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of the Hilbert transform; 5. Relationship when discussing applications to Analysis and between the Hilbert transform and some stochastic processes. common transforms; 6. The Hilbert transform 2009 228 x 152 mm 450pp Probability of periodic functions; 7. Inequalities for the 978-0-521-87607-0 Hardback c. £40.00 Hilbert transform; 8. Asymptotic behavior of www.cambridge.org/9780521876070 the Hilbert transform; 9. Hilbert transforms Graduate Textbook of some special functions; 10. Hilbert Lévy Processes and transforms involving distributions; 11. The Trends in Stochastic finite Hilbert transform; 12. Some singular Stochastic Calculus Analysis integral equations; 13. Discrete Hilbert Edited by Jochen Blath Second edition transforms; 14. Numerical evaluation of Technische Universität Berlin Hilbert transforms; References; Subject David Applebaum Peter Mörters University of Sheffield index; Author index. University of Bath A unique development of these two Encyclopedia of Mathematics and its and Michael Scheutzow Applications, 124 subjects contained in a single volume. Technische Universität Berlin 2009 234 x 156 mm 896pp 15 tables New topics featured in this fully revised Presenting important trends in the field edition include regular variation 350 exercises 80 figures 978-0-521-88762-5 Hardback £80.00 of stochastic analysis, this collection of and subexponential distributions, www.cambridge.org/9780521887625 thirteen articles provides an overview of characterisation of Lévy processes with recent developments and new results. finite variation, multiple Wiener-Lévy Leading experts discuss a wide range of integrals and chaos decomposition, and Hilbert Transforms topics, ranging from an alternative set- introductions to Malliavin calculus and Volume 2 up of rigorous probability to sampling of stability theory for Lévy-driven SDEs. Frederick W. King conditioned diffusions, from Feynmann Contents: Preface to second edition; University of Wisconsin, Eau Claire formulas to genetic inference. Preface to first edition; Overview; Notation; Contents: Preface; List of symbols; List London Mathematical Society Lecture Note 1. Lévy processes; 2. Martingales, stopping of abbreviations; Volume II: 15. Hilbert Series, 353 times and random measures; 3. Markov transforms in En; 16. Some further 2009 228 x 152 mm 396pp 9 tones processes, semigroups and generators; extensions of the classical Hilbert transform; 2 tables 30 worked examples 25 figures 4. Stochastic integration; 5. Exponential 17. Linear systems and causality; 18. The 978-0-521-71821-9 Paperback £38.00 martingales; 6. Stochastic differential Hilbert transform of waveforms and www.cambridge.org/9780521718219 equations; References; Index of notation; signal processing; 19. Kramers–Kronig Subject index. relations; 20. Dispersion relations for some Cambridge Studies in Advanced linear optical properties; 21. Dispersion Representation Mathematics, 116 relations for magneto-optical and natural Theorems in 2009 228 x 152 mm 490pp 130 exercises optical activity; 22. Dispersion relations Hardy Spaces 55 worked examples for nonlinear optical properties; 23. Some 978-0-521-73865-1 Paperback £35.00 further applications of Hilbert transforms; Javad Mashreghi Université Laval, Québec www.cambridge.org/9780521738651 Appendix 1. Table of selected Hilbert transforms; Appendix 2. Atlas of selected Gives a complete description of Hilbert transform pairs; References; Subject representation theorems with direct 2-Volume Set index; Author index. proofs for both classes of Hardy spaces. Hilbert Transforms Encyclopedia of Mathematics and its Clear and concise, it features over 300 Frederick W. King Applications, 125 exercises and is ideal for advanced University of Wisconsin, Eau Claire 2009 234 x 156 mm 698pp 145 exercises undergraduate and graduate students 50 figures Written in a style that suits a wide taking courses in Advanced Complex 978-0-521-51720-1 Hardback £75.00 Analysis, Function Theory or Theory of audience (including physical sciences), www.cambridge.org/9780521517201 this book will become the reference Hardy Spaces. of choice on the Hilbert transform, Contents: Preface; 1. Fourier series; whatever the subject background of Forthcoming 2. Abel–Poisson means; 3. Harmonic functions in the unit disc; 4. Logarithmic the reader. It explains all the common Multidimensional Hilbert transforms, mathematical convexity; 5. Analytic functions in the techniques for evaluating them, and has Stochastic Processes unit disc; 6. Norm inequalities for the conjugate function; 7. Blaschke products detailed discussions of their application. as Rough Paths and their applications; 8. Interpolating Theory and Applications Encyclopedia of Mathematics and its linear operators; 9. The Fourier transform; Applications Peter Friz 10. Poisson integrals; 11. Harmonic University of Cambridge 2009 234 x 156 mm 1440pp 500 exercises functions in the upper half plane; 12. The 130 figures and Nicolas Victoir Plancherel transform; 13. Analytic functions 978-0-521-51723-2 Set £140.00 J.P. Morgan, New York www.cambridge.org/9780521517232 in the upper half plane; 14. The Hilbert An appealing introduction to Lyons’ transform on R; A. Topics from real analysis; important theory and its applications. B. A panoramic view of the representation Hilbert Transforms Based on successful courses at the theorems; Bibliography; Index. Volume 1 graduate level, it presents the finite- London Mathematical Society Student Texts, 74 Frederick W. King dimensional story and emphasizes the University of Wisconsin, Eau Claire underlying geometry and algebra. This 2009 228 x 152 mm 384pp 16 tones 2 tables 335 exercises 45 figures Contents: Preface; List of symbols; List of viewpoint keeps the book as accessible as possible and is particularly powerful 978-0-521-51768-3 Hardback £60.00 abbreviations; Volume I: 1. Introduction; 978-0-521-73201-7 Paperback £23.99 2. Review of some background www.cambridge.org/9780521517683 mathematics; 3. Derivation of the Hilbert transform relations; 4. Some basic properties

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Groups and Analysis MAA Book functions; 16. Pi is irrational; 17. Planetary The Legacy of Hermann Weyl motion; 18. The logarithm and exponential Calculus Deconstructed functions; 19. Integration in elementary Edited by Katrin Tent A Second Course in First-Year terms; Part IV. Infinite Sequences Universität Bielefeld, Germany Calculus and Infinite Series: 20. Approximation The work of Hermann Weyl has Zbigniew H. Nitecki by polynomial functions; 21. e is had a lasting influence on areas of Tufts University, Massachusetts transcendental; 22. Infinite sequences; mathematics such as topological A thorough and mathematically rigorous 23. Infinite series; 24. Uniform convergence groups, Lie groups and representation exposition of single-variable calculus for and power series; 25. Complex numbers; theory, harmonic analysis, and on the readers with some previous experience 26. Complex functions; 27. Complex foundations of mathematics itself. In of calculus techniques. This book can be power series; Part V. Epilogue: 28. Fields; 29. Construction of the real numbers; this volume leading experts outline the used as a textbook for an undergraduate connections between Weyl’s theorems 30. Uniqueness of the real numbers; course on calculus or as a reference for Suggested reading; Answers (to selected and up-to-date results in many self-study. contemporary topics. problems); Glossary of symbols; Index. Contents: Preface; Contents; 1. Precalculus; 2006 252 x 225 mm 682pp 700 line figures London Mathematical Society Lecture Note 2. Sequences and their limits; 3. Continuity; Series, 354 978-0-521-86744-3 Hardback £29.99 4. Differentiation; 5. Integration; 6. Power www.cambridge.org/9780521867443 2008 228 x 152 mm 354pp 3 tables series; A. Methods of proof; B. Answers to 7 worked examples 2 figures selected problems; Bibliography; Index. 978-0-521-71788-5 Paperback £38.00 www.cambridge.org/9780521717885 Mathematical Association of America Textbooks Discrete 2009 247 x 170 mm 540pp Textbook 978-0-88385-756-4 Hardback c. £50.00 Mathematics www.cambridge.org/9780883857564 A Guide to Complex and Foundations Variables Steven G. Krantz Dynamics of Linear American Institute of Mathematics, Palo Alto Operators Graduate Textbook A quick and easy-to-use introduction Frédéric Bayart Combinatorics: to the key topics in complex variables, Université de Clermont-Ferrand II (Université Blaise Pascal), France The Rota Way providing a solid grounding in this Joseph P. S. Kung fundamental area. Its lively exposition, and Étienne Matheron Université d’Artois, France University of North Texas and wealth of figures and examples Gian-Carlo Rota make this book a useful companion The first book to assemble the wide to more daunting texts. A valuable body of theory which has rapidly and Catherine H. Yan Texas A & M University resource for mathematicians and non- developed on the dynamics of linear mathematicians alike. operators. Written for researchers in Gian-Carlo Rota was one of the most Dolciani Mathematical Expositions, 32 operator theory, but also accessible to original and colourful mathematicians of anyone with a reasonable background in the twentieth century. His work on the 2008 228 x 152 mm 200pp 978-0-88385-338-2 Hardback £25.99 functional analysis at the graduate level. foundations of combinatorics created www.cambridge.org/9780883853382 Cambridge Tracts in Mathematics, 179 a new area of algebraic combinatorics. 2009 228 x 152 mm 350pp 105 exercises The book is based upon his influential 25 worked examples graduate courses on the foundations Analysis in Positive 978-0-521-51496-5 Hardback c. £43.00 of combinatorics, that have influenced Characteristic Publication June 2009 generations of students. www.cambridge.org/9780521514965 Anatoly N. Kochubei Contents: 1. Sets, functions, and relations; National Academy of Sciences of Ukraine 2. Matching theory; 3. Partially ordered sets Devoted to counterparts of classical Recent Bestseller and lattices; 4. Generating functions and the umbral calculus; 5. Symmetric functions and structures of mathematical analysis Textbook in analysis over local fields of positive Baxter algebras; 6. Determinants, matrices, characteristic, this is one of the first Calculus and polynomials; 7. Selected solutions. books to treat positive characteristic Third edition Cambridge Mathematical Library phenomena from an analytic viewpoint. Michael Spivak 2009 228 x 152 mm 408pp 3 line figures The author’s development of the work Publish or Perish Inc, Houston, Texas 209 exercises begun by Carlitz provides a foundation 978-0-521-88389-4 Hardback £55.00 Spivak’s celebrated Calculus is ideal 978-0-521-73794-4 Paperback £22.99 for studying various special functions. for mathematics majors seeking an www.cambridge.org/9780521883894 Cambridge Tracts in Mathematics, 178 alternative to doorstop textbooks and 2009 228 x 152 mm 220pp formidable introductions to real analysis. Analytic Combinatorics 978-0-521-50977-0 Hardback £40.00 Contents: Preface; Part I. Prologue: www.cambridge.org/9780521509770 1. Basic properties of numbers; 2. Numbers Philippe Flajolet Institut National de Recherche en Informatique of various sorts; Part II. Foundations: et en Automatique (INRIA), Rocquencourt 3. Functions; 4. Graphs; 5. Limits; 6. Continuous functions; 7. Three hard and Robert Sedgewick Princeton University, New Jersey theorems; 8. Least upper bounds; Part III. Derivatives and Integrals: The definitive treatment of analytic 9. Derivatives; 10. Differentiation; combinatorics. This self-contained text 11. Significance of the derivative; 12. Inverse covers the mathematics underlying functions; 13. Integrals; 14. The fundamental the analysis of discrete structures, theorem of calculus; 15. The trigonometric with thorough treatment of a large Discrete Mathematics and Foundations 3 number of applications. Exercises, Textbook Topics in Topological examples, appendices and notes aid A Primer of Graph Theory understanding: ideal for individual self- Infinitesimal Analysis Edited by Lowell W. Beineke study or for advanced undergraduate or Purdue University, Indiana graduate courses. Second edition and Robin J. Wilson Contents: Preface; An invitation to John L. Bell The Open University, Milton Keynes University of Western Ontario analytic combinatorics; Part A. Symbolic Consultant Editor Jonathan L. Gross Methods: 1. Combinatorial structures and A rigorous, axiomatically formulated Columbia University, New York ordinary generating functions; 2. Labelled presentation of the ‘zero-square’, or Assisted by Thomas W. Tucker structures and exponential generating ‘nilpotent’ infinitesimal. Colgate University, New York functions; 3. Combinatorial parameters and multivariate generating functions; Part B. ‘This might turn out to be a boring, The use of topological ideas to explore Complex Asymptotics: 4. Complex analysis, shallow book review: I merely LOVED various aspects of graph theory, and rational and meromorphic asymptotics; the book...the explanations are so vice versa, is a fruitful area of research. 5. Applications of rational and meromorphic clear, so considerate; the author There are links with other areas of asymptotics; 6. Singularity analysis of must have taught the subject many mathematics, such as design theory and generating functions; 7. Applications times, since he anticipates virtually geometry, and increasingly with such of singularity analysis; 8. Saddle-Point every potential question, concern, areas as computer networks where asymptotics; Part C. Random Structures: and misconception in a student’s or symmetry is an important feature. reader’s mind.’ 9. Multivariate asymptotics and limit laws; Contents: Preface; Foreword; Introduction; MAA Reviews Part D. Appendices: Appendix A. Auxiliary 1. Embedding graphs on surfaces; elementary notions; Appendix B. Basic Contents: Introduction; 1. Basic features 2. Maximum genus; 3. Distributions complex analysis; Appendix C. Concepts of of smooth worlds; 2. Basic differential of embeddings; 4. Algorithms and probability theory; Bibliography; Index. calculus; 3. First applications of the obstructions for embeddings; 5. Graph 2009 247 x 174 mm 824pp 74 tones differential calculus; 4. Applications to minors: generalizing Kuratowski’s 50 tables 200 worked examples 190 figures physics; 5. Multivariable calculus and theorem; 6. Colouring graphs on surfaces; 978-0-521-89806-5 Hardback £45.00 applications; 6. The definite integral: Higher 7. Crossing numbers; 8. Representing eBook available order infinitesimals; 7. Synthetic geometry; graphs and maps; 9. Enumerating coverings; www.cambridge.org/9780521898065 8. Smooth infinitesimal analysis as an 10. Symmetric maps; 11. The genus of a axiomatic system; Appendix; Models for group; 12. Embeddings and geometries; 13. Embeddings and designs; 14. Infinite MAA Book smooth infinitesimal analysis. 2008 228 x 152 mm 140pp 54 exercises graphs and planar maps; 15. Open Graph Theory 978-0-521-88718-2 Hardback £30.00 problems; Notes on contributors; Index of A Problem Oriented Approach eBook available definitions. Daniel Marcus www.cambridge.org/9780521887182 Encyclopedia of Mathematics and its Applications, 128 A natural way to learn some of the 2009 234 x 156 mm 416pp 7 tones essential ideas of graph theory from first Association for Symbolic 15 tables 95 figures principles. Logic 978-0-521-80230-7 Hardback c. £60.00 Publication July 2009 Contents: Preface; A. Basic Concepts; B. Games, Scales and Isomorphic graphs; C. Bipartite graphs; www.cambridge.org/9780521802307 D. Trees and forests; E. Spanning tree Suslin Cardinals: algorithms; F. Euler paths; G. Hamilton The Cabal Seminar Association for Symbolic paths and cycles; H. Planar graphs; I. Volume I Logic Independence and covering; J. Connections and obstructions; K. Vertex coloring; L. Edge Edited by Alexander S. Kechris Subsystems of Second California Institute of Technology coloring; M. Matching theory for bipartite Order Arithmetic graphs; N. Applications of matching theory; Benedikt Löwe Second edition O. Cycle-Free digraphs; Answers to selected Universiteit van Amsterdam problems. and John R. Steel Stephen G. Simpson University of California, Berkeley Pennsylvania State University Mathematical Association of America Textbooks Presents seminal papers from the What are the appropriate axioms for 2008 228 x 152 mm 240pp 640 exercises Caltech-UCLA ‘Cabal Seminar’, mathematics? Through a series of case 450 figures unpublished material, and related new studies, this volume examines these 978-0-88385-753-3 Hardback £31.99 papers. axioms to prove particular theorems in www.cambridge.org/9780883857533 Lecture Notes in Logic core areas including algebra, analysis, 2008 228 x 152 mm 460pp and topology, focusing on the language 978-0-521-89951-2 Hardback £45.00 of second-order arithmetic, the weakest eBook available language rich enough to express and www.cambridge.org/9780521899512 develop the bulk of mathematics. 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

