in elementary terms; Part IV. Infinite Sequences and Infinite Series: 20. Approximation by polynomial functions; 21. e is transcendental; 22. Infinite sequences; 23. Infinite series; 24. Uniform convergence and power series; 25. Complex numbers; 26. Complex functions; 27. Complex power series; Part V. Epilogue: 28. Fields; 29. Construction of the real numbers; 30. Uniqueness of the real numbers; Suggested reading; Answers (to selected problems); Glossary of symbols; Index.

Recent Bestseller Textbook

Calculus Third edition Michael Spivak Publish or Perish Inc, Houston, Texas

Spivak’s celebrated Calculus is ideal for mathematics majors seeking an alternative to doorstop textbooks and formidable introductions to real analysis. Contents: Preface; Part I. Prologue: 1. Basic properties of numbers; 2. Numbers of various sorts; Part II. Foundations: 3. Functions; 4. Graphs; 5. Limits; 6. Continuous functions; 7. Three hard theorems; 8. Least upper bounds; Part III. Derivatives and Integrals: 9. Derivatives; 10. Differentiation; 11. Significance of the derivative; 12. Inverse functions; 13. Integrals; 14. The fundamental theorem of calculus; 15. The trigonometric

Texas A & M University

Gian-Carlo Rota was one of the most original and colourful mathematicians of the twentieth century. His work on the foundations of combinatorics created a new area of algebraic combinatorics. The book is based upon his influential graduate courses on the foundations of combinatorics, that have influenced generations of students. Contents: 1. Sets, functions, and relations; 2. Matching theory; 3. Partially ordered sets and lattices; 4. Generating functions and the umbral calculus; 5. Symmetric functions and Baxter algebras; 6. Determinants, matrices, and polynomials; 7. Selected solutions. Cambridge Mathematical Library

2009 228 x 152 mm 408pp 3 line figures 209 exercises 978-0-521-88389-4 Hardback £55.00 978-0-521-73794-4 Paperback £22.99 www.cambridge.org/9780521883894

Analytic Combinatorics Philippe Flajolet Institut National de Recherche en Informatique et en Automatique (INRIA), Rocquencourt

and Robert Sedgewick Princeton University, New Jersey

The definitive treatment of analytic combinatorics. This self-contained text covers the mathematics underlying the analysis of discrete structures, with thorough treatment of a large

Discrete Mathematics and Foundations number of applications. Exercises, examples, appendices and notes aid understanding: ideal for individual selfstudy or for advanced undergraduate or graduate courses. Contents: Preface; An invitation to analytic combinatorics; Part A. Symbolic Methods: 1. Combinatorial structures and ordinary generating functions; 2. Labelled structures and exponential generating functions; 3. Combinatorial parameters and multivariate generating functions; Part B. Complex Asymptotics: 4. Complex analysis, rational and meromorphic asymptotics; 5. Applications of rational and meromorphic asymptotics; 6. Singularity analysis of generating functions; 7. Applications of singularity analysis; 8. Saddle-Point asymptotics; Part C. Random Structures: 9. Multivariate asymptotics and limit laws; Part D. Appendices: Appendix A. Auxiliary elementary notions; Appendix B. Basic complex analysis; Appendix C. Concepts of probability theory; Bibliography; Index. 2009 247 x 174 mm 824pp 74 tones 50 tables 200 worked examples 190 figures 978-0-521-89806-5 Hardback £45.00 eBook available

www.cambridge.org/9780521898065

MAA Book

Graph Theory A Problem Oriented Approach Daniel Marcus

A natural way to learn some of the essential ideas of graph theory from first principles. Contents: Preface; A. Basic Concepts; B. Isomorphic graphs; C. Bipartite graphs; D. Trees and forests; E. Spanning tree algorithms; F. Euler paths; G. Hamilton paths and cycles; H. Planar graphs; I. Independence and covering; J. Connections and obstructions; K. Vertex coloring; L. Edge coloring; M. Matching theory for bipartite graphs; N. Applications of matching theory; O. Cycle-Free digraphs; Answers to selected problems. Mathematical Association of America Textbooks

2008 228 x 152 mm 240pp 640 exercises 450 figures 978-0-88385-753-3 Hardback £31.99 www.cambridge.org/9780883857533

Textbook

A Primer of Infinitesimal Analysis Second edition John L. Bell University of Western Ontario

A rigorous, axiomatically formulated presentation of the ‘zero-square’, or ‘nilpotent’ infinitesimal. ‘This might turn out to be a boring, shallow book review: I merely LOVED the book...the explanations are so clear, so considerate; the author must have taught the subject many times, since he anticipates virtually every potential question, concern, and misconception in a student’s or reader’s mind.’ MAA Reviews

Contents: Introduction; 1. Basic features of smooth worlds; 2. Basic differential calculus; 3. First applications of the differential calculus; 4. Applications to physics; 5. Multivariable calculus and applications; 6. The definite integral: Higher order infinitesimals; 7. Synthetic geometry; 8. Smooth infinitesimal analysis as an axiomatic system; Appendix; Models for smooth infinitesimal analysis. 2008 228 x 152 mm 140pp 54 exercises 978-0-521-88718-2 Hardback £30.00 eBook available

www.cambridge.org/9780521887182

Association for Symbolic Logic

Games, Scales and Suslin Cardinals: The Cabal Seminar Volume I Edited by Alexander S. Kechris California Institute of Technology

Benedikt Löwe Universiteit van Amsterdam

and John R. Steel

Topics in Topological Graph Theory Edited by Lowell W. Beineke Purdue University, Indiana

and Robin J. Wilson The Open University, Milton Keynes

Consultant Editor Jonathan L. Gross Columbia University, New York

Assisted by Thomas W. Tucker Colgate University, New York

The use of topological ideas to explore various aspects of graph theory, and vice versa, is a fruitful area of research. There are links with other areas of mathematics, such as design theory and geometry, and increasingly with such areas as computer networks where symmetry is an important feature. Contents: Preface; Foreword; Introduction; 1. Embedding graphs on surfaces; 2. Maximum genus; 3. Distributions of embeddings; 4. Algorithms and obstructions for embeddings; 5. Graph minors: generalizing Kuratowski’s theorem; 6. Colouring graphs on surfaces; 7. Crossing numbers; 8. Representing graphs and maps; 9. Enumerating coverings; 10. Symmetric maps; 11. The genus of a group; 12. Embeddings and geometries; 13. Embeddings and designs; 14. Infinite graphs and planar maps; 15. Open problems; Notes on contributors; Index of definitions. Encyclopedia of Mathematics and its Applications, 128

2009 234 x 156 mm 416pp 7 tones 15 tables 95 figures 978-0-521-80230-7 Hardback c. £60.00 Publication July 2009 www.cambridge.org/9780521802307

Association for Symbolic Logic

Subsystems of Second Order Arithmetic Second edition Stephen G. Simpson

University of California, Berkeley

Pennsylvania State University

Presents seminal papers from the Caltech-UCLA ‘Cabal Seminar’, unpublished material, and related new papers.

What are the appropriate axioms for mathematics? Through a series of case studies, this volume examines these axioms to prove particular theorems in core areas including algebra, analysis, and topology, focusing on the language of second-order arithmetic, the weakest language rich enough to express and develop the bulk of mathematics.

Lecture Notes in Logic

2008 228 x 152 mm 460pp 978-0-521-89951-2 Hardback £45.00 eBook available

www.cambridge.org/9780521899512

Perspectives in Logic

2009 228 x 152 mm 456pp 83 tables 4 exercises 978-0-521-88439-6 Hardback £50.00 Publication July 2009 www.cambridge.org/9780521884396

For regular email alerts visit www.cambridge.org/alerts

Discrete Mathematics and Foundations Surveys in Combinatorics 2009 Edited by Sophie Huczynska University of St Andrews, Scotland

James D. Mitchell University of St Andrews, Scotland

and Colva M. Roney-Dougal

Association for Symbolic Logic

Logic Colloquium 2006 Edited by S. Barry Cooper University of Leeds

Herman Geuvers Radboud Universiteit Nijmegen

University of St Andrews, Scotland

Anand Pillay

Survey articles based on the invited lectures given at the Twenty-second British Combinatorial Conference.

University of Leeds

Contents: Preface; 1. Graph decompositions and symmetry; 2. Combinatorics of optimal designs; 3. Regularity and the spectra of graphs; 4. Trades and t-designs; 5. Extremal graph packing problems: Ore-type versus Diractype; 6. Embedding large subgraphs into dense graphs; 7. Counting planar graphs and related families of graphs; 8. Metrics for sparse graphs; 9. Recent results on chromatic and flow roots of graphs and matroids. London Mathematical Society Lecture Note Series, 365

2009 228 x 152 mm 336pp 5 tones 50 worked examples 45 figures 978-0-521-74173-6 Paperback c. £40.00 Publication July 2009 www.cambridge.org/9780521741736

and Jouko Väänänen University of Amsterdam and University of Helsinki

The Annual European Meeting of the Association for Symbolic Logic, also known as the Logic Colloquium, is among the most prestigious annual meetings in the field. The current volume, Logic Colloquium 2006, with contributions from plenary speakers and selected special session speakers, contains both expository and research papers by some of the best logicians in the world. Lecture Notes in Logic

2009 234 x 156 mm 384pp 978-0-521-11081-5 Hardback c. £60.00 Publication July 2009 www.cambridge.org/9780521110815

Channel Codes Forthcoming

Algebraic Theories J. Adámek Technische Universität Carolo Wilhelmina zu Braunschweig, Germany

J. Rosick Masarykova Univerzita v Brnì, Czech Republic

and E. M. Vitale Université Catholique de Louvain, Belgium

First up-to-date treatment of this categorical way of describing sets with extra algebraic structure (data types), with applications in analysis, topology and number theory, geometry and mathematical physics. A must-read for graduate students and researchers in category theory, general algebra, theoretical computer science, and logic. Cambridge Tracts in Mathematics

2010 228 x 152 mm 200pp 978-0-521-11922-1 Hardback c. £40.00 Publication January 2010 www.cambridge.org/9780521119221

Classical and Modern William Ryan University of Arizona

and Shu Lin University of California, Davis

This detailed introduction presents the underlying theory and describes how to design and implement practical iterative codes. Including the latest information on modern channel codes plus 250 varied and stimulating end-of-chapter problems, this is an essential resource for students and practitioners alike. 2009 247 x 174 mm 700pp 35 tables 250 exercises 145 worked examples 219 figures 978-0-521-84868-8 Hardback c. £50.00 Publication October 2009 www.cambridge.org/9780521848688

Network Coding An Introduction Tracey Ho California Institute of Technology

and Desmond Lun Broad Institute of MIT and Harvard

Unified overview of the theory, applications, challenges and future directions of network coding for graduate students, researchers and practitioners. Contents: 1. Introduction; 2. Lossless multicast network coding; 3. Inter-session network coding; 4. Network coding in lossy networks; 5. Subgraph selection; 6. Security against adversarial errors. 2008 253 x 177 mm 184pp 47 line figures 978-0-521-87310-9 Hardback £30.00 eBook available

www.cambridge.org/9780521873109

Modern Coding Theory Tom Richardson and Ruediger Urbanke École Polytechnique Fédérale, Lausanne

Summary of the state-of-the-art in techniques to analyse and design practical iterative coding systems. ‘There is definitely a market for a book focusing on LDPC codes, and Tom Richardson and Reudiger Urbanke would be on anyone’s short list to write that book. They have made substantive contributions to the theory and practice of LDPC codes. I believe this book will become required reading for researchers in LDPC codes at universities and communications companies around the world.’ Thomas Fuja, University of Notre Dame

Contents: Preface; 1. Introduction; 2. Factor graphs; 3. Binary erasure channel; 4. Binary memoryless symmetric channels; 5. General channels ; 6. Convolutional codes and turbo codes; 7. General ensembles; 8. Expander codes and the flipping algorithm; Appendices: A. Encoding low-density parity-check codes; B. Efficient implementation of density evolution; C. Concentration inequalities; D. Formal power sums. 2008 247 x 174 mm 592pp 150 line figures 185 exercises 978-0-521-85229-6 Hardback £45.00 eBook available

www.cambridge.org/9780521852296

Algebra and Geometry / Number Theory and Algebra

Algebra and Geometry Directed Algebraic Topology Models of Non-Reversible Worlds Marco Grandis Università degli Studi di Genova

The first authored book to be dedicated to the new field of directed algebraic topology that arose in the 1990s, in homotopy theory and in the theory of concurrent processes. The author presents its mathematical foundations, demonstrating its relation to classical algebraic topology, and explores its varied applications. New Mathematical Monographs, 13

2009 228 x 152 mm 445pp 978-0-521-76036-2 Hardback c. £55.00 Publication October 2009 www.cambridge.org/9780521760362

Moduli Spaces and Vector Bundles Edited by Leticia Brambila-Paz Centro de Investigacíon en Matematicás (CIMAT), Mexico

Steven B. Bradlow University of Illinois, Urbana-Champaign

Oscar García-Prada Consejo Superior de Investigaciones Cientificas, Madrid

and applications of sub-Riemannian geometry for graduate students and researchers in pure and applied mathematics, theoretical physics, control theory, and thermodynamics. Potential applications include quantum mechanics and quantum field theory. Encyclopedia of Mathematics and its Applications, 126

2009 234 x 156 mm 370pp 52 line figures 978-0-521-89730-3 Hardback £55.00 Publication May 2009 www.cambridge.org/9780521897303

Forthcoming

Vector bundles and their associated moduli spaces are of fundamental importance in algebraic geometry. This volume, authored by some of the subject’s leading experts, covers foundational material as well as focusing on research topics currently at the forefront of the field. Suitable for both graduate students and more experienced researchers. London Mathematical Society Lecture Note Series, 359

2009 228 x 152 mm 512pp 9 tones 30 worked examples 10 figures 978-0-521-73471-4 Paperback c. £48.00 Publication June 2009 www.cambridge.org/9780521734714

Sub-Riemannian Geometry General Theory and Examples Ovidiu Calin

2008 228 x 152 mm 248pp 3 tables 150 exercises 6 figures 978-0-521-72236-0 Paperback £23.99 eBook available

www.cambridge.org/9780521722360

Analytic Number Theory Essays in Honour of Klaus Roth Edited by W. W. L. Chen

Daniel Huybrechts

University of Cambridge

and Manfred Lehn

Macquarie University, Sydney

W. T. Gowers H. Halberstam University of Illinois, Urbana-Champaign

Johannes Gutenberg Universität Mainz, Germany

W. M. Schmidt

Lucidly written, fully developed, the perfect exposition of this central area of current research in algebraic geometry.

University of Colorado, Boulder

2009 228 x 152 mm 300pp 978-0-521-13420-0 Paperback c. £35.00 Publication December 2009 www.cambridge.org/9780521134200

Leading lights in mathematics acknowledge the contribution of British mathematician, Klaus Roth, to number theory, diophantine approximation, sieve theory and beyond. Extensive lists of references make this a valuable source for research mathematicians in many areas and a suitable introductory overview of the subject for beginning research students.

Number Theory and Algebra

and S. Ramanan Chennai Mathematical Institute, India

Contents: Introduction; 1. Factorization and the primes; 2. Congruences; 3. Quadratic residues; 4. Continued fractions; 5. Sums of squares; 6. Quadratic forms; 7. Some Diophantine equations; 8. Computers and number theory; Exercises; Hints; Answers; Bibliography; Index; Additional notes.

