Mathematics Catalogue 2016

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MatheMatics 2016

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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.

http://www.cambridge.org/Mathematics2016

http://www.cambridge.org/Mathematics2016

http://www.cambridgeblog.org/category/mathematics/

see page 7

see page 1

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

Cover designed by Zoe Naylor.

The striking theorems showcased in this book are among the most profound results of twen-tieth-century analysis. The authors’ original ap-proach 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.

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

“There is a fi ne balance of methods of ‘hard’ and ‘soft’ analysis, which are often beautifully combined. The style is vivid and even enter-taining 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 profi t.”Gazette des mathématiciens

TWELVE LANDMARKS OF Twentieth-Century

AnalysisD. Choimet and H. Queffélec

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D. Choimet has spent all of his academic career in the French “Classes préparatoires”, an intensive two-year undergraduate programme leading to a nation-wide 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 Gradu-ate Engineering Schools. Choimet is also a member of the jury of the “Agrégation”, a competitive examination leading to professor-ship positions.

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 topologi-cal methods, as well as in number theory (Dirichlet series) and op-erator theory – more specifi cally, composition operators and their approximation numbers. He has also written fi ve textbooks and a research book on Banach spaces and probabilistic methods (in col-laboration 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.

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Contents General and recreational mathematics 1

Logic, categories and sets 2

Algebra 2

Number theory 3

Discrete mathematics, information theory and coding theory 4

Abstract analysis 6

Real and complex analysis 8

Topology and geometry 9

Differential and integral equations, dynamical systems and control 11

Mathematical physics 11

Mathematical modelling and methods 12

Fluid dynamics and solid mechanics 13

Numerical analysis 13

Computational science 13

History of mathematics 14

Optimization, OR and risk analysis 14

Mathematical finance 15

Also of interest 15

Information on related journals Inside back cover

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

Featured authors

TH E O N CE A N D FUTU RE

T U R INGE D I T E D B Y

S . BA R RY CO O P E R A N D A N D R E W H O D G ES

C O M P U T I N G T H E W O R L D

General and recreational mathematics 1

eBooks available at www.cambridge.org/ebookstore

General and recreational mathematics

HigHligHt

The Once and Future TuringComputing the WorldEdited by S. Barry CooperUniversity of Leeds

and Andrew HodgesUniversity 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 Penrose2016 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, seewww.cambridge.org/9781107010833

Computation, Proof, MachineMathematics Enters a New AgeGilles DowekEcole Polytechnique, Paris

Translated by Pierre Guillotand 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

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


available in PaPerback

Alan M. TuringCentenary EditionSara TuringAfterword by John F. TuringForeword by Lyn Irvineand Martin Davis

Containing never-before-published material, this fascinating account sheds new light on one of the greatest figures of the twentieth century.2014 216 x 140 mm 194pp 7 b/w illus. 978-1-107-52422-4 Paperback

£9.99 / US$15.99

Also available 978-1-107-02058-0 Hardback

£19.99 / US$29.99


Proofs and RefutationsThe Logic of Mathematical DiscoveryImre LakatosEdited by John Worralland 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

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


The G. H. Hardy ReaderEdited by Donald J. AlbersDover Publications, California

Gerald L. AlexandersonSanta Clara University, California

and William DunhamBryn 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


c. £50.00 / c. US$85.00

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

Publication January 2016


Knots and Borromean Rings, Rep-Tiles, and Eight QueensMartin Gardner’s Unexpected HangingMartin 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


£29.99 / US$44.99

978-0-521-75871-0 Paperback £12.99 / US$17.99


http://www.cambridge.org/9780521118019










2 Logic, categories and sets / Algebra

Logic, categories and sets

Type Theory and Formal ProofAn IntroductionRob NederpeltTechnische Universiteit Eindhoven, The Netherlands

and Herman GeuversRadboud 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


The Semantic Web ExplainedThe Technology and Mathematics behind Web 3.0Péter SzerediBudapest University of Technology and Economics