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Surveys in Association for Symbolic Network Coding Combinatorics 2009 Logic An Introduction Edited by Sophie Huczynska Logic Colloquium 2006 Tracey Ho University of St Andrews, Scotland Edited by S. Barry Cooper California Institute of Technology James D. Mitchell University of Leeds and Desmond Lun University of St Andrews, Scotland Herman Geuvers Broad Institute of MIT and Harvard and Colva M. Roney-Dougal Radboud Universiteit Nijmegen Unified overview of the theory, University of St Andrews, Scotland Anand Pillay applications, challenges and future Survey articles based on the invited University of Leeds directions of network coding for lectures given at the Twenty-second and Jouko Väänänen graduate students, researchers and British Combinatorial Conference. University of Amsterdam and University of practitioners. Helsinki Contents: Preface; 1. Graph Contents: 1. Introduction; 2. Lossless decompositions and symmetry; The Annual European Meeting of the multicast network coding; 3. Inter-session 2. Combinatorics of optimal designs; Association for Symbolic Logic, also network coding; 4. Network coding in lossy 3. Regularity and the spectra of graphs; known as the Logic Colloquium, is networks; 5. Subgraph selection; 6. Security 4. Trades and t-designs; 5. Extremal graph among the most prestigious annual against adversarial errors. packing problems: Ore-type versus Dirac- meetings in the field. The current 2008 253 x 177 mm 184pp 47 line figures type; 6. Embedding large subgraphs into volume, Logic Colloquium 2006, with 978-0-521-87310-9 Hardback £30.00 dense graphs; 7. Counting planar graphs contributions from plenary speakers eBook available and related families of graphs; 8. Metrics and selected special session speakers, www.cambridge.org/9780521873109 for sparse graphs; 9. Recent results on contains both expository and research chromatic and flow roots of graphs and papers by some of the best logicians in Modern Coding Theory matroids. the world. Tom Richardson London Mathematical Society Lecture Note Lecture Notes in Logic Series, 365 and Ruediger Urbanke 2009 234 x 156 mm 384pp École Polytechnique Fédérale, Lausanne 2009 228 x 152 mm 336pp 5 tones 978-0-521-11081-5 Hardback c. £60.00 50 worked examples 45 figures Publication July 2009 Summary of the state-of-the-art in 978-0-521-74173-6 Paperback c. £40.00 www.cambridge.org/9780521110815 techniques to analyse and design Publication July 2009 www.cambridge.org/9780521741736 practical iterative coding systems. Channel Codes ‘There is definitely a market for a Forthcoming Classical and Modern book focusing on LDPC codes, and William Ryan Tom Richardson and Reudiger Urbanke Algebraic Theories University of Arizona would be on anyone’s short list to J. Adámek and Shu Lin write that book. They have made Technische Universität Carolo Wilhelmina zu University of California, Davis substantive contributions to the Braunschweig, Germany theory and practice of LDPC codes. I This detailed introduction presents the J. Rosick believe this book will become required Masarykova Univerzita v Brnì, Czech Republic underlying theory and describes how to reading for researchers in LDPC codes design and implement practical iterative and E. M. Vitale at universities and communications Université Catholique de Louvain, Belgium codes. Including the latest information companies around the world.’ on modern channel codes plus 250 Thomas Fuja, University of Notre Dame First up-to-date treatment of this varied and stimulating end-of-chapter categorical way of describing sets with problems, this is an essential resource Contents: Preface; 1. Introduction; extra algebraic structure (data types), for students and practitioners alike. 2. Factor graphs; 3. Binary erasure channel; with applications in analysis, topology 4. Binary memoryless symmetric channels; and number theory, geometry and 2009 247 x 174 mm 700pp 35 tables 5. General channels ; 6. Convolutional 250 exercises 145 worked examples codes and turbo codes; 7. General mathematical physics. A must-read 219 figures for graduate students and researchers 978-0-521-84868-8 Hardback c. £50.00 ensembles; 8. Expander codes and the in category theory, general algebra, Publication October 2009 flipping algorithm; Appendices: A. Encoding theoretical computer science, and logic. www.cambridge.org/9780521848688 low-density parity-check codes; B. Efficient implementation of density evolution; C. Cambridge Tracts in Mathematics Concentration inequalities; D. Formal power 2010 228 x 152 mm 200pp sums. 978-0-521-11922-1 Hardback c. £40.00 Publication January 2010 2008 247 x 174 mm 592pp 150 line figures www.cambridge.org/9780521119221 185 exercises 978-0-521-85229-6 Hardback £45.00 eBook available www.cambridge.org/9780521852296 Algebra and Geometry / Number Theory and Algebra 5

and applications of sub-Riemannian Contents: Introduction; 1. Factorization and Algebra and geometry for graduate students the primes; 2. Congruences; 3. Quadratic and researchers in pure and applied residues; 4. Continued fractions; 5. Sums Geometry mathematics, theoretical physics, control of squares; 6. Quadratic forms; 7. Some theory, and thermodynamics. Potential Diophantine equations; 8. Computers and number theory; Exercises; Hints; Answers; Directed Algebraic applications include quantum mechanics and quantum field theory. Bibliography; Index; Additional notes. Topology Encyclopedia of Mathematics and its 2008 228 x 152 mm 248pp 3 tables Models of Non-Reversible Worlds Applications, 126 150 exercises 6 figures 978-0-521-72236-0 Paperback £23.99 Marco Grandis 2009 234 x 156 mm 370pp 52 line figures Università degli Studi di Genova 978-0-521-89730-3 Hardback £55.00 eBook available www.cambridge.org/9780521722360 The first authored book to be dedicated Publication May 2009 to the new field of directed algebraic www.cambridge.org/9780521897303 topology that arose in the 1990s, in Analytic Number homotopy theory and in the theory Forthcoming Theory of concurrent processes. The author Essays in Honour of Klaus Roth presents its mathematical foundations, The Geometry of Edited by W. W. L. Chen demonstrating its relation to classical Moduli Spaces Macquarie University, Sydney algebraic topology, and explores its of Sheaves W. T. Gowers varied applications. Daniel Huybrechts University of Cambridge New Mathematical Monographs, 13 Rheinische Friedrich-Wilhelms-Universität Bonn H. Halberstam 2009 228 x 152 mm 445pp and Manfred Lehn University of Illinois, Urbana-Champaign 978-0-521-76036-2 Hardback c. £55.00 Johannes Gutenberg Universität Mainz, Germany W. M. Schmidt Publication October 2009 University of Colorado, Boulder www.cambridge.org/9780521760362 Lucidly written, fully developed, the perfect exposition of this central area of and R. C. Vaughan current research in algebraic geometry. Pennsylvania State University Moduli Spaces and 2009 228 x 152 mm 300pp Leading lights in mathematics Vector Bundles 978-0-521-13420-0 Paperback c. £35.00 acknowledge the contribution of British Publication December 2009 mathematician, Klaus Roth, to number Edited by Leticia Brambila-Paz www.cambridge.org/9780521134200 Centro de Investigacíon en Matematicás theory, diophantine approximation, (CIMAT), Mexico sieve theory and beyond. Extensive Steven B. Bradlow lists of references make this a valuable University of Illinois, Urbana-Champaign Number Theory source for research mathematicians in Oscar García-Prada many areas and a suitable introductory Consejo Superior de Investigaciones Cientificas, and Algebra overview of the subject for beginning Madrid research students. and S. Ramanan Contributors: Roger Baker, Glyn Harman, Chennai Mathematical Institute, India Textbook William D. Banks, Igor E. Shparlinski, József Vector bundles and their associated The Higher Arithmetic Beck, Wesley Pegden, Sujith Vijay, Victor moduli spaces are of fundamental Beresnevich, Vasily Bernik, Maurice Dodson, importance in algebraic geometry. An Introduction to the Theory of Sanju Velani, J. Bourgain, T. D. Browning, This volume, authored by some of Numbers D. R. Heath-Brown, Jörg Brüdern, Yann the subject’s leading experts, covers Eighth edition Bugeaud, Bernard Chazelle, William Chen, foundational material as well as H. 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Algorithmic A Higher-Dimensional Graduate Textbook Number Theory Sieve Method Groups, Graphs Lattices, Number Fields, Curves With Procedures for Computing and Trees and Cryptography Sieve Functions An Introduction to the Geometry Edited by J.P. Buhler Harold G. Diamond of Infinite Groups Reed College, Oregon University of Illinois, Urbana-Champaign John Meier and P. Stevenhagen H. Halberstam Lafayette College, Pennsylvania Universiteit Leiden University of Illinois, Urbana-Champaign Accessible and engaging approach and William F. Galway This comprehensive introduction for to geometric group theory; ideal for beginning graduate students contains Modern and practical guide to higher advanced undergraduates. articles by the leading experts in dimensional sieve theory, with an the field. 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Benjamin Harvey Mudd College, California A collection of articles presenting the London Mathematical Society Student Texts, 73 and Ezra Brown state of the art in the topic of modular Virginia Polytechnic Institute and State University forms. 2008 228 x 152 mm 256pp 1 table 175 exercises 61 worked examples 95 figures An anthology of articles ideal for use 2008 228 x 152 mm 360pp 20 tables 55 graphs as a textbook supplement on a number 10 worked examples 1 figure 978-0-521-89545-3 Hardback £55.00 978-0-521-49354-3 Hardback £50.00 theory course. The editors have selected 978-0-521-71977-3 Paperback £19.99 well written bite-sized articles and notes eBook available eBook available www.cambridge.org/9780521493543 which aid an understanding of number www.cambridge.org/9780521895453 theory. 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Galois Groups and Words Scientific Fundamental Groups Notes on Verbal Width in Groups Tamás Szamuely Dan Segal Computing Hungarian Academy of Sciences, Budapest All Souls College, Oxford Ever since the concepts of Galois groups Spectacular new results in finite group in algebra and fundamental groups in theory can be accessed via the study Textbook topology emerged during the nineteenth of word-values in groups. This book New Edition century, mathematicians have known explores fundamental questions about of the strong analogies between the the behaviour of word-values in groups The Student’s two concepts. This book presents the and demonstrates the power of this Introduction to connection starting at an elementary approach. An accessible treatment MATHEMATICA® level and assuming as little technical suitable for research students and A Handbook for Precalculus, background as possible. experienced workers in group theory. Calculus, and Linear Algebra Cambridge Studies in Advanced London Mathematical Society Lecture Note Second edition Mathematics, 117 Series, 361 Bruce F. Torrence 2009 228 x 152 mm 140pp 30 exercises 2009 228 x 152 mm 304pp 60 exercises Randolph-Macon College, Virginia 90 worked examples 1 figure 978-0-521-88850-9 Hardback c. £30.00 978-0-521-74766-0 Paperback c. £24.99 and Eve A. Torrence Publication July 2009 Publication June 2009 Randolph-Macon College, Virginia www.cambridge.org/9780521888509 www.cambridge.org/9780521747660 A new edition of this well loved book completely rewritten for Mathematica 6. Unitary Reflection This book can be used in a variety of Differential Tensor courses, from precalculus to linear Algebras and their Groups algebra. Used as a supplementary text Module Categories Gustav I. Lehrer it will aid in bridging the gap between University of Sydney R. Bautista the mathematics in the course and National University of Mexico and Donald E. Taylor Mathematica. University of Sydney L. Salmerón National University of Mexico This book provides a complete ‘This book does a very good job of filling an important niche – giving and R. Zuazua classification of unitary reflection mathematics students a thorough National University of Mexico groups – which arise naturally in many areas of mathematics. Designed for introduction to Mathematica without This volume provides a systematic overwhelming them with the long graduate students, but also suitable for presentation of the theory of differential manual.’ researchers in algebra, topology and tensor algebras and their categories of Mathematics Teacher modules. The authors introduce new mathematical physics. findings and proofs as well as providing Australian Mathematical Society Lecture Contents: Preface; 1. Getting started; Series, 20 a fresh perspective on established 2. Working with Mathematica; 3. Functions results. 2009 228 x 152 mm 305pp 12 tables and their graphs; 4. Algebra; 5. Calculus; 110 exercises 6. Multivariable calculus; 7. Linear algebra; London Mathematical Society Lecture Note 978-0-521-74989-3 Paperback c. £35.00 8. Programming; Solutions to exercises; Series, 362 Publication June 2009 Index. 2009 228 x 152 mm 456pp 90 exercises www.cambridge.org/9780521749893 978-0-521-75768-3 Paperback c. £40.00 2009 246 x 189 mm 484pp 50 tones Publication September 2009 5 tables 220 exercises www.cambridge.org/9780521757683 978-0-521-71789-2 Paperback £25.99 Purity, Spectra www.cambridge.org/9780521717892 and Localisation Forthcoming Mike Prest University of Manchester Textbook Synthetic Geometry A unified, coherent account of the A First Course in the of Manifolds algebraic aspects and uses of the Numerical Analysis of Anders Kock Ziegler spectrum. It may be used as Aarhus Universitet, Denmark an introductory graduate-level text, Differential Equations User-friendly introduction to the providing relevant background material Second edition generalized context for modern research and a wealth of illustrated examples. Arieh Iserles on quantum field theory and higher An extensive index and thorough University of Cambridge category theory. referencing also make this book an ideal Extensively updated new edition Cambridge Tracts in Mathematics, 180 reference. including new chapters on emerging 2009 228 x 152 mm 300pp Encyclopedia of Mathematics and its subject areas: geometric numerical 978-0-521-11673-2 Hardback c. £50.00 Applications, 121 integration, spectral methods and Publication November 2009 2009 234 x 156 mm 792pp conjugate gradients. www.cambridge.org/9780521116732 115 worked examples 978-0-521-87308-6 Hardback c. £85.00 ‘A well written and exciting book … Publication June 2009 the exposition throughout is clear and www.cambridge.org/9780521873086 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 8 Scientific Computing / Dynamical Systems, Mechanics and Modelling

