Mathematics Catalogue 2016 by Cambridge University Press

Mathematics cambridge.org/mathematics2016

2016

Welcome to the Mathematics books catalogue 2016. Here you will find new and forthcoming titles, representing the highest level of academic research from renowned authors. Our highlights this year include The G. H. Hardy Reader, Prime Numbers and the Riemann Hypothesis, Fourier Analysis and Hausdorff Dimension, and Twelve Landmarks of Twentieth-Century Analysis. Our publications are available in a variety of formats, including ebooks and print, as well as online collections for institutional purchase via ebooks.cambridge.org. We also publish a range of leading journals including Acta Numerica and from 2016 we will be publishing the Nayoya Mathematical Journal. You can recommend our books and online collections to your librarian by filling out the form at the back of this catalogue. To see more book listings, product information, preview extracts and reviews, and to find out which conferences we are attending, you can find us online at www.cambridge.org/ mathematics2016. You can also keep up to date with the latest news and author views from our academic blog at http://www.cambridgeblog.org/category/mathematics/. We hope that you enjoy reading about our latest publications. For queries, suggestions or proposals, you can find a list of useful contacts at the back of this catalogue.

Be the first to hear about the academic products in your area of interest and receive 20% off your first online order

How to order books In the UK, Europe and rest of the world: www.cambridge.org/mathematics2016 +44 (0)1223 325566 internationaltrade2@cambridge.org In the Americas:

Cambridge Alerts

www.cambridge.org/mathematics2016 +1 212 924 3900 customer_service@cambridge.org

see page 1

Contents General and recreational mathematics 1 Logic, categories and sets

Algebra 2 Number theory

see page 3

Discrete mathematics, information theory and coding theory 4 Abstract analysis

Real and complex analysis

Topology and geometry

Differential and integral equations, dynamical systems and control

Mathematical physics

see page 7

Mathematical modelling and methods 12 Fluid dynamics and solid mechanics 13 13

Optimization, OR and risk analysis 14 Mathematical finance Also of interest

“There is a fine balance of methods of ‘hard’ and ‘soft’ analysis, which are often beautifully combined. The style is vivid and even entertaining at times ... [The review] can only give a glimpse of what this beautifully written, rich and almost unique monograph contains.” Zentralblatt MATH

“[makes] you want to read and learn ... those who love analysis and beautiful demonstrations will read and re-read with pleasure and profit.” Gazette des mathématiciens

Cover illustration: Image courtesy of Trinity College Library, Cambridge.

Information on related journals Inside back cover Cover designed by Zoe Naylor.

H. Queffélec shared his academic career between the universities of Paris-Sud and, later, Lille, where he is now an emeritus professor. He has written around 40 research papers in harmonic analysis and related probabilistic or topological methods, as well as in number theory (Dirichlet series) and operator theory – more specifically, composition operators and their approximation numbers. He has also written five textbooks and a research book on Banach spaces and probabilistic methods (in collaboration with D. Li). Queffélec has served on the committees for selecting secondary school professors (“Agrégation”), and for hiring university researchers. He was also a member of the CNU (National Council of Universities in France) which deals with the promotion of university members.

see page 8

TWELVE LANDMARKS OF

This edition extends the original French edition of 2009 with a new chapter on partitions, including the Hardy–Ramanujan theorem, and a significant expansion of the existing chapter on the Corona problem.

D. Choimet has spent all of his academic career in the French “Classes préparatoires”, an intensive two-year undergraduate programme leading to a nationwide competitive examination for enrolment in one of the “Grandes Écoles”. He currently teaches at the Lycée du Parc in Lyon, preparing students for the Écoles Normales Supérieures, the École Polytechnique and many Graduate Engineering Schools. Choimet is also a member of the jury of the “Agrégation”, a competitive examination leading to professorship positions.

Twentieth-Century Analysis

History of mathematics

The striking theorems showcased in this book are among the most profound results of twentieth-century analysis. The authors’ original approach combines rigorous mathematical proofs with commentary on the underlying ideas to provide a rich insight into these landmarks in mathematics. Results ranging from the proof of Littlewood’s conjecture to the Banach –Tarski paradox have been selected for their mathematical beauty as well as their educative value and historical role. Placing each theorem in historical perspective, the authors paint a coherent picture of modern analysis and its development, whilst maintaining mathematical rigour with the provision of complete proofs, alternative proofs, worked examples, and more than 150 exercises and solution hints.

Choimet and Queffélec

Computational science

9781107650343 Choimet & Queffélec PB C M Y K

Numerical analysis

TWELVE LANDMARKS OF

Twentieth-Century Analysis D. Choimet and H. Queffélec

Featured authors Barry Mazur, Harvard University, Massachusetts William Stein, University of Washington Authors of Prime Numbers and the Riemann Hypothesis We wrote our book to explain – in the most basic terms – the importance of the Riemann Hypothesis, one of the major unsolved problems in mathematics. We do this largely by displaying – visually, in graphs – the extraordinary phenomena offered by prime numbers, phenomena that lead to wonder and curiosity. I was delighted to write this book with William Stein, the developer of SageMath and one of the leading computational number theorists. We want to reach readers who have little background but general interest in mathematics, but we also want to engage readers with higher levels of mathematical experience. Our book comes, for that reason, in four parts, the first part meant to be a full introduction to the mystery of prime numbers and the essential reasons why mathematicians seek to solve this mystery. It is also meant to invite readers, particularly those who have little background, to experiment, to ask questions, to pay attention to the phenomena, and to enjoy it all, as we do.

Carola-Bibiane Schönlieb, Author of Partial Differential Equation Methods for Image Inpainting This book is concerned with digital image processing techniques that use partial differential equations (PDE) for the task of image ‘inpainting,’ an artistic term for virtual image restoration or interpolation, whereby missing or occluded parts in images are completed based on information provided by intact parts. Computer graphic designers, artists and photographers have long used manual inpainting to restore damaged paintings or manipulate photographs. Today, mathematicians apply powerful methods based on PDE to automate this task. This book introduces the mathematical concept of PDE for virtual image restoration. It gives the full picture, from the first modelling steps originating in Gestalt theory and arts restoration to the analysis of resulting PDE models, numerical realisation and real world application. This broad approach also gives insight into functional analysis, variational calculus, optimisation and numerical analysis and will appeal to researchers and graduate students in mathematics with an interest in image processing and mathematical analysis.

Visit www.cambridge.org/authorhub for a range of step-by-step guides for authors

General and recreational mathematics

General and recreational mathematics Highlight

The Once and Future Turing Computing the World Edited by S. Barry Cooper University of Leeds

and Andrew Hodges University of Oxford

Alan Turing made a seminal contribution to logic, computation, computer science, artificial intelligence, cryptography and theoretical biology. The articles here, by outstanding writers and thinkers, reflect on these contributions, how the subjects have developed since then, and how they might develop still further. Five themes are explored: language, universality and computation; computing and the brain; computing life and morphogenesis; quantum computing; and the challenge of incomputability. These essays will provoke and engross the reader who wishes to understand better the lasting significance of one of the twentieth century’s deepest thinkers. Contributors: S. Barry Cooper, Andrew Hodges, Martin Davis, J. M. E. Hyland, Andrew R. Booker, Ueli Maurer, Kanti V. Mardia, Stephen Wolfram, Christof Teuscher, Douglas Richard Hofstadter, Philip K. Maini, Thomas E. Woolley, Eamonn A. Gaffney, Ruth E. Baker, Richard Gordon, Stuart Kauffman, Scott Aaronson, Solomon Feferman, P. D. Welch, Roger Penrose 2016 247 x 174 mm 410pp 978-1-107-01083-3 Hardback c. £64.99 / c. US$100.00 978-0-521-28250-5 Paperback c. £24.99 / c. US$39.99 Publication March 2016 For all formats available, see

www.cambridge.org/9781107010833

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

Translated by Pierre Guillot and Marion Roman

Computation, calculation, algorithms – all have played an important role in mathematical progress from the beginning – but behind the scenes, their contribution was obscured in the enduring mathematical literature. To understand the future of mathematics, this fascinating book returns to its past,

tracing the hidden history that follows the thread of computation. ‘In this pithy, award-winning account of the growing role of computation in mathematics, Gilles Dowek adds further evidence, if any were needed, that the Age of the Algorithm is upon us. A master storyteller, the author takes the reader on an exhilarating journey through the history of mathematics, as he explains, in engaging, vivid prose, why to prove is to compute. A delightful read brimming with big ideas.’ Bernard Chazelle, Princeton University 2015 216 x 138 mm 158pp 6 b/w illus. 978-0-521-11801-9 Hardback £60.00 / US$120.00

Journal for the Philosophy of Science, that forms the greater part of this book, will be eager to read the supplementary material … the book, as it stands, is rich and stimulating, and, unlike most writings on the philosophy of mathematics, succeeds in making excellent use of detailed observations about mathematics as it is actually practised.’ Michael Dummett, Nature Cambridge Philosophy Classics

2015 228 x 152 mm 196pp 27 b/w illus. 2 tables 978-1-107-11346-6 Hardback £59.99 / US$89.99 For all formats available, see

www.cambridge.org/9781107113466

978-0-521-13377-7 Paperback £24.99 / US$39.99

The G. H. Hardy Reader

For all formats available, see

Edited by Donald J. Albers

www.cambridge.org/9780521118019

Dover Publications, California

THE ONCE AND FUTURE

TURING COMPUTING THE WORLD ED ITED BY

S. BA RRY CO O PER A N D ANDREW HODGES

Gerald L. Alexanderson available in Paperback

Alan M. Turing Centenary Edition Sara Turing Afterword by John F. Turing Foreword by Lyn Irvine and Martin Davis

Containing never-before-published material, this fascinating account sheds new light on one of the greatest figures of the twentieth century.

Santa Clara University, California

and William Dunham Bryn Mawr College, Pennsylvania

G. H. Hardy ranks among the great mathematicians of the twentieth century, doing essential research in number theory and analysis. This book is a feast of Hardy’s writing, featuring articles ranging from the serious to the humorous. The G. H. Hardy Reader is a worthy introduction to an extraordinary individual. Spectrum

2014 216 x 140 mm 194pp 7 b/w illus. 978-1-107-52422-4 Paperback £9.99 / US$15.99

2016 228 x 152 mm 380pp 24 b/w illus. 978-1-107-13555-0 Hardback c. £50.00 / c. US$85.00

Also available 978-1-107-02058-0 Hardback £19.99 / US$29.99

978-1-107-59464-7 Paperback c. £22.99 / c. US$34.99

For all formats available, see

www.cambridge.org/9781107524224

Proofs and Refutations The Logic of Mathematical Discovery Imre Lakatos Edited by John Worrall and Elie Zahar

Imre Lakatos’s influential and enduring work on the nature of mathematic discovery and development continues to be relevant to philosophers of mathematics. Including a specially commissioned Preface written by Paolo Mancosu, and presented in a fresh twenty-first-century series livery, it is now available for a new generation of readers. ‘For anyone interested in mathematics who has not encountered the work of the late Imre Lakatos before, this book is a treasure; and those who know well the famous dialogue, first published in 1963–4 in the British

Publication January 2016 For all formats available, see

www.cambridge.org/9781107135550

Knots and Borromean Rings, Rep-Tiles, and Eight Queens Martin Gardner’s Unexpected Hanging Martin Gardner

Find new twists on knotted molecules, the hangman’s paradox, cat’s cradle, gambling, peg solitaire, pi and e in this book. The New Martin Gardner Mathematical Library, 4

2014 216 x 138 mm 288pp 137 b/w illus. 978-0-521-75613-6 Hardback £29.99 / US$44.99 978-0-521-75871-0 Paperback £12.99 / US$17.99 For all formats available, see

www.cambridge.org/9780521756136

eBooks available at www.cambridge.org/ebookstore

Logic, categories and sets / Algebra

Logic, categories and sets Type Theory and Formal Proof An Introduction Rob Nederpelt Technische Universiteit Eindhoven, The Netherlands

and Herman Geuvers Radboud Universiteit Nijmegen

A gentle introduction for graduate students and researchers in the art of formalizing mathematics on the basis of type theory. 2014 247 x 174 mm 490pp 35 b/w illus. 125 exercises 978-1-107-03650-5 Hardback £50.00 / US$80.00 For all formats available, see

www.cambridge.org/9781107036505

The Semantic Web Explained The Technology and Mathematics behind Web 3.0 Péter Szeredi Budapest University of Technology and Economics

Gergely Lukácsy Cisco Systems, Ireland

and Tamás Benkő Digital Enterprise Research Institute, Ireland

With contributions by Zsolt Nagy

Describes the underlying theory as well as algorithms, optimisation ideas and implementation details. Includes numerous examples and exercises. 2014 247 x 174 mm 478pp 117 b/w illus. 195 exercises 978-0-521-70036-8 Paperback £39.99 / US$59.99 For all formats available, see

www.cambridge.org/9780521700368

Ordinal Definability and Recursion Theory The Cabal Seminar, Volume III Edited by Alexander S. Kechris California Institute of Technology

Benedikt Löwe Universiteit van Amsterdam

and John R. Steel University of California, Berkeley

Ordinal Definability and Recursion Theory is the third in a series of four books presenting the seminal papers from the Caltech-UCLA ‘Cabal Seminar’ with extensive unpublished material, new papers on related topics, and discussion of research developments

since the publication of the original volumes.