Gergely LukácsyCisco Systems, Ireland

and Tamás BenkőDigital 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


Ordinal Definability and Recursion TheoryThe Cabal Seminar, Volume IIIEdited by Alexander S. KechrisCalifornia Institute of Technology

Benedikt LöweUniversiteit van Amsterdam

and John R. SteelUniversity 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.Lecture Notes in Logic, 43


£110.00 / US$175.00

Publication December 2015


A Guide to NIP TheoriesPierre SimonUniversité 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


Pure Inductive LogicJeffrey ParisUniversity of Manchester

and Alena VencovskáUniversity 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.Perspectives in Logic


£79.99 / US$125.00


Algebra

A Concise Text on Advanced Linear AlgebraYisong YangPolytechnic School of Engineering, New York University

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


Classical Groups, Derangements and PrimesTimothy C. BurnessUniversity of Bristol

and Michael GiudiciUniversity 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



Representation TheoryA Combinatorial ViewpointAmritanshu PrasadInstitute 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














Algebra / Number theory 3

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Solving Polynomial Equation Systems IIIVolume 3: Algebraic SolvingTeo MoraUniversity 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.Encyclopedia of Mathematics and its Applications, 157


£79.99 / US$125.00


Solving Polynomial Equation Systems IVVolume 4: Buchberger Theory and BeyondTeo MoraUniversity 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


£110.00 / US$175.00



Groups St Andrews 2013Edited by C. M. CampbellUniversity of St Andrews, Scotland

M. R. QuickUniversity of St Andrews, Scotland

E. F. RobertsonUniversity of St Andrews, Scotland

and C. M. Roney-DougalUniversity 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

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


Pseudo-reductive GroupsSecond editionBrian ConradStanford University, California

Ofer GabberInstitut des Hautes Études Scientifiques, France

and Gopal PrasadUniversity of Michigan, Ann Arbor

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 pseudo-reductive groups.

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


Number theory

Prime Numbers and the Riemann HypothesisBarry MazurHarvard University, Massachusetts

and William SteinUniversity of Washington

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

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


Unit Equations in Diophantine Number TheoryJan-Hendrik EvertseUniversiteit Leiden

and Kálmán GyőryDebreceni 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













4 Number theory / Discrete mathematics, information theory and coding theory

Automorphic Forms and Galois RepresentationsVolume 1Edited by Fred DiamondKing’s College London

Payman L. KassaeiKing’s College London

and Minhyong KimUniversity 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


Automorphic Forms and Galois RepresentationsVolume 2Edited by Fred DiamondKing’s College London

Payman L. KassaeiKing’s College London

and Minhyong KimUniversity 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


The Bloch–Kato Conjecture for the Riemann Zeta FunctionEdited by John CoatesUniversity of Cambridge

A. RaghuramIndian Institute of Science Education and Research, Pune

Anupam SaikiaIndian Institute of Technology, Guwahati

and R. SujathaUniversity 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


Arithmetic and GeometryEdited by Luis DieulefaitUniversitat de Barcelona

Gerd FaltingsMax-Planck-Institut für Mathematik, Bonn

D. R. Heath-BrownUniversity of Oxford

Yu. V. ManinMax-Planck-Institut für Mathematik, Bonn

B. Z. MorozMax-Planck-Institut für Mathematik, Bonn

and Jean-Pierre WintenbergerUniversité 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


O-Minimality and Diophantine GeometryEdited by G. O. JonesUniversity of Manchester

and A. J. WilkieUniversity 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

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

£50.00 / US$80.00


Sheaves and Functions Modulo pLectures on the Woods Hole Trace FormulaLenny TaelmanUniversiteit van Amsterdam

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

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


Discrete mathematics, information theory and coding theory

Introduction to Random GraphsAlan FriezeCarnegie Mellon University, Pennsylvania

and Michal KarońskiUniwersytet 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


Analytic Pattern MatchingFrom DNA to TwitterPhilippe JacquetBell Laboratories

and Wojciech SzpankowskiPurdue University, Indiana

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.2015 247 x 174 mm 385pp 40 b/w illus. 110 exercises 978-0-521-87608-7 Hardback