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Soliton Equations glimpse of further developments in real manifolds; 12. Integration on manifolds; and Their Algebro- and complex one-dimensional dynamics. 13. An introduction to differential topology; Cambridge Studies in Advanced 14. Group and group representations; Geometric Solutions Mathematics, 115 15. Lie groups; 16. The geometry of Volume 2 2008 228 x 152 mm 208pp 56 exercises fibre bundles; 17. Complex analysis I; Fritz Gesztesy 25 worked examples 15 figures 18. Applications of complex variables; University of Missouri, Columbia 978-0-521-88861-5 Hardback £35.00 19. Special functions and complex variables; Helge Holden eBook available Appendixes; Reference; Index. 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These selected contributions Gaston Gonnet Eidgenössische Technische Hochschule Zürich Cambridge Studies in Advanced reflect different approaches to the and Ralf Scholl Mathematics, 114 integration of differential equations, 2008 228 x 152 mm 448pp originating from Differential Galois Using real-life applications, this 15 worked examples 4 figures Theory, Symmetry, Integrability and graduate-level textbook introduces 978-0-521-75308-1 Hardback £75.00 Soliton Theory. The ideas of several different mathematical methods eBook available mathematical communities are here of scientific computation to solve www.cambridge.org/9780521753081 brought together and connections minimization problems. Each chapter between them sought. solves several realistic problems, Also available London Mathematical Society Lecture Note allowing readers to see how the Series, 357 methods are put to use, making Soliton Equations 2008 228 x 152 mm 248pp it easier to grasp the basic ideas. and their Algebro- 80 worked examples Interactive exercises are available at 978-0-521-72008-3 Paperback £40.00 www.cambridge.org/9780521849890. Geometric Solutions www.cambridge.org/9780521720083 Volume 1 Contents: Preface; 1. Determination of the accurate location of an aircraft; Fritz Gesztesy 2. When to replace equipment; 3. SSP University of Missouri, Columbia Mathematics using LS and SVD; 4. SSP using least and Helge Holden squares and best basis; 5. SSP learning Norwegian University of Science and Technology, methods (nearest neighbours); 6. SSP with Trondheim for Physics and linear programming (LP); 7. Stock market This book offers a detailed treatment of prediction; 8. Phylogenetic tree construction; a class of algebro-geometric solutions Biology Appendixes; Index. and their representations. 2009 246 x 189 mm 216pp 13 tones Cambridge Studies in Advanced Graduate Textbook 978-0-521-84989-0 Hardback c. £35.00 Mathematics, 79 Publication August 2009 2003 228 x 152 mm 518pp Mathematics www.cambridge.org/9780521849890 978-0-521-75307-4 Hardback £80.00 for Physics eBook available A Guided Tour for Graduate www.cambridge.org/9780521753074 Textbook Students Michael Stone A First Course in Mathematical Tools University of Illinois, Urbana-Champaign String Theory for One-Dimensional and Paul Goldbart Second edition University of Illinois, Urbana-Champaign Dynamics Barton Zwiebach An engagingly-written account of Massachusetts Institute of Technology Edson de Faria mathematical tools and ideas, this book Universidade de São Paulo Zwiebach is once again faithful to his provides a graduate-level introduction goal of making string theory accessible and Welington de Melo IMPA, Rio de Janeiro to the mathematics used in research to undergraduates. This text now in physics. Topics are illustrated includes AdS/CFT correspondence, as Self-contained book presenting the through carefully chosen examples, well introducing superstrings. With mathematical tools necessary for the exercises and problems drawn from almost 300 problems and exercises study of complex dynamics. Detailing realistic physics settings. Solutions it is perfectly suited for introductory the latest research, it will appeal to to the exercises are available at courses for students with a background graduate students and researchers www.cambridge.org/9780521854030. in physics. working in dynamical systems and related fields. Carefully chosen exercises Contents: Preface; 1. Calculus of variations; 2. Function spaces; 3. Linear ‘A refreshingly different approach to aid understanding and provide a ordinary differential equations; 4. Linear string theory that requires remarkably differential operators; 5. Green functions; little previous knowledge of quantum theory or relativity. This highlights 6. Partial differential equations; 7. The fundamental features of the theory mathematics of real waves; 8. Special that make it so radically different functions; 9. Integral equations; 10. Vectors from theories based on point-like and tensors; 11. Differential calculus on

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particles. This book makes the subject Digital Image Textbook amenable to undergraduates but it will also appeal greatly to beginning Processing for Medical Probability and researchers who may be overwhelmed Applications Statistics by Example by the standard textbooks.’ Geoff Dougherty Volume 2: Markov Chains: A Primer in Professor Michael Green, University of California State University, Channel Islands Random Processes and their Applications Cambridge This practical book for advanced Yuri Suhov Contents: Foreword; Preface; undergraduates and graduate students University of Cambridge Acknowledgements; Part I. Basics: 1. A explains the concepts and the effective and Mark Kelbert brief introduction; 2. Special relativity and use of image processing tools for University of Wales, Swansea extra dimensions; 3. Electromagnetism medical applications. Real medical The subject is critical in many modern and gravitation in various dimensions; images and hands-on activities are applications such as mathematical 4. Nonrelativistic strings; 5. The relativistic used to develop the reader’s skill and finance, quantitative management, point particle; 6. Relativistic strings; confidence. All images, public-domain insurance and actuarial studies. 7. Strong parameterization and classical software and solutions available from Contents: Preface; Introduction: Andrei motion; 8. World-sheet currents; 9. Light- www.cambridge.org/books/dougherty. cone relativistic strings; 10. Light-cone fields Markov and his time; 1. Discrete-time 2009 247 x 174 mm 462pp 130 tones and particles; 11. The relativistic quantum Markov chains; 2. Continuous-time Markov 13 plates 17 tables 130 exercises chains: basic theory; 3. Statistics of discrete- point particle; 12, Relativistic quantum 13 worked examples 735 figures closed strings; 13. Relativistic quantum time Markov chains; Afterword: Pearson, 978-0-521-86085-7 Hardback £45.00 Maxwell and other famous Cambridge closed strings; 14. A look at relativistic www.cambridge.org/9780521860857 superstrings; Part II. Developments: Wranglers of the past: some lessons to be 15. D-branes and gauge fields; 16. String learned; Bibliography; Appendix; Index. charge and electric charge; 17. T-duality 2008 247 x 174 mm 498pp 151 line figures of closed strings; 18. T-duality of open Statistics, 190 worked examples strings; 19. Electromagnetism fields in 978-0-521-84767-4 Hardback £70.00 978-0-521-61234-0 Paperback £29.99 D-branes; 20. Nonlinear and Born-Infeld Applied electrodynamics; 21. Strong theory and eBook available particle physics; 22. String thermodynamics Probability and www.cambridge.org/9780521847674 and black holes; 23. Strong interactions and AdS/CFT; 24. Covariant string quantization; Finance New in Paperback 25. String interactions and Riemann surfaces; 26. Loop amplitudes in string Graduate Textbook theory; References; Index. Markov Chains and Statistical Models 2009 246 x 189 mm 696pp 86 tones Stochastic Stability A. C. Davison 180 exercises École Polytechnique Fédérale, Lausanne 978-0-521-88032-9 Hardback £40.00 Second edition eBook available Sean Meyn An integrated development of models www.cambridge.org/9780521880329 University of Illinois, Urbana-Champaign and likelihood that blends theory and Richard L. Tweedie and practice, suitable for advanced University of Minnesota undergraduate and graduate students, Chaos and Coarse Prologue by Peter W. Glynn researchers and practitioners. Each Graining in Statistical New up-to-date edition of this chapter contains a wide range of Mechanics influential classic on Markov chains in problems and exercises. A library of data sets accompanying the book is available Patrizia Castiglione general state spaces. Proofs are rigorous Editions Belin, Paris and concise, the range of applications over the web. is broad and knowledgeable, and key Massimo Falcioni ‘This is an excellent textbook on Università degli Studi di Roma ‘La Sapienza’, ideas are accessible to practitioners modern statistics.’ Italy with limited mathematical background. Zentralblatt MATH Annick Lesne New commentary by Sean Meyn, Centre National de la Recherche Scientifique including updated references, reflects Contents: 1. Introduction; 2. Variation; (CNRS), Paris developments since 1996. 3. Uncertainty; 4. Likelihood; 5. Models; and Angelo Vulpiani 6. Stochastic models; 7. Estimation and Università degli Studi di Roma ‘La Sapienza’, ‘This second edition remains true hypothesis testing; 8. Linear regression Italy to the remarkable standards of models; 9. Designed experiments; Presents concepts of chaotic systems for scholarship established by the first 10. Nonlinear regression models; researchers and graduate students in edition … it will no doubt be a very 11. Bayesian models; 12. Conditional and statistical mechanics and chaos. welcome addition to the literature.’ marginal inference. Peter W. Glynn, Prologue to the Second Edition 2008 247 x 174 mm 280pp 35 line figures Cambridge Series in Statistical and Probabilistic Mathematics, 11 978-0-521-89593-4 Hardback £65.00 Cambridge Mathematical Library 2008 253 x 177 mm 736pp 119 tables eBook available 2009 247 x 174 mm 622pp 4 tones 566 exercises www.cambridge.org/9780521895934 17 figures 978-0-521-73449-3 Paperback £29.99 978-0-521-73182-9 Paperback £30.00 www.cambridge.org/9780521734493 www.cambridge.org/9780521731829 Statistics, Applied Probability and Finance 13