Algebra

Lecture Notes in Logic, 43

Publication December 2015

A Concise Text on Advanced Linear Algebra

For all formats available, see

Yisong Yang

2015 228 x 152 mm 551pp 10 b/w illus. 978-1-107-03340-5 Hardback £110.00 / US$175.00

www.cambridge.org/9781107033405

Polytechnic School of Engineering, New York University

A Guide to NIP Theories

This engaging, well-motivated textbook helps advanced undergraduate students to grasp core concepts and reveals applications in mathematics and beyond.

Pierre Simon Université Lyon I

This book, the first on the rapidly expanding topic of NIP theories, gives an accessible introduction to the subject for students and researchers in model theory and related areas such as combinatorics and algebraic geometry. It covers the basic notions while presenting a concise, elegant tour through the main results. Lecture Notes in Logic, 44

2015 228 x 152 mm 166pp 50 exercises 978-1-107-05775-3 Hardback £79.99 / US$125.00 For all formats available, see

www.cambridge.org/9781107057753

Pure Inductive Logic Jeffrey Paris University of Manchester

and Alena Vencovská University of Manchester

This book establishes pure inductive logic as a contemporary branch of mathematical logic. Collecting together research from a wide range of sources within one unified context, it provides both a comprehensive account of the subject up to cutting-edge modern research, and an accessible reference for the philosopher or computer scientist.

2014 228 x 152 mm 334pp 390 exercises 978-1-107-08751-4 Hardback £70.00 / US$115.00 978-1-107-45681-5 Paperback £29.99 / US$55.00 For all formats available, see

www.cambridge.org/9781107087514

Classical Groups, Derangements and Primes Timothy C. Burness University of Bristol

and Michael Giudici University of Western Australia, Perth

This book provides an accessible graduate-level introduction to the finite classical groups and gives the first unified account of conjugacy and geometry of elements of prime order. The authors also provide a detailed discussion of derangements, making this book an essential resource for all researchers interested in permutation groups. Australian Mathematical Society Lecture Series, 25

2015 228 x 152 mm 350pp 3 b/w illus. 60 tables 978-1-107-62944-8 Paperback £50.00 / US$80.00

Perspectives in Logic

Publication December 2015

2015 228 x 152 mm 354pp 1 b/w illus. 978-1-107-04230-8 Hardback £79.99 / US$125.00

For all formats available, see

Representation Theory

www.cambridge.org/9781107042308

www.cambridge.org/9781107629448

A Combinatorial Viewpoint Amritanshu Prasad Institute of Mathematical Sciences, Chennai

This book discusses representation theory of symmetric groups, theory of symmetric functions and polynomial representation theory of general linear groups. Cambridge Studies in Advanced Mathematics, 147

2015 244 x 170 mm 202pp 978-1-107-08205-2 Hardback £50.00 / US$80.00 For all formats available, see

www.cambridge.org/9781107082052

Algebra / Number theory Solving Polynomial Equation Systems III Volume 3: Algebraic Solving Teo Mora University of Genoa

This third volume of four describes all the most important techniques, mainly based on Gröbner bases. It covers the ‘standard’ solutions (Gianni–Kalkbrener, Auzinger–Stetter, Cardinal–Mourrain) as well as the more innovative (Lazard– Rouillier, Giusti–Heintz–Pardo). The author also explores the historical background, from Bézout to Macaulay.

the 2013 meeting, covering a wide spectrum of modern group theory. London Mathematical Society Lecture Note Series, 422

2015 228 x 152 mm 500pp 15 b/w illus. 978-1-107-51454-6 Paperback £65.00 / US$115.00 For all formats available, see

www.cambridge.org/9781107514546

Pseudo-reductive Groups Second edition Brian Conrad

Encyclopedia of Mathematics and its Applications, 157

Stanford University, California

2015 234 x 156 mm 294pp 7 b/w illus. 978-0-521-81155-2 Hardback £79.99 / US$125.00

Institut des Hautes Études Scientifiques, France

For all formats available, see

This monograph provides a comprehensive treatment of the theory of pseudo-reductive groups and gives their classification in a usable form. This second edition has been revised and updated, with Chapter 9 being completely rewritten via the useful new notion of ‘minimal type’ for pseudoreductive groups.

www.cambridge.org/9780521811552

Solving Polynomial Equation Systems IV Volume 4: Buchberger Theory and Beyond Teo Mora University of Genoa

In this fourth and final volume the author covers extensions of Buchberger’s Algorithm, including a discussion of the most promising recent alternatives to Gröbner bases: Gerdt’s involutive bases and Faugère’s F4 and F5 algorithms. This completes the author’s comprehensive treatise, which is a fundamental reference for any mathematical library. Encyclopedia of Mathematics and its Applications, 158

2016 234 x 156 mm 800pp 40 b/w illus. 978-1-107-10963-6 Hardback £110.00 / US$175.00 Publication January 2016 For all formats available, see

www.cambridge.org/9781107109636

Groups St Andrews 2013 Edited by C. M. Campbell

Ofer Gabber and Gopal Prasad University of Michigan, Ann Arbor

Review of previous edition: ‘This book is an impressive piece of work; many hard technical difficulties are overcome in order to provide the general structure of pseudo-reductive groups and to elucidate their classification by means of reasonable data. In view of the importance of this class of algebraic groups … and of the impact of a better understanding of them on the general theory of linear algebraic groups, this book can be considered a fundamental reference in the area.’ Mathematical Reviews New Mathematical Monographs, 26

2015 228 x 152 mm 690pp 978-1-107-08723-1 Hardback £90.00 / US$145.00 For all formats available, see

www.cambridge.org/9781107087231

those with a minimal mathematical background. Advance praise: ‘This is an extraordinary book, really one of a kind. Written by two supreme experts, but aimed at the level of an undergraduate or curious amateur, it emphasizes the really powerful ideas, with the bare minimum of math notation and the maximum number of elegant and suggestive visuals. The authors explain why this legendary problem is so beautiful, why it is difficult, and why you should care.’ Will Hearst, Hearst Corporation 2016 228 x 152 mm 150pp 110 b/w illus. 132 colour illus. 978-1-107-10192-0 Hardback £39.99 / US$59.99 978-1-107-49943-0 Paperback £17.99 / US$24.99 Publication February 2016 For all formats available, see

www.cambridge.org/9781107101920

Unit Equations in Diophantine Number Theory Jan-Hendrik Evertse Universiteit Leiden

and Kálmán Győry Debreceni Egyetem, Hungary

Unit equations play a central role in Diophantine number theory. This book provides a comprehensive and up-to-date treatment of unit equations and their various applications. It brings together the most important results and gives an overview of the basic techniques, making it accessible to young researchers. Cambridge Studies in Advanced Mathematics, 146

2016 228 x 152 mm 384pp 978-1-107-09760-5 Hardback £49.99 / US$79.99 Publication January 2016 For all formats available, see

www.cambridge.org/9781107097605

University of St Andrews, Scotland

M. R. Quick University of St Andrews, Scotland

E. F. Robertson University of St Andrews, Scotland

and C. M. Roney-Dougal University of St Andrews, Scotland

Every four years, leading researchers gather to survey the latest developments in all aspects of group theory. This volume contains selected papers from

Number theory Prime Numbers and the Riemann Hypothesis Barry Mazur Harvard University, Massachusetts

and William Stein University of Washington

This book introduces prime numbers and explains the celebrated, unsolved Riemann hypothesis in a direct manner. Suitable for both scholars and

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

Number theory / Discrete mathematics, information theory and coding theory Automorphic Forms and Galois Representations Volume 1 Edited by Fred Diamond King’s College London

Payman L. Kassaei King’s College London

and Minhyong Kim University of Oxford

Part one of a two-volume collection exploring recent developments in number theory related to automorphic forms and Galois representations. London Mathematical Society Lecture Note Series, 414

2014 228 x 152 mm 390pp 978-1-107-69192-6 Paperback £50.00 / US$85.00 For all formats available, see

www.cambridge.org/9781107691926

Automorphic Forms and Galois Representations Volume 2 Edited by Fred Diamond King’s College London

Payman L. Kassaei King’s College London

and Minhyong Kim University of Oxford

Part two of a two-volume collection exploring recent developments in number theory related to automorphic forms and Galois representations. London Mathematical Society Lecture Note Series, 415

2014 228 x 152 mm 390pp 978-1-107-69363-0 Paperback £50.00 / US$85.00 For all formats available, see

www.cambridge.org/9781107693630

The Bloch–Kato Conjecture for the Riemann Zeta Function

Arithmetic and Geometry Edited by Luis Dieulefait Universitat de Barcelona

Gerd Faltings Max-Planck-Institut für Mathematik, Bonn

D. R. Heath-Brown University of Oxford

Yu. V. Manin Max-Planck-Institut für Mathematik, Bonn

with a Frobenius structure. It includes classical examples as well as new results on characteristic p zeta values. London Mathematical Society Lecture Note Series, 429

2015 228 x 152 mm 131pp 978-1-316-50259-4 Paperback £40.00 / US$70.00 For all formats available, see

www.cambridge.org/9781316502594

B. Z. Moroz Max-Planck-Institut für Mathematik, Bonn

and Jean-Pierre Wintenberger Université de Strasbourg

In this proceedings volume leading authorities describe the state of the art in number theory, particularly Diophantine and arithmetic geometry. The book gives an excellent overview of the subject for graduate students and it is essential reading for researchers wishing to keep abreast of recent developments. London Mathematical Society Lecture Note Series, 420

2015 228 x 152 mm 535pp 978-1-107-46254-0 Paperback £64.99 / US$115.00 For all formats available, see

www.cambridge.org/9781107462540

O-Minimality and Diophantine Geometry Edited by G. O. Jones University of Manchester

and A. J. Wilkie University of Manchester

This collection of articles brings the researcher up to date with recent applications of logic, specifically model theory, to conjectures associated with those of Manin–Mumford and André–Oort. Originating from a short course, it combines original papers with background articles on related topics. London Mathematical Society Lecture Note Series, 421

Discrete mathematics, information theory and coding theory Introduction to Random Graphs Alan Frieze Carnegie Mellon University, Pennsylvania

and Michal Karoński Uniwersytet im. Adama Mickiewicza w Poznaniu, Poland

The authors cover random graphs from the basic to the advanced and will appeal to anyone interested in combinatorics, applied probability or theoretical computer science. Having read this book, the reader should be in a good position to pursue research in the area. 2015 228 x 152 mm 478pp 25 b/w illus. 190 exercises 978-1-107-11850-8 Hardback £49.99 / US$79.99 For all formats available, see

www.cambridge.org/9781107118508

Analytic Pattern Matching From DNA to Twitter Philippe Jacquet

University of Cambridge

2015 228 x 152 mm 232pp 1 b/w illus. 30 exercises 978-1-107-46249-6 Paperback £50.00 / US$80.00

A. Raghuram

For all formats available, see

Purdue University, Indiana

Indian Institute of Science Education and Research, Pune

www.cambridge.org/9781107462496

How do you distinguish a cat from a dog by their DNA? Pattern matching problems like these play a key role in areas such as computer science, telecommunications and molecular biology. In this graduate-level book the authors present a unique probabilistic approach using analytic combinatorics and analytic information theory.