The Geometry of Moduli Spaces of Sheaves Rheinische Friedrich-Wilhelms-Universität Bonn

Textbook

The Higher Arithmetic An Introduction to the Theory of Numbers Eighth edition H. Davenport University of Cambridge

Classic text in number theory; this eighth edition contains new material on primality testing written by J. H. Davenport. ‘Although this book is not written as a textbook but rather as a work for the general reader, it could certainly be used as a textbook for an undergraduate course in number theory and, in the reviewer’s opinion, is far superior for this purpose to any other book in English.’ From a review of the first edition in Bulletin of the American Mathematical Society

and R. C. Vaughan Pennsylvania State University

Contributors: Roger Baker, Glyn Harman, William D. Banks, Igor E. Shparlinski, József Beck, Wesley Pegden, Sujith Vijay, Victor Beresnevich, Vasily Bernik, Maurice Dodson, Sanju Velani, J. Bourgain, T. D. Browning, D. R. Heath-Brown, Jörg Brüdern, Yann Bugeaud, Bernard Chazelle, William Chen, Giancarlo Travaglini, Harold G. Diamond, H. Halberstam, P. D. T. A. Elliott, Ben Green, Terence Tao, Nils Hebbinghaus, Tomasz Schoen, Anand Srivastav, H. A. Helfgott, A. Venkatesh, C. Hooley, Nicholas M. Katz, Sergei Konyagin, A. Lasjaunias, Michel Laurent, Helmut Maier, David Masser, Bernard de Mathan, Melvyn B. Nathanson, Erich Novak, Henryk Wózniakowski, A. Sárközy, C. L. Stewart, A. Schinzel, Jerzy Kaczorowski, Wolfgang M. Schmidt, Dinesh S. Thakur, R. C. Vaughan, Michel Waldschmidt, Umberto Zannier 2009 228 x 152 mm 510pp 1 tone 5 tables 20 worked examples 2 figures 978-0-521-51538-2 Hardback £60.00 www.cambridge.org/9780521515382

Eastern Michigan University

and Der-Chen Chang Georgetown University, Washington DC

Sub-Riemannian manifolds are manifolds with the Heisenberg principle built in. This comprehensive text and reference introduces the theory

Visit our website at www.cambridge.org

Number Theory and Algebra Algorithmic Number Theory

A Higher-Dimensional Sieve Method

Lattices, Number Fields, Curves and Cryptography Edited by J.P. Buhler

With Procedures for Computing Sieve Functions Harold G. Diamond

Reed College, Oregon

University of Illinois, Urbana-Champaign

and P. Stevenhagen

H. Halberstam

Universiteit Leiden

University of Illinois, Urbana-Champaign

This comprehensive introduction for beginning graduate students contains articles by the leading experts in the field. It covers basic topics such as algorithmic aspects of number fields, elliptic curves, and lattice basis reduction and advanced topics including cryptography, computational class field theory, zeta functions and L-series, and quantum computing.

and William F. Galway

Mathematical Sciences Research Institute Publications, 44

www.cambridge.org/9780521894876

2008 234 x 156 mm 662pp 978-0-521-80854-5 Hardback £50.00 www.cambridge.org/9780521808545

Modular Forms on Schiermonnikoog

Modern and practical guide to higher dimensional sieve theory, with an Appendix describing methods for computing sieve functions. Cambridge Tracts in Mathematics, 177

2008 228 x 152 mm 290pp 5 tones 15 tables 10 worked examples 15 figures 978-0-521-89487-6 Hardback £45.00 eBook available

Edited by Bas Edixhoven MAA Book

Biscuits of Number Theory Edited by Arthur T. Benjamin Harvey Mudd College, California

and Ezra Brown Virginia Polytechnic Institute and State University

An anthology of articles ideal for use as a textbook supplement on a number theory course. The editors have selected well written bite-sized articles and notes which aid an understanding of number theory. Dolciani Mathematical Expositions

2009 253 x 177 mm 326pp 978-0-88385-340-5 Hardback £40.00 www.cambridge.org/9780883853405

Elliptic Curves and Big Galois Representations Daniel Delbourgo Monash University, Victoria

Describes the arithmetic of modular forms and elliptic curves; self-contained and ideal for both graduate students and professional number theorists. London Mathematical Society Lecture Note Series, 356

2008 228 x 152 mm 288pp 70 line figures 1 table 5 exercises 15 worked examples 5 figures 2 graphs 978-0-521-72866-9 Paperback £35.00 www.cambridge.org/9780521728669

Universiteit Leiden

Gerard van der Geer Universiteit van Amsterdam

and Ben Moonen Universiteit van Amsterdam

A collection of articles presenting the state of the art in the topic of modular forms. 2008 228 x 152 mm 360pp 20 tables 10 worked examples 1 figure 978-0-521-49354-3 Hardback £50.00 eBook available

www.cambridge.org/9780521493543

MAA Book

Visual Group Theory Nathan Carter Bentley College, Massachusetts

This text approaches the learning of group theory visually. It allows the student to see groups, experiment with groups and understand their significance. It is ideal as a supplement for a first course in group theory or alternatively as recreational reading. Contents: Preface; Overview; 1. What is a group?; 2. What do groups look like?; 3. Why study groups?; 4. Algebra at last; 5. Five families; 6. Subgroups; 7. Products and quotients; 8. The power of homomorphisms; 9. Sylow Theory; 10. Galois theory. Classroom Resource Materials

2009 247 x 170 mm 340pp 978-0-88385-757-1 Hardback £40.00 www.cambridge.org/9780883857571

Graduate Textbook

Groups, Graphs and Trees An Introduction to the Geometry of Infinite Groups John Meier Lafayette College, Pennsylvania

Accessible and engaging approach to geometric group theory; ideal for advanced undergraduates. ‘Meier has the rare ability to make complex concepts accessible to novices while simultaneously challenging the experienced. … With well-chosen illustrations and examples, Meier succeeds brilliantly in this unique approach.’ SciTech Book News

Contents: Preface; 1. Cayley’s theorems; 2. Groups generated by reflections; 3. Groups acting on trees; 4. BaumslagSolitar groups; 5. Words and Dehn’s word problem; 6. A finitely-generated, infinite, Torsion group; 7. Regular languages and normal forms; 8. The Lamplighter group; 9. The geometry of infinite groups; 10. Thompson’s group; 11. The large-scale geometry of groups; Bibliography; Index. London Mathematical Society Student Texts, 73

2008 228 x 152 mm 256pp 1 table 175 exercises 61 worked examples 95 figures 55 graphs 978-0-521-89545-3 Hardback £55.00 978-0-521-71977-3 Paperback £19.99 eBook available

www.cambridge.org/9780521895453

The Monster Group and Majorana Involutions A. A. Ivanov Imperial College of Science, Technology and Medicine, London

The first book containing a rigorous construction and uniqueness proof for the largest and most famous sporadic simple group, the Monster. The author provides a systematic exposition of the theory of the Monster group, which so far remains largely unpublished, and explores the theory of groups generated by Majorana involutions. Cambridge Tracts in Mathematics, 176

2009 228 x 152 mm 266pp 15 tables 978-0-521-88994-0 Hardback £50.00 www.cambridge.org/9780521889940

Number Theory and Algebra / Scientific Computing Galois Groups and Fundamental Groups Tamás Szamuely

Words Notes on Verbal Width in Groups Dan Segal

Hungarian Academy of Sciences, Budapest

All Souls College, Oxford

Ever since the concepts of Galois groups in algebra and fundamental groups in topology emerged during the nineteenth century, mathematicians have known of the strong analogies between the two concepts. This book presents the connection starting at an elementary level and assuming as little technical background as possible.

Spectacular new results in finite group theory can be accessed via the study of word-values in groups. This book explores fundamental questions about the behaviour of word-values in groups and demonstrates the power of this approach. An accessible treatment suitable for research students and experienced workers in group theory.

Cambridge Studies in Advanced Mathematics, 117

London Mathematical Society Lecture Note Series, 361

2009 228 x 152 mm 304pp 60 exercises 90 worked examples 978-0-521-88850-9 Hardback c. £30.00 Publication July 2009 www.cambridge.org/9780521888509

2009 228 x 152 mm 140pp 30 exercises 1 figure 978-0-521-74766-0 Paperback c. £24.99 Publication June 2009 www.cambridge.org/9780521747660

Differential Tensor Algebras and their Module Categories

Unitary Reflection Groups

R. Bautista National University of Mexico

L. Salmerón National University of Mexico

and R. Zuazua National University of Mexico

This volume provides a systematic presentation of the theory of differential tensor algebras and their categories of modules. The authors introduce new findings and proofs as well as providing a fresh perspective on established results. London Mathematical Society Lecture Note Series, 362

2009 228 x 152 mm 456pp 90 exercises 978-0-521-75768-3 Paperback c. £40.00 Publication September 2009 www.cambridge.org/9780521757683

Forthcoming

Synthetic Geometry of Manifolds Anders Kock Aarhus Universitet, Denmark

User-friendly introduction to the generalized context for modern research on quantum field theory and higher category theory. Cambridge Tracts in Mathematics, 180

2009 228 x 152 mm 300pp 978-0-521-11673-2 Hardback c. £50.00 Publication November 2009 www.cambridge.org/9780521116732

Gustav I. Lehrer University of Sydney

and Donald E. Taylor University of Sydney

This book provides a complete classification of unitary reflection groups – which arise naturally in many areas of mathematics. Designed for graduate students, but also suitable for researchers in algebra, topology and mathematical physics. Australian Mathematical Society Lecture Series, 20

2009 228 x 152 mm 305pp 12 tables 110 exercises 978-0-521-74989-3 Paperback c. £35.00 Publication June 2009 www.cambridge.org/9780521749893

Purity, Spectra and Localisation Mike Prest University of Manchester

A unified, coherent account of the algebraic aspects and uses of the Ziegler spectrum. It may be used as an introductory graduate-level text, providing relevant background material and a wealth of illustrated examples. An extensive index and thorough referencing also make this book an ideal reference. Encyclopedia of Mathematics and its Applications, 121

2009 234 x 156 mm 792pp 115 worked examples 978-0-521-87308-6 Hardback c. £85.00 Publication June 2009 www.cambridge.org/9780521873086

Scientific Computing Textbook New Edition

The Student’s Introduction to MATHEMATICA® A Handbook for Precalculus, Calculus, and Linear Algebra Second edition Bruce F. Torrence Randolph-Macon College, Virginia

and Eve A. Torrence Randolph-Macon College, Virginia

A new edition of this well loved book completely rewritten for Mathematica 6. This book can be used in a variety of courses, from precalculus to linear algebra. Used as a supplementary text it will aid in bridging the gap between the mathematics in the course and Mathematica. ‘This book does a very good job of filling an important niche – giving mathematics students a thorough introduction to Mathematica without overwhelming them with the long manual.’ Mathematics Teacher

Contents: Preface; 1. Getting started; 2. Working with Mathematica; 3. Functions and their graphs; 4. Algebra; 5. Calculus; 6. Multivariable calculus; 7. Linear algebra; 8. Programming; Solutions to exercises; Index. 2009 246 x 189 mm 484pp 50 tones 5 tables 220 exercises 978-0-521-71789-2 Paperback £25.99 www.cambridge.org/9780521717892

Textbook

A First Course in the Numerical Analysis of Differential Equations Second edition Arieh Iserles University of Cambridge

Extensively updated new edition including new chapters on emerging subject areas: geometric numerical integration, spectral methods and conjugate gradients. ‘A well written and exciting book … the exposition throughout is clear and very lively. The author’s enthusiasm and wit are obvious on almost every page and I recommend the text very strongly indeed.’ Proceedings of the Edinburgh Mathematical Society

eBooks available at www.cambridge.org/online

Scientific Computing / Dynamical Systems, Mechanics and Modelling Contents: Preface to the first edition; Preface to the second edition; Flowchart of contents; Part I. Ordinary differential equations: 1. Euler’s method and beyond; 2. Multistep methods; 3. Runge–Kutta methods; 4. Stiff equations; 5. Geometric numerical integration; 6. Error control; 7. Nonlinear algebraic systems; Part II. The Poisson equation: 8. Finite difference schemes; 9. The finite element method; 10. Spectral methods; 11. Gaussian elimination for sparse linear equations; 12. Classical iterative methods for sparse linear equations; 13. Multigrid techniques; 14. Conjugate gradients; 15. Fast Poisson solvers; Part III. Partial differential equations of evolution: 16. The diffusion equation; 17. Hyperbolic equations; Appendix. Bluffer’s guide to useful mathematics: A.1. Linear algebra; A.2. Analysis; Bibliography; Index. Cambridge Texts in Applied Mathematics, 44

2008 247 x 174 480pp 4 tones 163 exercises 120 figures 978-0-521-73490-5 Paperback £29.99 www.cambridge.org/9780521734905

Acta Numerica 2008 Volume 17 Edited by A. Iserles University of Cambridge

A high-impact, prestigious, annual publication containing invited surveys by subject leaders: essential reading for all practitioners and researchers. Acta Numerica, 17

2008 247 x 174 mm 416pp 50 figures 978-0-521-51642-6 Hardback £70.00 www.cambridge.org/9780521516426

A Compendium of Partial Differential Equation Models Method of Lines Analysis with Matlab William E. Schiesser Lehigh University, Pennsylvania

and Graham W. Griffiths City University, London

Explains numerical methods, and associated computer codes in Matlab, for the solution of a spectrum of models expressed as ordinary and partial differential equations. The authors focus on the well-established method of lines, making the code easy to understand, implement, and modify. 2009 253 x 215 mm 488pp 43 line figures 15 tones 2 plates 43 tables 978-0-521-51986-1 Hardback £55.00 www.cambridge.org/9780521519861

Numerical Recipes The Art of Scientific Computing Third edition William H. Press University of Texas, Austin

Saul A. Teukolsky Cornell University, New York

William T. Vetterling ZINK Imaging. LLC

and Brian P. Flannery

Numerical Recipes Source Code CD-ROM Third edition William H. Press University of Texas, Austin

Saul A. Teukolsky Cornell University, New York

William T. Vetterling Polaroid Corporation, Cambridge, Massachusetts

and Brian P. Flannery

Exxon Mobil Corporation

Exxon Research and Engineering, New Jersey

The third edition of Numerical Recipes has wider coverage than ever before. New chapters cover classification and inference and computational geometry; new sections include MCMC, interior point methods, and an updated, expanded treatment of ODEs, all with completely new routines in C++. For more information, or to buy the book, visit www.cambridge.org/ numericalrecipes. For support, or to subscribe to an online version, please visit www.nr.com.