Textbook Graduate Textbook Stochastic Statistical Models Elementary Probability Approximation Theory and Practice for Applications A Dynamical Systems Viewpoint Second edition Rick Durrett Vivek S. Borkar David Freedman Cornell University, New York Tata Institute of Fundamental Research, Mumbai, India University of California, Berkeley This clear, lively introduction to This lively and engaging book explains probability concentrates on the results Simple, compact toolkit for designing the basic ideas of association and that are the most useful for applications. and analyzing algorithms, with regression, and tells you the things you It is designed for a one-semester course concrete examples from control and have to know in order to read empirical for students who have some familiarity communications engineering, artificial papers in the social and health sciences, with basic calculus. Reflecting the intelligence, economic modelling. as well as the techniques you need to author’s philosophy that the best way Contents: Preface; 1. Introduction; build statistical models of your own. to learn probability is to see it in action, 2. Basic convergence analysis; 3. Stability there are more than 350 problems and criteria; 4. Lock-in probability; 5. Stochastic ‘At last, a second course in statistics 200 examples. recursive inclusions; 6. Multiple timescales; that is serious, correct, and interesting. 7. Asynchronous schemes; 8. A limit The book teaches regression, causal ‘The book has a nice interplay theorem for fluctuations; 9. Constant modeling, maximum likelihood, and between probability modeling and stepsize algorithms; 10. Applications; the bootstrap. Everyone who analyzes scientific applications, whether from 11. Appendices; References; Index. real data should read this book.’ biology, sports, or discussions of 2008 228 x 152 mm 176pp Persi Diaconis, Professor of Mathematics and China’s one-child policy. Many of the 978-0-521-51592-4 Hardback £35.00 Statistics, Stanford University examples are thought provoking, www.cambridge.org/9780521515924 including ones on DNA samples for 2009 253 x 177 mm 456pp 21 line figures paternity cases and others about the 11 tables 404 exercises Recent Bestseller 978-0-521-11243-7 Hardback £70.00 O. J. Simpson trial. As an instructor, 978-0-521-74385-3 Paperback £24.99 I enjoy digging into these examples Textbook Publication June 2009 in class. And the large selection of www.cambridge.org/9780521112437 interesting problems builds basic skills A First Course and deepens or extends the main in Statistical ideas.’ A Quantitative Tour of Professor Michael Phelan, University of Programming with R California, Irvine W. John Braun the Social Sciences University of Western Ontario Edited by Andrew Gelman 2009 247 x 187 mm 296pp 55 line figures and Duncan J. Murdoch Columbia University, New York 80 tables 355 exercises University of Western Ontario and Jeronimo Cortina 978-0-521-86756-6 Hardback c. £35.00 Publication September 2009 The only introduction you’ll need to start This overview by prominent social www.cambridge.org/9780521867566 programming in R. scientists gives a friendly, non-technical sense of how quantitative research is ‘… with this book, you can be up and done in different areas. Readers will find Bayesian running, doing very advanced work out about models and ways of thinking Nonparametrics with R in a matter of minutes. Using a series of code examples, the authors in economics, history, sociology, political Edited by Nils Lid Hjort take you through many of the basic science, and psychology, which in turn Universitetet i Oslo they can bring back to their own work. capabilities of the package. All that Chris Holmes is needed to follow the examples University of Oxford ‘A marvelous sampler of quantitative is a basic understanding of control Peter Müller approaches to social science across constructs such as the if-then, loops University of Texas, M. D. Anderson Cancer and functions as well as knowledge of a range of disciplines. The authors Center forsake the dry and mechanical the underlying mathematics.’ overviews that typify introductory and Stephen Walker Charles Ashbacher, Journal of Recreational University of Kent, Canterbury texts in favor of focused forays Mathematics into specific problems, deemed Bayesian nonparametrics works. Contents: 1. Getting started; representative of their discipline’s Applications are appearing in such 2. Introduction to the R language; theoretical and empirical output. disciplines as information retrieval, NLP, 3. Programming statistical graphics; These engrossing stories of research machine vision, computational biology, 4. Programming with R; 5. Simulation; make the volume a lively and cognitive science, signal processing. In informative read.’ 6. Computational linear algebra; this coherent introduction, the editors 7. Numerical optimization; Appendix. John Gerring, author of Social Science weave together tutorial chapters by Methodology and Case Study Research: Review of random variables and Principles and Practices Ghosal, Lijoi and Prünster, Dunson, and distributions; Index. Teh and Jordan, giving direct access to 2007 246 x 189 mm 174pp 39 line figures Contents: 1. Models and methods in the these exciting ideas and methods. 160 exercises 64 worked examples social sciences; 2. History; 3. 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Recent Bestseller Contents: 1. Introduction; 2. Probabilistic Contents: Preface; Acknowledgements; Graduate Textbook framework; 3. Markov optimal stopping 1. Risk; 2. Pricing methodologies and theory; 4. Sequential detection; 5. Bayesian arbitrage; 3. Trees and option pricing; Data Analysis and quickest detection; 6. Non-bayesian quickest 4. Practicalities; 5. The Ito calculus; 6. Risk Graphics Using R detection; 7. Additional topics. neutrality and martingale measures; 7. The practical pricing of a European option; An Example-based Approach 2008 247 x 174 mm 244pp 17 figures 978-0-521-62104-5 Hardback £45.00 8. Continuous barrier options; 9. Multi- Second edition eBook available look exotic options; 10. Static replication; John Maindonald www.cambridge.org/9780521621045 11. Multiple sources of risk; 12. Options Australian National University, Canberra with early exercise features; 13. Interest rate and John Braun derivatives; 14. The pricing of exotic interest University of Western Ontario Mathematical Finance rate derivatives; 15. Incomplete markets and Hands-on guide to the R system for jump-diffusion processes; 16. Stochastic data analysis for scientists, students and volatility; 17. Variance gamma models; practising statisticians. Synthetic CDOs 18. Smile dynamics and the pricing of Modelling, Valuation and Risk exotic options; Appendix A. Financial and From reviews of previous edition: Management mathematical jargon; Appendix B. Computer ‘I would strongly recommend the book C. C. Mounfield projects; Appendix C. Elements of probability to scientists who have already had a Barclays Capital, London theory; Appendix D. Hints and answers to exercises; Bibliography; Index. regression or a linear models course Details the latest models and techniques and who wish to learn to use R … an Mathematics, Finance and Risk, 8 easy-to-read and an understandable in quantitative and computational modelling of synthetic Collateralised 2008 247 x 174 mm 560pp 202 exercises reference on the use of R for practical 978-0-521-51408-8 Hardback £40.00 data analysis.’ Debt Obligations. www.cambridge.org/9780521514088 R News Contents: Acknowledgements; Dedication; Preface; 1. A primer on collateralised debt Contents: Preface; 1. A brief introduction obligations; 2. The modelling of obligor Interest Rates and to R; 2. Styles of data analysis; 3. Statistical default; 3. Valuation of credit default Coupon Bonds in models; 4. An introduction to formal swaps; 4. Credit indices; 5. Valuation of inference; 5. Regression with a single default baskets; 6. Synthetic CDO valuation Quantum Finance predictor; 6. Multiple linear regression; methodologies; 7. Phenomenology of Belal E. Baaquie 7. Exploiting the linear model framework; the standard market model; 8. Risk National University of Singapore 8. Generalized linear models and survival quantification and sensitivities of synthetic The economic crisis of 2008 has analysis; 9. Time series models; 10. Multi- CDOs; 9. Implied and base correlations; shown that the capital markets need level models and repeated measures; 10. Extensions of the standard market new theoretical and mathematical 11. Tree-based classification and regression; model; 11. Exotic CDOs; 12. Correlation concepts to describe and price financial 12. Multivariate data exploration and trading of synthetic CDO tranches; instruments. This ground-breaking discrimination; 13. Regression on principal 13. Risk management of a portfolio of book will provide physicists and component or discriminant scores; 14. The synthetic CDOs; 14. Hedging simulation of R system – additional topics; Epilogue – mathematicians researching in finance, structured credit products; A. Explanation of and professionals working in the finance models; References; Index of R symbols and common notation; B. Simulated annealing; industry, with a completely different functions; Index of terms; Index of names. References. perspective on finance. Cambridge Series in Statistical and Mathematics, Finance and Risk, 7 Probabilistic Mathematics, 10 Contents: 1. Synopsis; 2. Interest rates 2008 247 x 174 mm 386pp 90 tones and coupon bonds; 3. Options and option 2007 247 x 174 mm 528pp 12 plates 25 tables 130 figures 15 graphs 50 tables 150 exercises 150 figures 978-0-521-89788-4 Hardback £45.00 theory; 4. Interest rate and coupon bond 978-0-521-86116-8 Hardback £43.00 options; 5. Quantum field theory of bond eBook available eBook available www.cambridge.org/9780521897884 forward interest rates; 6. Libor Market www.cambridge.org/9780521861168 Model of interest rates; 7. Empirical analysis of forward interest rates; 8. Libor New Edition Market Model of interest rate options; Quickest Detection 9. Numeraires for bond forward interest H. Vincent Poor The Concepts rates; 10. Empirical analysis of interest Princeton University, New Jersey and Practice of rate caps; 11. Coupon bond European and and Olympia Hadjiliadis Mathematical Finance Asian options; 12. Empirical analysis of Brooklyn College, City University of New York interest rate swaptions; 13. Correlation of Second edition This unified treatment of the quickest coupon bond options; 14. Hedging interest Mark S. Joshi rate options; 15. Interest rate Hamiltonian detection problem provides the University of Melbourne background necessary to design, and option theory; 16. American options analyze, and understand quickest Second edition of successful text for coupon bonds and interest rates; detection algorithms. providing the working knowledge 17. Hamiltonian derivation of coupon bond needed to become a good quantitative options; Appendixes; Glossaries; List of ‘Nothing endures but change. This analyst. symbols; Reference; Index. timely book applies Heraclitus’ 2009 247 x 174 mm 550pp 25 tones fundamental principle to the processes ‘The book is intended as an 978-0-521-88928-5 Hardback c. £50.00 used to describe change itself. As introduction for a numerate person Publication October 2009 financial markets ebb and flow, to the discipline of mathematical www.cambridge.org/9780521889285 practitioners schooled in quickest finance. 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MAA Book Actuarial Contents: 1. Introduction; 2. Preliminary mathematics; 3. Principles of financial Mathematical Mathematics for Life valuation; 4. Interest rate models; Interest Theory Contingent Risks 5. Mathematics of asset pricing; Leslie Vaaler David C. M. Dickson 6. Bibliography. University of Texas, Austin University of Melbourne 2009 228 x 152 mm 350pp 16 tables and James Daniel Mary R. Hardy 978-0-521-06679-2 Paperback £16.99 University of Texas, Austin University of Waterloo, Ontario www.cambridge.org/9780521066792 Mathematical Interest Theory gives an and Howard Waters Heriot-Watt University, Edinburgh introduction to how investments vary Textbook over time, and this book provides a Life contingencies within the modern solid foundation for readers embarking framework of multiple-state models. Financial Products on actuarial careers. It is among the Balancing rigor and intuition, with An Introduction using recommended reading options for the an emphasis on applications, this Mathematics and Excel Society of Actuaries/Casualty Actuarial textbook is ideal for university courses Bill Dalton Society FM/2 exam. and individual exam preparation. All A step-by-step guide to some of the Contents: An introduction to the Texas necessary theoretical material, many most important ideas in financial Instruments BA II Plus; 1. The growth of worked examples and exercises, and mathematics, including options, future money; 2. Equations of value and yield computational practice, using Excel, contracts, bonds and derivatives. teaching practical skills in simulation rates; 3. Annuities; 4. Annuities with Contents: Introduction; An introduction to and projection. different payment and conversion periods; Excel; 1. A foundation; 2. Forward contracts; 5. Loan repayment; 6. Bonds; 7. Stocks and International Series on Actuarial Science 3. The futures market; 4. Bonds; 5. The financial markets; 8. Arbitrage, the term 2009 228 x 152 mm 600pp forward rate, forward rate agreements, structure of interest rates, and derivatives; 978-0-521-11825-5 Hardback c. £50.00 swaps, caps and floors; 6. Options; 7. Option 9. Interest rate sensitivity; Appendices: A. Publication October 2009 pricing; 8. Credit derivatives; Solutions; www.cambridge.org/9780521118255 Some useful formulas; B. Answers to end of Index. chapter problems; Bibliography; Index. 2008 247 x 174 mm 408pp 189 line figures Mathematical Association of America 4 tables 8 exercises 189 figures 50 graphs Textbooks New in Paperback 978-0-521-86358-2 Hardback £60.00 2009 247 x 170 mm 494pp Financial Derivatives 978-0-521-68222-0 Paperback £23.99 978-0-88385-754-0 Hardback £50.00 Pricing, Applications, and eBook available www.cambridge.org/9780883857540 Mathematics www.cambridge.org/9780521863582 Jamil Baz Nonlife Actuarial PIMCO Europe, Ltd. London Advances in Credit Models and George Chacko Harvard Business School Risk Modelling and Theory, Methods and Evaluation Corporate Bankruptcy Yiu-Kuen Tse This book is a graduate level manual on Singapore Management University the pricing of financial derivatives. It Prediction allows the reader with basic knowledge Actuaries must pass exams, but more Edited by Stewart Jones of finance, calculus, and probability University of Sydney than that: they must put knowledge and statistics to understand the most into practice. This coherent textbook and David A. Hensher powerful tools in applied finance. The University of Sydney gives complete syllabus coverage for focus is on equity derivatives, interest Exam C of the Society of Actuaries (SOA) A compendium of credit risk modelling rate markets, and the mathematics of while emphasizing the concepts and approaches, including several new pricing. practical application of nonlife actuarial techniques that extend the horizons of future research and practice. models. It has also been class-tested for ‘This introduction to the modeling undergraduate university courses. of financial derivatives is ideal for ‘… if you wish to learn more about International Series on Actuarial Science quantitatively oriented traders, bank the nature of the financial instruments 2009 228 x 152 mm 544pp 1 tone researchers, and masters or doctoral that have brought the world to its 55 tables 350 exercises 155 worked examples students in this field. 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Non- parametric 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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8. Credit derivatives: current practices and Functions of Matrices 5. Linear elasticity; 6. Stokes flow; controversies; 9. Local government distress Theory and Computation 7. Navier–Stokes flow; 8. Flow in porous in Australia: a latent class regression media; Appendix A. Quadrature rules; Nicholas J. Higham analysis; 10. A belief-function perspective to Appendix B. DG codes; Appendix C. An University of Manchester credit risk assessments; Index. approximation result; Bibliography; Index. Quantitative Methods for Applied Economics A thorough treatment of the theory Frontiers in Applied Mathematics, 35 of matrix functions and numerical and Business Research 2008 247 x 174 mm 210pp 2008 247 x 174 mm 312pp 18 line figures methods for computing them, including 978-0-89871-656-6 Paperback £35.00 39 tables 18 figures 11 graphs an overview of applications, new and www.cambridge.org/9780898716566 978-0-521-86928-7 Hardback £60.00 unpublished research results, and 978-0-521-68954-0 Paperback £23.99 improved algorithms. Ideal for advanced eBook available courses and for self-study, its broad Graduate Textbook www.cambridge.org/9780521869287 content, references and appendix also Scientific Computing make this book a convenient general with Case Studies reference. Dianne P. O’Leary 2008 247 x 174 mm 450pp SIAM books University of Maryland, College Park 978-0-89871-646-7 Hardback £38.00 www.cambridge.org/9780898716467 A practical guide to solving linear A First Course in and nonlinear equations, differential equations, optimization problems, and Order Statistics Numerical Methods eigenvalue problems. The case studies Barry C. Arnold for Evolutionary illustrate mathematical modeling and University of California, Riverside Differential Equations algorithm design, for problems in N. Balakrishnan physics, engineering, epidemiology, McMaster University, Ontario Uri M. Ascher University of British Columbia, Vancouver chemistry, and biology. For advanced and H. N. Nagaraja undergraduates and beginning graduate Develops, analyses, and applies Ohio State University students, and scientists whose work numerical methods for evolutionary, or A simple introduction to the general involves numerical computing. time-dependent, differential problems. theory of order statistics and their 2009 247 x 174 mm 395pp applications, requiring no advanced Contents: List of figures; List of tables; 978-0-89871-666-5 Paperback £60.00 mathematical or statistical background. Preface; Introduction; 1. Ordinary differential www.cambridge.org/9780898716665 equations; 2. On problem atability; 3. Basic Contents: Preface to classics edition; methods, Basic concepts; 4. One-step Further reading; Preface; Acknowledgments; methods; 5. Linear multistep methods; Evaluating Derivatives Notations and abbreviations; Errata; 6. More boundary value problem theory and 1. Introduction and preview; 2. Basic Principles and Techniques of applications; 7. Shooting; 8. Finite difference distribution theory; 3. Discrete order Algorithmic Differentiation methods for boundary value problems; statistics; 4. Order statistics from Second edition 9. More on differential-algebraic equations; some specific distributions; 5. Moment Andreas Griewank 10. Numerical methods for differential- relations, bounds, and approximations; Humboldt-Universität zu Berlin algebraic equations; Bibliography; Index. 6. Characterizations using order statistics; and Andrea Walther Computational Science and Engineering 7. Order statistics in statistical inference; Technische Universität, Dresden 2008 247 x 174 mm 410pp 8. Asymptotic theory; 9. Record values; A comprehensive treatment Bibliography; Author index; Subject index. 978-0-89871-652-8 Paperback £51.00 www.cambridge.org/9780898716528 of algorithmic, or automatic, Classics in Applied Mathematics, 54 differentiation. 2008 247 x 174 mm 300pp Contents: Rules; Preface; Prologue; 978-0-89871-648-1 Paperback £47.00 Discontinuous www.cambridge.org/9780898716481 Mathematical symbols; 1. Introduction; Galerkin Methods for 2. A framework for evaluating functions; Solving Elliptic and 3. Fundamentals of forward and reverse; Generalized Inverses of Parabolic Equations 4. Memory issues and complexity bounds; Linear Transformations 5. Repeating and extending reverse; Theory and Implementation 6. Implementation and software; 7. Sparse Stephen L. Campbell Béatrice M. Rivière forward and reverse; 8. Exploiting sparsity North Carolina State University Rice University, Houston by compression; 9. Going beyond forward and Carl D. Meyer Focuses on three primal DG methods, and reverse; 10. Jacobian and Hessian North Carolina State University covering both theory and computation, accumulation; 11. Observations on This reference book provides and providing the basic tools for efficiency; 12. Reversal schedules and comprehensive coverage of the analysis. checkpointing; 13. Taylor and tensor mathematical theory of generalized coefficients; 14. Differentiation without Contents: List of figures; List of tables; inverses coupled with a wide range of differentiability; 15. Implicit and iterative List of algorithms; Preface; Part I. Elliptic important and practical applications. differentiation; Epilogue; List of figures; Problems: 1. One-dimensional problem; List of tables; Assumptions and definitions; It will be useful as a reference text for 2. Higher dimensional problem; applied scientists and engineers. Propositions, corollaries, and lemmas; Part II. Parabolic Problems: 3. Purely Bibliography; Index. Classics in Applied Mathematics parabolic problems; 4. Parabolic problems 2008 247 x 174 mm 460pp 2009 247 x 170 mm 275pp with convection; Part III. Applications: 978-0-89871-659-7 Paperback £48.00 978-0-89871-671-9 Paperback £45.00 www.cambridge.org/9780898716597 www.cambridge.org/9780898716719 SIAM books 17