£45.00 / US$75.00














Discrete mathematics, information theory and coding theory 5

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Catalan NumbersRichard P. StanleyMassachusetts 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


Applied Algebra and Number TheoryEdited by Gerhard LarcherJohannes Kepler Universität Linz

Friedrich PillichshammerJohannes Kepler Universität Linz

Arne WinterhofAustrian Academy of Sciences, Linz

and Chaoping XingNanyang 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


Erdős–Ko–Rado Theorems: Algebraic ApproachesChristopher GodsilUniversity of Waterloo, Ontario

and Karen MeagherUniversity 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


Topics in Chromatic Graph TheoryEdited by Lowell W. BeinekePurdue University, Indiana

and Robin J. WilsonThe 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 JensenEncyclopedia of Mathematics and its Applications, 156


£79.99 / US$130.00


Combinatorics, Words and Symbolic DynamicsEdited by Valérie BerthéUniversité Paris Diderot – Paris 7

and Michel RigoUniversité 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

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


£99.99 / US$155.00



The Surprising Mathematics of Longest Increasing SubsequencesDan RomikUniversity 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

Institute of Mathematical Statistics Textbooks, 4


£65.00 / US$99.00

978-1-107-42882-9 Paperback £27.99 / US$39.99












6 Discrete mathematics, information theory and coding theory / Abstract analysis

Inequalities for Graph EigenvaluesZoran StanićUniverzitet 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


Surveys in Combinatorics 2015Edited by Artur CzumajUniversity of Warwick

Agelos GeorgakopoulosUniversity of Warwick

Daniel KrálUniversity of Warwick

Vadim LozinUniversity of Warwick

and Oleg PikhurkoUniversity 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 in-depth analysis of recent developments.London Mathematical Society Lecture Note Series, 424


£55.00 / US$90.00


Random Graphs, Geometry and Asymptotic StructureMichael KrivelevichTel-Aviv University

Konstantinos PanagiotouUniversität Munchen

Mathew PenroseUniversity of Bath

and Colin McDiarmidUniversity of Oxford

Edited by Nikolaos FountoulakisUniversity of Birmingham

and Dan HefetzUniversity 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


Finite Geometry and Combinatorial ApplicationsSimeon BallUniversitat 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


£79.99 / US$120.00

978-1-107-51843-8 Paperback £27.99 / US$44.99


Games of No Chance 4Edited by Richard J. NowakowskiDalhousie 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


£59.99 / US$94.99


Abstract analysis

The Cambridge Dictionary of Probability and Its ApplicationsDavid StirzakerSt 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












Abstract analysis 7


Probability: The Classical Limit TheoremsHenry McKeanNew 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


Quantum StochasticsMou-Hsiung ChangMathematical Sciences Division, US Army Research Office

This book provides a systematic, self-contained treatment of the theory of quantum probability and quantum Markov processes.Cambridge Series in Statistical and Probabilistic Mathematics, 37

2015 253 x 177 mm 424pp 978-1-107-06919-0 Hardback

£55.00 / US$85.00


Introduction to Model Spaces and their OperatorsStephan Ramon GarciaPomona College, California

Javad MashreghiUniversité Laval, Québec

and William T. RossUniversity of Richmond, Virginia

The study of model spaces is a broad field with connections to complex analysis, operator theory, engineering and mathematical physics. This self-contained 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


£49.99 / US$79.99



Fourier Analysis and Hausdorff DimensionPertti MattilaUniversity 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.Cambridge Studies in Advanced Mathematics, 150


£49.99 / US$79.99


Foundations of Ergodic TheoryMarcelo VianaInstituto Nacional de Matemática Pura e Aplicada (IMPA), Rio de Janeiro

and Krerley OliveiraUniversidade 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


£79.99 / US$120.00



Random Matrix Theory, Interacting Particle Systems, and Integrable SystemsEdited by Percy DeiftNew York University, Courant Institute of Mathematical Sciences

and Peter ForresterUniversity 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


The Theory of H(b) SpacesEmmanuel FricainUniversité de Lille 1

and Javad MashreghiUniversité 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