Edited by John Coates

Anupam Saikia Indian Institute of Technology, Guwahati

and R. Sujatha University of British Columbia, Vancouver

A graduate-level account of an important recent result concerning the Riemann zeta function. London Mathematical Society Lecture Note Series, 418

2015 228 x 152 mm 320pp 978-1-107-49296-7 Paperback £50.00 / US$80.00 For all formats available, see

www.cambridge.org/9781107492967

Sheaves and Functions Modulo p Lectures on the Woods Hole Trace Formula Lenny Taelman Universiteit van Amsterdam

This graduate-level introduction describes a version of the sheavesfunctions dictionary of Deligne, relating characteristic-p-valued functions on the rational points of varieties over finite fields to coherent modules equipped

Bell Laboratories

and Wojciech Szpankowski

2015 247 x 174 mm 385pp 40 b/w illus. 110 exercises 978-0-521-87608-7 Hardback £45.00 / US$75.00 For all formats available, see

www.cambridge.org/9780521876087

Discrete mathematics, information theory and coding theory Catalan Numbers Richard P. Stanley Massachusetts Institute of Technology

Catalan numbers are probably the most ubiquitous sequence of numbers in mathematics. This book gives some basic background and then presents more than 250 exercises and solutions on the properties and applications of these numbers, with difficulty levels ranging from recreational to research. 2015 228 x 152 mm 224pp 150 b/w illus. 282 exercises 978-1-107-07509-2 Hardback £44.99 / US$74.99 978-1-107-42774-7 Paperback £19.99 / US$29.99 For all formats available, see

www.cambridge.org/9781107075092

Applied Algebra and Number Theory Edited by Gerhard Larcher Johannes Kepler Universität Linz

Friedrich Pillichshammer Johannes Kepler Universität Linz

Arne Winterhof Austrian Academy of Sciences, Linz

and Chaoping Xing Nanyang Technological University, Singapore

This book contains survey articles on modern topics related to the work of Harald Niederreiter, written by close colleagues and leading experts. 2014 228 x 152 mm 345pp 25 b/w illus. 5 colour illus. 978-1-107-07400-2 Hardback £65.00 / US$99.00 For all formats available, see

www.cambridge.org/9781107074002

Erdős–Ko–Rado Theorems: Algebraic Approaches Christopher Godsil University of Waterloo, Ontario

and Karen Meagher University of Regina, Saskatchewan, Canada

The Erdős–Ko–Rado Theorem is a fundamental result in combinatorics. Aimed at graduate students and researchers, this comprehensive text shows how tools from algebraic graph theory can be applied to prove the EKR Theorem and its generalizations. Readers can test their understanding at every step with the end-of-chapter exercises. Cambridge Studies in Advanced Mathematics, 149

2015 228 x 152 mm 350pp 5 b/w illus. 170 exercises 978-1-107-12844-6 Hardback £49.99 / US$79.99 For all formats available, see

www.cambridge.org/9781107128446

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

and Robin J. Wilson The Open University, Milton Keynes

Chromatic graph theory is a thriving area that uses various ideas of ‘colouring’ (of vertices, edges, and so on) to explore aspects of graph theory. It has links with other areas of mathematics, including topology, algebra and geometry, and is increasingly used in such areas as computer networks, where colouring algorithms form an important feature. While other books cover portions of the material, no other title has such a wide scope as this one, in which acknowledged international experts in the field provide a broad survey of the subject. All fifteen chapters have been carefully edited, with uniform notation and terminology applied throughout. Bjarne Toft (Odense, Denmark), widely recognized for his substantial contributions to the area, acted as academic consultant. The book serves as a valuable reference for researchers and graduate students in graph theory and combinatorics and as a useful introduction to the topic for mathematicians in related fields. Contributors: Bjarne Toft, Lowell W. Beineke, Robin J. Wilson, Bojan Mohar, Michael Stiebitz, Bill Jackson, Ken-ichi Kawarabayashi, Jessica McDonald, Margit Voigt, Nicolas Trotignon, Alexander Soifer, Hongjian Lai, Rong Luo, Cun-Quan Zhang, Ross J. Kang, Colin McDiarmid, Csilla Bujtas, Zsolt Tuza, Vitaly Voloshin, Dominique de Werra, Alain Hertz, Thore Husfeldt, Xuding Zhu, Tommy Jensen Encyclopedia of Mathematics and its Applications, 156

2015 234 x 156 mm 386pp 65 b/w illus. 978-1-107-03350-4 Hardback £79.99 / US$130.00 For all formats available, see

www.cambridge.org/9781107033504

subshifts, dynamical systems, ergodic theory or probabilistic models. Encyclopedia of Mathematics and its Applications, 159

2016 234 x 156 mm 490pp 135 b/w illus. 75 exercises 978-1-107-07702-7 Hardback £99.99 / US$155.00 Publication January 2016 For all formats available, see

www.cambridge.org/9781107077027

The Surprising Mathematics of Longest Increasing Subsequences Dan Romik University of California, Davis

This book presents for the first time to a graduate-level readership recent groundbreaking developments in probability and combinatorics related to the longest increasing subsequence problem. Its detailed, playful presentation provides a motivating entry to elegant mathematical ideas that are of interest to every mathematician and to many computer scientists, physicists and statisticians. ‘The story of longest monotone subsequences in permutations has been, for six decades, one of the most beautiful in mathematics, ranging from the very pure to the applied and featuring many terrific mathematicians, starting with Erdős– Szekeres’s ‘happy end theorem’ and continuing through the Tracy–Widom distribution and the breakthrough of Baik–Deift–Johansson. With its connections to many areas of mathematics, to the Riemann hypothesis, and to high-energy physics we cannot foresee where the story is heading. Dan Romik tells the tale thus far – and teaches its rich multifaceted mathematics, a blend of probability, combinatorics, analysis, and algebra – in a wonderful way.’ Gil Kalai, Hebrew University

Combinatorics, Words and Symbolic Dynamics Edited by Valérie Berthé Université Paris Diderot – Paris 7

and Michel Rigo Université de Liège, Belgium

This survey volume looks at developing trends in combinatorics with applications in the study of words and in symbolic dynamics. It will appeal to graduate students, research mathematicians and computer scientists working in combinatorics, graph theory, theory of computation, multidimensional

Institute of Mathematical Statistics Textbooks, 4

2015 228 x 152 mm 366pp 3 b/w illus. 94 exercises 978-1-107-07583-2 Hardback £65.00 / US$99.00 978-1-107-42882-9 Paperback £27.99 / US$39.99 For all formats available, see

www.cambridge.org/9781107075832

Visit our website at www.cambridge.org/academic

Discrete mathematics, information theory and coding theory / Abstract analysis Inequalities for Graph Eigenvalues Zoran Stanić Univerzitet u Beogradu, Serbia

Written for mathematicians working with the theory of graph spectra, this book explores more than 400 inequalities for eigenvalues of the six matrices associated with graphs. It presents the main results and then details their proofs, discussions, comparisons, examples, and exercises. Open problems and pointers to the literature are provided. London Mathematical Society Lecture Note Series, 423

2015 228 x 152 mm 312pp 35 b/w illus. 7 tables 90 exercises 978-1-107-54597-7 Paperback £55.00 / US$90.00 For all formats available, see

www.cambridge.org/9781107545977

Surveys in Combinatorics 2015 Edited by Artur Czumaj University of Warwick

Agelos Georgakopoulos University of Warwick

Daniel Král University of Warwick

Vadim Lozin University of Warwick

and Oleg Pikhurko

Random Graphs, Geometry and Asymptotic Structure Michael Krivelevich Tel-Aviv University

Konstantinos Panagiotou Universität Munchen

Mathew Penrose University of Bath

and Colin McDiarmid University of Oxford

Edited by Nikolaos Fountoulakis University of Birmingham

and Dan Hefetz University of Birmingham

A self-contained and concise introduction to recent developments, particularly those of a geometric and topological nature, in the theory of random graphs. Such material is seldom covered in the formative study of young combinatorialists and probabilists, making this essential reading for beginning researchers in these fields. London Mathematical Society Student Texts

2016 228 x 152 mm 160pp 2 b/w illus. 1 table 978-1-107-13657-1 Hardback c. £50.00 / c. US$85.00 978-1-316-50191-7 Paperback c. £24.99 / c. US$39.99 Publication April 2016 For all formats available, see

www.cambridge.org/9781107136571

University of Warwick

This book consists of nine survey papers by internationally renowned mathematicians. It will be of interest to researchers in combinatorics, from graduate students who want an overview of several areas to advanced researchers who want to have an indepth analysis of recent developments. London Mathematical Society Lecture Note Series, 424

2015 228 x 152 mm 334pp 20 b/w illus. 978-1-107-46250-2 Paperback £55.00 / US$90.00 For all formats available, see

www.cambridge.org/9781107462502

Finite Geometry and Combinatorial Applications Simeon Ball Universitat Politècnica de Catalunya, Barcelona

For students and researchers interested in algebraic combinatorics, this book not only provides an introduction to the geometries arising from vector spaces over finite fields but also shows how these geometries can be applied to various combinatorial objects. More than 100 exercises and solutions are provided. London Mathematical Society Student Texts, 82

2015 228 x 152 mm 298pp 35 b/w illus. 105 exercises 978-1-107-10799-1 Hardback £79.99 / US$120.00 978-1-107-51843-8 Paperback £27.99 / US$44.99 For all formats available, see

www.cambridge.org/9781107107991

Games of No Chance 4 Edited by Richard J. Nowakowski Dalhousie University, Nova Scotia

This book includes a tutorial for analysing misère impartial games and how it can be used for misère partisan games. Hex and Go are featured, along with new games: Toppling Dominoes and Maze. Updated versions of Unsolved Problems in Combinatorial Game Theory and the Combinatorial Games Bibliography complete the volume. Mathematical Sciences Research Institute Publications, 63

2015 234 x 156 mm 350pp 70 b/w illus. 23 tables 978-1-107-01103-8 Hardback £59.99 / US$94.99 For all formats available, see

www.cambridge.org/9781107011038

Abstract analysis The Cambridge Dictionary of Probability and Its Applications David Stirzaker St John’s College, Oxford

Probability comes of age with this, the first dictionary of probability and its applications in English, which supplies a guide to the concepts and vocabulary of this rapidly expanding field. Besides the basic theory of probability and random processes, applications covered here include financial and insurance mathematics, operations research (including queueing, reliability, and inventories), decision and game theory, optimization, time series, networks, and communication theory, as well as classic problems and paradoxes. The dictionary is reliable, stable, concise, and cohesive. Each entry provides a rigorous definition, a sketch of the context, and a reference pointing the reader to the wider literature. Judicious use of figures makes complex concepts easier to follow without oversimplifying. As the only dictionary on the market, this will be a guiding reference for all those working in, or learning, probability together with its applications. 2015 246 x 189 mm 426pp 80 b/w illus. 978-1-107-07516-0 Hardback £120.00 / US$195.00 For all formats available, see

www.cambridge.org/9781107075160

Abstract analysis Probability: The Classical Limit Theorems Henry McKean New York University

A leading authority sheds light on a variety of interesting topics in which probability theory plays a key role. 2014 228 x 152 mm 488pp 122 b/w illus. 260 exercises 978-1-107-05321-2 Hardback £60.00 / US$99.00 978-1-107-62827-4 Paperback £27.99 / US$45.99 For all formats available, see

Fourier Analysis and Hausdorff Dimension Pertti Mattila University of Helsinki

During the past two decades there has been active interplay between geometric measure theory and Fourier analysis. This book for graduate students and researchers describes part of that development, concentrating on the relationship between the Fourier transform and Hausdorff dimension. It covers classical results as well as cutting-edge research.

www.cambridge.org/9781107053212

Cambridge Studies in Advanced Mathematics, 150

Quantum Stochastics

2015 228 x 152 mm 452pp 5 b/w illus. 978-1-107-10735-9 Hardback £49.99 / US$79.99

Mou-Hsiung Chang Mathematical Sciences Division, US Army Research Office

For all formats available, see

www.cambridge.org/9781107107359

This book provides a systematic, self-contained treatment of the theory of quantum probability and quantum Markov processes.