2007 978-0-521-70685-8 3rd Edition £45.00 www.cambridge.org/9780521706858

Contents: 1. Preliminaries; 2. Solution of linear algebraic equations; 3. Interpolation and extrapolation; 4. Integration of functions; 5. Evaluation of functions; 6. Special functions; 7. Random numbers; 8. Sorting and selection; 9. Root finding and nonlinear sets of equations; 10. Minimization or maximization of functions; 11. Eigensystems; 12. Fast Fourier transform; 13. Fourier and spectral applications; 14. Statistical description of data; 15. Modeling of data; 16. Classification and inference; 17. Integration of ordinary differential equations; 18. Two point boundary value problems; 19. Integral equations and inverse theory; 20. Partial differential equations; 21. Computational geometry; 22. Lessnumerical algorithms; References. 2007 253 x 177 mm 1256pp 37 tables 978-0-521-88068-8 3rd Edition £45.00 www.cambridge.org/9780521880688

Numerical Recipes with Source Code CD-ROM Third edition William H. Press University of Texas, Austin

Saul A. Teukolsky Cornell University, New York

William T. Vetterling Zink Imaging, Cambridge, Massachusetts

and Brian P. Flannery Exxon Mobil Corporation, New Jersey 2007 978-0-521-88407-5 3rd Edition £80.00 www.cambridge.org/9780521884075

Dynamical Systems, Mechanics and Modelling New DVD Edition

Multimedia Fluid Mechanics Second edition Edited by G. M. Homsy University of California, Santa Barbara

Inspired in large part by the very favourable reception of the first edition, this second edition of Multimedia Fluid Mechanics continues to exploit the moving image and interactivity of multimedia to improve the teaching and learning of fluid mechanics by illustrating fundamental phenomena and conveying fascinating fluid flows. • Now covers all standard topics taught in a fluid mechanics or hydrology course • 1000 videos; 20 virtual labs and dozens of new demos and animations with greatly improved search and browse to find your way round • Movie playlist tool lets you plan video sequences ahead of time ‘Homsy and his colleagues have now provided us with a new and powerful teaching aid ... This CD is an ambitious project, and, in my view, it has been accomplished with remarkable success … I have no doubt that this CD-ROM should be regarded as a ‘set text’ for viscous fluid mechanics courses at the undergraduate or starting graduate levels.’ Journal of Fluid Mechanics 2008 978-0-521-72169-1 DVD ROM £16.99 www.cambridge.org/9780521721691

Dynamical Systems, Mechanics and Modelling Graduate Textbook

Applied Solid Mechanics Peter Howell University of Oxford

Gregory Kozyreff University of Oxford

and John Ockendon University of Oxford

The power of mathematics to provide quantitative insights across the whole area of solid mechanics is emphasised in this unique book. Without heavy theory, the authors relate theory to practical applications and provide over 100 carefully chosen exercises. With minimal prerequisites this is accessible to third year undergraduates and above. Contents: List of illustrations; Prologue; 1. Modelling solids; 2. Linear elastostatics; 3. Linear elastodynamics; 4. Approximate theories; 5. Nonlinear elasticity; 6. Asymptotic analysis; 7. Fracture and contact; 8. Plasticity; 9. More general theories; Epilogue; Appendix 1. Orthogonal curvilinear coordinates; References. Cambridge Texts in Applied Mathematics, 43

2008 247 x 174 mm 466pp 18 tones 1 table 134 exercises 128 figures 978-0-521-85489-4 Hardback £70.00 978-0-521-67109-5 Paperback £29.99 www.cambridge.org/9780521854894

Homogeneous Turbulence Dynamics Pierre Sagaut Université de Paris VI (Pierre et Marie Curie)

and Claude Cambon Ecole Centrale de Lyon

This book summarizes the most recent theoretical, computational, and experimental results dealing with homogeneous turbulence dynamics. 2008 253 x 177 mm 480pp 123 line figures 20 tones 27 tables 978-0-521-85548-8 Hardback £65.00 eBook available

www.cambridge.org/9780521855488

Computational Continuum Mechanics Ahmed A. Shabana University of Illinois, Chicago

This book covers nonlinear continuum mechanics theory and its use in nonlinear computer formulations.

www.cambridge.org/9780521885690

Partial Differential Equations in Fluid Dynamics Isom H. Herron Rensselaer Polytechnic Institute, New York

and Michael R. Foster Rensselaer Polytechnic Institute, New York

This book concerns partial differential equations applied to fluids problems in science and engineering. Contents: 1. Review of analytic function theory; 2. Special functions; 3. Eigenvalue problems and eigenfunction expansions; 4. Green’s functions for boundary-value problems; 5. Laplace transform methods; 6. Fourier transform methods; 7. Particular physical problems; 8. Asymptotic expansions of integrals. 2008 253 x 177 mm 296pp 43 line figures 978-0-521-88824-0 Hardback £45.00 eBook available

www.cambridge.org/9780521888240

Recent Bestseller

Classical Mechanics R. Douglas Gregory University of Manchester

‘The writing here is a picture of clarity and directness … The exercises include plenty of interesting and challenging problems … an attractive and well-written exposition of classical mechanics. I wish it had been my textbook when I was a student.’ Mathematical Association of America

Contents: Part I. Newtonian Mechanics of a Single Particle; Part II. Multi-particle Systems; Part III. Analytical mechanics; Part IV. Further Topics. 2006 247 x 174 mm 608pp 193 line figures 3 tables 348 exercises 181 worked examples 978-0-521-53409-3 Paperback £29.99 eBook available

www.cambridge.org/9780521534093

Non-equilibrium Statistical Mechanics and Turbulence John Cardy University of Oxford

Gregory Falkovich Weizmann Institute of Science, Israel

and Krzysztof Gawedzki Ecole Normale Supérieure, Lyon

Edited by Sergey Nazarenko University of Warwick

and Oleg V. Zaboronski University of Warwick

This self-contained volume introduces modern methods of statistical mechanics in turbulence, with three harmonised lecture courses by world class experts. Contents: 1. Preface; 2. Introduction to turbulence theory; 3. Soluble models of turbulent transport; 3. Reaction-diffusion processes. London Mathematical Society Lecture Note Series, 355

2008 228 x 152 mm 172pp 3 tones 35 exercises 30 figures 978-0-521-71514-0 Paperback £25.99 www.cambridge.org/9780521715140

W. T. Koiter’s Elastic Stability of Solids and Structures Edited by Arnold M. A. van der Heijden Technische Universiteit Delft, The Netherlands

This book covers elastic stability of solids and structures, Warner Koiter’s area of special expertise. 2008 253 x 177 mm 240pp 978-0-521-51528-3 Hardback £45.00 eBook available

www.cambridge.org/9780521515283

Textbook

Introduction to Continuum Mechanics Sudhakar Nair Illinois Institute of Technology

This text treats solids and fluids in a balanced manner, using thermodynamic restrictions on the relation between applied forces and material responses. It has many examples and over 150 exercises. This subject is essential for

Contents: 1. Introduction; 2. Kinematics; 3. Forces and stresses; 4. Constitutive equations; 5. Plasticity formulations; 6. Finite element formulation: large deformation, large rotation problem; 7. Finite element formulation: small deformation, large rotation problem. 2008 253 x 177 mm 348pp 102 exercises 978-0-521-88569-0 Hardback £60.00 eBook available

Visit our website at www.cambridge.org

Dynamical Systems, Mechanics and Modelling experimental or numerical modeling of material behavior. Contents: 1. Introduction; 2. Cartesian tensors; 3. General tensors; 4. Integral theorems; 5. Deformation; 6. Motion; 7. Fundamental laws of mechanics; 8. Stress tensor; 9. Energy and entropy constraints; 10. Constitutive relations; 11. Hyperelastic materials; 12. Fluid dynamics; 13. Viscoelasticity; 14. Plasticity. 2009 253 x 215 mm 256pp 60 line figures 149 exercises 978-0-521-87562-2 Hardback £40.00 www.cambridge.org/9780521875622

Fundamentals of Fluid Power Control John Watton Cardiff University

This exciting new reference text is concerned with fluid power control. It is an ideal reference for the practicing engineer and a textbook for advanced courses in fluid power control. In applications in which large forces and/ or torques are required, often with a fast response time, oil-hydraulic control systems are essential. 2009 253 x 215 mm 528pp 381 line figures 61 tones 21 tables 978-0-521-76250-2 Hardback c. £65.00 Publication September 2009 www.cambridge.org/9780521762502

Non-linear Modeling and Analysis of Solids and Structures Steen Krenk Technical University of Denmark, Lyngby

This book presents a theoretical treatment of nonlinear behaviour of solids and structures in such a way that it is suitable for numerical computation, typically using the Finite Element Method. This self-contained and rigorous account of the basic methods contains exercises, examples and algorithms throughout. 2009 247 x 174 mm 370pp 3 tones 5 tables 70 exercises 25 worked examples 105 figures 978-0-521-83054-6 Hardback c. £40.00 Publication June 2009 www.cambridge.org/9780521830546

Continuum Mechanics and Thermodynamics Joanne Wegner University of Victoria, British Columbia

and James Haddow University of Victoria, British Columbia

This text provides a modern and integrated treatment of the foundations and applications of continuum mechanics, especially to microscale phenomena. The text includes numerous

examples and exercises and a chapter on continuum thermodynamics, including entropy production in Newtonian viscous fluid flow and thermoelasticity. Computer solutions use Mathematica®. 2009 253 x 215 mm 280pp 35 line figures 2 tables 978-0-521-86632-3 Hardback £40.00 Publication May 2009 www.cambridge.org/9780521866323

Waves and Mean Flows Oliver Bühler New York University

A modern account of the nonlinear interactions between waves and mean flows such as shear flows and vortices. It can be used as a fundamental reference, a course text, or by geophysicists and physicists needing an introduction to this important area in fundamental fluid dynamics and atmosphere-ocean science. Cambridge Monographs on Mechanics

2009 247 x 174 mm 370pp 10 tones 25 figures 978-0-521-86636-1 Hardback c. £55.00 Publication August 2009 www.cambridge.org/9780521866361

Graduate Textbook

Geological Fluid Dynamics Sub-surface Flow and Reactions Owen M. Phillips

fundamental problem-solving tools, including numerical examples, and serves both as a graduate-level textbook and as a reference for earth scientists and engineers. 2009 247 x 174 mm 328pp 85 line figures 3 tones 3 plates 1 table 88 figures 978-0-521-89853-9 Hardback £70.00 Publication May 2009 www.cambridge.org/9780521898539

Nonlinear Vibrations and Stability of Shells and Plates Marco Amabili Università degli Studi, Parma

This book covers theoretical and experimental aspects of nonlinear vibrations and stability of shells and plates including recent progresses in nonlinear vibrations and stability, advanced problems of shells with fluidstructure interaction, and many practical concepts, diagrams, and numerical results. 2008 253 x 177 mm 390pp 10 tables 978-0-521-88329-0 Hardback £65.00 eBook available

www.cambridge.org/9780521883290

Graduate Textbook

Numerical Solution of Hyperbolic Partial Differential Equations John A. Trangenstein

The Johns Hopkins University

Duke University, North Carolina

This book describes essential scientific concepts and tools for hydrologists and public health ecologists concerned with fluid flow, transport and contamination in rocks and sediments, and for geologists who interpret patterns of mineralization. It is ideal for graduate students and professionals in hydrology, water resources, and aqueous geochemistry.

Numerical Solution of Hyperbolic Partial Differential Equations is a new type of graduate textbook, comprising print, and interactive electronic components (on CD). It is a comprehensive presentation of the modern theory and numerics with a range of applications broad enough to engage most engineering disciplines and many areas of applied mathematics.

Contents: Preface; 1. Introduction; 2. The basic principles; 3. Patterns of flow; 4. Flows with buoyancy variations; 5. Patterns of reaction with flow; 6. Extensions and examples; References; Index. 2009 247 x 174 mm 298pp 6 tones 78 figures 978-0-521-86555-5 Hardback £40.00 www.cambridge.org/9780521865555

Viscoelastic Waves in Layered Media Roger D. Borcherdt United States Geological Survey, California

This is the first book to explain the mathematical theory and corresponding numerical results for wave propagation in layered media with arbitrary amounts of intrinsic absorption. It provides

Contents: Preface; 1. Introduction to partial differential equations; 2. Scalar hyperbolic conservations laws; 3. Nonlinear scalar laws; 4, Nonlinear hyperbolic systems; 5. Methods for scalar laws; 6. Methods for hyperbolic systems; 7. Methods in multiple dimensions; 8. Adaptive mesh refinement; Bibliography; Index. 2009 247 x 174 mm 616pp 113 line figures 2 tables 141 exercises 56 worked examples 978-0-521-87727-5 Hardback £40.00 Publication June 2009 www.cambridge.org/9780521877275

Dynamical Systems, Mechanics and Modelling / Mathematics for Physics and Biology Soliton Equations and Their AlgebroGeometric Solutions

glimpse of further developments in real and complex one-dimensional dynamics.

Volume 2 Fritz Gesztesy University of Missouri, Columbia

2008 228 x 152 mm 208pp 56 exercises 25 worked examples 15 figures 978-0-521-88861-5 Hardback £35.00

Helge Holden

eBook available

Cambridge Studies in Advanced Mathematics, 115

Norwegian University of Science and Technology, Trondheim

www.cambridge.org/9780521888615

Johanna Michor and Gerald Teschl

Algebraic Theory of Differential Equations

Universität Wien, Austria

Edited by Malcolm A. H. MacCallum

Detailed treatment of the class of algebro-geometric solutions and their representations in terms of Riemann theta functions.

Queen Mary, University of London

Universität Wien, Austria

Cambridge Studies in Advanced Mathematics, 114

2008 228 x 152 mm 448pp 15 worked examples 4 figures 978-0-521-75308-1 Hardback £75.00 eBook available

www.cambridge.org/9780521753081

Also available

Soliton Equations and their AlgebroGeometric Solutions Volume 1 Fritz Gesztesy University of Missouri, Columbia

and Helge Holden Norwegian University of Science and Technology, Trondheim

This book offers a detailed treatment of a class of algebro-geometric solutions and their representations. Cambridge Studies in Advanced Mathematics, 79

2003 228 x 152 mm 518pp 978-0-521-75307-4 Hardback £80.00 eBook available

www.cambridge.org/9780521753074

Mathematical Tools for One-Dimensional Dynamics Edson de Faria Universidade de São Paulo

and Welington de Melo IMPA, Rio de Janeiro

Self-contained book presenting the mathematical tools necessary for the study of complex dynamics. Detailing the latest research, it will appeal to graduate students and researchers working in dynamical systems and related fields. Carefully chosen exercises aid understanding and provide a

and Alexander V. Mikhailov University of Leeds

These selected contributions reflect different approaches to the integration of differential equations, originating from Differential Galois Theory, Symmetry, Integrability and Soliton Theory. The ideas of several mathematical communities are here brought together and connections between them sought. London Mathematical Society Lecture Note Series, 357

2008 228 x 152 mm 248pp 80 worked examples 978-0-521-72008-3 Paperback £40.00 www.cambridge.org/9780521720083

Mathematics for Physics and Biology Graduate Textbook

Mathematics for Physics A Guided Tour for Graduate Students Michael Stone University of Illinois, Urbana-Champaign

and Paul Goldbart University of Illinois, Urbana-Champaign

An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. Topics are illustrated through carefully chosen examples, exercises and problems drawn from realistic physics settings. Solutions to the exercises are available at www.cambridge.org/9780521854030. Contents: Preface; 1. Calculus of variations; 2. Function spaces; 3. Linear ordinary differential equations; 4. Linear differential operators; 5. Green functions; 6. Partial differential equations; 7. The mathematics of real waves; 8. Special functions; 9. Integral equations; 10. Vectors and tensors; 11. Differential calculus on

manifolds; 12. Integration on manifolds; 13. An introduction to differential topology; 14. Group and group representations; 15. Lie groups; 16. The geometry of fibre bundles; 17. Complex analysis I; 18. Applications of complex variables; 19. Special functions and complex variables; Appendixes; Reference; Index. 2009 246 x 189 mm 760pp 100 tones 313 exercises 978-0-521-85403-0 Hardback c. £45.00 Publication July 2009 www.cambridge.org/9780521854030

Graduate Textbook

Scientific Computation Gaston Gonnet Eidgenössische Technische Hochschule Zürich

and Ralf Scholl

Using real-life applications, this graduate-level textbook introduces different mathematical methods of scientific computation to solve minimization problems. Each chapter solves several realistic problems, allowing readers to see how the methods are put to use, making it easier to grasp the basic ideas. Interactive exercises are available at www.cambridge.org/9780521849890. Contents: Preface; 1. Determination of the accurate location of an aircraft; 2. When to replace equipment; 3. SSP using LS and SVD; 4. SSP using least squares and best basis; 5. SSP learning methods (nearest neighbours); 6. SSP with linear programming (LP); 7. Stock market prediction; 8. Phylogenetic tree construction; Appendixes; Index. 2009 246 x 189 mm 216pp 13 tones 978-0-521-84989-0 Hardback c. £35.00 Publication August 2009 www.cambridge.org/9780521849890

Textbook

A First Course in String Theory Second edition Barton Zwiebach Massachusetts Institute of Technology

Zwiebach is once again faithful to his goal of making string theory accessible to undergraduates. This text now includes AdS/CFT correspondence, as well introducing superstrings. With almost 300 problems and exercises it is perfectly suited for introductory courses for students with a background in physics. ‘A refreshingly different approach to string theory that requires remarkably little previous knowledge of quantum theory or relativity. This highlights fundamental features of the theory that make it so radically different from theories based on point-like

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Mathematics for Physics and Biology / Statistics, Applied Probability and Finance particles. This book makes the subject amenable to undergraduates but it will also appeal greatly to beginning researchers who may be overwhelmed by the standard textbooks.’