The Theory of H(b) SpacesVolume 1Emmanuel FricainUniversité de Lille 1


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,












8 Abstract analysis / Real and complex analysis

making the book suitable for graduate courses.New Mathematical Monographs, 20


£99.00 / US$150.00



The Theory of H(b) SpacesVolume 2Emmanuel FricainUniversité de Lille I


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


£110.00 / US$175.00



Sobolev Spaces on Metric Measure SpacesAn Approach Based on Upper GradientsJuha HeinonenPekka KoskelaUniversity of Jyväskylä, Finland

Nageswari ShanmugalingamUniversity of Cincinnati

and Jeremy T. TysonUniversity 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


£80.00 / US$130.00


Convergence of One-parameter Operator SemigroupsIn Models of Mathematical Biology and ElsewhereAdam BobrowskiPolitechnika Lubelska, Poland

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.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



Real and complex analysis

Twelve Landmarks of Twentieth-Century AnalysisD. ChoimetLycée du Parc, Lyon

and H. QueffélecUniversité 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


textbook

Numbers and FunctionsSteps into AnalysisThird editionR. P. BurnUniversity 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












Topology and geometry 9


Topology and geometry

Hyperbolic ManifoldsAn Introduction in 2 and 3 DimensionsAlbert MardenUniversity 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.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



new in PaPerback

Indra’s PearlsThe Vision of Felix KleinDavid MumfordBrown University, Rhode Island

Caroline SeriesUniversity of Warwick

and David WrightOklahoma State University

Felix Klein, one of the great nineteenth-century 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 step-by-step instructions for writing programs that generate the images. Others can see how the images relate to ideas at the forefront of research.

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

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


£49.99 / US$84.99


Cox RingsIvan ArzhantsevMoscow State University

Ulrich DerenthalLeibniz Universität Hannover

Jürgen HausenEberhard-Karls-Universität Tübingen, Germany

and Antonio LafaceUniversidad de Concepción, Chile

This book provides a largely self-contained 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


Constructing Dynamic Triangles TogetherThe Development of Mathematical Group CognitionGerry StahlDrexel 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,

mathematics education, and human-computer interaction.Learning in Doing: Social, Cognitive and Computational Perspectives


£69.99 / US$110.00


Recent Advances in Algebraic GeometryA Volume in Honor of Rob Lazarsfeld’s 60th BirthdayEdited by Christopher D. HaconUniversity of Utah

Mircea MustaţăUniversity of Michigan, Ann Arbor

and Mihnea PopaUniversity 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


£65.00 / US$99.00


Geometry, Topology, and Dynamics in Negative CurvatureEdited by C. S. AravindaTIFR Centre for Applicable Mathematics, Bangalore, India

F. T. FarrellTsinghua University, Beijing

and J.-F. LafontOhio 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


£60.00 / US$99.00













10 Topology and geometry

Recent Advances in Hodge TheoryPeriod Domains, Algebraic Cycles, and ArithmeticEdited by Matt KerrWashington University, St Louis

and Gregory PearlsteinTexas 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


£65.00 / US$115.00



Geometry in a Fréchet ContextA Projective Limit ApproachC. T. J. DodsonUniversity of Manchester

George GalanisHellenic Naval Academy, Piraeus, Greece

and Efstathios VassiliouUniversity 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



The Geometry of Celestial MechanicsHansjörg GeigesUniversität 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.London Mathematical Society Student Texts


c. £65.00 / c. US$110.00

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



Symplectic, Poisson, and Noncommutative GeometryEdited by Tohru EguchiRikkyo University, Japan

Yakov EliashbergStanford University, California

and Yoshiaki MaedaTokyo 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


£60.00 / US$99.00


Cubical Homotopy TheoryBrian A. MunsonUnited States Naval Academy, Maryland

and Ismar VolićWellesley 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


£79.99 / US$125.00


Symplectic Topology and Floer HomologyYong-Geun OhPohang 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

comprehensive resource suitable for experts and newcomers alike.New Mathematical Monographs