Graduate Textbook Linear and Nonlinear 11. Navier–Stokes equations; 12. Motion planning for PDEs; 13. Adaptive control Numerical Methods in Optimization for PDEs; 14. Towards nonlinear PDEs; Scientific Computing Second edition Appendix. Bessel functions; Bibliography; Volume 1 Igor Griva Index. George Mason University, Virginia Germund Dahlquist Advances in Design and Control, 16 Royal Institute of Technology, Stockholm Stephen G. Nash 2008 247 x 174 mm 200pp George Mason University, Virginia and Åke Björck 978-0-89871-650-4 Hardback £58.00 Linköping University, Sweden and Ariela Sofer www.cambridge.org/9780898716504 George Mason University, Virginia This book from the authors of the classic Numerical Methods addresses Flexible graduate textbook that introduces the applications, theory, Stochastic Processes, the growing role of numerical methods Estimation, in science and engineering. With better and algorithms of linear and nonlinear organization and coverage than any optimization in a clear succinct style, and Control modern book in the field, it includes supported by numerous examples Jason L. Speyer topics not typically covered in numerical and exercises. It introduces important University of California, Los Angeles analysis texts (e.g. interval arithmetic realistic applications and explains how and Walter H. Chung and elementary functions). optimization can address them. University of California, Los Angeles Contents: Preface; Part I. Basics: Covers stochastic systems beginning ‘This work is a monumental 1. Optimization models; 2. Fundamentals with the foundations of probability and undertaking and represents the most of optimization; 3. Representation of linear ending with stochastic optimal control. comprehensive textbook survey of constraints; Part II. Linear Programming: Contents: Preface; 1. Probability theory; numerical analysis to date. It will be 4. Geometry of linear programming; 5. The 2. Random variables and stochastic an important reference in the field for simplex method; 6. Duality and sensitivity; processes; 3. Conditional expectations and many years to come.’ 7. Enhancements of the simplex method; discrete-time Kalman filtering; 4. Least Nicholas J. Higham, University of Manchester 8. Network problems; 9. Computational squares, the orthogonal projection lemma, complexity of linear programming; Contents: List of figures; List of tables; and discrete-time Kalman filtering; 10. Interior-point methods of linear List of conventions; Preface; 1. Principles 5. Stochastic processes and stochastic programming; Part III. Unconstrained of numerical calculations; 2. How to obtain calculus; 6. Continuous-time Gauss-Markov Optimization: 11. Basics of unconstrained and estimate accuracy; 3. Series, operators systems: continuous-time Kalman filter, optimization; 12. Methods for unconstrained and continued fractions; 4. Interpolation and stationarity, power spectral density, and the optimization; 13. Low-storage methods for approximation; 5. Numerical integration; Wiener filter; 7. The extended Kalman filter; unconstrained problems; Part IV. Nonlinear 6. Solving scalar nonlinear equations; 8. A selection of results from estimation Optimization: 14. Optimality conditions Bibliography; Index; Online appendix A. theory; 9. Stochastic control and the linear for constrained problems; 15. Feasible- Introduction to matrix computations; Online quadratic Gaussian control problem; point methods; 16. Penalty and barrier appendix B. A MATLAB multiple precision 10. Linear exponential Gaussian control and methods; Part V. Appendices: Appendix package; Online appendix C. Guide to estimation; Bibliography; Index. A. Topics from linear algebra; Appendix B. literature. Other fundamentals; Appendix C. Software; Advances in Design and Control, 17 2008 247 x 174 mm 746pp Bibliography; Index. 2008 247 x 174 mm 400pp 978-0-89871-644-3 Hardback £70.00 978-0-89871-655-9 Paperback £55.00 2009 247 x 174 mm 764pp www.cambridge.org/9780898716443 www.cambridge.org/9780898716559 978-0-89871-661-0 Hardback £61.00 www.cambridge.org/9780898716610 Introduction to Lagrange Multiplier Derivative-Free Boundary Control Approach to Optimization of PDEs Variational Problems Andrew R. Conn A Course on Backstepping and Applications IBM T. J. Watson Research Center, New York Designs Kazufumi Ito Katya Scheinberg Miroslav Krstic North Carolina State University IBM T. J. Watson Research Center, New York University of California, San Diego and Karl Kunisch and Luís N. Vicente and Andrey Smyshlyaev Karl-Franzens-Universität Graz, Austria Universidade de Coimbra, Portugal University of California, San Diego Analyses Lagrange multiplier theory The first contemporary comprehensive A clear and concise introduction to and demonstrates its impact on the treatment of optimization without backstepping, an elegant new approach development of numerical algorithms for derivatives. This text explains how to boundary control of partial differential variational problems in function spaces. sampling and model techniques are equations (PDEs). Contents: Preface; 1. Existence of Lagrange used in derivative-free methods and how Contents: List of figures; List of tables; multipliers; 2. Sensitivity analysis; 3. First they are designed to solve optimization Preface; 1. Introduction; 2. Lyapunov Order augmented Lagrangians for equality problems. It is designed to be readily stability; 3. Exact solutions to PDEs; and finite rank inequality constraints; accessible to both researchers and 4. Parabolic PDEs: reaction-advection- 4. Augmented Lagrangian methods those with a modest background in diffusion and other equations; 5. Observer for nonsmooth, convex optimization; computational mathematics. design; 6. Complex-valued PDEs: 5. Newton and SQP methods; 6. Augmented 2009 247 x 170 mm 295pp Schrödinger and Ginzburg–Landau Lagrangian-SQP methods; 7. The primal-dual 978-0-89871-668-9 Paperback £47.00 equations; 7. Hyperbolic PDEs: wave www.cambridge.org/9780898716689 equations; 8. Beam equations; 9. First- order hyperbolic PDEs and delay equations; 10. Kuramoto–Sivashinsky, Korteweg–de Vries, and other ‘exotic’ equations;