Digital Image Processing for Medical Applications

Professor Michael Green, University of Cambridge

California State University, Channel Islands

Contents: Foreword; Preface; Acknowledgements; Part I. Basics: 1. A brief introduction; 2. Special relativity and extra dimensions; 3. Electromagnetism and gravitation in various dimensions; 4. Nonrelativistic strings; 5. The relativistic point particle; 6. Relativistic strings; 7. Strong parameterization and classical motion; 8. World-sheet currents; 9. Lightcone relativistic strings; 10. Light-cone fields and particles; 11. The relativistic quantum point particle; 12, Relativistic quantum closed strings; 13. Relativistic quantum closed strings; 14. A look at relativistic superstrings; Part II. Developments: 15. D-branes and gauge fields; 16. String charge and electric charge; 17. T-duality of closed strings; 18. T-duality of open strings; 19. Electromagnetism fields in D-branes; 20. Nonlinear and Born-Infeld electrodynamics; 21. Strong theory and particle physics; 22. String thermodynamics and black holes; 23. Strong interactions and AdS/CFT; 24. Covariant string quantization; 25. String interactions and Riemann surfaces; 26. Loop amplitudes in string theory; References; Index. 2009 246 x 189 mm 696pp 86 tones 180 exercises 978-0-521-88032-9 Hardback £40.00 eBook available

www.cambridge.org/9780521880329

Chaos and Coarse Graining in Statistical Mechanics Patrizia Castiglione Editions Belin, Paris

Massimo Falcioni Università degli Studi di Roma ‘La Sapienza’, Italy

Annick Lesne Centre National de la Recherche Scientifique (CNRS), Paris

and Angelo Vulpiani Università degli Studi di Roma ‘La Sapienza’, Italy

Presents concepts of chaotic systems for researchers and graduate students in statistical mechanics and chaos. 2008 247 x 174 mm 280pp 35 line figures 978-0-521-89593-4 Hardback £65.00 eBook available

www.cambridge.org/9780521895934

Geoff Dougherty

This practical book for advanced undergraduates and graduate students explains the concepts and the effective use of image processing tools for medical applications. Real medical images and hands-on activities are used to develop the reader’s skill and confidence. All images, public-domain software and solutions available from www.cambridge.org/books/dougherty. 2009 247 x 174 mm 462pp 130 tones 13 plates 17 tables 130 exercises 13 worked examples 735 figures 978-0-521-86085-7 Hardback £45.00 www.cambridge.org/9780521860857

Statistics, Applied Probability and Finance

Textbook

Probability and Statistics by Example Volume 2: Markov Chains: A Primer in Random Processes and their Applications Yuri Suhov University of Cambridge

and Mark Kelbert University of Wales, Swansea

The subject is critical in many modern applications such as mathematical finance, quantitative management, insurance and actuarial studies. Contents: Preface; Introduction: Andrei Markov and his time; 1. Discrete-time Markov chains; 2. Continuous-time Markov chains: basic theory; 3. Statistics of discretetime Markov chains; Afterword: Pearson, Maxwell and other famous Cambridge Wranglers of the past: some lessons to be learned; Bibliography; Appendix; Index. 2008 247 x 174 mm 498pp 151 line figures 190 worked examples 978-0-521-84767-4 Hardback £70.00 978-0-521-61234-0 Paperback £29.99 eBook available

www.cambridge.org/9780521847674

New in Paperback Graduate Textbook

Markov Chains and Stochastic Stability Second edition Sean Meyn University of Illinois, Urbana-Champaign

and Richard L. Tweedie University of Minnesota

Prologue by Peter W. Glynn

New up-to-date edition of this influential classic on Markov chains in general state spaces. Proofs are rigorous and concise, the range of applications is broad and knowledgeable, and key ideas are accessible to practitioners with limited mathematical background. New commentary by Sean Meyn, including updated references, reflects developments since 1996. ‘This second edition remains true to the remarkable standards of scholarship established by the first edition … it will no doubt be a very welcome addition to the literature.’ Peter W. Glynn, Prologue to the Second Edition Cambridge Mathematical Library

2009 247 x 174 mm 622pp 4 tones 17 figures 978-0-521-73182-9 Paperback £30.00 www.cambridge.org/9780521731829

Statistical Models A. C. Davison École Polytechnique Fédérale, Lausanne

An integrated development of models and likelihood that blends theory and practice, suitable for advanced undergraduate and graduate students, researchers and practitioners. Each chapter contains a wide range of problems and exercises. A library of data sets accompanying the book is available over the web. ‘This is an excellent textbook on modern statistics.’ Zentralblatt MATH

Contents: 1. Introduction; 2. Variation; 3. Uncertainty; 4. Likelihood; 5. Models; 6. Stochastic models; 7. Estimation and hypothesis testing; 8. Linear regression models; 9. Designed experiments; 10. Nonlinear regression models; 11. Bayesian models; 12. Conditional and marginal inference. Cambridge Series in Statistical and Probabilistic Mathematics, 11

2008 253 x 177 mm 736pp 119 tables 566 exercises 978-0-521-73449-3 Paperback £29.99 www.cambridge.org/9780521734493

Statistics, Applied Probability and Finance Textbook

Statistical Models Theory and Practice Second edition David Freedman University of California, Berkeley

This lively and engaging book explains the basic ideas of association and regression, and tells you the things you have to know in order to read empirical papers in the social and health sciences, as well as the techniques you need to build statistical models of your own. ‘At last, a second course in statistics that is serious, correct, and interesting. The book teaches regression, causal modeling, maximum likelihood, and the bootstrap. Everyone who analyzes real data should read this book.’ Persi Diaconis, Professor of Mathematics and Statistics, Stanford University 2009 253 x 177 mm 456pp 21 line figures 11 tables 404 exercises 978-0-521-11243-7 Hardback £70.00 978-0-521-74385-3 Paperback £24.99 Publication June 2009 www.cambridge.org/9780521112437

A Quantitative Tour of the Social Sciences Edited by Andrew Gelman Columbia University, New York

and Jeronimo Cortina

This overview by prominent social scientists gives a friendly, non-technical sense of how quantitative research is done in different areas. Readers will find out about models and ways of thinking in economics, history, sociology, political science, and psychology, which in turn they can bring back to their own work. ‘A marvelous sampler of quantitative approaches to social science across a range of disciplines. The authors forsake the dry and mechanical overviews that typify introductory texts in favor of focused forays into specific problems, deemed representative of their discipline’s theoretical and empirical output. These engrossing stories of research make the volume a lively and informative read.’ John Gerring, author of Social Science Methodology and Case Study Research: Principles and Practices

Contents: 1. Models and methods in the social sciences; 2. History; 3. Economics; 4. Sociology; 5. Political science; 6. Psychology; 7. To treat or not to treat: casual inference in the social science.

Graduate Textbook

Elementary Probability for Applications Rick Durrett Cornell University, New York

This clear, lively introduction to probability concentrates on the results that are the most useful for applications. It is designed for a one-semester course for students who have some familiarity with basic calculus. Reflecting the author’s philosophy that the best way to learn probability is to see it in action, there are more than 350 problems and 200 examples. ‘The book has a nice interplay between probability modeling and scientific applications, whether from biology, sports, or discussions of China’s one-child policy. Many of the examples are thought provoking, including ones on DNA samples for paternity cases and others about the O. J. Simpson trial. As an instructor, I enjoy digging into these examples in class. And the large selection of interesting problems builds basic skills and deepens or extends the main ideas.’ Professor Michael Phelan, University of California, Irvine 2009 247 x 187 mm 296pp 55 line figures 80 tables 355 exercises 978-0-521-86756-6 Hardback c. £35.00 Publication September 2009 www.cambridge.org/9780521867566

Bayesian Nonparametrics Edited by Nils Lid Hjort Universitetet i Oslo

Chris Holmes University of Oxford

Peter Müller University of Texas, M. D. Anderson Cancer Center

and Stephen Walker University of Kent, Canterbury

Bayesian nonparametrics works. Applications are appearing in such disciplines as information retrieval, NLP, machine vision, computational biology, cognitive science, signal processing. In this coherent introduction, the editors weave together tutorial chapters by Ghosal, Lijoi and Prünster, Dunson, and Teh and Jordan, giving direct access to these exciting ideas and methods. 2009 253 x 177 mm 272pp 978-0-521-51346-3 Hardback c. £35.00 www.cambridge.org/9780521513463

Stochastic Approximation A Dynamical Systems Viewpoint Vivek S. Borkar Tata Institute of Fundamental Research, Mumbai, India

Simple, compact toolkit for designing and analyzing algorithms, with concrete examples from control and communications engineering, artificial intelligence, economic modelling. Contents: Preface; 1. Introduction; 2. Basic convergence analysis; 3. Stability criteria; 4. Lock-in probability; 5. Stochastic recursive inclusions; 6. Multiple timescales; 7. Asynchronous schemes; 8. A limit theorem for fluctuations; 9. Constant stepsize algorithms; 10. Applications; 11. Appendices; References; Index. 2008 228 x 152 mm 176pp 978-0-521-51592-4 Hardback £35.00 www.cambridge.org/9780521515924

Recent Bestseller Textbook

A First Course in Statistical Programming with R W. John Braun University of Western Ontario

and Duncan J. Murdoch University of Western Ontario

The only introduction you’ll need to start programming in R. ‘… with this book, you can be up and running, doing very advanced work with R in a matter of minutes. Using a series of code examples, the authors take you through many of the basic capabilities of the package. All that is needed to follow the examples is a basic understanding of control constructs such as the if-then, loops and functions as well as knowledge of the underlying mathematics.’ Charles Ashbacher, Journal of Recreational Mathematics

Contents: 1. Getting started; 2. Introduction to the R language; 3. Programming statistical graphics; 4. Programming with R; 5. Simulation; 6. Computational linear algebra; 7. Numerical optimization; Appendix. Review of random variables and distributions; Index. 2007 246 x 189 mm 174pp 39 line figures 160 exercises 64 worked examples 978-0-521-69424-7 Paperback £24.99 www.cambridge.org/9780521694247

2009 228 x 152 mm 368pp 49 line figures 32 tables 63 exercises 978-0-521-86198-4 Hardback £50.00 978-0-521-68003-5 Paperback £17.99 Publication May 2009 www.cambridge.org/9780521861984

eBooks available at www.cambridge.org/online

Statistics, Applied Probability and Finance Recent Bestseller Graduate Textbook

Data Analysis and Graphics Using R An Example-based Approach Second edition John Maindonald Australian National University, Canberra

and John Braun University of Western Ontario

Hands-on guide to the R system for data analysis for scientists, students and practising statisticians. From reviews of previous edition: ‘I would strongly recommend the book to scientists who have already had a regression or a linear models course and who wish to learn to use R … an easy-to-read and an understandable reference on the use of R for practical data analysis.’ R News

Contents: Preface; 1. A brief introduction to R; 2. Styles of data analysis; 3. Statistical models; 4. An introduction to formal inference; 5. Regression with a single predictor; 6. Multiple linear regression; 7. Exploiting the linear model framework; 8. Generalized linear models and survival analysis; 9. Time series models; 10. Multilevel models and repeated measures; 11. Tree-based classification and regression; 12. Multivariate data exploration and discrimination; 13. Regression on principal component or discriminant scores; 14. The R system – additional topics; Epilogue – models; References; Index of R symbols and functions; Index of terms; Index of names. Cambridge Series in Statistical and Probabilistic Mathematics, 10

2007 247 x 174 mm 528pp 12 plates 50 tables 150 exercises 150 figures 978-0-521-86116-8 Hardback £43.00 eBook available

www.cambridge.org/9780521861168

Quickest Detection H. Vincent Poor Princeton University, New Jersey

and Olympia Hadjiliadis Brooklyn College, City University of New York

This unified treatment of the quickest detection problem provides the background necessary to design, analyze, and understand quickest detection algorithms. ‘Nothing endures but change. This timely book applies Heraclitus’ fundamental principle to the processes used to describe change itself. As financial markets ebb and flow, practitioners schooled in quickest detection stand the greatest chance for survival.’ Peter Carr, Head of Quantitative Financial Research, Bloomberg

Contents: 1. Introduction; 2. Probabilistic framework; 3. Markov optimal stopping theory; 4. Sequential detection; 5. Bayesian quickest detection; 6. Non-bayesian quickest detection; 7. Additional topics. 2008 247 x 174 mm 244pp 17 figures 978-0-521-62104-5 Hardback £45.00 eBook available

www.cambridge.org/9780521621045

Mathematical Finance Synthetic CDOs Modelling, Valuation and Risk Management C. C. Mounfield Barclays Capital, London

Details the latest models and techniques in quantitative and computational modelling of synthetic Collateralised Debt Obligations. Contents: Acknowledgements; Dedication; Preface; 1. A primer on collateralised debt obligations; 2. The modelling of obligor default; 3. Valuation of credit default swaps; 4. Credit indices; 5. Valuation of default baskets; 6. Synthetic CDO valuation methodologies; 7. Phenomenology of the standard market model; 8. Risk quantification and sensitivities of synthetic CDOs; 9. Implied and base correlations; 10. Extensions of the standard market model; 11. Exotic CDOs; 12. Correlation trading of synthetic CDO tranches; 13. Risk management of a portfolio of synthetic CDOs; 14. Hedging simulation of structured credit products; A. Explanation of common notation; B. Simulated annealing; References. Mathematics, Finance and Risk, 7

2008 247 x 174 mm 386pp 90 tones 25 tables 130 figures 15 graphs 978-0-521-89788-4 Hardback £45.00 eBook available

www.cambridge.org/9780521897884

New Edition

The Concepts and Practice of Mathematical Finance Second edition Mark S. Joshi University of Melbourne

Second edition of successful text providing the working knowledge needed to become a good quantitative analyst. ‘The book is intended as an introduction for a numerate person to the discipline of mathematical finance. In this, Mark Joshi succeeds admirably – an excellent starting point for a numerate person in the field of mathematical finance.’ Risk Magazine

Contents: Preface; Acknowledgements; 1. Risk; 2. Pricing methodologies and arbitrage; 3. Trees and option pricing; 4. Practicalities; 5. The Ito calculus; 6. Risk neutrality and martingale measures; 7. The practical pricing of a European option; 8. Continuous barrier options; 9. Multilook exotic options; 10. Static replication; 11. Multiple sources of risk; 12. Options with early exercise features; 13. Interest rate derivatives; 14. The pricing of exotic interest rate derivatives; 15. Incomplete markets and jump-diffusion processes; 16. Stochastic volatility; 17. Variance gamma models; 18. Smile dynamics and the pricing of exotic options; Appendix A. Financial and mathematical jargon; Appendix B. Computer projects; Appendix C. Elements of probability theory; Appendix D. Hints and answers to exercises; Bibliography; Index. Mathematics, Finance and Risk, 8

2008 247 x 174 mm 560pp 202 exercises 978-0-521-51408-8 Hardback £40.00 www.cambridge.org/9780521514088

Interest Rates and Coupon Bonds in Quantum Finance Belal E. Baaquie National University of Singapore

The economic crisis of 2008 has shown that the capital markets need new theoretical and mathematical concepts to describe and price financial instruments. This ground-breaking book will provide physicists and mathematicians researching in finance, and professionals working in the finance industry, with a completely different perspective on finance. Contents: 1. Synopsis; 2. Interest rates and coupon bonds; 3. Options and option theory; 4. Interest rate and coupon bond options; 5. Quantum field theory of bond forward interest rates; 6. Libor Market Model of interest rates; 7. Empirical analysis of forward interest rates; 8. Libor Market Model of interest rate options; 9. Numeraires for bond forward interest rates; 10. Empirical analysis of interest rate caps; 11. Coupon bond European and Asian options; 12. Empirical analysis of interest rate swaptions; 13. Correlation of coupon bond options; 14. Hedging interest rate options; 15. Interest rate Hamiltonian and option theory; 16. American options for coupon bonds and interest rates; 17. Hamiltonian derivation of coupon bond options; Appendixes; Glossaries; List of symbols; Reference; Index. 2009 247 x 174 mm 550pp 25 tones 978-0-521-88928-5 Hardback c. £50.00 Publication October 2009 www.cambridge.org/9780521889285