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


Symplectic Topology and Floer HomologyVolume 1: Symplectic Geometry and Pseudoholomorphic CurvesYong-Geun OhPohang 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


£89.99 / US$140.00


Symplectic Topology and Floer HomologyVolume 2: Floer Homology and its ApplicationsYong-Geun OhPohang 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


£89.99 / US$140.00














Differential and integral equations, dynamical systems and control / Mathematical physics 11


Differential and integral equations, dynamical systems and control

new in PaPerback

textbook

Introduction to Dynamical SystemsMichael BrinUniversity of Maryland, College Park

and Garrett StuckUniversity 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. Low-dimensional dynamics; 8. Complex dynamics; 9. Measure-theoretic entropy; Bibliography; Index.2015 228 x 152 mm 256pp 35 b/w illus. 305 exercises 978-1-107-53894-8 Paperback

£34.99 / US$59.99


£49.99 / US$84.99


Isolated Singularities in Partial Differential InequalitiesMarius GherguUniversity College Dublin

and Steven D. TaliaferroTexas 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

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


£79.99 / US$125.00



Reversibility in Dynamics and Group TheoryAnthony G. O’FarrellNational University of Ireland, Maynooth

and Ian ShortThe 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


£40.00 / US$65.00


The Cauchy Problem for Non-Lipschitz Semi-Linear Parabolic Partial Differential EquationsJ. C. MeyerUniversity of Birmingham

and D. J. NeedhamUniversity of Birmingham

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 semi-linear 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.London Mathematical Society Lecture Note Series, 419

2015 228 x 152 mm 173pp 978-1-107-47739-1 Paperback

£44.99 / US$69.99


Recent Progress in the Theory of the Euler and Navier–Stokes EquationsEdited by James C. RobinsonUniversity of Warwick

José L. RodrigoUniversity of Warwick

Witold SadowskiUniwersytet Warszawski, Poland

and Alejandro Vidal-LópezXi’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


£50.00 / US$80.00



Mathematical physics

Electricity and Magnetism for MathematiciansA Guided Path from Maxwell’s Equations to Yang–MillsThomas A. GarrityWilliams 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












12 Mathematical physics / Mathematical modelling and methods

Advanced Concepts in Quantum MechanicsGiampiero EspositoUniversità degli Studi di Napoli ‘Federico II’

Giuseppe MarmoUniversità degli Studi di Napoli ‘Federico II’

Gennaro MieleUniversità degli Studi di Napoli ‘Federico II’

and George SudarshanUniversity 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


Mathematical modelling and methods

A Guided Tour of Mathematical Methods for the Physical SciencesThird editionRoel SniederColorado School of Mines

and Kasper van WijkUniversity 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


Introduction to Atmospheric ModellingDouw G. SteynUniversity 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


£15.99 / US$25.99


Partial Differential Equation Methods for Image InpaintingCarola-Bibiane SchönliebUniversity 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


£64.99 / US$99.99


An Introduction to Stochastic DynamicsJinqiao DuanIllinois 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


£94.99 / US$150.00

978-1-107-42820-1 Paperback £41.99 / US$64.99


Singularities: Formation, Structure, and PropagationJ. EggersUniversity of Bristol

and M. A. FontelosUniversidad 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


£79.99 / US$130.00

978-1-107-48549-5 Paperback £39.99 / US$74.99












Fluid dynamics and solid mechanics / Numerical analysis / Computational science 13


Fluid dynamics and solid mechanics

MagnetoconvectionN. O. WeissUniversity of Cambridge

and M. R. E. ProctorUniversity 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


£75.00 / US$120.00


Lectures on the Theory of Water WavesEdited by Thomas J. BridgesUniversity of Surrey

Mark D. GrovesUniversität des Saarlandes, Saarbrücken, Germany

and David P. NichollsUniversity 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


£55.00 / US$90.00



Numerical analysis

textbook

Elements of Numerical AnalysisSecond editionRadhey S. GuptaIndian 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

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


Acta Numerica 2015Volume 24Edited by Arieh IserlesUniversity 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.Acta Numerica, 24