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active set method; 8. Semismooth Newton Feedback Systems Elementary Calculus of methods I; 9. Semismooth Newton methods Input-Output Properties II: applications; 10. Parabolic variational Financial Mathematics Charles A. Desoer inequalities; 11. Shape optimization; A. J. Roberts University of California, Berkeley Bibliography; Index. University of Adelaide and M. Vidyasagar Advances in Design and Control, 15 This book introduces the fascinating Tata Institute of Fundamental Research, area of financial mathematics and 2008 247 x 174 mm 360pp Mumbai, India 978-0-89871-649-8 Paperback £64.00 its calculus in an accessible manner www.cambridge.org/9780898716498 This book was the first and remains for undergraduate students. Using the only book to give a comprehensive little high-level mathematics, the treatment of the behaviour of linear author presents the basic methods for Approximation or nonlinear systems when they are evaluating financial options and building of Large-Scale connected in a closed-loop fashion, with financial simulations. the output of one system forming the Dynamical Systems Contents: Preface; List of algorithms; input of the other. Athanasios C. Antoulas 1. Financial indices appear to be stochastic Rice University Contents: Preface to the Classics edition; processes; 2. Ito’s stochastic calculus Preface; Acknowledgments; Note to the Approximation of Large-Scale Dynamical introduced; 3. The Fokker–Planck equation reader; List of symbols; 1. Memoryless describes the probability distribution; Systems provides a comprehensive nonlinearities; 2. Norms; 3. General picture of model reduction, combining 4. Stochastic integration proves Ito’s theorems; 4. Linear systems; 5. Applications formula; Appendix A. Extra MATLAB/SCILAB system theory with numerical of the small gain theorem; 6. Passivity; code; Appendix B. Two alternate proofs; linear algebra and computational Appendix A. Integrals and series; Bibliography; Index. considerations. It addresses the issue of Appendix B. Fourier transforms; Appendix Monographs on Mathematical Modeling and model reduction and the resulting trade- C. Convolution; Appendix D. Algebras; Computation offs between accuracy and complexity. Appendix E. Bellman-Gronwall Lemma; 2009 247 x 170 mm 140pp Special attention is given to numerical References; Index. 978-0-89871-667-2 Paperback £30.00 aspects, simulation questions, and Classics in Applied Mathematics www.cambridge.org/9780898716672 practical applications. 2009 247 x 170 mm 284pp 978-0-89871-670-2 Paperback £40.00 ‘… this book contains a wealth of www.cambridge.org/9780898716702 Graduate Textbook useful information and is the most authoritative presentation of the Introduction to the approximation techniques for large- UAV Cooperative Numerical Analysis scale dynamical systems available Decision and Control of Incompressible at the moment. The book is highly recommended to graduate students Challenges and Practical Viscous Flows and researchers in the fields of system Approaches William Layton and control theory, and numerical Steven Rasmussen University of Pittsburgh analysis.’ and Tal Shima A unified treatment of fluid mechanics, Petko Petkov, Mathematical Reviews Technion – Israel Institute of Technology, Haifa analysis and numerical analysis Contents: Preface; Part I. Introduction: Unmanned aerial vehicles (UAVs) appropriate for first year graduate 1. Introduction; 2. Motivating examples; are increasingly used in military students. Part II. Preliminaries: 3. Tools from matrix missions. This text is aimed at helping Contents: Foreword; Preface; theory; 4. Linear dynamical systems, Part practitioners, students, and academics 1. Mathematical preliminaries: energy and 1; 5. Linear dynamical systems, Part 2; alike to better understand what stress; 2. Approximating scalars; 3. Vector 6. Sylvester and Lyapunov equations; cooperative decision and control is and tensor analysis; 4. Approximating vector Part III. SVD-based Approximation and its applications and methods for functions; 5. The equations of fluid motion; Methods: 7. Balancing and balanced implementing algorithms that make 6. The steady Navier–Stokes equations; approximations; 8. Hankel-norm cooperative UAV operations possible. 7. Approximating steady flows; 8. The approximation; 9. Special topics in Contents: Preface; 1. Introduction; time-dependent Navier–Stokes equations; SVD-based approximation methods; 2. Challenges; 3. Single task tours; 9. Approximating time-dependent flows; Part IV. Krylov-based Approximation 4. Multiple assignments; 5. Simultaneous 10. Models of turbulent flow; Appendix. Methods: 10. Eigenvalue computations; multiple assignments; 6. Estimation Computational Science and Engineering 11. Model reduction using Krylov methods; algorithms for improved cooperation under 2008 247 x 174 mm 233pp Part V. SVD-Krylov Methods and Case uncertainty; 7. Effectiveness measures 978-0-89871-657-3 Paperback £43.00 / TBA Studies: 12. SVD-Krylov methods; 13. Case for operations in uncertain environments; www.cambridge.org/9780898716573 studies; 14. Epilogue; 15. Problems; Appendix A. MultiUAV simulation; Appendix Bibliography; Index. B. Path planning for UAVs; Index. A Unified Approach Advances in Design and Control, 6 Advances in Design and Control 2009 247 x 174 mm 510pp 2009 247 x 170 mm 198pp to Boundary 978-0-89871-658-0 Paperback £64.00 978-0-89871-664-1 Hardback £55.00 Value Problems www.cambridge.org/9780898716580 www.cambridge.org/9780898716641 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 19 method is unique in also yielding novel as if that were possible for a much sequences and applications; 19. Finite integral representations for linear PDEs. admired book. In particular, the new fields; 20. Algorithms for finite fields; chapter on case studies looks quite 21. Deterministic primality testing; • Unifies the most extensively used interesting with its useful applications. Appendix: Some useful facts; Bibliography; techniques for solving boundary value In addition, new treatments of new Index of notation; Index. problems for linear PDEs functions and features like nested 2008 247 x 174 mm 598pp 650 exercises • Includes a new approach to an functions, ODE as well as DDE 280 worked examples important medical imaging technique functions will be of great interest.’ 978-0-521-51644-0 Hardback £35.00 Floyd B. Hanson, Ph.D., Professor of www.cambridge.org/9780521516440 • Unique in presenting an extension of Mathematics, Department of Mathematics, the inverse scattering method from Statistics, and Computer Science, University of initial value problems to boundary Illinois at Chicago Textbook value problems Contents: Preface; 1. A brief tutorial; Quantum Computing CBMS-NSF Regional Conference Series in 2. Basics; 3. Distinctive features of MATLAB; Applied Mathematics, 78 for Computer 4. Arithmetic; 5. Matrices; 6. Operators 2008 247 x 174 mm 356pp and flow control; 7. M-files; 8. Graphics; Scientists 978-0-89871-651-1 Paperback £49.00 9. Linear algebra; 10. More on functions; Noson S. Yanofsky www.cambridge.org/9780898716511 11. Numerical methods Part I; 12. Numerical Brooklyn College, City University of New York methods Part II; 13. Input and output; and Mirco A. Mannucci Hidden Markov 14. Troubleshooting; 15. Sparse matrices; HoloMathics, LLC, Virginia 16. Further M-files; 17. Handle graphics; Models and Finally, a textbook that explains 18. Other data types and multidimensional quantum computing using techniques Dynamical Systems arrays; 19. The symbolic math toolbox; and concepts familiar to computer Andrew M. Fraser 20. Optimizing M-files; 21. Tricks and tips; scientists. Los Alamos National Laboratory 22. Case studies; Appendices; Bibliography; An introduction to hidden Markov Index. ‘The book has the potential to fill a models for the dynamical systems 2005 228 x 152 mm 406pp void that needs to be filled: to bring community. The book presents 978-0-89871-578-1 Hardback £30.00 the excitement of quantum computing www.cambridge.org/9780898715781 algorithms for using HMMs and explains to undergraduate computing majors, especially those with modest math the derivation of those algorithms. backgrounds.’ It provides introductory material for Professor Stephen Fenner, Department of undergraduate study in engineering, Computer Computer Science and Engineering, University mathematics, or science that includes of South Carolina work in probability, linear algebra and Science differential equations. Contents: 1. Complex numbers; 2. Complex vector spaces; 3. The leap from Contents: Preface; 1. Introduction; 2. Basic classical to quantum; 4. Basic quantum algorithms; 3. Variants and generalizations; Graduate Textbook theory; 5. Architecture; 6. Algorithms; 4. Continuous states and observations and A Computational 7. Programming languages; 8. Theoretical Kalman filtering; 5. Performance bounds and computer science; 9. Cryptography; a toy problem; 6. Obstructive sleep apnea; Introduction to 10. Information theory; 11. Hardware. Appendix A. Formulas for matrices and Number Theory Gaussians; Appendix B. Notes on software; 2008 253 x 177 mm 368pp 4 tones and Algebra 245 exercises Bibliography; Index. Second edition 978-0-521-87996-5 Hardback £38.00 2009 247 x 174 mm 143pp Victor Shoup www.cambridge.org/9780521879965 978-0-89871-665-8 Paperback £35.00 New York University www.cambridge.org/9780898716658 Introductory graduate-level text Graduate Textbook emphasizing algorithms and Recent Bestseller applications. This second edition now A Second Course in Textbook includes over 200 new exercises and Formal Languages and examples. MATLAB Guide Automata Theory Contents: Preface; Preliminaries; 1. Basic Second edition Jeffrey Shallit properties of the integers; 2. Congruences; University of Waterloo, Ontario Desmond J. Higham 3. Computing with large integers; 4. Euclid’s University of Strathclyde A textbook for a graduate course algorithm; 5. The distribution of primes; on formal languages and automata and Nicholas J. Higham 6. Abelian groups; 7. Rings; 8. Finite theory, building on prior knowledge of University of Manchester and discrete probability distributions; theoretical computer models. This second edition remains a lively, 9. Probabilistic algorithms; 10. Probabilistic concise introduction to the important primality testing; 11. Finding generators and Contents: 1. Review of formal languages features of MATLAB 7 and the Symbolic discrete logarithms in Z*p; 12. Quadratic and automata theory; 2. Combinatorics Math Toolbox. reciprocity and computing modular on words; 3. 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This first textbook on demonstrated by applying them to the topic explains these innovations Encyclopedia of Mathematics and its Applications, 127 concrete problems. carefully and shows the reader, whether 2009 228 x 152 mm 496pp 2 tones a student or a developer, how to build 2009 228 x 152 mm 216pp 12 line figures 12 tables 40 figures 168 exercises their own translation system. 978-0-521-51926-7 Hardback c. £65.00 978-0-521-88427-3 Hardback c. £40.00 Contents: Preface; Part I. Foundations: Publication June 2009 Publication July 2009 1. Introduction; 2. Words, sentences, www.cambridge.org/9780521519267 www.cambridge.org/9780521884273 corpora; 3. Probability theory; Part II. Core Methods: 4. Word-based models; 5. Phrase- New in Paperback based models; 6. Decoding; 7. Language Algorithmic Aspects models; 8. Evaluation; Part III. Advanced Geometric Folding of Graph Connectivity Topics: 9. Discriminative training; Algorithms Hiroshi Nagamochi 10. Integrating linguistic information; Kyoto University, Japan Linkages, Origami, Polyhedra 11. Tree-based models; Bibliography; Author and Toshihide Ibaraki index; Index. Erik D. Demaine Kwansei Gakuin University, Japan Massachusetts Institute of Technology 2009 247 x 174 mm 488pp 24 tones and Joseph O’Rourke The first really thorough book to discuss 70 exercises 143 figures this central notion in graph and network 978-0-521-87415-1 Hardback c. £35.00 Smith College, Massachusetts theory, emphasising its algorithmic Publication August 2009 Lavishly illustrated and entertaining aspects. www.cambridge.org/9780521874151 account of the surprising and useful Encyclopedia of Mathematics and its results of the maths of folding and Applications, 123 unfolding. Algebraic Geometry 2008 234 x 156 mm 392pp 1 table and Statistical ‘Demaine and O’Rourke are among 978-0-521-87864-7 Hardback £50.00 www.cambridge.org/9780521878647 Learning Theory the best-qualified authors for a book Sumio Watanabe on this subject; and the book that Tokyo Institute of Technology they have written is a delight … it Graduate Textbook is exceptionally clear and readable. Sure to be influential, this book lays It could be read for pleasure by Computational the foundations for the use of algebraic any mathematics undergraduate, Complexity geometry in statistical learning theory. and much of it (though not all) Many widely used statistical models by amateurs with a high school A Modern Approach are singular: mixture models, neural mathematics background … although Sanjeev Arora networks, HMMs, and Bayesian there are sections that some amateurs Princeton University, New Jersey networks are major examples. The will skip, the level is always kept and Boaz Barak theory achieved here underpins accurate as elementary as locally possible. Princeton University, New Jersey This book should be in all university Describes recent achievements and libraries, and many professional and classical results of computational amateur mathematicians will want to complexity theory, including interactive add it to their personal collections.’ proofs, PCP, derandomization, and Robert Dawson (Halifax), Zentralblatt Math quantum computation. It can be used Computer Science / General and Recreational Maths 21 as a reference, for self-study, or as a General and Naive Decision Making beginning graduate textbook. More than Mathematics Applied to the 300 exercises are included. Recreational Social World Contents: Part I. Basic Complexity T. W. Körner Classes: 1. The computational model – Maths University of Cambridge and why it doesn’t matter; 2. NP and NP How should one choose the best completeness; 3. 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Algebraic computation models; undergraduate degree in mathematics? book that will excite anyone prepared Part III. Advanced Topics: 17. Complexity This friendly companion eases beginning to open their mind to the ways in which a mathematical approach can of counting; 18. Average case students into real mathematical help us make better choices in an complexity: Levin’s theory; 19. Hardness thinking, unlocking important uncertain world.’ amplification and error correcting codes; techniques for effective mathematics Significance 20. Derandomization; 21. Pseudorandom so you can communicate with clarity, constructions: expanders and extractors; solve problems, and explore the world 2008 228 x 152 mm 400pp 17 tables 22. Proofs of PCP theorems and the Fourier of definitions, theorems and proofs with 405 exercises 10 worked examples 4 figures transform technique; 23. Why are circuit real confidence. 978-0-521-51616-7 Hardback £60.00 lower bounds so difficult?; Appendix A: 978-0-521-73163-8 Paperback £21.99 mathematical background. Contents: 0. Preface; Part I. Study eBook available Skills For Mathematicians: 1. Sets and 2009 253 x 215 mm 608pp 72 line figures www.cambridge.org/9780521516167 1 tone 6 tables 307 exercises functions; 2. Reading mathematics; 978-0-521-42426-4 Hardback £32.50 3. Writing mathematics I; 4. Writing Publication May 2009 mathematics II; 5. How to solve problems; New Series www.cambridge.org/9780521424264 Part II. How To Think Logically: 6. Making a statement; 7. Implications; 8. Finer points concerning implications; 9. Converse The New Martin Forthcoming and equivalence; 10. Quantifiers – For Gardner Mathematical Computation, all and There exists; 11. Complexity and negation of quantifiers; 12. Examples and Library Proof, Machine counterexamples; 13. Summary of logic; Series Editors: Donald J. Albers Mathematics Enters a New Age Part III. Definitions, Theorems and Proofs: Menlo College, California Gilles Dowek 14. Definitions, theorems and proofs; Gerald L. Alexanderson Ecole Polytechnique, Paris 15. How to read a definition; 16. How to Santa Clara University, California Translated by Pierre Guillot read a theorem; 17. Proof; 18. How to John H. Conway and Marion Roman read a proof; 19. A study of Pythagoras’ Princeton University, New Jersey Theorem; Part IV. Techniques of Proof: Richard K. Guy Mathematics has entered the age of the 20. Techniques of proof I: direct method; University of Calgary algorithm. How, why, what next? 2007 21. Some common mistakes; 22. Techniques Donald E. Knuth Grand Prix de Philosophie de l’Académie of proof II: proof by cases; 23. Techniques Stanford University, California Francaise. of proof III: Contradiction; 24. Techniques Peter L. Renz 2009 228 x 152 mm 200pp of proof IV: Induction; 25. 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Greek alphabet; B. added and old ones improved, and Commonly used symbols and notation; C. the bibliographies have been greatly How to prove that …; Index. expanded throughout. 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