Statistics, Applied Probability and Finance MAA Book

Mathematical Interest Theory Leslie Vaaler

Actuarial Mathematics for Life Contingent Risks David C. M. Dickson

University of Texas, Austin

University of Melbourne

and James Daniel

Mary R. Hardy

University of Texas, Austin

University of Waterloo, Ontario

Mathematical Interest Theory gives an introduction to how investments vary over time, and this book provides a solid foundation for readers embarking on actuarial careers. It is among the recommended reading options for the Society of Actuaries/Casualty Actuarial Society FM/2 exam.

and Howard Waters

Contents: An introduction to the Texas Instruments BA II Plus; 1. The growth of money; 2. Equations of value and yield rates; 3. Annuities; 4. Annuities with different payment and conversion periods; 5. Loan repayment; 6. Bonds; 7. Stocks and financial markets; 8. Arbitrage, the term structure of interest rates, and derivatives; 9. Interest rate sensitivity; Appendices: A. Some useful formulas; B. Answers to end of chapter problems; Bibliography; Index. Mathematical Association of America Textbooks

Heriot-Watt University, Edinburgh

Life contingencies within the modern framework of multiple-state models. Balancing rigor and intuition, with an emphasis on applications, this textbook is ideal for university courses and individual exam preparation. All necessary theoretical material, many worked examples and exercises, and computational practice, using Excel, teaching practical skills in simulation and projection. International Series on Actuarial Science

2009 228 x 152 mm 600pp 978-0-521-11825-5 Hardback c. £50.00 Publication October 2009 www.cambridge.org/9780521118255

New in Paperback

Contents: 1. Introduction; 2. Preliminary mathematics; 3. Principles of financial valuation; 4. Interest rate models; 5. Mathematics of asset pricing; 6. Bibliography. 2009 228 x 152 mm 350pp 16 tables 978-0-521-06679-2 Paperback £16.99 www.cambridge.org/9780521066792

Textbook

Financial Products An Introduction using Mathematics and Excel Bill Dalton

A step-by-step guide to some of the most important ideas in financial mathematics, including options, future contracts, bonds and derivatives. Contents: Introduction; An introduction to Excel; 1. A foundation; 2. Forward contracts; 3. The futures market; 4. Bonds; 5. The forward rate, forward rate agreements, swaps, caps and floors; 6. Options; 7. Option pricing; 8. Credit derivatives; Solutions; Index. 2008 247 x 174 mm 408pp 189 line figures 4 tables 8 exercises 189 figures 50 graphs 978-0-521-86358-2 Hardback £60.00 978-0-521-68222-0 Paperback £23.99

2009 247 x 170 mm 494pp 978-0-88385-754-0 Hardback £50.00 www.cambridge.org/9780883857540

Financial Derivatives

eBook available

Nonlife Actuarial Models

Pricing, Applications, and Mathematics Jamil Baz PIMCO Europe, Ltd. London

Advances in Credit Risk Modelling and Corporate Bankruptcy Prediction

Theory, Methods and Evaluation Yiu-Kuen Tse Singapore Management University

Actuaries must pass exams, but more than that: they must put knowledge into practice. This coherent textbook gives complete syllabus coverage for Exam C of the Society of Actuaries (SOA) while emphasizing the concepts and practical application of nonlife actuarial models. It has also been class-tested for undergraduate university courses. International Series on Actuarial Science

2009 228 x 152 mm 544pp 1 tone 55 tables 350 exercises 155 worked examples 30 figures 978-0-521-76465-0 Hardback c. £40.00 Publication October 2009 www.cambridge.org/9780521764650

and George Chacko Harvard Business School

This book is a graduate level manual on the pricing of financial derivatives. It allows the reader with basic knowledge of finance, calculus, and probability and statistics to understand the most powerful tools in applied finance. The focus is on equity derivatives, interest rate markets, and the mathematics of pricing. ‘This introduction to the modeling of financial derivatives is ideal for quantitatively oriented traders, bank researchers, and masters or doctoral students in this field. The book has an elegant balance of concepts and applications that allows a full understanding of why the models work, without an overburden of technical details. Broader than its title suggests, the book contains a strong grounding in models of stochastic processes for financial applications, including portfolio choice and asset pricing theory.’ Darrell Duffie, Stanford University

www.cambridge.org/9780521863582

Edited by Stewart Jones University of Sydney

and David A. Hensher University of Sydney

A compendium of credit risk modelling approaches, including several new techniques that extend the horizons of future research and practice. ‘… if you wish to learn more about the nature of the financial instruments that have brought the world to its knees, then this … is a useful starting point.’ Times Higher Education

Contents: List of figures; List of tables; List of contributors; Introduction; 1. A statistical model for credit scoring; 2. Mixed Logit and error component models of corporate insolvency and bankruptcy risk; 3. An evaluation of open and closed form distress prediction models: the nested Logit and latent class models; 4. Survival analysis and omitted dividends; 5. Nonparametric methods for credit risk analysis: neural networks and recursive partitioning techniques; 6. Bankruptcy prediction and structural credit risk models; 7. Default recovery rates and LGD in credit risk modeling and practice: an updated review of the literature and empirical evidence;

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Statistics, Applied Probability and Finance / SIAM books 8. Credit derivatives: current practices and controversies; 9. Local government distress in Australia: a latent class regression analysis; 10. A belief-function perspective to credit risk assessments; Index. Quantitative Methods for Applied Economics and Business Research

2008 247 x 174 mm 312pp 18 line figures 39 tables 18 figures 11 graphs 978-0-521-86928-7 Hardback £60.00 978-0-521-68954-0 Paperback £23.99 eBook available

www.cambridge.org/9780521869287

SIAM books A First Course in Order Statistics Barry C. Arnold University of California, Riverside

N. Balakrishnan McMaster University, Ontario

and H. N. Nagaraja Ohio State University

A simple introduction to the general theory of order statistics and their applications, requiring no advanced mathematical or statistical background. Contents: Preface to classics edition; Further reading; Preface; Acknowledgments; Notations and abbreviations; Errata; 1. Introduction and preview; 2. Basic distribution theory; 3. Discrete order statistics; 4. Order statistics from some specific distributions; 5. Moment relations, bounds, and approximations; 6. Characterizations using order statistics; 7. Order statistics in statistical inference; 8. Asymptotic theory; 9. Record values; Bibliography; Author index; Subject index. Classics in Applied Mathematics, 54

2008 247 x 174 mm 300pp 978-0-89871-648-1 Paperback £47.00 www.cambridge.org/9780898716481

Generalized Inverses of Linear Transformations Stephen L. Campbell North Carolina State University

and Carl D. Meyer North Carolina State University

This reference book provides comprehensive coverage of the mathematical theory of generalized inverses coupled with a wide range of important and practical applications. It will be useful as a reference text for applied scientists and engineers. Classics in Applied Mathematics

2009 247 x 170 mm 275pp 978-0-89871-671-9 Paperback £45.00 www.cambridge.org/9780898716719

Functions of Matrices Theory and Computation Nicholas J. Higham University of Manchester

A thorough treatment of the theory of matrix functions and numerical methods for computing them, including an overview of applications, new and unpublished research results, and improved algorithms. Ideal for advanced courses and for self-study, its broad content, references and appendix also make this book a convenient general reference. 2008 247 x 174 mm 450pp 978-0-89871-646-7 Hardback £38.00 www.cambridge.org/9780898716467

Numerical Methods for Evolutionary Differential Equations Uri M. Ascher University of British Columbia, Vancouver

Develops, analyses, and applies numerical methods for evolutionary, or time-dependent, differential problems. Contents: List of figures; List of tables; Preface; Introduction; 1. Ordinary differential equations; 2. On problem atability; 3. Basic methods, Basic concepts; 4. One-step methods; 5. Linear multistep methods; 6. More boundary value problem theory and applications; 7. Shooting; 8. Finite difference methods for boundary value problems; 9. More on differential-algebraic equations; 10. Numerical methods for differentialalgebraic equations; Bibliography; Index. Computational Science and Engineering

2008 247 x 174 mm 410pp 978-0-89871-652-8 Paperback £51.00 www.cambridge.org/9780898716528

Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations Theory and Implementation Béatrice M. Rivière Rice University, Houston

Focuses on three primal DG methods, covering both theory and computation, and providing the basic tools for analysis. Contents: List of figures; List of tables; List of algorithms; Preface; Part I. Elliptic Problems: 1. One-dimensional problem; 2. Higher dimensional problem; Part II. Parabolic Problems: 3. Purely parabolic problems; 4. Parabolic problems with convection; Part III. Applications:

5. Linear elasticity; 6. Stokes flow; 7. Navier–Stokes flow; 8. Flow in porous media; Appendix A. Quadrature rules; Appendix B. DG codes; Appendix C. An approximation result; Bibliography; Index. Frontiers in Applied Mathematics, 35

2008 247 x 174 mm 210pp 978-0-89871-656-6 Paperback £35.00 www.cambridge.org/9780898716566

Graduate Textbook

Scientific Computing with Case Studies Dianne P. O’Leary University of Maryland, College Park

A practical guide to solving linear and nonlinear equations, differential equations, optimization problems, and eigenvalue problems. The case studies illustrate mathematical modeling and algorithm design, for problems in physics, engineering, epidemiology, chemistry, and biology. For advanced undergraduates and beginning graduate students, and scientists whose work involves numerical computing. 2009 247 x 174 mm 395pp 978-0-89871-666-5 Paperback £60.00 www.cambridge.org/9780898716665

Evaluating Derivatives Principles and Techniques of Algorithmic Differentiation Second edition Andreas Griewank Humboldt-Universität zu Berlin

and Andrea Walther Technische Universität, Dresden

A comprehensive treatment of algorithmic, or automatic, differentiation. Contents: Rules; Preface; Prologue; Mathematical symbols; 1. Introduction; 2. A framework for evaluating functions; 3. Fundamentals of forward and reverse; 4. Memory issues and complexity bounds; 5. Repeating and extending reverse; 6. Implementation and software; 7. Sparse forward and reverse; 8. Exploiting sparsity by compression; 9. Going beyond forward and reverse; 10. Jacobian and Hessian accumulation; 11. Observations on efficiency; 12. Reversal schedules and checkpointing; 13. Taylor and tensor coefficients; 14. Differentiation without differentiability; 15. Implicit and iterative differentiation; Epilogue; List of figures; List of tables; Assumptions and definitions; Propositions, corollaries, and lemmas; Bibliography; Index. 2008 247 x 174 mm 460pp 978-0-89871-659-7 Paperback £48.00 www.cambridge.org/9780898716597

SIAM books Graduate Textbook

Numerical Methods in Scientific Computing Volume 1 Germund Dahlquist Royal Institute of Technology, Stockholm

and Åke Björck

Linear and Nonlinear Optimization Second edition Igor Griva George Mason University, Virginia

Stephen G. Nash George Mason University, Virginia

11. Navier–Stokes equations; 12. Motion planning for PDEs; 13. Adaptive control for PDEs; 14. Towards nonlinear PDEs; Appendix. Bessel functions; Bibliography; Index. Advances in Design and Control, 16

2008 247 x 174 mm 200pp 978-0-89871-650-4 Hardback £58.00 www.cambridge.org/9780898716504

Linköping University, Sweden

and Ariela Sofer

This book from the authors of the classic Numerical Methods addresses the growing role of numerical methods in science and engineering. With better organization and coverage than any modern book in the field, it includes topics not typically covered in numerical analysis texts (e.g. interval arithmetic and elementary functions).

Flexible graduate textbook that introduces the applications, theory, and algorithms of linear and nonlinear optimization in a clear succinct style, supported by numerous examples and exercises. It introduces important realistic applications and explains how optimization can address them.

Stochastic Processes, Estimation, and Control

Contents: Preface; Part I. Basics: 1. Optimization models; 2. Fundamentals of optimization; 3. Representation of linear constraints; Part II. Linear Programming: 4. Geometry of linear programming; 5. The simplex method; 6. Duality and sensitivity; 7. Enhancements of the simplex method; 8. Network problems; 9. Computational complexity of linear programming; 10. Interior-point methods of linear programming; Part III. Unconstrained Optimization: 11. Basics of unconstrained optimization; 12. Methods for unconstrained optimization; 13. Low-storage methods for unconstrained problems; Part IV. Nonlinear Optimization: 14. Optimality conditions for constrained problems; 15. Feasiblepoint methods; 16. Penalty and barrier methods; Part V. Appendices: Appendix A. Topics from linear algebra; Appendix B. Other fundamentals; Appendix C. Software; Bibliography; Index.

Covers stochastic systems beginning with the foundations of probability and ending with stochastic optimal control.

‘This work is a monumental undertaking and represents the most comprehensive textbook survey of numerical analysis to date. It will be an important reference in the field for many years to come.’ Nicholas J. Higham, University of Manchester

Contents: List of figures; List of tables; List of conventions; Preface; 1. Principles of numerical calculations; 2. How to obtain and estimate accuracy; 3. Series, operators and continued fractions; 4. Interpolation and approximation; 5. Numerical integration; 6. Solving scalar nonlinear equations; Bibliography; Index; Online appendix A. Introduction to matrix computations; Online appendix B. A MATLAB multiple precision package; Online appendix C. Guide to literature. 2008 247 x 174 mm 746pp 978-0-89871-644-3 Hardback £70.00 www.cambridge.org/9780898716443

Introduction to Derivative-Free Optimization Andrew R. Conn IBM T. J. Watson Research Center, New York

Katya Scheinberg IBM T. J. Watson Research Center, New York

and Luís N. Vicente Universidade de Coimbra, Portugal

The first contemporary comprehensive treatment of optimization without derivatives. This text explains how sampling and model techniques are used in derivative-free methods and how they are designed to solve optimization problems. It is designed to be readily accessible to both researchers and those with a modest background in computational mathematics. 2009 247 x 170 mm 295pp 978-0-89871-668-9 Paperback £47.00 www.cambridge.org/9780898716689

George Mason University, Virginia

2009 247 x 174 mm 764pp 978-0-89871-661-0 Hardback £61.00 www.cambridge.org/9780898716610

Boundary Control of PDEs A Course on Backstepping Designs Miroslav Krstic University of California, San Diego

and Andrey Smyshlyaev University of California, San Diego

A clear and concise introduction to backstepping, an elegant new approach to boundary control of partial differential equations (PDEs). Contents: List of figures; List of tables; Preface; 1. Introduction; 2. Lyapunov stability; 3. Exact solutions to PDEs; 4. Parabolic PDEs: reaction-advectiondiffusion and other equations; 5. Observer design; 6. Complex-valued PDEs: Schrödinger and Ginzburg–Landau equations; 7. Hyperbolic PDEs: wave equations; 8. Beam equations; 9. Firstorder hyperbolic PDEs and delay equations; 10. Kuramoto–Sivashinsky, Korteweg–de Vries, and other ‘exotic’ equations;

Jason L. Speyer University of California, Los Angeles

and Walter H. Chung University of California, Los Angeles

Contents: Preface; 1. Probability theory; 2. Random variables and stochastic processes; 3. Conditional expectations and discrete-time Kalman filtering; 4. Least squares, the orthogonal projection lemma, and discrete-time Kalman filtering; 5. Stochastic processes and stochastic calculus; 6. Continuous-time Gauss-Markov systems: continuous-time Kalman filter, stationarity, power spectral density, and the Wiener filter; 7. The extended Kalman filter; 8. A selection of results from estimation theory; 9. Stochastic control and the linear quadratic Gaussian control problem; 10. Linear exponential Gaussian control and estimation; Bibliography; Index. Advances in Design and Control, 17

2008 247 x 174 mm 400pp 978-0-89871-655-9 Paperback £55.00 www.cambridge.org/9780898716559