£114.00 / US$195.00


Multiscale Methods for Fredholm Integral EquationsZhongying ChenSun Yat-Sen University, Guangzhou, China

Charles A. MicchelliState University of New York, Albany

and Yuesheng XuSun 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

course for advanced undergraduates or beginning graduates.Cambridge Monographs on Applied and Computational Mathematics, 28


£99.99 / US$155.00


Computational science

Passive Imaging with Ambient NoiseJosselin GarnierUniversité de Paris VII (Denis Diderot)

and George PapanicolaouStanford University, California

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.2016 247 x 174 mm 288pp 15 b/w illus. 48 colour illus. 978-1-107-13563-5 Hardback

£89.99 / US$150.00



Probabilistic Forecasting and Bayesian Data AssimilationSebastian ReichUniversität Potsdam, Germany and University of Reading

and Colin CotterImperial 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.











14 Computational science / History of mathematics / Optimization, OR and risk analysis


£69.99 / US$115.00

978-1-107-66391-6 Paperback £34.99 / US$54.99


A Student’s Guide to Numerical MethodsIan H. HutchinsonMassachusetts 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


Ridge FunctionsAllan PinkusTechnion – 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


£79.99 / US$125.00


History of mathematics

Applied Nonparametric EconometricsDaniel J. HendersonUniversity of Alabama

and Christopher F. ParmeterUniversity 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


Optimization, OR and risk analysis

A Course on Cooperative Game TheorySatya R. ChakravartyIndian Statistical Institute

Manipushpak MitraIndian Statistical Institute

and Palash SarkarIndian 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


textbook

Chance, Strategy, and ChoiceAn Introduction to the Mathematics of Games and ElectionsSamuel Bruce SmithSt 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


An Introduction to Polynomial and Semi-Algebraic OptimizationJean Bernard LasserreCentre 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













Optimization, OR and risk analysis / Mathematical finance / Also of interest 15


HigHligHt

Repeated GamesJean-François MertensSylvain SorinUniversité de Paris VI (Pierre et Marie Curie)

and Shmuel ZamirHebrew 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.Econometric Society Monographs, 55


£75.00 / US$125.00

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


Mathematical finance

Algorithmic and High-Frequency TradingÁlvaro CarteaUniversity College London

Sebastian JaimungalUniversity of Toronto

and José PenalvaUniversidad 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

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


Stochastic Interest RatesDaragh McInerneyAGH University of Science and Technology, Krakow

and Tomasz ZastawniakUniversity of York

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.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


Also of interest

The Computing UniverseA Journey through a RevolutionTony HeyMicrosoft Research, Washington

and Gyuri PápayUniversity 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

978-0-521-15018-7 Paperback £24.99 / US$39.99


HigHligHt

Entertainment Industry EconomicsA Guide for Financial AnalysisNinth editionHarold 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


Mathematical Foundations of Infinite-Dimensional Statistical ModelsEvarist GinéUniversity of Connecticut

and Richard NicklUniversity 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 self-contained, 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













16 Also of interest

Mathematics and the BodyMaterial Entanglements in the ClassroomElizabeth de FreitasAdelphi University, Garden City, New York

and Nathalie SinclairSimon 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


£65.00 / US$99.00


Granularity Theory with Applications to Finance and InsurancePatrick GagliardiniUniversita della Svizzera Italiana, Switzerland

and Christian GouriérouxUniversity 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


£55.00 / US$90.00

978-1-107-66288-9 Paperback £21.99 / US$34.99






Index 17


A Acta Numerica 2015 .............................13Advanced Concepts in Quantum

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

Representations....................................4

B Ball, Simeon ............................................6Beineke, Lowell W. ...................................5Benkő, Tamás ..........................................2Berthé, Valérie .........................................5Bloch–Kato Conjecture for the Riemann

Zeta Function, The ................................4Bobrowski, Adam ....................................8Bridges, Thomas J. .................................13Brin, Michael .........................................11Burn, R. P. ...............................................8Burness, Timothy C. .................................2