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Hexaflexagons, Sphere Packing, Lewis MAA Book Probability Paradoxes, Carroll, and Reversi Proof and Other and the Tower of Hanoi Martin Gardner’s New Dilemmas Martin Gardner’s First Book of Mathematical Diversions Mathematics and Philosophy Mathematical Puzzles and Games Martin Gardner Bonnie Gold Martin Gardner Martin Gardner returns to charm readers Monmouth University, New Jersey This is the first book of the updated with the latest on packing spheres, and Roger Simons collection of Mathematical Games from Reversi, braids, polyominoes, board This collection of sixteen original essays Martin Gardner, the king of recreational games, and the puzzles of Lewis Carroll. is the first to explore a range of new mathematics. 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MAA Book Leibniz MAA Book The Contest An Intellectual Biography Who Gave you Problem Book IX Maria Rosa Antognazza the Epsilon? American Mathematics In this first intellectual biography of & Other Tales of Mathematical Competitions (AMC 12) 2001– Gottfried Wilhelm Leibniz (1646–1716), History 2007 Contests Maria Rosa Antognazza surveys the full Marlow Anderson Edited by David M. Wells range of the philosopher’s interests and Colorado College Pennsylvania State University activities and offers a unified portrait of Victor Katz and J. Douglas Faires a unique thinker, identifying the master University of the District of Columbia, Youngstown State University project that inspired and coordinated his Washington DC A compilation of 325 problems and huge range of apparently miscellaneous and Robin Wilson solutions previously featured in the endeavours. Keble College, Oxford American Mathematics Competitions for 2008 228 x 152 mm 652pp 8 line figures This book picks up the history of students of all abilities in American and 1 map mathematics from where Sherlock 978-0-521-80619-0 Hardback £25.00 Holmes in Babylon left it. The 40 Canadian high schools. A problem index www.cambridge.org/9780521806190 at the back of the book breaks major articles of Who Gave You the Epsilon? subject areas into subcategories and continue the story of the development cross-references for ease of use. MAA Book of mathematics into the nineteenth and twentieth centuries. It is ideal for those MAA Problem Book Series Uncommon 2008 228 x 152 mm 230pp interested in the history of mathematics. 978-0-88385-826-4 Paperback £25.99 Mathematical Spectrum www.cambridge.org/9780883858264 Excursions 2009 253 x 177 mm 440pp Polynomia and Related Realms 978-0-88385-569-0 Hardback £45.00 www.cambridge.org/9780883855690 Rigorous Mathematical Dan Kalman American University, Washington DC Thinking This text serves as a guide to little MAA Book Conceptual Formation in the known corners of the mathematical Mathematics Classroom landscape, not far from the main byways When Less is More James T. Kinard of algebra, geometry, and calculus. It is Visualizing Basic Inequalities Institute for Cognitive Literacy, Chicago for the seasoned mathematical traveller Claudi Alsina and Alex Kozulin who has visited these subjects many Universitat Politècnica de Catalunya, Barcelona International Center for the Enhancement of and Roger Nelsen Learning Potential, Jerusalem times and is ready to venture abroad off the beaten track. Lewis and Clark College, Portland The first book to present mathematics Dolciani Mathematical Expositions An introduction to basic inequalities teaching from Vygotsky’s socio-cultural in mathematics (including numbers, theory of learning perspective. The 2009 253 x 177 mm 282pp 978-0-88385-341-2 Hardback £30.00 functions and geometry) motivated and authors introduce a RMT program that www.cambridge.org/9780883853412 illustrated by drawings that make it helps students to gain general thinking possible to ‘see’ the results in an elegant skills essential for all types of problem manner. Applications of the inequalities, solving. They show how mathematics MAA Book historical details, and exercises for the standards can be reached by students Problems from reader (with solutions) are also included. considered to be ‘underachievers’. Murray Klamkin Dolciani Mathematical Expositions 2008 228 x 152 mm 216pp 34 line figures The Canadian Collection 2009 247 x 170 mm 250pp 2 tones 978-0-88385-342-9 Hardback £30.00 978-0-521-87685-8 Hardback £40.00 Andy Liu www.cambridge.org/9780883853429 978-0-521-70026-9 Paperback £15.99 University of Alberta eBook available and Bruce Shawyer www.cambridge.org/9780521876858 Memorial University of Newfoundland Recent Bestseller A collection of problems proposed Music: A Mathematical Ludic Proof by Murray Klamkin over his career. It contains the ‘quickies’ (problems with Offering Greek Mathematics and the Dave Benson Alexandrian Aesthetic quick and neat solutions) he proposed in ‘Crux Mathematicorum,’ his longer University of Aberdeen Reviel Netz Benson provides a wealth of information Stanford University, California problems, and also problems which were proposed in tribute to him after he died. for the teacher, the student, or the Describes the relationship between Solutions are provided. interested amateur to understand, science and poetry in the Hellenistic MAA Problem Book Series at varying levels of technicality, period by analysing the stylistic features the interplay between two ancient of Hellenistic mathematics and then 2009 253 x 177 mm 266pp 978-0-88385-828-8 Hardback £30.00 disciplines. A must-have book if you showing how they can be understood www.cambridge.org/9780883858288 want to know about the music of the within the context of Hellenistic poetry. spheres or digital music and much in The result transforms our understanding between. of the origins of Western mathematics. 2009 228 x 152 mm 272pp ‘… informative and well-written … 978-0-521-89894-2 Hardback £55.00 Not only does this book cover basic Publication May 2009 material thoroughly, it also presents www.cambridge.org/9780521898942 much of interest to those already familiar with the area of math and

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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 25

A Chang, Der-Chen...... 5 Falkovich, Gregory...... 9 Acta Numerica 2008...... 8 Channel Codes...... 4 Feedback Systems...... 18 Actuarial Mathematics for Life Chaos and Coarse Graining in Statistical Financial Derivatives...... 15 Contingent Risks...... 15 Mechanics...... 12 Financial Products...... 15 Adámek, J...... 4 Chen, W. W. L...... 5 First Course in Order Statistics, A...... 16 Advances in Credit Risk Modelling and Chung, Walter H...... 17 First Course in Statistical Programming Corporate Bankruptcy Prediction...... 15 Classical Mechanics...... 9 with R, A...... 13 Aggregation Functions...... 20 Combinatorics: The Rota Way...... 2 First Course in String Theory, A...... 11 Aha! Solutions...... 22 Compendium of Partial Differential First Course in the Numerical Analysis of Algebraic Geometry and Statistical Equation Models, A...... 8 Differential Equations, A...... 7 Learning Theory...... 20 Computation, Proof, Machine...... 21 Flajolet, Philippe...... 2 Algebraic Theories...... 4 Computational Complexity...... 20 Flannery, Brian P...... 8 Algebraic Theory of Differential Computational Continuum Mechanics...... 9 Fokas, Athanassios S...... 18 Equations...... 11 Computational Introduction to Number Foster, Michael R...... 9 Algorithmic Aspects of Graph Theory and Algebra, A...... 19 Fraser, Andrew M...... 19 Connectivity...... 20 Concentration of Measure for the Freedman, David...... 13 Algorithmic Number Theory...... 6 Analysis of Randomized Algorithms...... 20 Friz, Peter...... 1 Alsina, Claudi...... 23 Concepts and Practice of Mathematical Functions of Matrices...... 16 Amabili, Marco...... 10 Finance, The...... 14 Fundamentals of Fluid Power Control.....10 Analysis in Positive Characteristic...... 2 Conn, Andrew R...... 17 Analytic Combinatorics...... 2 Contest Problem Book IX, The...... 23 G Contest Problem Book VIII, The...... 22 Analytic Number Theory...... 5 Galois Groups and Fundamental Groups...7 Continuum Mechanics and Anderson, Marlow...... 23 Galway, William F...... 6 Thermodynamics...... 10 Antognazza, Maria Rosa...... 23 Games, Scales and Suslin Cardinals: The Cooper, S. Barry...... 4 Antoulas, Athanasios C...... 18 Cabal Seminar Volume I...... 3 Cortina, Jeronimo...... 13 Applebaum, David...... 1 García-Prada, Oscar...... 5 Creative Mathematics...... 22 Applied Solid Mechanics...... 9 Gardner, Martin...... 22 Approximation of Large-Scale Dynamical Gawedzki, Krzysztof...... 9 Systems...... 18 D Gelman, Andrew...... 13 Arnold, Barry C...... 16 Dahlquist, Germund ...... 17 Generalized Inverses of Linear Arora, Sanjeev...... 20 Dalton, Bill...... 15 Transformations...... 16 Ascher, Uri M...... 16 Daniel, James...... 15 Geological Fluid Dynamics...... 10 Data Analysis and Graphics Using R...... 14 Geometric Folding Algorithms...... 20 B Davenport, H...... 5 Geometry of Moduli Spaces of Sheaves, Baaquie, Belal E...... 14 Davison, A. C...... 12 The...... 5 Balakrishnan, N...... 16 de Faria, Edson...... 11 Gesztesy, Fritz...... 11 Barak, Boaz...... 20 de Melo, Welington...... 11 Geuvers, Herman...... 4 Bautista, R...... 7 Delbourgo, Daniel...... 6 Glynn, Peter W...... 12 Bayart, Frédéric...... 2 Demaine, Erik D...... 20 Gold, Bonnie...... 22 Bayesian Nonparametrics...... 13 Desoer , Charles A...... 18 Goldbart, Paul...... 11 Baz, Jamil...... 15 Diamond, Harold G...... 6 Gonnet, Gaston...... 11 Beineke, Lowell W...... 3 Dickson, David C. M...... 15 Gowers, W. T...... 5 Bell, John L...... 3 Differential Tensor Algebras and their Grabisch, Michel...... 20 Benjamin, Arthur T...... 6 Module Categories...... 7 Grandis, Marco...... 5 Benson, Dave...... 24 Digital Image Processing for Medical Graph Theory...... 3 Biscuits of Number Theory...... 6 Applications...... 12 Gregory, R. Douglas...... 9 Björck, Åke ...... 17 Directed Algebraic Topology...... 5 Griewank, Andreas...... 16 Blath, Jochen...... 1 Discontinuous Galerkin Methods Griffiths, Graham W...... 8 Borcherdt, Roger D...... 10 for Solving Elliptic and Parabolic Griva, Igor...... 17 Borkar, Vivek S...... 13 Equations...... 16 Gross, Jonathan L...... 3 Boundary Control of PDEs...... 17 Dougherty, Geoff...... 12 Groups and Analysis...... 2 Bradlow, Steven B...... 5 Dowek, Gilles...... 21 Groups, Graphs and Trees...... 6 Brambila-Paz, Leticia...... 5 Dubhashi, Devdatt...... 20 Guide to Complex Variables, A...... 2 Braun, John...... 14 Durrett, Rick...... 13 Guillot, Pierre...... 21 Braun, W. John...... 13 Dynamics of Linear Operators...... 2 Brown, Ezra...... 6 H Buhler, J.P...... 6 E Haddow, James...... 10 Bühler, Oliver...... 10 Edixhoven, Bas...... 6 Hadjiliadis, Olympia...... 14 Elementary Calculus of Financial Halberstam, H...... 5, 6 C Mathematics...... 18 Handbook of Practical Logic and Calculus...... 2 Elementary Probability for Applications...13 Automated Reasoning...... 20 Calculus Deconstructed...... 2 Elliptic Curves and Big Galois Hardy, Mary R...... 15 Calin, Ovidiu...... 5 Representations...... 6 Harrison, John...... 20 Cambon, Claude...... 9 Erickson, Martin...... 22 Hensher, David A...... 15 Campbell, Stephen L...... 16 Evaluating Derivatives ...... 16 Herron, Isom H...... 9 Cardy, John...... 9 Hexaflexagons, Probability Paradoxes, Carter, Nathan ...... 6 F and the Tower of Hanoi...... 22 Hidden Markov Models and Dynamical Castiglione, Patrizia...... 12 Faires, J. Douglas...... 22, 23 Systems...... 19 Chacko, George...... 15 Falcioni, Massimo...... 12