Lagrange Multiplier Approach to Variational Problems and Applications Kazufumi Ito North Carolina State University

and Karl Kunisch Karl-Franzens-Universität Graz, Austria

Analyses Lagrange multiplier theory and demonstrates its impact on the development of numerical algorithms for variational problems in function spaces. Contents: Preface; 1. Existence of Lagrange multipliers; 2. Sensitivity analysis; 3. First Order augmented Lagrangians for equality and finite rank inequality constraints; 4. Augmented Lagrangian methods for nonsmooth, convex optimization; 5. Newton and SQP methods; 6. Augmented Lagrangian-SQP methods; 7. The primal-dual

Visit our website at www.cambridge.org

SIAM books active set method; 8. Semismooth Newton methods I; 9. Semismooth Newton methods II: applications; 10. Parabolic variational inequalities; 11. Shape optimization; Bibliography; Index. Advances in Design and Control, 15

2008 247 x 174 mm 360pp 978-0-89871-649-8 Paperback £64.00 www.cambridge.org/9780898716498

Approximation of Large-Scale Dynamical Systems Athanasios C. Antoulas Rice University

Approximation of Large-Scale Dynamical Systems provides a comprehensive picture of model reduction, combining system theory with numerical linear algebra and computational considerations. It addresses the issue of model reduction and the resulting tradeoffs between accuracy and complexity. Special attention is given to numerical aspects, simulation questions, and practical applications. ‘… this book contains a wealth of useful information and is the most authoritative presentation of the approximation techniques for largescale dynamical systems available at the moment. The book is highly recommended to graduate students and researchers in the fields of system and control theory, and numerical analysis.’ Petko Petkov, Mathematical Reviews

Contents: Preface; Part I. Introduction: 1. Introduction; 2. Motivating examples; Part II. Preliminaries: 3. Tools from matrix theory; 4. Linear dynamical systems, Part 1; 5. Linear dynamical systems, Part 2; 6. Sylvester and Lyapunov equations; Part III. SVD-based Approximation Methods: 7. Balancing and balanced approximations; 8. Hankel-norm approximation; 9. Special topics in SVD-based approximation methods; Part IV. Krylov-based Approximation Methods: 10. Eigenvalue computations; 11. Model reduction using Krylov methods; Part V. SVD-Krylov Methods and Case Studies: 12. SVD-Krylov methods; 13. Case studies; 14. Epilogue; 15. Problems; Bibliography; Index. Advances in Design and Control, 6

2009 247 x 174 mm 510pp 978-0-89871-658-0 Paperback £64.00 www.cambridge.org/9780898716580

Feedback Systems Input-Output Properties Charles A. Desoer University of California, Berkeley

and M. Vidyasagar Tata Institute of Fundamental Research, Mumbai, India

This book was the first and remains the only book to give a comprehensive treatment of the behaviour of linear or nonlinear systems when they are connected in a closed-loop fashion, with the output of one system forming the input of the other. Contents: Preface to the Classics edition; Preface; Acknowledgments; Note to the reader; List of symbols; 1. Memoryless nonlinearities; 2. Norms; 3. General theorems; 4. Linear systems; 5. Applications of the small gain theorem; 6. Passivity; Appendix A. Integrals and series; Appendix B. Fourier transforms; Appendix C. Convolution; Appendix D. Algebras; Appendix E. Bellman-Gronwall Lemma; References; Index. Classics in Applied Mathematics

2009 247 x 170 mm 284pp 978-0-89871-670-2 Paperback £40.00 www.cambridge.org/9780898716702

UAV Cooperative Decision and Control Challenges and Practical Approaches Steven Rasmussen and Tal Shima Technion – Israel Institute of Technology, Haifa

Unmanned aerial vehicles (UAVs) are increasingly used in military missions. This text is aimed at helping practitioners, students, and academics alike to better understand what cooperative decision and control is and its applications and methods for implementing algorithms that make cooperative UAV operations possible. Contents: Preface; 1. Introduction; 2. Challenges; 3. Single task tours; 4. Multiple assignments; 5. Simultaneous multiple assignments; 6. Estimation algorithms for improved cooperation under uncertainty; 7. Effectiveness measures for operations in uncertain environments; Appendix A. MultiUAV simulation; Appendix B. Path planning for UAVs; Index. Advances in Design and Control

2009 247 x 170 mm 198pp 978-0-89871-664-1 Hardback £55.00 www.cambridge.org/9780898716641

Elementary Calculus of Financial Mathematics A. J. Roberts University of Adelaide

This book introduces the fascinating area of financial mathematics and its calculus in an accessible manner for undergraduate students. Using little high-level mathematics, the author presents the basic methods for evaluating financial options and building financial simulations. Contents: Preface; List of algorithms; 1. Financial indices appear to be stochastic processes; 2. Ito’s stochastic calculus introduced; 3. The Fokker–Planck equation describes the probability distribution; 4. Stochastic integration proves Ito’s formula; Appendix A. Extra MATLAB/SCILAB code; Appendix B. Two alternate proofs; Bibliography; Index. Monographs on Mathematical Modeling and Computation

2009 247 x 170 mm 140pp 978-0-89871-667-2 Paperback £30.00 www.cambridge.org/9780898716672

Graduate Textbook

Introduction to the Numerical Analysis of Incompressible Viscous Flows William Layton University of Pittsburgh

A unified treatment of fluid mechanics, analysis and numerical analysis appropriate for first year graduate students. Contents: Foreword; Preface; 1. Mathematical preliminaries: energy and stress; 2. Approximating scalars; 3. Vector and tensor analysis; 4. Approximating vector functions; 5. The equations of fluid motion; 6. The steady Navier–Stokes equations; 7. Approximating steady flows; 8. The time-dependent Navier–Stokes equations; 9. Approximating time-dependent flows; 10. Models of turbulent flow; Appendix. Computational Science and Engineering

2008 247 x 174 mm 233pp 978-0-89871-657-3 Paperback £43.00 / TBA www.cambridge.org/9780898716573

A Unified Approach to Boundary Value Problems Athanassios S. Fokas University of Cambridge

Explains a new approach to analysing initial-boundary value problems for integrable partial differential equations (PDEs) in two dimensions, based on ideas of the inverse scattering transform that the author introduced in 1997. This

SIAM books / Computer Science method is unique in also yielding novel integral representations for linear PDEs. • Unifies the most extensively used techniques for solving boundary value problems for linear PDEs • Includes a new approach to an important medical imaging technique • Unique in presenting an extension of the inverse scattering method from initial value problems to boundary value problems CBMS-NSF Regional Conference Series in Applied Mathematics, 78

2008 247 x 174 mm 356pp 978-0-89871-651-1 Paperback £49.00 www.cambridge.org/9780898716511

Hidden Markov Models and Dynamical Systems Andrew M. Fraser Los Alamos National Laboratory

An introduction to hidden Markov models for the dynamical systems community. The book presents algorithms for using HMMs and explains the derivation of those algorithms. It provides introductory material for undergraduate study in engineering, mathematics, or science that includes work in probability, linear algebra and differential equations. Contents: Preface; 1. Introduction; 2. Basic algorithms; 3. Variants and generalizations; 4. Continuous states and observations and Kalman filtering; 5. Performance bounds and a toy problem; 6. Obstructive sleep apnea; Appendix A. Formulas for matrices and Gaussians; Appendix B. Notes on software; Bibliography; Index. 2009 247 x 174 mm 143pp 978-0-89871-665-8 Paperback £35.00 www.cambridge.org/9780898716658

Recent Bestseller Textbook

MATLAB Guide Second edition Desmond J. Higham University of Strathclyde

and Nicholas J. Higham University of Manchester

This second edition remains a lively, concise introduction to the important features of MATLAB 7 and the Symbolic Math Toolbox. ‘I use the Higham brothers’ MATLAB Guide as a reference for myself and my students in all my applied mathematics and computational science courses. The clarity and usefulness of their writing are major attractions for using their books. Consequently, I look forward to the very much improved second edition,

as if that were possible for a much admired book. In particular, the new chapter on case studies looks quite interesting with its useful applications. In addition, new treatments of new functions and features like nested functions, ODE as well as DDE functions will be of great interest.’ Floyd B. Hanson, Ph.D., Professor of Mathematics, Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago

Contents: Preface; 1. A brief tutorial; 2. Basics; 3. Distinctive features of MATLAB; 4. Arithmetic; 5. Matrices; 6. Operators and flow control; 7. M-files; 8. Graphics; 9. Linear algebra; 10. More on functions; 11. Numerical methods Part I; 12. Numerical methods Part II; 13. Input and output; 14. Troubleshooting; 15. Sparse matrices; 16. Further M-files; 17. Handle graphics; 18. Other data types and multidimensional arrays; 19. The symbolic math toolbox; 20. Optimizing M-files; 21. Tricks and tips; 22. Case studies; Appendices; Bibliography; Index. 2005 228 x 152 mm 406pp 978-0-89871-578-1 Hardback £30.00 www.cambridge.org/9780898715781

Computer Science Graduate Textbook

A Computational Introduction to Number Theory and Algebra Second edition Victor Shoup

sequences and applications; 19. Finite fields; 20. Algorithms for finite fields; 21. Deterministic primality testing; Appendix: Some useful facts; Bibliography; Index of notation; Index. 2008 247 x 174 mm 598pp 650 exercises 280 worked examples 978-0-521-51644-0 Hardback £35.00 www.cambridge.org/9780521516440

Textbook

Quantum Computing for Computer Scientists Noson S. Yanofsky Brooklyn College, City University of New York

and Mirco A. Mannucci HoloMathics, LLC, Virginia

Finally, a textbook that explains quantum computing using techniques and concepts familiar to computer scientists. ‘The book has the potential to fill a void that needs to be filled: to bring the excitement of quantum computing to undergraduate computing majors, especially those with modest math backgrounds.’ Professor Stephen Fenner, Department of Computer Science and Engineering, University of South Carolina

Contents: 1. Complex numbers; 2. Complex vector spaces; 3. The leap from classical to quantum; 4. Basic quantum theory; 5. Architecture; 6. Algorithms; 7. Programming languages; 8. Theoretical computer science; 9. Cryptography; 10. Information theory; 11. Hardware. 2008 253 x 177 mm 368pp 4 tones 245 exercises 978-0-521-87996-5 Hardback £38.00 www.cambridge.org/9780521879965

New York University

Introductory graduate-level text emphasizing algorithms and applications. This second edition now includes over 200 new exercises and examples. Contents: Preface; Preliminaries; 1. Basic properties of the integers; 2. Congruences; 3. Computing with large integers; 4. Euclid’s algorithm; 5. The distribution of primes; 6. Abelian groups; 7. Rings; 8. Finite and discrete probability distributions; 9. Probabilistic algorithms; 10. Probabilistic primality testing; 11. Finding generators and discrete logarithms in Z*p; 12. Quadratic reciprocity and computing modular square roots; 13. Modules and vector spaces; 14. Matrices; 15. Subexponentialtime discrete logarithms and factoring; 16. More rings; 17. Polynomial arithmetic and applications; 18. Linearly generated

Graduate Textbook

A Second Course in Formal Languages and Automata Theory Jeffrey Shallit University of Waterloo, Ontario

A textbook for a graduate course on formal languages and automata theory, building on prior knowledge of theoretical computer models. Contents: 1. Review of formal languages and automata theory; 2. Combinatorics on words; 3. Finite automata and regular languages; 4. Context-free grammars and languages; 5. Parsing and recognition; 6. Turing machines; 7. Other language classes. 2008 228 x 152 mm 252pp 12 tables 241 exercises 978-0-521-86572-2 Hardback £30.00 eBook available

www.cambridge.org/9780521865722

eBooks available at www.cambridge.org/online

Computer Science Handbook of Practical Logic and Automated Reasoning

estimation techniques in the presence of singularities.

John Harrison

2009 228 x 152 mm 288pp 13 tones 55 worked examples 40 figures 978-0-521-86467-1 Hardback c. £45.00 Publication August 2009 www.cambridge.org/9780521864671

Intel Corporation, Portland, Oregon

A self-contained and broad-based account of the concepts, the machinery and the use of automated reasoning. It’s ideal for those seeking a one-stop source for the subject. The approach is constructive, concrete and algorithmic: importantly, methods are described with reference to actual implementations (for which code is supplied). 2009 247 x 174 mm 702pp 10 tables 155 exercises 978-0-521-89957-4 Hardback £75.00 www.cambridge.org/9780521899574

Statistical Machine Translation Philipp Koehn University of Edinburgh

Automatic language translation systems like those used by Google, have been revolutionized by recent advances in the methods used in statistical machine translation. This first textbook on the topic explains these innovations carefully and shows the reader, whether a student or a developer, how to build their own translation system. Contents: Preface; Part I. Foundations: 1. Introduction; 2. Words, sentences, corpora; 3. Probability theory; Part II. Core Methods: 4. Word-based models; 5. Phrasebased models; 6. Decoding; 7. Language models; 8. Evaluation; Part III. Advanced Topics: 9. Discriminative training; 10. Integrating linguistic information; 11. Tree-based models; Bibliography; Author index; Index. 2009 247 x 174 mm 488pp 24 tones 70 exercises 143 figures 978-0-521-87415-1 Hardback c. £35.00 Publication August 2009 www.cambridge.org/9780521874151

Algebraic Geometry and Statistical Learning Theory Sumio Watanabe Tokyo Institute of Technology

Sure to be influential, this book lays the foundations for the use of algebraic geometry in statistical learning theory. Many widely used statistical models are singular: mixture models, neural networks, HMMs, and Bayesian networks are major examples. The theory achieved here underpins accurate

Cambridge Monographs on Applied and Computational Mathematics, 25

2008 253 x 177 mm 496pp 330 plates 16 tables 978-0-521-71522-5 Paperback £29.99 www.cambridge.org/9780521715225

Aggregation Functions

Concentration of Measure for the Analysis of Randomized Algorithms

Michel Grabisch

Devdatt Dubhashi

Université de Paris I

Jean-Luc Marichal Université du Luxembourg

Radko Mesiar Slovenská Technická Univerzita

Chalmers University of Technology, Gothenberg

and Alessandro Panconesi Università degli Studi di Roma ‘La Sapienza’, Italy

Encyclopedia of Mathematics and its Applications, 127

Randomized algorithms have become a central part of the algorithms curriculum, based on their increasingly widespread use in modern. This book presents a coherent and unified account of classical and more advanced techniques for analyzing the performance of such algorithms. The presentation emphasizes discrete settings and elementary notions of probability, making it accessible to computer scientists and applied discrete mathematicians. The relative strengths and weaknesses of the methods are demonstrated by applying them to concrete problems.

2009 228 x 152 mm 496pp 2 tones 12 tables 40 figures 978-0-521-51926-7 Hardback c. £65.00 Publication June 2009 www.cambridge.org/9780521519267

2009 228 x 152 mm 216pp 12 line figures 168 exercises 978-0-521-88427-3 Hardback c. £40.00 Publication July 2009 www.cambridge.org/9780521884273

and Endre Pap University of Novi Sad, Serbia

Aggregation is the process of combining several numerical values into a single representative value, and an aggregation function performs this operation. This readable book provides a comprehensive, rigorous and selfcontained exposition of aggregation functions. It is ideal for graduate students and a unique resource for researchers.