C Cambridge Dictionary of Probability and

Its Applications, The ..............................6Campbell, C. M. .......................................3Cartea, Álvaro .......................................15Catalan Numbers ....................................5Cauchy Problem for Non-Lipschitz Semi-

Linear Parabolic Partial Differential Equations, The ....................................11

Chakravarty, Satya R. .............................14Chance, Strategy, and Choice .................14Chang, Mou-Hsiung ................................7Chen, Zhongying ...................................13Choimet, D. .............................................8Classical Groups, Derangements and

Primes ..................................................2Coates, John ...........................................4Combinatorics, Words and Symbolic

Dynamics .............................................5Computation, Proof, Machine ..................1Computing Universe, The .......................15Concise Text on Advanced Linear

Algebra, A ............................................2Conrad, Brian ..........................................3Constructing Dynamic Triangles Together .9Convergence of One-parameter

Operator Semigroups ............................8Cooper, S. Barry .......................................1Cotter, Colin ..........................................13Course on Cooperative Game Theory, A ..14Cox Rings................................................9Cubical Homotopy Theory ......................10Czumaj, Artur ..........................................6

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

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

E Eggers, J. ...............................................12Eguchi, Tohru ........................................10Electricity and Magnetism for

Mathematicians ..................................11Elements of Numerical Analysis..............13Eliashberg, Yakov...................................10Entertainment Industry Economics .........15Erdős–Ko–Rado Theorems: Algebraic

Approaches ..........................................5Esposito, Giampiero ...............................12Evertse, Jan-Hendrik ................................3

F Faltings, Gerd ..........................................4Farrell, F. T................................................9Finite Geometry and Combinatorial

Applications .........................................6Fontelos, M. A. ......................................12Forrester, Peter ........................................7Foundations of Ergodic Theory .................7Fountoulakis, Nikolaos .............................6Fourier Analysis and Hausdorff Dimension 7Fricain, Emmanuel ............................... 7, 8Frieze, Alan .............................................4

G G. H. Hardy Reader, The ...........................1Gabber, Ofer ............................................3Gagliardini, Patrick ................................16Galanis, George .....................................10Games of No Chance 4............................6Garcia, Stephan Ramon ...........................7Gardner, Martin .......................................1Garnier, Josselin ....................................13Garrity, Thomas A. .................................11Geiges, Hansjörg ...................................10Geometry in a Fréchet Context ...............10Geometry of Celestial Mechanics, The ....10Geometry, Topology, and Dynamics in

Negative Curvature ...............................9Georgakopoulos, Agelos ..........................6Geuvers, Herman .....................................2Ghergu, Marius .....................................11Giné, Evarist ..........................................15Giudici, Michael ......................................2Godsil, Christopher ..................................5Gouriéroux, Christian .............................16Granularity Theory with Applications to

Finance and Insurance ........................16Groups St Andrews 2013 .........................3Groves, Mark D. .....................................13Guide to NIP Theories, A ..........................2Guided Tour of Mathematical Methods

for the Physical Sciences, A .................12Guillot, Pierre ..........................................1Gupta, Radhey S. ...................................13Győry, Kálmán .........................................3

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

I Indra’s Pearls ...........................................9Inequalities for Graph Eigenvalues ...........6Introduction to Atmospheric Modelling ..12Introduction to Dynamical Systems ........11Introduction to Model Spaces and their

Operators .............................................7Introduction to Polynomial and Semi-

Algebraic Optimization, An .................14Introduction to Random Graphs ...............4Introduction to Stochastic Dynamics, An .12Irvine, Lyn ................................................1Iserles, Arieh ..........................................13Isolated Singularities in Partial

Differential Inequalities .......................11

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

K Karoński, Micha .....................................4Kassaei, Payman L. ..................................4Kechris, Alexander S. ................................2Kerr, Matt ..............................................10Kim, Minhyong ........................................4Knots and Borromean Rings, Rep-Tiles,

and Eight Queens .................................1Koskela, Pekka ........................................8Král, Daniel .............................................6Krivelevich, Michael .................................6