Foundations of Ergodic Theory

Cambridge Series in Statistical and Probabilistic Mathematics, 37

Instituto Nacional de Matemática Pura e Aplicada (IMPA), Rio de Janeiro

2015 253 x 177 mm 424pp 978-1-107-06919-0 Hardback £55.00 / US$85.00

and Krerley Oliveira

For all formats available, see

www.cambridge.org/9781107069190

Introduction to Model Spaces and their Operators Stephan Ramon Garcia Pomona College, California

Javad Mashreghi Université Laval, Québec

and William T. Ross University of Richmond, Virginia

The study of model spaces is a broad field with connections to complex analysis, operator theory, engineering and mathematical physics. This selfcontained text is the ideal introduction for newcomers, quickly taking them through the history of the subject and then pointing towards areas of future research. Cambridge Studies in Advanced Mathematics, 148

2016 228 x 152 mm 335pp 10 b/w illus. 978-1-107-10874-5 Hardback £49.99 / US$79.99 Publication March 2016 For all formats available, see

www.cambridge.org/9781107108745

Marcelo Viana

Universidade Federal de Alagoas, Brazil

Rich with examples, applications and over 400 exercises, this textbook provides a coherent and self-contained introduction to ergodic theory, suitable for a variety of one- or two-semester courses. It requires few prerequisites, beginning with elementary material suitable for undergraduate students and gradually building up to more sophisticated topics. Cambridge Studies in Advanced Mathematics, 151

2015 228 x 152 mm 625pp 35 b/w illus. 410 exercises 978-1-107-12696-1 Hardback £79.99 / US$120.00 Publication December 2015 For all formats available, see

www.cambridge.org/9781107126961

Random Matrix Theory, Interacting Particle Systems, and Integrable Systems Edited by Percy Deift New York University, Courant Institute of Mathematical Sciences

and Peter Forrester University of Melbourne

This volume includes review articles and research contributions on long-standing questions on universalities of Wigner matrices and beta-ensembles. Mathematical Sciences Research Institute Publications, 65

2015 234 x 156 mm 540pp 978-1-107-07992-2 Hardback £75.00 / US$120.00 For all formats available, see

www.cambridge.org/9781107079922

The Theory of H(b) Spaces Emmanuel Fricain Université de Lille 1

and Javad Mashreghi Université Laval, Québec

This comprehensive treatment in two volumes is accessible to graduate students as well as researchers. It covers all of the preliminary subjects required to fully understand and appreciate this beautiful branch of mathematics, such as Hardy spaces, Fourier analysis and Carleson measures. Each volume contains hundreds of exercises and hints. New Mathematical Monographs

2016 228 x 152 mm 1200pp 30 b/w illus. 420 exercises 978-1-107-11941-3 2 Volume Hardback Set c. £180.00 / US$270.00 Publication February 2016 For all formats available, see

www.cambridge.org/9781107119413

The Theory of H(b) Spaces Volume 1 Emmanuel Fricain Université de Lille 1

and Javad Mashreghi Université Laval, Québec

This comprehensive treatment is accessible to graduate students as well as researchers. It covers all of the preliminary subjects needed to fully understand and appreciate this beautiful subject, such as Hardy spaces, Fourier analysis and Carleson measures. Hundreds of exercises are also included,

eBooks available at www.cambridge.org/ebookstore

Abstract analysis / Real and complex analysis making the book suitable for graduate courses. New Mathematical Monographs, 20

2015 228 x 152 mm 700pp 30 b/w illus. 320 exercises 978-1-107-02777-0 Hardback £99.00 / US$150.00

Convergence of One-parameter Operator Semigroups In Models of Mathematical Biology and Elsewhere Adam Bobrowski

Publication December 2015

Politechnika Lubelska, Poland

For all formats available, see

Written by a leading expert in the field, this book presents the classical theory of convergence of semigroups and then uses real examples to show how it can be applied to models of mathematical biology as well as other branches of mathematics.

www.cambridge.org/9781107027770

The Theory of H(b) Spaces Volume 2 Emmanuel Fricain Université de Lille I

and Javad Mashreghi Université Laval, Québec

This comprehensive treatment in two volumes is accessible to graduate students as well as researchers. It covers all of the preliminary subjects required to fully understand and appreciate this beautiful branch of mathematics, such as Hardy spaces, Fourier analysis and Carleson measures, and it contains hundreds of exercises and hints. New Mathematical Monographs, 21

2016 228 x 152 mm 690pp 1 b/w illus. 100 exercises 978-1-107-02778-7 Hardback £110.00 / US$175.00 Publication February 2016 For all formats available, see

www.cambridge.org/9781107027787

Sobolev Spaces on Metric Measure Spaces An Approach Based on Upper Gradients Juha Heinonen Pekka Koskela University of Jyväskylä, Finland

Nageswari Shanmugalingam University of Cincinnati

and Jeremy T. Tyson University of Illinois, Urbana-Champaign

This coherent treatment from first principles is an ideal introduction for graduate students and a useful reference for experts. New Mathematical Monographs, 27

2015 228 x 152 mm 448pp 4 b/w illus. 978-1-107-09234-1 Hardback £80.00 / US$130.00 For all formats available, see

www.cambridge.org/9781107092341

New Mathematical Monographs, 30

2016 228 x 152 mm 439pp 60 b/w illus. 9 colour illus. 160 exercises 978-1-107-13743-1 Hardback £89.99 / US$140.00 Publication February 2016 For all formats available, see

www.cambridge.org/9781107137431

Real and complex analysis Twelve Landmarks of Twentieth-Century Analysis D. Choimet Lycée du Parc, Lyon

and H. Queffélec Université de Lille

The authors combine rigorous mathematical proofs with commentary on the underlying ideas to provide a rich insight into some of the most profound results of twentieth-century analysis. This English edition contains a new chapter on partitions and significantly expands the existing chapter on the Corona problem. 2015 228 x 152 mm 521pp 25 b/w illus. 153 exercises 978-1-107-05945-0 Hardback £69.99 / US$110.00 978-1-107-65034-3 Paperback £24.99 / US$39.99 For all formats available, see

www.cambridge.org/9781107059450

Textbook

Numbers and Functions Steps into Analysis Third edition R. P. Burn University of Exeter

Revised and updated edition. Hundreds of exercises to help students gradually transition from school to university-level calculus. ‘This third edition of Numbers and Functions continues the author’s long-term commitment to support every reader in making sense of mathematics by responding to a succession of well-chosen questions that encourage personal reflection and discussion with others. Groups of questions are followed by a summary to build the bigger picture. Every chapter includes details of the historical development and ends with a full list of solutions. The author is aware of the difficulties that students encounter with the complexity of the limit concept and begins with a pragmatic approach to null sequences. This broadens into a full study of limits of sequences, completeness, and a full range of tests for convergence of infinite series … This latest edition maintains the original chapters of the original, while benefiting from detailed improvements that have arisen from the experience of many readers. Thoroughly recommended.’ David Tall, University of Warwick

Contents: Preface to first edition; Preface to second edition; Preface to third edition; Glossary; Part I. Numbers: 1 Mathematical induction; 2. Inequalities; 3. Sequences: a first bite at infinity; 4. Completeness: what the rational numbers lack; 5. Series: infinite sums; Part II. Functions: 6. Functions and continuity: neighbourhoods, limits of functions; 7. Continuity and completeness: functions on intervals; 8. Derivatives: tangents; 9. Differentiation and completeness: mean value theorems, Taylor’s Theorem; 10. Integration: the fundamental theorem of calculus; 11. Indices and circle functions; 12. Sequences of functions; Appendix 1. Properties of the real numbers; Appendix 2. Geometry and intuition; Appendix 3. Questions for student investigation and discussion; Bibliography; Index. 2015 228 x 152 mm 374pp 65 b/w illus. 800 exercises 978-1-107-44453-9 Paperback £34.99 / US$69.99 For all formats available, see

www.cambridge.org/9781107444539

Topology and geometry

Topology and geometry Hyperbolic Manifolds An Introduction in 2 and 3 Dimensions Albert Marden University of Minnesota

This richly illustrated study of hyperbolic geometry in low dimensions takes the reader from first principles to the current state of knowledge. Marden begins by explaining basic ideas and techniques before applying them to the description and classification of the interiors of 3-dimensional objects. Each chapter ends with exercises and explorations.

right down to the level of computer programs (written in pseudo-code, and easy to translate into any computer language) … the reader who attempts any substantial subset of [the projects] will gain enormously … Even those who are convinced they have no ability to visualize may change their minds … It is almost required reading for the experts in the field … I truly love this book.’ John H. Hubbard, The American Mathematical Monthly 2015 246 x 189 mm 414pp 55 b/w illus. 150 colour illus. 75 exercises 978-1-107-56474-9 Paperback £36.99 / US$59.99 Also available 978-0-521-35253-6 Hardback £49.99 / US$84.99 For all formats available, see

2015 247 x 174 mm 550pp 55 b/w illus. 21 colour illus. 250 exercises 978-1-107-11674-0 Hardback £49.99 / US$99.99

www.cambridge.org/9781107564749

Publication December 2015

Ivan Arzhantsev

For all formats available, see

Moscow State University

www.cambridge.org/9781107116740

Cox Rings Ulrich Derenthal Leibniz Universität Hannover

New in Paperback

Indra’s Pearls The Vision of Felix Klein David Mumford Brown University, Rhode Island

Caroline Series University of Warwick

and David Wright Oklahoma State University

Felix Klein, one of the great nineteenthcentury geometers, discovered in mathematics an idea prefigured in Buddhist mythology: the heaven of Indra contained a net of pearls, each of which was reflected in its neighbour, so that the whole Universe was mirrored in each pearl. Klein studied infinitely repeated reflections and was led to forms with multiple coexisting symmetries. For a century, these images barely existed outside the imagination of mathematicians. However, in the 1980s, the authors embarked on the first computer exploration of Klein’s vision, and in doing so found many further extraordinary images. Join the authors on the path from basic mathematical ideas to the simple algorithms that create the delicate fractal filigrees, most of which have never appeared in print before. Beginners can follow the stepby-step instructions for writing programs that generate the images. Others can see how the images relate to ideas at the forefront of research.

Jürgen Hausen Eberhard-Karls-Universität Tübingen, Germany

and Antonio Laface Universidad de Concepción, Chile

This book provides a largely selfcontained introduction to Cox rings and their applications in algebraic and arithmetic geometry. Cambridge Studies in Advanced Mathematics, 144

2014 228 x 152 mm 472pp 19 tables 120 exercises 978-1-107-02462-5 Hardback £50.00 / US$80.00

mathematics education, and humancomputer interaction. Learning in Doing: Social, Cognitive and Computational Perspectives

2015 228 x 152 mm 294pp 40 b/w illus. 63 tables 978-1-107-12791-3 Hardback £69.99 / US$110.00 For all formats available, see

www.cambridge.org/9781107127913

Recent Advances in Algebraic Geometry A Volume in Honor of Rob Lazarsfeld’s 60th Birthday Edited by Christopher D. Hacon University of Utah

Mircea Mustaţă University of Michigan, Ann Arbor

and Mihnea Popa University of Illinois, Chicago

A comprehensive collection of expository articles on cutting-edge topics at the forefront of research in algebraic geometry. London Mathematical Society Lecture Note Series, 417

2015 228 x 152 mm 447pp 12 b/w illus. 9 tables 978-1-107-64755-8 Paperback £65.00 / US$99.00 For all formats available, see

www.cambridge.org/9781107647558

Geometry, Topology, and Dynamics in Negative Curvature Edited by C. S. Aravinda TIFR Centre for Applicable Mathematics, Bangalore, India

For all formats available, see

F. T. Farrell

www.cambridge.org/9781107024625

Tsinghua University, Beijing

and J.-F. Lafont

Constructing Dynamic Triangles Together The Development of Mathematical Group Cognition Gerry Stahl Drexel University, Philadelphia

A longitudinal study of eight sessions of online teamwork by three girls learning geometry as novices, this book presents innovative approaches and persuasive insights into computer-supported collaborative learning of mathematics. It offers valuable resources for researchers, instructors, and students interested in group cognition, educational technology,

Ohio State University

Negative curvature arises in several mathematical areas, including geometry, topology, dynamics, and number theory. This volume contains survey articles around this common theme, which should help mathematicians interested in transitioning between these areas, as well as graduate students entering this interdisciplinary subject. London Mathematical Society Lecture Note Series, 425