eBooks available at www.cambridge.org/online 26 Index

Higham, Desmond J...... 19 Löwe, Benedikt...... 3 O Higham, Nicholas J...... 16, 19 Ludic Proof...... 23 O’Leary, Dianne P...... 16 Higher Arithmetic, The...... 5 Lun, Desmond...... 4 O’Rourke, Joseph...... 20 Higher-Dimensional Sieve Method, A...... 6 Ockendon, John...... 9 Hilbert Transforms...... 1 M Origami, Eleusis, and the Soma Cube...... 22 Hjort, Nils Lid...... 13 MacCallum, Malcolm A. H...... 11 Ho, Tracey...... 4 Maindonald, John...... 14 Holden, Helge...... 11 P Mannucci, Mirco A...... 19 Holmes, Chris...... 13 Panconesi, Alessandro...... 20 Marcus, Daniel...... 3 Homogeneous Turbulence Dynamics...... 9 Pap, Endre...... 20 Marichal, Jean-Luc...... 20 Homsy, G. M...... 8 Partial Differential Equations in Fluid Markov Chains and Stochastic Stability...12 Houston, Kevin...... 21 Dynamics...... 9 Mashreghi, Javad...... 1 How to Think Like a Mathematician...... 21 Phillips, Owen M...... 10 Mathematical Interest Theory...... 15 Howell, Peter...... 9 Pillay, Anand...... 4 Mathematical Tools for One- Huczynska, Sophie...... 4 Poor, H. Vincent...... 14 Dimensional Dynamics...... 11 Huybrechts, Daniel ...... 5 Press, William H...... 8 Mathematics for Physics...... 11 Prest, Mike...... 7 Matheron, Étienne...... 2 Primer of Infinitesimal Analysis, A...... 3 I MATLAB Guide...... 19 Probability and Statistics by Example...... 12 Ibaraki, Toshihide...... 20 Meier, John...... 6 Problems from Murray Klamkin...... 23 Interest Rates and Coupon Bonds in Mesiar, Radko...... 20 Proof and Other Dilemmas...... 22 Quantum Finance...... 14 Meyer, Carl D...... 16 Purity, Spectra and Localisation...... 7 Introduction to Continuum Mechanics...... 9 Meyn, Sean...... 12 Introduction to Derivative-Free Michor, Johanna...... 11 Optimization...... 17 Mikhailov, Alexander V...... 11 Q Introduction to the Numerical Analysis Mitchell, James D...... 4 Quantitative Tour of the Social Sciences, of Incompressible Viscous Flows...... 18 Modern Coding Theory...... 4 A...... 13 Iserles, A...... 8 Modular Forms on Schiermonnikoog...... 6 Quantum Computing for Computer Iserles, Arieh...... 7 Moduli Spaces and Vector Bundles...... 5 Scientists...... 19 Ito, Kazufumi ...... 17 Monster Group and Majorana Quickest Detection...... 14 Ivanov, A. A...... 6 Involutions, The...... 6 Moonen, Ben...... 6 R J Mörters, Peter...... 1 Ramanan, S...... 5 Mounfield, C. C...... 14 Jones, Stewart...... 15 Rasmussen, Steven...... 18 Müller, Peter...... 13 Joshi, Mark S...... 14 Representation Theorems in Hardy Spaces.1 Multidimensional Stochastic Processes Richardson, Tom...... 4 as Rough Paths...... 1 Rigorous Mathematical Thinking...... 23 K Multimedia Fluid Mechanics...... 8 Rivière, Béatrice M...... 16 Kalman, Dan...... 23 Murdoch, Duncan J...... 13 Roberts, A. J...... 18 Katz, Victor ...... 23 Music: A Mathematical Offering...... 24 Roman, Marion...... 21 Kechris, Alexander S...... 3 Roney-Dougal, Colva M...... 4 Kelbert, Mark...... 12 N Rosick , J...... 4 Kendig, Keith...... 22 Nagamochi, Hiroshi...... 20 Rota, Gian-Carlo...... 2 Kinard, James T...... 23 Nagaraja, H. N...... 16 Ryan, William...... 4 King, Frederick W...... 1 Nair, Sudhakar...... 9 Kochubei, Anatoly N...... 2 Naive Decision Making...... 21 Kock, Anders...... 7 S Nash, Stephen G...... 17 Koehn, Philipp...... 20 Sagaut, Pierre...... 9 Nazarenko, Sergey...... 9 Körner, T. W...... 21 Salmerón, L...... 7 Nelsen, Roger...... 23 Kozulin, Alex...... 23 Scheinberg, Katya ...... 17 Network Coding...... 4 Kozyreff, Gregory...... 9 Scheutzow, Michael...... 1 Netz, Reviel...... 23 Krantz, Steven G...... 2 Schiesser, William E...... 8 Nitecki, Zbigniew H...... 2 Krenk, Steen...... 10 Schmidt, W. M...... 5 Non-equilibrium Statistical Mechanics Krstic, Miroslav...... 17 Scholl, Ralf...... 11 and Turbulence...... 9 Kung, Joseph P. S...... 2 Scientific Computation...... 11 Non-linear Modeling and Analysis of Kunisch, Karl...... 17 Scientific Computing with Case Studies...16 Solids and Structures...... 10 Second Course in Formal Languages Nonlife Actuarial Models...... 15 and Automata Theory, A...... 19 L Nonlinear Vibrations and Stability of Sedgewick, Robert...... 2 Lagrange Multiplier Approach to Shells and Plates...... 10 Segal, Dan...... 7 Variational Problems and Applications .17 Numerical Methods for Evolutionary Shabana, Ahmed A...... 9 Layton, William...... 18 Differential Equations...... 16 Shallit, Jeffrey...... 19 Lehn, Manfred...... 5 Numerical Methods in Scientific Shawyer, Bruce...... 23 Lehrer, Gustav I...... 7 Computing...... 17 Shima, Tal...... 18 Leibniz...... 23 Numerical Recipes...... 8 Shoup, Victor...... 19 Lesne, Annick...... 12 Numerical Recipes Source Code CD-ROM.8 Simons, Roger...... 22 Lévy Processes and Stochastic Calculus.....1 Numerical Recipes with Source Code Simpson, Stephen G...... 3 Lin, Shu...... 4 CD-ROM...... 8 Sink or Float...... 22 Linear and Nonlinear Optimization...... 17 Numerical Solution of Hyperbolic Partial Smyshlyaev, Andrey...... 17 Liu, Andy...... 23 Differential Equations...... 10 Sofer, Ariela...... 17 Logic Colloquium 2006...... 4 Index 27

Soliton Equations and their Algebro- Torrence, Eve A...... 7 W Geometric Solutions...... 11 Trangenstein, John A...... 10 W. T. Koiter’s Elastic Stability of Solids Speyer, Jason L...... 17 Trends in Stochastic Analysis...... 1 and Structures...... 9 Sphere Packing, Lewis Carroll, and Tse, Yiu-Kuen...... 15 Walker, Stephen...... 13 Reversi...... 22 Tucker, Thomas W...... 3 Wall, H. S...... 22 Spivak, Michael...... 2 Tweedie, Richard L...... 12 Walther, Andrea...... 16 Statistical Machine Translation...... 20 Watanabe, Sumio...... 20 Statistical Models...... 12, 13 U Waters, Howard...... 15 Steel, John R...... 3 UAV Cooperative Decision and Control...18 Watton, John...... 10 Stevenhagen, P...... 6 Uncommon Mathematical Excursions...... 23 Waves and Mean Flows...... 10 Stochastic Approximation...... 13 Unified Approach to Boundary Value Wegner, Joanne...... 10 Stochastic Processes, Estimation, and Problems, A...... 18 Wells, David M...... 22, 23 Control...... 17 Unitary Reflection Groups...... 7 When Less is More...... 23 Stone, Michael...... 11 Urbanke, Ruediger...... 4 Who Gave you the Epsilon?...... 23 Student’s Introduction to Wilson, Robin...... 23 MATHEMATICA, The...... 7 Wilson, Robin J...... 3 Sub-Riemannian Geometry...... 5 V Words...... 7 Subsystems of Second Order Arithmetic....3 Vaaler, Leslie...... 15 Suhov, Yuri...... 12 Väänänen, Jouko...... 4 Surveys in Combinatorics 2009...... 4 van der Geer, Gerard...... 6 Y Synthetic CDOs...... 14 van der Heijden, Arnold M. A...... 9 Yan, Catherine H...... 2 Synthetic Geometry of Manifolds...... 7 Vaughan, R. C...... 5 Yanofsky, Noson S...... 19 Szamuely, Tamás...... 7 Vetterling, William T...... 8 Vicente, Luís N...... 17 Z T Victoir, Nicolas...... 1 Zaboronski, Oleg V...... 9 Vidyasagar, M...... 18 Taylor, Donald E...... 7 Zuazua, R...... 7 Viscoelastic Waves in Layered Media...... 10 Tent, Katrin...... 2 Zwiebach, Barton...... 11 Visual Group Theory...... 6 Teschl, Gerald...... 11 Vitale, E. M...... 4 Teukolsky, Saul A...... 8 Vulpiani, Angelo...... 12 Topics in Topological Graph Theory...... 3 Torrence, Bruce F...... 7

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Mathematics 2009 Cambridge University Press MULTIMEDIA FLUID MECHANICS, Second Edition al. etHomsy G. M. Homsy et al. Allows students to: • Gain insight into and develop intuition about fluid flows • See the mathematical relationships brought to life through movies Customer Services Bookshop • Conduct simulations to show the effect of parameter variation.

This completely new edition, now on DVD, has: FLUIDMECHANICS MULTIMEDIA • Twice the coverage, with new modules on turbulence, control volumes, Cambridge University Press Bookshop 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 occupies the historic site of 1 Trinity • Dozens of new interactive demonstrations and animations Additional new features: Booksellers • Much-improved navigation via side bars that provide rapid overview of modules and guided browsing Street, Cambridge CB2 1SZ, where • Media libraries giving a snapshot of movies, each with descriptive labels • Facility to create movie playlists, which are invaluable in teaching For order processing and customer service, please contact: the complete range of titles is on sale. • Higher-resolution graphics, with full- or part-screen viewing options MULTIMEDIA G. M. Homsy, University of California, Santa Barbara; H. Aref, Virginia Praise for the first edition: Polytechnic Institute and Technical FLUID MECHANICS Catherine Atkins Phone + 44 (0)1223 325566 / 325577 “Homsy and his colleagues have now provided us with a University of Denmark; K. S, Breuer, Bookshop Manager: Cathy Ashbee Brown University; John W. M. Bush, new and powerful teaching aid... This CD is an ambitious Massachusetts Institute of project, and, in my view, it has been accomplished with Technology; Christophe Clanet, Ecole Second Edition remarkable success ... I have no doubt that this CD-ROM Polytechnique, Paris; Marc Fermigier, Fax + 44 (0)1223 325959 / 325151 Phone + 44 (0)1223 333333 should be regarded as a ‘set text’ for viscous fluid ESPCI, Paris; Simone Hochgreb, mechanics courses at the undergraduate or starting University of Cambridge; J. R. Koseff, • A perfect complement to any course in Fluid Mechanics graduate levels.” –Journal of Fluid Mechanics Stanford University; B. R. Munson, Email [email protected] Fax + 44 (0)1223 332954 Iowa State University; K. G. Powell, • Now with four times more movies “… a superb rendition of some of the most important University of Michigan; David Quere,

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Cambridge University Press MULTIMEDIA FLUID MECHANICS, Second Edition al. etHomsy G. M. Homsy et al. Allows students to: • Gain insight into and develop intuition about fluid flows • See the mathematical relationships brought to life through movies Customer Services Bookshop • Conduct simulations to show the effect of parameter variation.

This completely new edition, now on DVD, has: FLUIDMECHANICS MULTIMEDIA • Twice the coverage, with new modules on turbulence, control volumes, Cambridge University Press Bookshop 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 occupies the historic site of 1 Trinity • Dozens of new interactive demonstrations and animations Additional new features: Booksellers • Much-improved navigation via side bars that provide rapid overview of modules and guided browsing Street, Cambridge CB2 1SZ, where • Media libraries giving a snapshot of movies, each with descriptive labels • Facility to create movie playlists, which are invaluable in teaching For order processing and customer service, please contact: the complete range of titles is on sale. • Higher-resolution graphics, with full- or part-screen viewing options MULTIMEDIA G. M. Homsy, University of California, Santa Barbara; H. Aref, Virginia Praise for the first edition: Polytechnic Institute and Technical FLUID MECHANICS Catherine Atkins Phone + 44 (0)1223 325566 / 325577 “Homsy and his colleagues have now provided us with a University of Denmark; K. S, Breuer, Bookshop Manager: Cathy Ashbee Brown University; John W. M. Bush, new and powerful teaching aid... This CD is an ambitious Massachusetts Institute of project, and, in my view, it has been accomplished with Technology; Christophe Clanet, Ecole Second Edition remarkable success ... I have no doubt that this CD-ROM Polytechnique, Paris; Marc Fermigier, Fax + 44 (0)1223 325959 / 325151 Phone + 44 (0)1223 333333 should be regarded as a ‘set text’ for viscous fluid ESPCI, Paris; Simone Hochgreb, mechanics courses at the undergraduate or starting University of Cambridge; J. R. Koseff, • A perfect complement to any course in Fluid Mechanics graduate levels.” –Journal of Fluid Mechanics Stanford University; B. R. Munson, Email [email protected] Fax + 44 (0)1223 332954 Iowa State University; K. G. Powell, • Now with four times more movies “… a superb rendition of some of the most important University of Michigan; David Quere,

concepts in fluid mechanics… This reviewer estimates ESPCI and Ecole Polytechnique, Paris; Edition Second • Twice as many topics covered the ration (educational value to cost) to be (almost) J. J. Riley, University of Washington; [email protected] Email [email protected] infinite… this reviewer highly recommends the CD C. R. Robertson, Stanford University; • Now more than 20 virtual labs and simulations– to instructors as well as students… Multimedia Fluid A. J. Smits, Princeton University; S. T. Thoroddsen, National University a threefold increase Mechanics is an excellent study-companion… it is also of Singapore; J. M. Wallace, University [email protected] a bargain.” – Applied Mechanics Review of Maryland. • Much-improved navigation • Now compatible with Windows XP and Mac OSX 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 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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