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

M Maeda, Yoshiaki ....................................10Magnetoconvection ...............................13Manin, Yu. V. ...........................................4Marden, Albert ........................................9Marmo, Giuseppe ..................................12Mashreghi, Javad ................................ 7, 8Mathematical Foundations of Infinite-

Dimensional Statistical Models ............15Mathematics and the Body ....................16Mattila, Pertti ..........................................7

18 Index

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

Integral Equations ..............................13Mumford, David ......................................9Munson, Brian A. ...................................10Mustaţă, Mircea ......................................9

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

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

P Panagiotou, Konstantinos ........................6Papanicolaou, George............................13Pápay, Gyuri ..........................................15Paris, Jeffrey ............................................2Parmeter, Christopher F. .........................14Partial Differential Equation Methods for

Image Inpainting ................................12Passive Imaging with Ambient Noise ......13Pearlstein, Gregory ................................10Penalva, José .........................................15Penrose, Mathew.....................................6Pikhurko, Oleg .........................................6Pillichshammer, Friedrich ..........................5Pinkus, Allan .........................................14Popa, Mihnea ..........................................9Prasad, Amritanshu .................................2Prasad, Gopal ..........................................3Prime Numbers and the Riemann

Hypothesis ...........................................3Probabilistic Forecasting and Bayesian

Data Assimilation ...............................13Probability: The Classical Limit Theorems ..7Proctor, M. R. E. .....................................13Proofs and Refutations ............................1Pseudo-reductive Groups .........................3Pure Inductive Logic ................................2

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

R Raghuram, A. ..........................................4Random Graphs, Geometry and

Asymptotic Structure ............................6Random Matrix Theory, Interacting

Particle Systems, and Integrable Systems ................................................7

Recent Advances in Algebraic Geometry ...9Recent Advances in Hodge Theory ..........10Recent Progress in the Theory of the

Euler and Navier–Stokes Equations .....11Reich, Sebastian ....................................13Repeated Games ...................................15Representation Theory .............................2Reversibility in Dynamics and Group

Theory ................................................11Ridge Functions.....................................14Rigo, Michel ............................................5Robertson, E. F. ........................................3Robinson, James C. ................................11Rodrigo, José L. .....................................11Roman, Marion .......................................1Romik, Dan .............................................5Roney-Dougal, C. M. ................................3Ross, William T. ........................................7

S Sadowski, Witold...................................11Saikia, Anupam .......................................4Sarkar, Palash ........................................14Schönlieb, Carola-Bibiane ......................12Semantic Web Explained, The ..................2Series, Caroline........................................9Shanmugalingam, Nageswari ..................8Sheaves and Functions Modulo p .............4Short, Ian ..............................................11Simon, Pierre ...........................................2Sinclair, Nathalie....................................16Singularities: Formation, Structure, and

Propagation .......................................12Smith, Samuel Bruce ..............................14Snieder, Roel .........................................12Sobolev Spaces on Metric Measure

Spaces .................................................8Solving Polynomial Equation Systems III ...3Solving Polynomial Equation Systems IV ...3Sorin, Sylvain .........................................15Stahl, Gerry .............................................9Stanić, Zoran ...........................................6Stanley, Richard P. ...................................5Steel, John R. ..........................................2Stein, William ..........................................3Steyn, Douw G. ......................................12Stirzaker, David ........................................6Stochastic Interest Rates ........................15Stuck, Garrett ........................................11Student’s Guide to Numerical Methods,

A .......................................................14

Sudarshan, George ................................12Sujatha, R. ..............................................4Surprising Mathematics of Longest

Increasing Subsequences, The ...............5Surveys in Combinatorics 2015 ................6Symplectic Topology and Floer

Homology ..........................................10Symplectic, Poisson, and

Noncommutative Geometry ................10Szeredi, Péter ..........................................2Szpankowski, Wojciech ............................4

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

Analysis ...............................................8Type Theory and Formal Proof ..................2Tyson, Jeremy T. .......................................8

U Unit Equations in Diophantine Number

Theory ..................................................3

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

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

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

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

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

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