2016 228 x 152 mm 358pp 25 b/w illus. 978-1-107-52900-7 Paperback £60.00 / US$99.00 Publication January 2016 For all formats available, see

www.cambridge.org/9781107529007

‘[This book is] richly illustrated with these wonderful and mysterious pictures and gives detailed instructions for recreating them,

Visit our website at www.cambridge.org/academic

Topology and geometry Recent Advances in Hodge Theory Period Domains, Algebraic Cycles, and Arithmetic Edited by Matt Kerr Washington University, St Louis

and Gregory Pearlstein Texas A & M University

Hodge theory lies at the heart of modern algebraic geometry and this volume explores the many contexts in which it arises, including theoretical physics. The book will be of value to graduate students and seasoned researchers alike, for its mixture of cutting-edge research and expository articles. London Mathematical Society Lecture Note Series, 427

2016 228 x 152 mm 528pp 10 b/w illus. 7 tables 978-1-107-54629-5 Paperback £65.00 / US$115.00 Publication January 2016 For all formats available, see

www.cambridge.org/9781107546295

Geometry in a Fréchet Context A Projective Limit Approach C. T. J. Dodson University of Manchester

George Galanis Hellenic Naval Academy, Piraeus, Greece

and Efstathios Vassiliou University of Athens, Greece

Aimed at researchers and graduate students, this book presents a new approach to studying Fréchet geometry which overcomes deficiencies of the Fréchet space theory, such as the lack of a general solvability theory for differential equations. The book concludes with a series of open problems and suggestions for further research. London Mathematical Society Lecture Note Series, 428

2015 228 x 152 mm 314pp 978-1-316-60195-2 Paperback £55.00 / US$90.00 Publication December 2015 For all formats available, see

www.cambridge.org/9781316601952

The Geometry of Celestial Mechanics Hansjörg Geiges Universität zu Köln

A geometric introduction to celestial mechanics, for advanced undergraduate and beginning graduate students. This textbook introduces the geometric concepts underlying celestial mechanics and their applications, making it suitable for traditional geometry courses or as supplementary material. Numerous

exercises and extensive historical notes also support self-study.

comprehensive resource suitable for experts and newcomers alike.

London Mathematical Society Student Texts

New Mathematical Monographs

2016 228 x 152 mm 235pp 39 b/w illus. 112 exercises 978-1-107-12540-7 Hardback c. £65.00 / c. US$110.00

2015 228 x 152 mm 886pp 45 b/w illus. 100 exercises 978-1-107-53568-8 2 Volume Hardback Set £145.00 / US$225.00

978-1-107-56480-0 Paperback c. £26.99 / c. US$44.99

For all formats available, see

www.cambridge.org/9781107535688

Publication February 2016 For all formats available, see

www.cambridge.org/9781107125407

Symplectic, Poisson, and Noncommutative Geometry Edited by Tohru Eguchi Rikkyo University, Japan

Yakov Eliashberg Stanford University, California

and Yoshiaki Maeda Tokyo University of Science

This volume contains seven chapters based on lectures given by invited speakers at two May 2010 workshops held at the Mathematical Sciences Research Institute. Mathematical Sciences Research Institute Publications

2014 234 x 156 mm 304pp 23 b/w illus. 978-1-107-05641-1 Hardback £60.00 / US$99.00 For all formats available, see

www.cambridge.org/9781107056411

Cubical Homotopy Theory Brian A. Munson United States Naval Academy, Maryland

and Ismar Volić Wellesley College, Massachusetts

Graduate students and researchers alike will benefit from this modern treatment of classical and cutting-edge topics in topology. It provides detailed explanations of many fundamental results with 300 examples. Readers hoping to enter some of the most exciting research areas in topology will find the necessary background here. New Mathematical Monographs, 25

2015 228 x 152 mm 644pp 20 b/w illus. 978-1-107-03025-1 Hardback £79.99 / US$125.00 For all formats available, see

www.cambridge.org/9781107030251

Symplectic Topology and Floer Homology Yong-Geun Oh Pohang University of Science and Technology, Republic of Korea

This is the first systematic exposition of basic Floer homology theory and its applications to symplectic topology as a whole. In two volumes, it provides a

Symplectic Topology and Floer Homology Volume 1: Symplectic Geometry and Pseudoholomorphic Curves Yong-Geun Oh Pohang University of Science and Technology, Republic of Korea

Published in two volumes, this is the first book to provide a systematic explanation of symplectic topology, and the analytical details and techniques used in applying the machinery arising from Floer theory as a whole. Volume 1 covers the basic materials of Hamiltonian dynamics and symplectic geometry and the analytic foundations of Gromov’s pseudoholomorphic curve theory. New Mathematical Monographs, 28

2015 228 x 152 mm 420pp 35 b/w illus. 50 exercises 978-1-107-07245-9 Hardback £89.99 / US$140.00 For all formats available, see

www.cambridge.org/9781107072459

Symplectic Topology and Floer Homology Volume 2: Floer Homology and its Applications Yong-Geun Oh Pohang University of Science and Technology, Republic of Korea

Published in two volumes, this is the first book to provide a systematic explanation of symplectic topology, and the analytical details and techniques used in applying the machinery arising from Floer theory as a whole. Volume 2 provides a comprehensive introduction to both Hamiltonian Floer theory and Lagrangian Floer theory. New Mathematical Monographs, 29

2015 228 x 152 mm 472pp 10 b/w illus. 50 exercises 978-1-107-10967-4 Hardback £89.99 / US$140.00 For all formats available, see

www.cambridge.org/9781107109674

Differential and integral equations, dynamical systems and control / Mathematical physics

Differential and integral equations, dynamical systems and control New in Paperback Textbook

Introduction to Dynamical Systems Michael Brin University of Maryland, College Park

and Garrett Stuck University of Maryland, College Park

This introduction to the subject of dynamical systems is ideal for a one-year graduate course. From chapter one, the authors use examples to motivate, clarify and develop the theory. The book rounds off with beautiful and remarkable applications to such areas as number theory, data storage, and Internet search engines. ‘… an ideal choice for a graduate course on dynamical systems … warmly recommended …’ Acta Scientiarum Mathematicarum

Contents: Introduction; 1. Examples and basic concepts; 2. Topological dynamics; 3. Symbolic dynamics; 4. Ergodic theory; 5. Hyperbolic dynamics; 6. Ergodicity of Anosov diffeomorphisms; 7. Lowdimensional dynamics; 8. Complex dynamics; 9. Measure-theoretic entropy; Bibliography; Index.

will appeal to researchers and graduate students interested in analysis. Encyclopedia of Mathematics and its Applications, 161

2016 234 x 156 mm 344pp 4 b/w illus. 978-1-107-13838-4 Hardback £79.99 / US$125.00

University of Warwick

www.cambridge.org/9781107138384

Witold Sadowski Uniwersytet Warszawski, Poland

Reversibility in Dynamics and Group Theory Anthony G. O’Farrell National University of Ireland, Maynooth

and Ian Short The Open University, Milton Keynes

The powerful and far-reaching concept of reversibility is treated for the first time in book form. The authors establish basic principles of reversibility and demonstrate its impact in group theory, geometry, complex analysis and number theory, while describing open research problems throughout. Accessible at the advanced undergraduate level and above. London Mathematical Society Lecture Note Series, 416

2015 228 x 152 mm 292pp 38 b/w illus. 11 tables 978-1-107-44288-7 Paperback £40.00 / US$65.00

University College Dublin

and Steven D. Taliaferro Texas A & M University

Singularities are a common feature of the qualitative side of mathematics. In this monograph, the authors present some powerful methods for dealing with singularities in elliptic and parabolic partial differential inequalities, which

and Alejandro Vidal-López Xi’an Jiaotong-Liverpool University, P. R. China

This survey volume provides an accessible summary of a wide range of active research topics written by leaders in their field, together with some exciting new results. It serves both as a helpful overview for graduate students new to the area and as a useful resource for more established researchers. London Mathematical Society Lecture Note Series, 430

2016 228 x 152 mm 245pp 10 b/w illus. 978-1-107-55497-9 Paperback £50.00 / US$80.00 Publication February 2016 For all formats available, see

www.cambridge.org/9781107554979

Mathematical physics

For all formats available, see

www.cambridge.org/9781107442887

The Cauchy Problem for Non-Lipschitz Semi-Linear Parabolic Partial Differential Equations

Reaction-diffusion theory is a rapidly developing topic with important applications. This monograph, which includes significant new results, provides a general approach to the study of semilinear parabolic equations with Hölder and/or upper Lipschitz continuous nonlinearities, a scenario that occurs often in reaction-diffusion models in chemical kinetics, biochemical systems and population dynamics.

Marius Ghergu

University of Warwick

José L. Rodrigo

Also available 978-0-521-80841-5 Hardback £49.99 / US$84.99

Isolated Singularities in Partial Differential Inequalities

Edited by James C. Robinson

For all formats available, see

J. C. Meyer

www.cambridge.org/9781107538948

Recent Progress in the Theory of the Euler and Navier– Stokes Equations

Publication February 2016

2015 228 x 152 mm 256pp 35 b/w illus. 305 exercises 978-1-107-53894-8 Paperback £34.99 / US$59.99

For all formats available, see

University of Birmingham

and D. J. Needham University of Birmingham

Electricity and Magnetism for Mathematicians A Guided Path from Maxwell’s Equations to Yang–Mills Thomas A. Garrity Williams College, Massachusetts

Maxwell’s equations have led to many important mathematical discoveries. This text introduces mathematics students to some of their wonders. 2015 228 x 152 mm 296pp 81 b/w illus. 2 colour illus. 211 exercises 978-1-107-07820-8 Hardback £60.00 / US$99.00 978-1-107-43516-2 Paperback £24.99 / US$39.99 For all formats available, see

www.cambridge.org/9781107078208

London Mathematical Society Lecture Note Series, 419

2015 228 x 152 mm 173pp 978-1-107-47739-1 Paperback £44.99 / US$69.99 For all formats available, see

www.cambridge.org/9781107477391

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

Mathematical physics / Mathematical modelling and methods Advanced Concepts in Quantum Mechanics Giampiero Esposito Università degli Studi di Napoli ‘Federico II’

Giuseppe Marmo Università degli Studi di Napoli ‘Federico II’

Gennaro Miele Università degli Studi di Napoli ‘Federico II’

and George Sudarshan University of Texas, Austin

This book introduces a geometric view of fundamental physics, ideal for advanced undergraduate and graduate students in quantum mechanics and mathematical physics. 2014 246 x 189 mm 397pp 25 b/w illus. 79 exercises 978-1-107-07604-4 Hardback £55.00 / US$85.00 For all formats available, see

www.cambridge.org/9781107076044

Mathematical modelling and methods A Guided Tour of Mathematical Methods for the Physical Sciences Third edition Roel Snieder Colorado School of Mines

and Kasper van Wijk University of Auckland

This completely revised edition provides a comprehensive tour of mathematical knowledge and techniques needed by students across the physical sciences. 2015 253 x 177 mm 584pp 153 b/w illus. 10 tables 978-1-107-08496-4 Hardback £75.00 / US$130.00 978-1-107-64160-0 Paperback £37.99 / US$65.00 For all formats available, see

www.cambridge.org/9781107084964

Introduction to Atmospheric Modelling Douw G. Steyn University of British Columbia, Vancouver

This graduate-level introduction shows how mathematical modelling helps us to understand atmospheric phenomena. Written for students with backgrounds in mathematics, physics and engineering, this book will be a

valuable resource as they begin studying atmospheric science. AIMS Library of Mathematical Sciences

2015 216 x 138 mm 116pp 27 b/w illus. 978-1-107-49979-9 Paperback £15.99 / US$25.99 For all formats available, see

www.cambridge.org/9781107499799

Partial Differential Equation Methods for Image Inpainting Carola-Bibiane Schönlieb University of Cambridge