New in Paperback

Geometric Folding Algorithms Linkages, Origami, Polyhedra Erik D. Demaine Massachusetts Institute of Technology

and Joseph O’Rourke Smith College, Massachusetts

Lavishly illustrated and entertaining account of the surprising and useful results of the maths of folding and unfolding. ‘Demaine and O’Rourke are among the best-qualified authors for a book on this subject; and the book that they have written is a delight … it is exceptionally clear and readable. It could be read for pleasure by any mathematics undergraduate, and much of it (though not all) by amateurs with a high school mathematics background … although there are sections that some amateurs will skip, the level is always kept as elementary as locally possible. This book should be in all university libraries, and many professional and amateur mathematicians will want to add it to their personal collections.’ Robert Dawson (Halifax), Zentralblatt Math

Algorithmic Aspects of Graph Connectivity Hiroshi Nagamochi Kyoto University, Japan

and Toshihide Ibaraki Kwansei Gakuin University, Japan

The first really thorough book to discuss this central notion in graph and network theory, emphasising its algorithmic aspects. Encyclopedia of Mathematics and its Applications, 123

2008 234 x 156 mm 392pp 1 table 978-0-521-87864-7 Hardback £50.00 www.cambridge.org/9780521878647

Graduate Textbook

Computational Complexity A Modern Approach Sanjeev Arora Princeton University, New Jersey

and Boaz Barak Princeton University, New Jersey

Describes recent achievements and classical results of computational complexity theory, including interactive proofs, PCP, derandomization, and quantum computation. It can be used

Computer Science / General and Recreational Maths as a reference, for self-study, or as a beginning graduate textbook. More than 300 exercises are included. Contents: Part I. Basic Complexity Classes: 1. The computational model – and why it doesn’t matter; 2. NP and NP completeness; 3. Diagonalization; 4. Space complexity; 5. The polynomial hierarchy and alternations; 6. Boolean circuits; 7. Randomized computation; 8. Interactive proofs; 9. Cryptography; 10. Quantum computation; 11. PCP theorem and hardness of approximation: an introduction; Part II. Lower Bounds for Concrete Computational Models: 12. Decision trees; 13. Communication complexity; 14. Circuit lower bounds; 15. Proof complexity; 16. Algebraic computation models; Part III. Advanced Topics: 17. Complexity of counting; 18. Average case complexity: Levin’s theory; 19. Hardness amplification and error correcting codes; 20. Derandomization; 21. Pseudorandom constructions: expanders and extractors; 22. Proofs of PCP theorems and the Fourier transform technique; 23. Why are circuit lower bounds so difficult?; Appendix A: mathematical background. 2009 253 x 215 mm 608pp 72 line figures 1 tone 6 tables 307 exercises 978-0-521-42426-4 Hardback £32.50 Publication May 2009 www.cambridge.org/9780521424264

Forthcoming

Computation, Proof, Machine Mathematics Enters a New Age Gilles Dowek Ecole Polytechnique, Paris

Translated by Pierre Guillot and Marion Roman

Mathematics has entered the age of the algorithm. How, why, what next? 2007 Grand Prix de Philosophie de l’Académie Francaise. 2009 228 x 152 mm 200pp 978-0-521-11801-9 Hardback c. £60.00 978-0-521-13377-7 Paperback c. £23.99 Publication November 2009 www.cambridge.org/9780521118019

General and Recreational Maths Textbook

How to Think Like a Mathematician A Companion to Undergraduate Mathematics Kevin Houston University of Leeds

Looking for a head start in your undergraduate degree in mathematics? This friendly companion eases beginning students into real mathematical thinking, unlocking important techniques for effective mathematics so you can communicate with clarity, solve problems, and explore the world of definitions, theorems and proofs with real confidence. Contents: 0. Preface; Part I. Study Skills For Mathematicians: 1. Sets and functions; 2. Reading mathematics; 3. Writing mathematics I; 4. Writing mathematics II; 5. How to solve problems; Part II. How To Think Logically: 6. Making a statement; 7. Implications; 8. Finer points concerning implications; 9. Converse and equivalence; 10. Quantifiers – For all and There exists; 11. Complexity and negation of quantifiers; 12. Examples and counterexamples; 13. Summary of logic; Part III. Definitions, Theorems and Proofs: 14. Definitions, theorems and proofs; 15. How to read a definition; 16. How to read a theorem; 17. Proof; 18. How to read a proof; 19. A study of Pythagoras’ Theorem; Part IV. Techniques of Proof: 20. Techniques of proof I: direct method; 21. Some common mistakes; 22. Techniques of proof II: proof by cases; 23. Techniques of proof III: Contradiction; 24. Techniques of proof IV: Induction; 25. More sophisticated induction techniques; 26. Techniques of proof V: Contrapositive method; Part V. Mathematics That All Good Mathematicians Need: 27. Divisors; 28. The Euclidean Algorithm; 29. Modular arithmetic; 30. Injective, surjective, bijective – and a bit about infinity; 31. Equivalence relations; Part VI. Closing Remarks: 32. Putting it all together; 33. Generalization and specialization; 34. True understanding; 35. The biggest secret; Appendices: A. Greek alphabet; B. Commonly used symbols and notation; C. How to prove that …; Index. 2009 246 x 189 mm 278pp 1 tone 10 tables 335 exercises 195 worked examples 20 figures 978-0-521-89546-0 Hardback £45.00 978-0-521-71978-0 Paperback £18.99 www.cambridge.org/9780521895460

Naive Decision Making Mathematics Applied to the Social World T. W. Körner University of Cambridge

How should one choose the best restaurant to eat in? Can one really predict the future? Professor Körner presents the mathematical basis for making good decisions. Readers will gain insight into mathematics in general as they are taken on an enjoyable journey through aspects of mathematical decision making. ‘This is a highly readable and erudite book that will excite anyone prepared to open their mind to the ways in which a mathematical approach can help us make better choices in an uncertain world.’ Significance 2008 228 x 152 mm 400pp 17 tables 405 exercises 10 worked examples 4 figures 978-0-521-51616-7 Hardback £60.00 978-0-521-73163-8 Paperback £21.99 eBook available

www.cambridge.org/9780521516167

New Series The New Martin Gardner Mathematical Library Series Editors: Donald J. Albers Menlo College, California

Gerald L. Alexanderson Santa Clara University, California

John H. Conway Princeton University, New Jersey

Richard K. Guy University of Calgary

Donald E. Knuth Stanford University, California

Peter L. Renz

The books based on Martin Gardner’s enormously popular Scientific American columns and puzzles continue to challenge and fascinate readers. In these new editions, the author, in consultation with experts, has written updates to all the chapters, including new game variations, new mathematical proofs, and connections to recent developments and discoveries. New diagrams and illustrations have been added and old ones improved, and the bibliographies have been greatly expanded throughout.

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General and Recreational Maths Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi Martin Gardner’s First Book of Mathematical Puzzles and Games Martin Gardner

This is the first book of the updated collection of Mathematical Games from Martin Gardner, the king of recreational mathematics. As well as the classic puzzles, Gardner has added lots of exclusive new material (game variations, proofs and more). If you like Martin Gardner, you’ll love these books. ‘Gardner’s monthly romp through recreational math and logic ran in Scientific American for 25 years, from the Sputnik splash to the Reagan reign, and nobody has been able to match it since. ‘Mathematical Games’ was an orgy of right-brain tomfoolery that could be approached for superficial fun or deep insight, or both at the same time … I can’t think of a better present for a clever 12-year old, bored undergraduate, restless retiree, or stay-at-home parent fearing intellectual stagnation.’ David Brooks, The Telegraph The New Martin Gardner Mathematical Library, 1

2008 216 x 138 mm 208pp 1 tone 978-0-521-75615-0 Hardback £25.00 978-0-521-73525-4 Paperback £8.99 www.cambridge.org/9780521756150

Origami, Eleusis, and the Soma Cube Martin Gardner’s Mathematical Diversions Martin Gardner

The second of fifteen updated editions of the collected Mathematical Games of Martin Gardner, king of recreational mathematics. ‘I recommend you approach this book on a Sunday afternoon, with paper and pen, a few biscuits for brainpower and a good hour to spare for puzzling. It is worth it.’ Charlotte Mulcare, Plus Magazine The New Martin Gardner Mathematical Library, 2

2008 216 x 138 mm 246pp 7 tones 978-0-521-75610-5 Hardback £25.00 978-0-521-73524-7 Paperback £8.99 www.cambridge.org/9780521756105

Sphere Packing, Lewis Carroll, and Reversi Martin Gardner’s New Mathematical Diversions Martin Gardner

Martin Gardner returns to charm readers with the latest on packing spheres, Reversi, braids, polyominoes, board games, and the puzzles of Lewis Carroll. Read about Knuth’s Word Ladders program, new ways of finding the digits of pi, and much much more. ‘Martin Gardner’s fifteen volumes about Mathematical Games are The Canon – timeless classics that are always worth reading and rereading.’ Don Knuth The New Martin Gardner Mathematical Library, 3

MAA Book

Proof and Other Dilemmas Mathematics and Philosophy Bonnie Gold Monmouth University, New Jersey

and Roger Simons

This collection of sixteen original essays is the first to explore a range of new developments in the philosophy of mathematics, in a way mathematicians will understand. Coverage includes emerging questions in the field as well as recent thinking on classical ideas, all relevant to the teaching of mathematics. Spectrum

2009 253 x 177 mm 350pp 978-0-88385-567-6 Hardback £27.99 www.cambridge.org/9780883855676

2009 5 1/2 x 8 1/2 in 296pp 119 line figures 11 tones 978-0-521-75607-5 Hardback c. £25.00 978-0-521-74701-1 Paperback c. £8.99 Publication August 2009 www.cambridge.org/9780521756075

Sink or Float

Aha! Solutions

Cleveland State University

Martin Erickson Truman State University

Mathematicians (beginner, amateur, and professional alike) thrill to find simple, elegant solutions to seemingly difficult problems. Such happy resolutions are called ‘aha! solutions,’ a phrase popularized by mathematics and science writer Martin Gardner. Aha! solutions reveal the beauty of mathematics. This book is a collection of problems with aha! solutions. MAA Problem Book Series

2009 228 x 152 mm 220pp 978-0-88385-829-5 Hardback £30.00 www.cambridge.org/9780883858295

MAA Book

Creative Mathematics H. S. Wall University of Texas, Austin

Developed over a period of many years of working with students at the University of Texas, Austin, this book cultivates mathematical creativity and independence. The book is self contained, and assumes little formal mathematical background on the part of the reader. Classroom Resource Materials

2009 228 x 152 mm 218pp 978-0-88385-750-2 Hardback £27.99 www.cambridge.org/9780883857502

MAA Book Thought Problems in Math and Physics Keith Kendig

Over 250 problems drawn from mathematics and the real world revealing just how much can be learned by using everyday common sense. The author’s easily understandable style will engage school students as well as professional mathematicians. Covers a wide range of classical maths and physics, with solutions and explanations provided. Dolciani Mathematical Expositions, 33

2009 253 x 177 mm 390pp 978-0-88385-339-9 Hardback £31.99 www.cambridge.org/9780883853399

MAA Book

The Contest Problem Book VIII American Mathematics Competitions (AMC 10) 2000– 2007 Contests Edited by J. Douglas Faires Youngstown State University

and David M. Wells Pennsylvania State University

A compilation of 350 problems and solutions previously featured in the American Mathematics Competitions and aimed at students in the first two years of high school. A Problem Index at the back of the book breaks major subject areas into subcategories and cross-references for ease of use. MAA Problem Book Series

2008 228 x 152 mm 228pp 978-0-88385-825-7 Paperback £25.99 www.cambridge.org/9780883858257

General and Recreational Maths MAA Book

The Contest Problem Book IX American Mathematics Competitions (AMC 12) 2001– 2007 Contests Edited by David M. Wells Pennsylvania State University

and J. Douglas Faires Youngstown State University

A compilation of 325 problems and solutions previously featured in the American Mathematics Competitions for students of all abilities in American and Canadian high schools. A problem index at the back of the book breaks major subject areas into subcategories and cross-references for ease of use. MAA Problem Book Series

2008 228 x 152 mm 230pp 978-0-88385-826-4 Paperback £25.99 www.cambridge.org/9780883858264

Rigorous Mathematical Thinking Conceptual Formation in the Mathematics Classroom James T. Kinard Institute for Cognitive Literacy, Chicago

and Alex Kozulin International Center for the Enhancement of Learning Potential, Jerusalem

The first book to present mathematics teaching from Vygotsky’s socio-cultural theory of learning perspective. The authors introduce a RMT program that helps students to gain general thinking skills essential for all types of problem solving. They show how mathematics standards can be reached by students considered to be ‘underachievers’. 2008 228 x 152 mm 216pp 34 line figures 2 tones 978-0-521-87685-8 Hardback £40.00 978-0-521-70026-9 Paperback £15.99 eBook available

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Ludic Proof Greek Mathematics and the Alexandrian Aesthetic Reviel Netz Stanford University, California

Describes the relationship between science and poetry in the Hellenistic period by analysing the stylistic features of Hellenistic mathematics and then showing how they can be understood within the context of Hellenistic poetry. The result transforms our understanding of the origins of Western mathematics. 2009 228 x 152 mm 272pp 978-0-521-89894-2 Hardback £55.00 Publication May 2009 www.cambridge.org/9780521898942

Leibniz An Intellectual Biography Maria Rosa Antognazza

In this first intellectual biography of Gottfried Wilhelm Leibniz (1646–1716), Maria Rosa Antognazza surveys the full range of the philosopher’s interests and activities and offers a unified portrait of a unique thinker, identifying the master project that inspired and coordinated his huge range of apparently miscellaneous endeavours. 2008 228 x 152 mm 652pp 8 line figures 1 map 978-0-521-80619-0 Hardback £25.00 www.cambridge.org/9780521806190

MAA Book

Uncommon Mathematical Excursions Polynomia and Related Realms Dan Kalman

MAA Book

Who Gave you the Epsilon? & Other Tales of Mathematical History Marlow Anderson Colorado College

Victor Katz University of the District of Columbia, Washington DC

and Robin Wilson Keble College, Oxford

This book picks up the history of mathematics from where Sherlock Holmes in Babylon left it. The 40 articles of Who Gave You the Epsilon? continue the story of the development of mathematics into the nineteenth and twentieth centuries. It is ideal for those interested in the history of mathematics. Spectrum

2009 253 x 177 mm 440pp 978-0-88385-569-0 Hardback £45.00 www.cambridge.org/9780883855690

American University, Washington DC

This text serves as a guide to little known corners of the mathematical landscape, not far from the main byways of algebra, geometry, and calculus. It is for the seasoned mathematical traveller who has visited these subjects many times and is ready to venture abroad off the beaten track. Dolciani Mathematical Expositions

2009 253 x 177 mm 282pp 978-0-88385-341-2 Hardback £30.00 www.cambridge.org/9780883853412

MAA Book

Problems from Murray Klamkin The Canadian Collection Andy Liu University of Alberta

and Bruce Shawyer Memorial University of Newfoundland

A collection of problems proposed by Murray Klamkin over his career. It contains the ‘quickies’ (problems with quick and neat solutions) he proposed in ‘Crux Mathematicorum,’ his longer problems, and also problems which were proposed in tribute to him after he died. Solutions are provided. MAA Problem Book Series

2009 253 x 177 mm 266pp 978-0-88385-828-8 Hardback £30.00 www.cambridge.org/9780883858288

MAA Book

When Less is More Visualizing Basic Inequalities Claudi Alsina Universitat Politècnica de Catalunya, Barcelona

and Roger Nelsen Lewis and Clark College, Portland

An introduction to basic inequalities in mathematics (including numbers, functions and geometry) motivated and illustrated by drawings that make it possible to ‘see’ the results in an elegant manner. Applications of the inequalities, historical details, and exercises for the reader (with solutions) are also included. Dolciani Mathematical Expositions

2009 247 x 170 mm 250pp 978-0-88385-342-9 Hardback £30.00 www.cambridge.org/9780883853429

Recent Bestseller

Music: A Mathematical Offering Dave Benson University of Aberdeen

Benson provides a wealth of information for the teacher, the student, or the interested amateur to understand, at varying levels of technicality, the interplay between two ancient disciplines. A must-have book if you want to know about the music of the spheres or digital music and much in between. ‘… informative and well-written … Not only does this book cover basic material thoroughly, it also presents much of interest to those already familiar with the area of math and

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General and Recreational Maths music. And the author provides a wealth of citations to the often scattered literature on the subject.’ Zentralblatt MATH 2006 247 x 174 mm 426pp 260 line figures 20 tones 978-0-521-61999-8 Paperback £25.99 www.cambridge.org/9780521619998