This book introduces the mathematical concept of partial differential equations (PDEs) for virtual image restoration. It provides insight in mathematical modelling, partial differential equations, functional analysis, variational calculus, optimisation and numerical analysis. It is addressed towards generally informed mathematicians and graduate students in mathematics with an interest in image processing and mathematical analysis. ‘Since the late 1990s, there has been a substantial amount of academic works on the application of partial differential equations (PDEs) to the restoration of missing parts in images, which is usually referred to as the ‘inpainting problem’. This book provides a very comprehensive, clear, and well-written account of the use of PDEs for inpainting, and this is no minor feat, given the sizable literature on the subject and the mathematical complexity of many of the techniques described.’ Marcelo Bertalmío, Universitat Pompeu Fabra Cambridge Monographs on Applied and Computational Mathematics, 29

2015 228 x 152 mm 272pp 69 b/w illus. 34 colour illus. 15 exercises 978-1-107-00100-8 Hardback £64.99 / US$99.99 For all formats available, see

www.cambridge.org/9781107001008

An Introduction to Stochastic Dynamics Jinqiao Duan Illinois Institute of Technology

This book serves as a concise introductory text on stochastic dynamics for applied mathematicians. Rich with examples, illustrations, and exercises with their solutions, this book provides an accessible introduction to concepts and techniques for describing, quantifying, and understanding dynamics under uncertainty, from

analytical, deterministic, structural and numerical perspectives. ‘Jinqiao Duan’s book introduces the reader to the actively developing theory of stochastic dynamics through well-chosen examples that provide an overview, useful insights, and intuitive understanding of an often technically complicated topic.’ P. E. Kloeden, Goethe University, Frankfurt am Main Cambridge Texts in Applied Mathematics, 51

2015 247 x 174 mm 312pp 60 b/w illus. 100 exercises 978-1-107-07539-9 Hardback £94.99 / US$150.00 978-1-107-42820-1 Paperback £41.99 / US$64.99 For all formats available, see

www.cambridge.org/9781107075399

Singularities: Formation, Structure, and Propagation J. Eggers University of Bristol

and M. A. Fontelos Universidad Autónoma de Madrid

Many natural phenomena are described as singularities, for example, the formation of drops and bubbles, or the motion of cracks. Aimed at a broad audience of students and researchers in mathematics, physics and engineering, this book provides mathematical tools for understanding all aspects of singularities. Cambridge Texts in Applied Mathematics, 53

2015 228 x 152 mm 467pp 125 b/w illus. 8 colour illus. 180 exercises 978-1-107-09841-1 Hardback £79.99 / US$130.00 978-1-107-48549-5 Paperback £39.99 / US$74.99 For all formats available, see

www.cambridge.org/9781107098411

Fluid dynamics and solid mechanics / Numerical analysis / Computational science

Fluid dynamics and solid mechanics Magnetoconvection N. O. Weiss University of Cambridge

and M. R. E. Proctor University of Cambridge

Leading experts present the current state of knowledge of the subject of magnetoconvection from the viewpoint of applied mathematics. Cambridge Monographs on Mechanics

2014 247 x 174 mm 432pp 220 b/w illus. 978-0-521-19055-8 Hardback £75.00 / US$120.00 For all formats available, see

www.cambridge.org/9780521190558

Lectures on the Theory of Water Waves Edited by Thomas J. Bridges University of Surrey

Mark D. Groves Universität des Saarlandes, Saarbrücken, Germany

and David P. Nicholls University of Illinois, Chicago

In the summer of 2014 experts were invited to give introductory-level talks on active topics in the theory of water waves. This compilation is an ideal introduction for PhD students and researchers. It may also be used as a supplementary text for advanced courses in mathematics or fluid dynamics. London Mathematical Society Lecture Note Series, 426

2016 228 x 152 mm 300pp 50 b/w illus. 978-1-107-56556-2 Paperback £55.00 / US$90.00

courses in science and engineering for Indian universities. The mathematical derivations discussed here are presented in a simplified and systematic manner. Contents: Preface; 1. Errors in computation; 2. Linear equations and eigenvalue problem; 3. Nonlinear equations; 4. Interpolation; 5. Numerical differentiation; 6. Numerical integration; 7. Ordinary differential equations; 8. Splines and their applications; 9. Method of least squares and Chebyshev approximation; 10. Eigenvalues of symmetric matrices; 11. Partial differential equations; 12. Finite element method; 13. Integral equations; 14. Difference equations; 15. Fourier series, discrete Fourier transform and fast Fourier transform; 16. Free and moving boundary problems: a brief introduction; Appendices; Index. 2015 244 x 170 mm 774pp 978-1-107-50049-5 Paperback £49.99 / US$79.99

Volume 24 Edited by Arieh Iserles University of Cambridge

Acta Numerica is an annual publication containing invited survey papers by leading researchers in numerical mathematics and scientific computing. The papers present overviews of recent developments in their area and provide state-of-the-art techniques and analysis.

Computational science Passive Imaging with Ambient Noise Josselin Garnier Université de Paris VII (Denis Diderot)

and George Papanicolaou

2016 247 x 174 mm 288pp 15 b/w illus. 48 colour illus. 978-1-107-13563-5 Hardback £89.99 / US$150.00 Publication March 2016

2015 247 x 174 mm 381pp 50 b/w illus. 978-1-107-11258-2 Hardback £114.00 / US$195.00

For all formats available, see

Probabilistic Forecasting and Bayesian Data Assimilation

www.cambridge.org/9781107112582

Sun Yat-Sen University, Guangzhou, China

Second edition Radhey S. Gupta

www.cambridge.org/9781107103474

Acta Numerica, 24

Zhongying Chen

Elements of Numerical Analysis

For all formats available, see

This multidisciplinary book, for researchers and graduate students, presents the mathematical underpinnings in the analysis of passive sensor array imaging using ambient noise sources. It also covers a range of related topics, including conventional sensor array imaging, wave propagation in random media, and high frequency wave propagation.

www.cambridge.org/9781107565562

Textbook

2015 228 x 152 mm 552pp 25 b/w illus. 25 tables 978-1-107-10347-4 Hardback £99.99 / US$155.00

Stanford University, California

For all formats available, see

Numerical analysis

Cambridge Monographs on Applied and Computational Mathematics, 28

www.cambridge.org/9781107500495

Multiscale Methods for Fredholm Integral Equations

Publication February 2016

course for advanced undergraduates or beginning graduates.

For all formats available, see

Acta Numerica 2015

Charles A. Micchelli State University of New York, Albany

and Yuesheng Xu Sun Yat-Sen University, Guangzhou, China

The authors present the state of the art in fast multiscale methods, from traditional numerical methods to the recently developed wavelet-based approach. Theorems of functional analysis used throughout the book are summarised in an appendix. Selected chapters are suitable for a one-semester

www.cambridge.org/9781107135635

Sebastian Reich Universität Potsdam, Germany and University of Reading

and Colin Cotter Imperial College London

This book focuses on the Bayesian approach to data assimilation, outlining the subject’s key ideas and concepts, and explaining how to implement specific data assimilation algorithms. It is an ideal introduction for graduate students in applied mathematics, computer science, engineering, geoscience and other emerging application areas.

Indian Institute of Technology, Roorkee

This textbook introduces the basic concepts of numerical analysis conforming to the module syllabus designed by the University Grant Commission (UGC) for undergraduate

eBooks available at www.cambridge.org/ebookstore

Computational science / History of mathematics / Optimization, OR and risk analysis 2015 247 x 174 mm 308pp 70 b/w illus. 7 colour illus. 70 exercises 978-1-107-06939-8 Hardback £69.99 / US$115.00 978-1-107-66391-6 Paperback £34.99 / US$54.99 For all formats available, see

www.cambridge.org/9781107069398

History of mathematics Applied Nonparametric Econometrics Daniel J. Henderson

A Student’s Guide to Numerical Methods Ian H. Hutchinson Massachusetts Institute of Technology

Written for senior undergraduates in all disciplines of physical science and engineering, the plain language style of this concise guide to numerical methods concentrates on developing computational skills and avoids potentially intimidating formal mathematical proofs. Including numerous worked examples and exercises, this textbook explains the practical realities of numerical techniques. 2015 228 x 152 mm 221pp 73 b/w illus. 978-1-107-09567-0 Hardback £39.99 / US$69.99 978-1-107-47950-0 Paperback £17.99 / US$29.99 For all formats available, see

www.cambridge.org/9781107095670

Ridge Functions Allan Pinkus Technion – Israel Institute of Technology, Haifa

The first book devoted to ridge functions presents the state of the art and provides a solid theoretical foundation for researchers who encounter ridge functions in approximation theory or data science. It includes an extensive bibliography and discusses some of the unresolved questions in the field. Cambridge Tracts in Mathematics, 205

2015 228 x 152 mm 218pp 4 b/w illus. 978-1-107-12439-4 Hardback £79.99 / US$125.00 For all formats available, see

www.cambridge.org/9781107124394

University of Alabama

and Christopher F. Parmeter University of Miami

Bridging the gap between applied economists and theoretical nonparametric econometricians, this book explains basic to advanced nonparametric methods with applications. 2015 253 x 177 mm 380pp 81 b/w illus. 34 tables 978-1-107-01025-3 Hardback £75.00 / US$125.00 978-0-521-27968-0 Paperback £30.00 / US$49.99 For all formats available, see

www.cambridge.org/9781107010253

Optimization, OR and risk analysis A Course on Cooperative Game Theory Satya R. Chakravarty Indian Statistical Institute

Manipushpak Mitra Indian Statistical Institute

and Palash Sarkar Indian Statistical Institute

This book deals with situations where objectives of participants of the game are partially cooperative and partially conflicting. 2015 234 x 156 mm 273pp 978-1-107-05879-8 Hardback £65.00 / US$95.00 For all formats available, see

www.cambridge.org/9781107058798

Textbook

Chance, Strategy, and Choice An Introduction to the Mathematics of Games and Elections Samuel Bruce Smith St Joseph’s University, Philadelphia

This classroom-tested undergraduate textbook is intended for a general education course in game theory at the freshman or sophomore level. While it

starts off with the basics and introduces the reader to mathematical proofs, this text also presents several advanced topics, including accessible proofs of the Sprague–Grundy theorem and Arrow’s impossibility theorem. ‘Sam Smith’s book offers an intriguing juxtaposition of chance, strategy, and elections. The mathematical analysis is rigorous without being too formal or forbidding. The applications to topics in economics and political science – including auctions, power, and voting – as well as to parlor games like poker will engage both students and professionals.’ Steven Brams, New York University

Contents: 1. Introduction; 2. Games and elections; 3. Chance; 4. Strategy; 5. Choice; 6. Strategy and choice; 7. Choice and chance; 8. Chance and strategy; 9. Nash equilibria; 10. Proofs and counterexamples; 11. Laws of probability; 12. Fairness in elections; 13. Weighted voting; 14. Gambling games; 15. Zero-sum games; 16. Partial conflict games; 17. Take-away games; 18. Fairness and impossibility; 19. Paradoxes and puzzles in probability; 20. Combinatorial games; 21. Borda versus Condorcet; 22. The Sprague–Grundy theorem; 23. Arrow’s impossibility theorem. Cambridge Mathematical Textbooks

2015 253 x 177 mm 352pp 60 b/w illus. 243 tables 300 exercises 978-1-107-08452-0 Hardback £29.99 / US$49.99 For all formats available, see

www.cambridge.org/9781107084520

An Introduction to Polynomial and Semi-Algebraic Optimization Jean Bernard Lasserre Centre National de la Recherche Scientifique (CNRS), Toulouse

The first comprehensive introduction to the powerful moment approach for solving global optimization problems. Cambridge Texts in Applied Mathematics, 52

2015 228 x 152 mm 354pp 15 b/w illus. 2 colour illus. 978-1-107-06057-9 Hardback £70.00 / US$120.00 978-1-107-63069-7 Paperback £35.00 / US$60.00 For all formats available, see

www.cambridge.org/9781107060579

Optimization, OR and risk analysis / Mathematical finance / Also of interest Highlight

Repeated Games Jean-François Mertens Sylvain Sorin Université de Paris VI (Pierre et Marie Curie)

and Shmuel Zamir Hebrew University of Jerusalem and University of Exeter

This landmark work significantly advances the literature on game theory with a masterful conceptual presentation of the CORE working papers published in 1994.

it highly to students or practitioners interested in mathematical models used in algorithmic trading.’ Thierry Foucault, HEC Paris 2015 247 x 174 mm 356pp 5 b/w illus. 75 colour illus. 35 tables 978-1-107-09114-6 Hardback £44.99 / US$64.99 For all formats available, see

www.cambridge.org/9781107091146

Stochastic Interest Rates

Econometric Society Monographs, 55

Daragh McInerney

2015 228 x 152 mm 598pp 22 b/w illus. 18 exercises 978-1-107-03020-6 Hardback £75.00 / US$125.00

AGH University of Science and Technology, Krakow

978-1-107-66263-6 Paperback £39.99 / US$59.99

Designed for Master’s students and final-year undergraduates, this book strikes the right balance between mathematical rigour and practical application. Carefully chosen examples and exercises help students acquire the necessary skills to deal with interest rate modelling in a real-world setting.

For all formats available, see

www.cambridge.org/9781107030206

Mathematical finance Algorithmic and High-Frequency Trading Álvaro Cartea University College London

Sebastian Jaimungal

and Tomasz Zastawniak University of York

Mastering Mathematical Finance

2015 228 x 152 mm 170pp 25 b/w illus. 10 tables 60 exercises 978-1-107-00257-9 Hardback £49.99 / US$79.99 978-0-521-17569-2 Paperback £23.99 / US$39.99 For all formats available, see

www.cambridge.org/9781107002579

University of Toronto

and José Penalva Universidad Carlos III de Madrid

This cutting-edge textbook shows how to build the advanced mathematical models that underpin modern trading algorithms. If you need to understand how modern electronic markets operate, what information provides a trading edge, and how other market participants may affect the profitability of the algorithms, then this book is for you. ‘[This book] is an important and timely textbook on algorithmic trading. Human traders in financial markets are an endangered species, gradually replaced by computers and algorithms. In this new world, designing and coding trading strategies requires knowledge of market microstructure, basic economic principles governing price formation in financial markets, and stylized facts about price dynamics and trading activity. It also requires specific mathematical tools, such as stochastic control, and understanding of how these tools are used to solve trading problems. Algorithmic and High-Frequency Trading is unique in that it provides a unified treatment of these topics. I enjoyed reading it and recommend

Also of interest The Computing Universe A Journey through a Revolution Tony Hey Microsoft Research, Washington

and Gyuri Pápay University of Southampton

This exciting and accessible book takes us on a journey from the early days of computers to the cutting-edge research of the present day. 2015 297 x 210 mm 424pp 596 colour illus. 20 tables 978-0-521-76645-6 Hardback £50.00 / US$85.00

Highlight

Entertainment Industry Economics A Guide for Financial Analysis Ninth edition Harold L. Vogel

Fully updated, this ninth edition remains the definitive source on the economics of entertainment in the United States and overseas. 2015 228 x 152 mm 680pp 95 b/w illus. 73 tables 978-1-107-07529-0 Hardback £45.00 / US$70.00 For all formats available, see

www.cambridge.org/9781107075290

Mathematical Foundations of Infinite-Dimensional Statistical Models Evarist Giné University of Connecticut

and Richard Nickl University of Cambridge

High-dimensional and nonparametric statistical models are ubiquitous in modern data science. This book develops a mathematically coherent and objective approach to statistical inference in such models, with a focus on function estimation problems arising from random samples (density estimation) or from Gaussian regression/signal in white noise problems. Advance praise: ‘Finally – a book that goes all the way in the mathematics of nonparametric statistics. It is reasonably selfcontained, despite its depth and breadth, including accessible overviews of the necessary analysis and approximation theory.’ Aad van der Vaart, Leiden University Cambridge Series in Statistical and Probabilistic Mathematics, 40

2016 253 x 177 mm 720pp 978-1-107-04316-9 Hardback £59.99 / US$99.99 Publication January 2016 For all formats available, see

www.cambridge.org/9781107043169

978-0-521-15018-7 Paperback £24.99 / US$39.99 For all formats available, see

www.cambridge.org/9780521766456

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

Also of interest Mathematics and the Body Material Entanglements in the Classroom Elizabeth de Freitas Adelphi University, Garden City, New York

and Nathalie Sinclair Simon Fraser University, British Columbia

This book expands the landscape of research in mathematics education by analyzing how the body influences mathematical thinking. Innovations in Curriculum Studies, Division B Outstanding Book Award, American Educational Research Association 2015 – Honourable mention Learning in Doing: Social, Cognitive and Computational Perspectives

2014 228 x 152 mm 284pp 65 b/w illus. 2 tables 978-1-107-03948-3 Hardback £65.00 / US$99.00 For all formats available, see

www.cambridge.org/9781107039483

Granularity Theory with Applications to Finance and Insurance Patrick Gagliardini Universita della Svizzera Italiana, Switzerland

and Christian Gouriéroux University of Toronto

This book provides the first comprehensive overview of the granularity theory and its usefulness for risk analysis, statistical estimation, and derivative pricing. Themes in Modern Econometrics

2014 228 x 152 mm 202pp 36 b/w illus. 12 tables 978-1-107-07083-7 Hardback £55.00 / US$90.00 978-1-107-66288-9 Paperback £21.99 / US$34.99 For all formats available, see

www.cambridge.org/9781107070837

Index A Acta Numerica 2015..............................13 Advanced Concepts in Quantum Mechanics...........................................12 Alan M. Turing..........................................1 Albers, Donald J........................................1 Alexanderson, Gerald L.............................1 Algorithmic and High-Frequency Trading.15 Analytic Pattern Matching........................4 Applied Algebra and Number Theory.........5 Applied Nonparametric Econometrics......14 Aravinda, C. S...........................................9 Arithmetic and Geometry..........................4 Arzhantsev, Ivan.......................................9 Automorphic Forms and Galois Representations....................................4

B Ball, Simeon.............................................6 Beineke, Lowell W.....................................5 Benkő, Tamás...........................................2 Berthé, Valérie..........................................5 Bloch–Kato Conjecture for the Riemann Zeta Function, The.................................4 Bobrowski, Adam.....................................8 Bridges, Thomas J...................................13 Brin, Michael..........................................11 Burn, R. P.................................................8 Burness, Timothy C...................................2

C Cambridge Dictionary of Probability and Its Applications, The...............................6 Campbell, C. M.........................................3 Cartea, Álvaro........................................15 Catalan Numbers.....................................5 Cauchy Problem for Non-Lipschitz SemiLinear Parabolic Partial Differential Equations, The.....................................11 Chakravarty, Satya R...............................14 Chance, Strategy, and Choice..................14 Chang, Mou-Hsiung.................................7 Chen, Zhongying....................................13 Choimet, D...............................................8 Classical Groups, Derangements and Primes...................................................2 Coates, John............................................4 Combinatorics, Words and Symbolic Dynamics..............................................5 Computation, Proof, Machine...................1 Computing Universe, The........................15 Concise Text on Advanced Linear Algebra, A.............................................2 Conrad, Brian...........................................3 Constructing Dynamic Triangles Together..9 Convergence of One-parameter Operator Semigroups.............................8 Cooper, S. Barry........................................1 Cotter, Colin...........................................13 Course on Cooperative Game Theory, A...14 Cox Rings................................................9 Cubical Homotopy Theory.......................10 Czumaj, Artur...........................................6

D Davis, Martin............................................1 de Freitas, Elizabeth................................16 Deift, Percy...............................................7

Derenthal, Ulrich......................................9 Diamond, Fred..........................................4 Dieulefait, Luis.........................................4 Dodson, C. T. J........................................10 Dowek, Gilles...........................................1 Duan, Jinqiao.........................................12 Dunham, William......................................1

E Eggers, J.................................................12 Eguchi, Tohru.........................................10 Electricity and Magnetism for Mathematicians...................................11 Elements of Numerical Analysis..............13 Eliashberg, Yakov...................................10 Entertainment Industry Economics..........15 Erdős–Ko–Rado Theorems: Algebraic Approaches...........................................5 Esposito, Giampiero................................12 Evertse, Jan-Hendrik.................................3

F Faltings, Gerd...........................................4 Farrell, F. T................................................9 Finite Geometry and Combinatorial Applications..........................................6 Fontelos, M. A........................................12 Forrester, Peter.........................................7 Foundations of Ergodic Theory..................7 Fountoulakis, Nikolaos..............................6 Fourier Analysis and Hausdorff Dimension.7 Fricain, Emmanuel................................ 7, 8 Frieze, Alan..............................................4

G G. H. Hardy Reader, The............................1 Gabber, Ofer.............................................3 Gagliardini, Patrick.................................16 Galanis, George......................................10 Games of No Chance 4............................6 Garcia, Stephan Ramon............................7 Gardner, Martin........................................1 Garnier, Josselin.....................................13 Garrity, Thomas A...................................11 Geiges, Hansjörg....................................10 Geometry in a Fréchet Context................10 Geometry of Celestial Mechanics, The.....10 Geometry, Topology, and Dynamics in Negative Curvature................................9 Georgakopoulos, Agelos...........................6 Geuvers, Herman......................................2 Ghergu, Marius......................................11 Giné, Evarist...........................................15 Giudici, Michael.......................................2 Godsil, Christopher...................................5 Gouriéroux, Christian..............................16 Granularity Theory with Applications to Finance and Insurance.........................16 Groups St Andrews 2013..........................3 Groves, Mark D.......................................13 Guide to NIP Theories, A...........................2 Guided Tour of Mathematical Methods for the Physical Sciences, A..................12 Guillot, Pierre...........................................1 Gupta, Radhey S.....................................13 Győry, Kálmán..........................................3

H Hacon, Christopher D................................9 Hausen, Jürgen........................................9 Heath-Brown, D. R....................................4 Hefetz, Dan..............................................6 Heinonen, Juha........................................8 Henderson, Daniel J................................14 Hey, Tony...............................................15 Hodges, Andrew.......................................1 Hutchinson, Ian H...................................14 Hyperbolic Manifolds................................9

I Indra’s Pearls............................................9 Inequalities for Graph Eigenvalues............6 Introduction to Atmospheric Modelling...12 Introduction to Dynamical Systems.........11 Introduction to Model Spaces and their Operators..............................................7 Introduction to Polynomial and SemiAlgebraic Optimization, An..................14 Introduction to Random Graphs................4 Introduction to Stochastic Dynamics, An.. 12 Irvine, Lyn.................................................1 Iserles, Arieh...........................................13 Isolated Singularities in Partial Differential Inequalities........................11

J Jacquet, Philippe......................................4 Jaimungal, Sebastian..............................15 Jones, G. O...............................................4

K Karoński, Micha ......................................4 Kassaei, Payman L....................................4 Kechris, Alexander S..................................2 Kerr, Matt...............................................10 Kim, Minhyong.........................................4 Knots and Borromean Rings, Rep-Tiles, and Eight Queens..................................1 Koskela, Pekka.........................................8 Král, Daniel..............................................6 Krivelevich, Michael..................................6

L Laface, Antonio........................................9 Lafont, J.-F................................................9 Lakatos, Imre...........................................1 Larcher, Gerhard.......................................5 Lasserre, Jean Bernard............................14 Lectures on the Theory of Water Waves...13 Löwe, Benedikt.........................................2 Lozin, Vadim.............................................6 Lukácsy, Gergely.......................................2

M Maeda, Yoshiaki.....................................10 Magnetoconvection................................13 Manin, Yu. V.............................................4 Marden, Albert.........................................9 Marmo, Giuseppe...................................12 Mashreghi, Javad................................. 7, 8 Mathematical Foundations of InfiniteDimensional Statistical Models.............15 Mathematics and the Body.....................16 Mattila, Pertti...........................................7

Visit our website at www.cambridge.org/academic

Index Mazur, Barry.............................................3 McDiarmid, Colin.....................................6 McInerney, Daragh.................................15 McKean, Henry.........................................7 Meagher, Karen........................................5 Mertens, Jean-François...........................15 Meyer, J. C..............................................11 Micchelli, Charles A................................13 Miele, Gennaro.......................................12 Mitra, Manipushpak...............................14 Mora, Teo.................................................3 Moroz, B. Z...............................................4 Multiscale Methods for Fredholm Integral Equations...............................13 Mumford, David.......................................9 Munson, Brian A.....................................10 Mustaţă, Mircea.......................................9

N Nagy, Zsolt...............................................2 Nederpelt, Rob.........................................2 Needham, D. J........................................11 Nicholls, David P.....................................13 Nickl, Richard.........................................15 Nowakowski, Richard J.............................6 Numbers and Functions............................8