Index A Acta Numerica 2008................................8 Actuarial Mathematics for Life Contingent Risks.................................15 Adámek, J................................................4 Advances in Credit Risk Modelling and Corporate Bankruptcy Prediction..........15 Aggregation Functions...........................20 Aha! Solutions.......................................22 Algebraic Geometry and Statistical Learning Theory...................................20 Algebraic Theories....................................4 Algebraic Theory of Differential Equations............................................11 Algorithmic Aspects of Graph Connectivity........................................20 Algorithmic Number Theory......................6 Alsina, Claudi.........................................23 Amabili, Marco.......................................10 Analysis in Positive Characteristic..............2 Analytic Combinatorics.............................2 Analytic Number Theory............................5 Anderson, Marlow..................................23 Antognazza, Maria Rosa.........................23 Antoulas, Athanasios C...........................18 Applebaum, David....................................1 Applied Solid Mechanics...........................9 Approximation of Large-Scale Dynamical Systems...............................................18 Arnold, Barry C.......................................16 Arora, Sanjeev........................................20 Ascher, Uri M..........................................16

B Baaquie, Belal E.....................................14 Balakrishnan, N......................................16 Barak, Boaz............................................20 Bautista, R...............................................7 Bayart, Frédéric........................................2 Bayesian Nonparametrics.......................13 Baz, Jamil...............................................15 Beineke, Lowell W.....................................3 Bell, John L...............................................3 Benjamin, Arthur T....................................6 Benson, Dave.........................................24 Biscuits of Number Theory........................6 Björck, Åke . ..........................................17 Blath, Jochen...........................................1 Borcherdt, Roger D.................................10 Borkar, Vivek S........................................13 Boundary Control of PDEs......................17 Bradlow, Steven B.....................................5 Brambila-Paz, Leticia................................5 Braun, John............................................14 Braun, W. John.......................................13 Brown, Ezra..............................................6 Buhler, J.P.................................................6 Bühler, Oliver..........................................10

C Calculus...................................................2 Calculus Deconstructed............................2 Calin, Ovidiu............................................5 Cambon, Claude......................................9 Campbell, Stephen L...............................16 Cardy, John..............................................9 Carter, Nathan ........................................6 Castiglione, Patrizia................................12 Chacko, George......................................15

Chang, Der-Chen......................................5 Channel Codes.........................................4 Chaos and Coarse Graining in Statistical Mechanics...........................................12 Chen, W. W. L...........................................5 Chung, Walter H.....................................17 Classical Mechanics..................................9 Combinatorics: The Rota Way....................2 Compendium of Partial Differential Equation Models, A...............................8 Computation, Proof, Machine.................21 Computational Complexity.....................20 Computational Continuum Mechanics......9 Computational Introduction to Number Theory and Algebra, A..........................19 Concentration of Measure for the Analysis of Randomized Algorithms......20 Concepts and Practice of Mathematical Finance, The........................................14 Conn, Andrew R.....................................17 Contest Problem Book IX, The.................23 Contest Problem Book VIII, The...............22 Continuum Mechanics and Thermodynamics.................................10 Cooper, S. Barry........................................4 Cortina, Jeronimo...................................13 Creative Mathematics.............................22

D Dahlquist, Germund ..............................17 Dalton, Bill.............................................15 Daniel, James.........................................15 Data Analysis and Graphics Using R........14 Davenport, H............................................5 Davison, A. C..........................................12 de Faria, Edson.......................................11 de Melo, Welington................................11 Delbourgo, Daniel....................................6 Demaine, Erik D......................................20 Desoer , Charles A..................................18 Diamond, Harold G...................................6 Dickson, David C. M...............................15 Differential Tensor Algebras and their Module Categories................................7 Digital Image Processing for Medical Applications........................................12 Directed Algebraic Topology......................5 Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations............................................16 Dougherty, Geoff....................................12 Dowek, Gilles.........................................21 Dubhashi, Devdatt..................................20 Durrett, Rick...........................................13 Dynamics of Linear Operators...................2

E Edixhoven, Bas.........................................6 Elementary Calculus of Financial Mathematics.......................................18 Elementary Probability for Applications...13 Elliptic Curves and Big Galois Representations....................................6 Erickson, Martin.....................................22 Evaluating Derivatives ...........................16

F Faires, J. Douglas.............................. 22, 23 Falcioni, Massimo...................................12

Falkovich, Gregory....................................9 Feedback Systems..................................18 Financial Derivatives...............................15 Financial Products..................................15 First Course in Order Statistics, A............16 First Course in Statistical Programming with R, A.............................................13 First Course in String Theory, A................11 First Course in the Numerical Analysis of Differential Equations, A........................7 Flajolet, Philippe.......................................2 Flannery, Brian P.......................................8 Fokas, Athanassios S...............................18 Foster, Michael R......................................9 Fraser, Andrew M....................................19 Freedman, David....................................13 Friz, Peter.................................................1 Functions of Matrices.............................16 Fundamentals of Fluid Power Control.....10

G Galois Groups and Fundamental Groups...7 Galway, William F......................................6 Games, Scales and Suslin Cardinals: The Cabal Seminar Volume I.........................3 García-Prada, Oscar..................................5 Gardner, Martin......................................22 Gawedzki, Krzysztof.................................9 Gelman, Andrew....................................13 Generalized Inverses of Linear Transformations...................................16 Geological Fluid Dynamics......................10 Geometric Folding Algorithms.................20 Geometry of Moduli Spaces of Sheaves, The.......................................................5 Gesztesy, Fritz........................................11 Geuvers, Herman......................................4 Glynn, Peter W........................................12 Gold, Bonnie..........................................22 Goldbart, Paul........................................11 Gonnet, Gaston......................................11 Gowers, W. T.............................................5 Grabisch, Michel.....................................20 Grandis, Marco.........................................5 Graph Theory............................................3 Gregory, R. Douglas..................................9 Griewank, Andreas.................................16 Griffiths, Graham W..................................8 Griva, Igor..............................................17 Gross, Jonathan L.....................................3 Groups and Analysis.................................2 Groups, Graphs and Trees.........................6 Guide to Complex Variables, A..................2 Guillot, Pierre.........................................21

H Haddow, James......................................10 Hadjiliadis, Olympia................................14 Halberstam, H...................................... 5, 6 Handbook of Practical Logic and Automated Reasoning.........................20 Hardy, Mary R........................................15 Harrison, John........................................20 Hensher, David A....................................15 Herron, Isom H.........................................9 Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi.......................22 Hidden Markov Models and Dynamical Systems...............................................19

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Index Higham, Desmond J................................19 Higham, Nicholas J........................... 16, 19 Higher Arithmetic, The..............................5 Higher-Dimensional Sieve Method, A........6 Hilbert Transforms....................................1 Hjort, Nils Lid.........................................13 Ho, Tracey.................................................4 Holden, Helge........................................11 Holmes, Chris.........................................13 Homogeneous Turbulence Dynamics.........9 Homsy, G. M.............................................8 Houston, Kevin.......................................21 How to Think Like a Mathematician........21 Howell, Peter............................................9 Huczynska, Sophie....................................4 Huybrechts, Daniel ..................................5

I Ibaraki, Toshihide...................................20 Interest Rates and Coupon Bonds in Quantum Finance................................14 Introduction to Continuum Mechanics......9 Introduction to Derivative-Free Optimization.......................................17 Introduction to the Numerical Analysis of Incompressible Viscous Flows...........18 Iserles, A..................................................8 Iserles, Arieh.............................................7 Ito, Kazufumi . .......................................17 Ivanov, A. A..............................................6

J Jones, Stewart........................................15 Joshi, Mark S..........................................14

K Kalman, Dan..........................................23 Katz, Victor ...........................................23 Kechris, Alexander S..................................3 Kelbert, Mark.........................................12 Kendig, Keith..........................................22 Kinard, James T.......................................23 King, Frederick W......................................1 Kochubei, Anatoly N.................................2 Kock, Anders............................................7 Koehn, Philipp........................................20 Körner, T. W.............................................21 Kozulin, Alex..........................................23 Kozyreff, Gregory......................................9 Krantz, Steven G.......................................2 Krenk, Steen...........................................10 Krstic, Miroslav.......................................17 Kung, Joseph P. S......................................2 Kunisch, Karl..........................................17

L Lagrange Multiplier Approach to Variational Problems and Applications .17 Layton, William......................................18 Lehn, Manfred..........................................5 Lehrer, Gustav I........................................7 Leibniz...................................................23 Lesne, Annick.........................................12 Lévy Processes and Stochastic Calculus.....1 Lin, Shu....................................................4 Linear and Nonlinear Optimization.........17 Liu, Andy................................................23 Logic Colloquium 2006............................4

Löwe, Benedikt.........................................3 Ludic Proof.............................................23 Lun, Desmond..........................................4

M MacCallum, Malcolm A. H.......................11 Maindonald, John..................................14 Mannucci, Mirco A.................................19 Marcus, Daniel.........................................3 Marichal, Jean-Luc.................................20 Markov Chains and Stochastic Stability...12 Mashreghi, Javad.....................................1 Mathematical Interest Theory..................15 Mathematical Tools for OneDimensional Dynamics.........................11 Mathematics for Physics.........................11 Matheron, Étienne....................................2 MATLAB Guide.......................................19 Meier, John..............................................6 Mesiar, Radko........................................20 Meyer, Carl D..........................................16 Meyn, Sean............................................12 Michor, Johanna.....................................11 Mikhailov, Alexander V............................11 Mitchell, James D.....................................4 Modern Coding Theory.............................4 Modular Forms on Schiermonnikoog.........6 Moduli Spaces and Vector Bundles............5 Monster Group and Majorana Involutions, The.....................................6 Moonen, Ben...........................................6 Mörters, Peter..........................................1 Mounfield, C. C......................................14 Müller, Peter...........................................13 Multidimensional Stochastic Processes as Rough Paths.....................................1 Multimedia Fluid Mechanics.....................8 Murdoch, Duncan J. . .............................13 Music: A Mathematical Offering..............24

N Nagamochi, Hiroshi................................20 Nagaraja, H. N. .....................................16 Nair, Sudhakar..........................................9 Naive Decision Making...........................21 Nash, Stephen G.....................................17 Nazarenko, Sergey....................................9 Nelsen, Roger.........................................23 Network Coding.......................................4 Netz, Reviel............................................23 Nitecki, Zbigniew H..................................2 Non-equilibrium Statistical Mechanics and Turbulence......................................9 Non-linear Modeling and Analysis of Solids and Structures...........................10 Nonlife Actuarial Models........................15 Nonlinear Vibrations and Stability of Shells and Plates.................................10 Numerical Methods for Evolutionary Differential Equations..........................16 Numerical Methods in Scientific Computing..........................................17 Numerical Recipes....................................8 Numerical Recipes Source Code CD-ROM.8 Numerical Recipes with Source Code CD-ROM...............................................8 Numerical Solution of Hyperbolic Partial Differential Equations..........................10

O O’Leary, Dianne P....................................16 O’Rourke, Joseph....................................20 Ockendon, John.......................................9 Origami, Eleusis, and the Soma Cube......22

P Panconesi, Alessandro............................20 Pap, Endre..............................................20 Partial Differential Equations in Fluid Dynamics..............................................9 Phillips, Owen M....................................10 Pillay, Anand............................................4 Poor, H. Vincent......................................14 Press, William H........................................8 Prest, Mike...............................................7 Primer of Infinitesimal Analysis, A..............3 Probability and Statistics by Example......12 Problems from Murray Klamkin...............23 Proof and Other Dilemmas.....................22 Purity, Spectra and Localisation.................7

Q Quantitative Tour of the Social Sciences, A........................................................13 Quantum Computing for Computer Scientists.............................................19 Quickest Detection.................................14

R Ramanan, S..............................................5 Rasmussen, Steven.................................18 Representation Theorems in Hardy Spaces.1 Richardson, Tom.......................................4 Rigorous Mathematical Thinking.............23 Rivière, Béatrice M..................................16 Roberts, A. J...........................................18 Roman, Marion......................................21 Roney-Dougal, Colva M............................4 Rosick , J..................................................4 Rota, Gian-Carlo......................................2 Ryan, William...........................................4

S Sagaut, Pierre...........................................9 Salmerón, L..............................................7 Scheinberg, Katya . ................................17 Scheutzow, Michael..................................1 Schiesser, William E..................................8 Schmidt, W. M..........................................5 Scholl, Ralf.............................................11 Scientific Computation...........................11 Scientific Computing with Case Studies...16 Second Course in Formal Languages and Automata Theory, A.......................19 Sedgewick, Robert....................................2 Segal, Dan...............................................7 Shabana, Ahmed A...................................9 Shallit, Jeffrey.........................................19 Shawyer, Bruce.......................................23 Shima, Tal..............................................18 Shoup, Victor..........................................19 Simons, Roger........................................22 Simpson, Stephen G.................................3 Sink or Float...........................................22 Smyshlyaev, Andrey................................17 Sofer, Ariela............................................17

Index Soliton Equations and their AlgebroGeometric Solutions............................11 Speyer, Jason L.......................................17 Sphere Packing, Lewis Carroll, and Reversi................................................22 Spivak, Michael........................................2 Statistical Machine Translation................20 Statistical Models............................. 12, 13 Steel, John R............................................3 Stevenhagen, P.........................................6 Stochastic Approximation.......................13 Stochastic Processes, Estimation, and Control................................................17 Stone, Michael.......................................11 Student’s Introduction to MATHEMATICA, The..............................7 Sub-Riemannian Geometry.......................5 Subsystems of Second Order Arithmetic....3 Suhov, Yuri.............................................12 Surveys in Combinatorics 2009.................4 Synthetic CDOs......................................14 Synthetic Geometry of Manifolds..............7 Szamuely, Tamás......................................7

T Taylor, Donald E........................................7 Tent, Katrin..............................................2 Teschl, Gerald.........................................11 Teukolsky, Saul A......................................8 Topics in Topological Graph Theory...........3 Torrence, Bruce F......................................7

Torrence, Eve A.........................................7 Trangenstein, John A...............................10 Trends in Stochastic Analysis.....................1 Tse, Yiu-Kuen..........................................15 Tucker, Thomas W......................................3 Tweedie, Richard L..................................12

U UAV Cooperative Decision and Control...18 Uncommon Mathematical Excursions......23 Unified Approach to Boundary Value Problems, A.........................................18 Unitary Reflection Groups.........................7 Urbanke, Ruediger....................................4

V Vaaler, Leslie..........................................15 Väänänen, Jouko......................................4 van der Geer, Gerard................................6 van der Heijden, Arnold M. A....................9 Vaughan, R. C..........................................5 Vetterling, William T..................................8 Vicente, Luís N........................................17 Victoir, Nicolas.........................................1 Vidyasagar, M.........................................18 Viscoelastic Waves in Layered Media.......10 Visual Group Theory.................................6 Vitale, E. M...............................................4 Vulpiani, Angelo.....................................12

W W. T. Koiter’s Elastic Stability of Solids and Structures.......................................9 Walker, Stephen.....................................13 Wall, H. S...............................................22 Walther, Andrea.....................................16 Watanabe, Sumio...................................20 Waters, Howard.....................................15 Watton, John..........................................10 Waves and Mean Flows..........................10 Wegner, Joanne......................................10 Wells, David M................................. 22, 23 When Less is More.................................23 Who Gave you the Epsilon?....................23 Wilson, Robin.........................................23 Wilson, Robin J.........................................3 Words......................................................7

Y Yan, Catherine H......................................2 Yanofsky, Noson S..................................19

Z Zaboronski, Oleg V....................................9 Zuazua, R.................................................7 Zwiebach, Barton...................................11

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MULTIMEDIA FLUID MECHANICS Second Edition • A perfect complement to any course in Fluid Mechanics • Now with four times more movies • Twice as many topics covered

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Contents Analysis and Probability 1 Discrete Mathematics and Foundations 2 Algebra and Geometry 4 Number Theory and Algebra 5 Scientific Computing 7 Dynamical Systems, Mechanics and Modelling 8 Mathematics for Physics and Biology 10 Statistics, Applied Probability and Finance 11 Mathematical Finance 13 SIAM books 15 Computer Science 18 General and Recreational Maths 20 New Series 20 Information on related journals Inside back cover

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