O O-Minimality and Diophantine Geometry..4 O’Farrell, Anthony G...............................11 Oh, Yong-Geun.......................................10 Oliveira, Krerley........................................7 Once and Future Turing, The.....................1 Ordinal Definability and Recursion Theory.2

P Panagiotou, Konstantinos.........................6 Papanicolaou, George............................13 Pápay, Gyuri...........................................15 Paris, Jeffrey.............................................2 Parmeter, Christopher F...........................14 Partial Differential Equation Methods for Image Inpainting.................................12 Passive Imaging with Ambient Noise.......13 Pearlstein, Gregory.................................10 Penalva, José..........................................15 Penrose, Mathew.....................................6 Pikhurko, Oleg..........................................6 Pillichshammer, Friedrich...........................5 Pinkus, Allan..........................................14 Popa, Mihnea...........................................9 Prasad, Amritanshu..................................2 Prasad, Gopal...........................................3 Prime Numbers and the Riemann Hypothesis............................................3 Probabilistic Forecasting and Bayesian Data Assimilation................................13 Probability: The Classical Limit Theorems...7 Proctor, M. R. E.......................................13 Proofs and Refutations.............................1 Pseudo-reductive Groups..........................3 Pure Inductive Logic.................................2

Q Quantum Stochastics................................7 Queffélec, H.............................................8 Quick, M. R..............................................3

R Raghuram, A............................................4 Random Graphs, Geometry and Asymptotic Structure.............................6 Random Matrix Theory, Interacting Particle Systems, and Integrable Systems.................................................7 Recent Advances in Algebraic Geometry....9 Recent Advances in Hodge Theory...........10 Recent Progress in the Theory of the Euler and Navier–Stokes Equations......11 Reich, Sebastian.....................................13 Repeated Games....................................15 Representation Theory..............................2 Reversibility in Dynamics and Group Theory.................................................11 Ridge Functions.....................................14 Rigo, Michel.............................................5 Robertson, E. F..........................................3 Robinson, James C..................................11 Rodrigo, José L.......................................11 Roman, Marion........................................1 Romik, Dan..............................................5 Roney-Dougal, C. M..................................3 Ross, William T..........................................7

S Sadowski, Witold...................................11 Saikia, Anupam........................................4 Sarkar, Palash.........................................14 Schönlieb, Carola-Bibiane.......................12 Semantic Web Explained, The...................2 Series, Caroline........................................9 Shanmugalingam, Nageswari...................8 Sheaves and Functions Modulo p..............4 Short, Ian...............................................11 Simon, Pierre............................................2 Sinclair, Nathalie....................................16 Singularities: Formation, Structure, and Propagation........................................12 Smith, Samuel Bruce...............................14 Snieder, Roel..........................................12 Sobolev Spaces on Metric Measure Spaces..................................................8 Solving Polynomial Equation Systems III....3 Solving Polynomial Equation Systems IV....3 Sorin, Sylvain..........................................15 Stahl, Gerry..............................................9 Stanić, Zoran............................................6 Stanley, Richard P.....................................5 Steel, John R............................................2 Stein, William...........................................3 Steyn, Douw G........................................12 Stirzaker, David.........................................6 Stochastic Interest Rates.........................15 Stuck, Garrett.........................................11 Student’s Guide to Numerical Methods, A........................................................14

Sudarshan, George.................................12 Sujatha, R................................................4 Surprising Mathematics of Longest Increasing Subsequences, The................5 Surveys in Combinatorics 2015.................6 Symplectic Topology and Floer Homology...........................................10 Symplectic, Poisson, and Noncommutative Geometry.................10 Szeredi, Péter...........................................2 Szpankowski, Wojciech.............................4

T Taelman, Lenny........................................4 Taliaferro, Steven D.................................11 Theory of H(b) Spaces, The.................... 7, 8 Topics in Chromatic Graph Theory.............5 Turing, John F...........................................1 Turing, Sara..............................................1 Twelve Landmarks of Twentieth-Century Analysis................................................8 Type Theory and Formal Proof...................2 Tyson, Jeremy T.........................................8

U Unit Equations in Diophantine Number Theory...................................................3

V van Wijk, Kasper....................................12 Vassiliou, Efstathios................................10 Vencovská, Alena.....................................2 Viana, Marcelo.........................................7 Vidal-López, Alejandro............................11 Vogel, Harold L.......................................15 Volić, Ismar............................................10

W Weiss, N. O.............................................13 Wilkie, A. J................................................4 Wilson, Robin J.........................................5 Wintenberger, Jean-Pierre.........................4 Winterhof, Arne........................................5 Worrall, John............................................1 Wright, David...........................................9

X Xing, Chaoping........................................5 Xu, Yuesheng.........................................13

Y Yang, Yisong............................................2

Z Zahar, Elie................................................1 Zamir, Shmuel........................................15 Zastawniak, Tomasz...............................15

FAO: Acquisitions Librarian LIBRARY RECOMMENDATION FORM I would like to recommend the following titles/online products published by Cambridge University Press for the library ISBN Author Title

_________________ __________________ _________________________ _________________

__________________

_________________________

_________________ __________________ _________________________ _________________ __________________ _________________________ _________________ __________________ _________________________ _________________ __________________ _________________________ _________________ __________________ _________________________ _________________ __________________ _________________________ _________________ __________________ _________________________ _________________ __________________ _________________________ _________________ __________________ _________________________ _________________ __________________ _________________________

Name

Position

Department

Date

Signature

Please pass this form to your librarian

FAO: Acquisitions Librarian

Cambridge University Press Bookshop

Customer Services

Cambridge University Press Bookshop occupies the historic site of 1 Trinity Street, Cambridge CB2 1SZ, where the complete range of titles is on sale. Bookshop Manager: Cathy Ashbee Phone + 44 (0)1223 333333 Fax + 44 (0)1223 332954 Email bookshop@cambridge.org

Booksellers For customer service, please contact: UK, Europe - internationaltrade2@cambridge.org Middle East, North Africa & Japan - internationaltrade1@cambridge.org North America - customer_service@cambridge.org Central & South America, Caribbean - internationalorders@cambridge.org Asia - asia@cambridge.org Account-holding booksellers can order online at www.PubEasy.com

Cambridge University Press Around the World Cambridge University Press has offices, representatives and distributors in some 60 countries around the world; our publications are available through bookshops in virtually every country.

United Kingdom and Ireland

The Americas

Academic Sales Department Cambridge University Press, University Printing House, Cambridge CB2 8BS, UK Email academicsales@cambridge.org Web www.cambridge.org/emea

North, Central, South America and Caribbean Cambridge University Press 32 Avenue of the Americas, New York, NY 10013-2473, USA Phone + 1 212 924 3900 Fax + 1 212 691 3239 Email customer_service@cambridge.org Web www.cambridge.org

Europe (excluding Iberia), Middle East and North Africa Academic Sales Department Cambridge University Press, University Printing House, Cambridge CB2 8BS, UK Email academicsales@cambridge.org Web www.cambridge.org/emea

Iberia Cambridge University Press Iberian Branch Basílica 17, 1º-, 28020 Madrid, Spain Phone + 34 91 360 46 06 Fax + 34 91 360 45 70 Email iberia@cambridge.org Web www.cambridge.org/emea

Asia 79 Anson Road Unit #06-04/06 Singapore 079906 Phone + 65 6323 2701 Fax + 65 6323 2370 Email singapore@cambridge.org Web www.cambridge.org/asia

Sub-Saharan Africa and English-speaking Caribbean Cambridge University Press African Branch Lower Ground Floor, Nautica Building, The Water Club, Beach Road, Granger Bay – 8005, Cape Town, South Africa Phone + 27 21 412 7800 Fax + 27 21 419 8418 Email information@cambridge.org Web www.cambridge.org/africa

Australia and New Zealand Cambridge University Press Australian Branch 477 Williamstown Road, Port Melbourne, VIC 3207, Australia Phone +61 3 8671 1411 Fax +61 3 9676 9966 Email info@cambridge.edu.au Web www.cambridge.org/aus

Institutional ebook access If you’re interested in institution-wide access to ebooks, or other Cambridge digital publications, please contact online@cambridge.org in the Americas or library.sales@cambridge.org in the rest of the world.

Connect with our Authors

Join in the conversation

www.cambridgeblog.org How to order books

Read exclusive articles and interviews

Further information

In the UK, Europe and rest of the world:

Please contact information@cambridge.org

www.cambridge.org/mathematics2016

Inspection Copies

+44 (0)1223 325566 internationaltrade2@cambridge.org In the Americas: www.cambridge.org/mathematics2016 +1 212 924 3900 customer_service@cambridge.org

EBooks For individuals: you can find information about ebook availability for Cambridge publications at www.cambridge.org/mathematics2016 For institutions: Cambridge publications are also available for institutional purchase as online collections and packages. Visit www.universitypublishingonline.org/list

Please order your inspection copies by visiting www.cambridge.org/textbooks If you experience problems with ordering your inspection copy via our website, or have any questions, please contact our Customer Services team at internationaltrade2@cambridge.org or on +44 (0)1223 325566 Our inspection copy policy • Inspection copies are available to lecturers who regard the textbook as potentially suitable for adoption • We will only supply inspection copies to a campus address • We will only process requests which contain a complete university or college address and course information • Books not yet published will be sent in the month of publication • Inspection copies are sent at the discretion of Cambridge University Press and we reserve the right to decline requests without explanation

Review enquiries For further information please email reviewcopy@cambridge.org

Press and media enquiries For further information please visit www.cambridge.org/academic/journalist

Translation Rights For enquiries regarding translation rights, please contact foreignrights@cambridge.org

Book proposals For information about submitting book proposals, please visit www.cambridge.org/proposals

Pricing and availability Prices are correct at time of going to press but are subject to alteration without notice. Publication dates indicate anticipated first publication date, but are subject to alteration without notice and may differ by country.

EXCEPTIONAL

Pure and Applied Mathematics Research READ AND PUBLISH IN THE HIGHEST QUALITY JOURNALS: u Acta Numerica u Advances in Applied

Mathematics and Mechanics u Advances in Applied Probability â&#x20AC;&#x201C; New in 2016 u Annals of Actuarial Science u ASTIN Bulletin u Bulletin of the Australian Mathematical Society u Combinatorics, Probability and Computing u Communications in Computational Physics u Compositio Mathematica u East Asian Journal on Applied Mathematics u Ergodic Theory and Dynamical Systems u European Journal of Applied Mathematics u Forum of Mathematics, Pi u Forum of Mathematics, Sigma u Glasgow Mathematical Journal u Journal of Applied Probability - New in 2016 u Journal of the Australian Mathematical Society u Journal of Fluid Mechanics

u Journal of the Institute of Mathematics of Jussieu u Mathematical Proceedings of the Cambridge

Philosophical Society u Mathematical Structures in Computer Science u Mathematika u Nagoya Mathematical Journal â&#x20AC;&#x201C; New in 2016 u Network Science u Numerical

Mathematics: Theory, Methods and Applications u Probability in the Engineering and Informational Sciences u Proceedings of the Edinburgh Mathematical Society u Proceedings of the Royal Society of Edinburgh, Section A: Mathematics u The ANZIAM journal u The Bulletin of Symbolic Logic u The Journal of Symbolic Logic u The Mathematical Gazette u The Review of Symbolic Logic

journals.cambridge.org/maths

A world of learning and research inspired by Cambridge At Cambridge University Press, our mission is to unlock people’s potential with the best learning and research solutions. Our success is driven by academic pedigree, innovation, unparalleled editorial experience and quality production processes. Do you want to publish with us? If you are thinking about getting your research published, we want to hear from you. • You will join a distinguished group of authors, including over 60 Nobel Prize Laureates, whose work has helped to shape the world we live in today. • With over 30,000 ebooks available we are proud of our digital publishing, and we can offer you the best combination of print and digital formats for your publication. • We draw on a range of marketing methods, including social media, e-marketing, author videos, and book trailers to promote titles across the world. • You will have access to Author Hub, an online resource designed to help you connect with the wider academic community.

To find out more, go to cambridge.org/getpublished

We further the mission of the University of Cambridge by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence.

Printed in the United Kingdom, 2016.