PUBLICATIONS OF

the American Mathematical Society

Spring 2017

TABLE OF CONTENTS Special Note to AMS Members

AMS members qualify for a discount on the price of AMS

1 HIGHLIGHTS publications. Please provide your membership number when

8 ALGEBRA & ALGEBRAIC GEOMETRY making your purchase.

9 ANALYSIS

11 APPLIED MATHEMATICS AMS eBooks

13 DIFFERENTIAL EQUATIONS

14 DISCRETE MATHEMATICS The AMS offers several of its most popular series in eBook

& COMBINATORICS format. Titles may be purchased as complete backfiles or current-

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17 GEOMETRY & TOPOLOGY simultaneous access, and without DRM.

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19 MATHEMATICAL PHYSICS

20 MATHEMATICS EDUCATION To set up a standing order for any series in this

22 NUMBER THEORY catalogue, please email:

23 PROBABILITY & STATISTICS [email protected]

25 CONTEMPORARY MATHEMATICS

SERIES

27 MEMOIRS OF THE AMERICAN

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Applied Mathematics AM

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HIGHLIGHTS 1

IT’S ABOUT TIME

Elementary Mathematical Aspects of Relativity

Roger Cooke

Apr 2017 410pp

9781470434830 Hardback £76.50 / €84.00

This book has three main goals. First, it explores a selection of topics from the early period of the

theory of relativity, focusing on particular aspects that are interesting or unusual. These include

the twin paradox; relativistic mechanics and its interaction with Maxwell’s laws; the earliest

triumphs of general relativity relating to the orbit of Mercury and the deflection of light passing

near the sun; and the surprising bizarre metric of Kurt Gödel, in which time travel is possible.

Second, it provides an exposition of the differential geometry needed to understand these

topics on a level that is intended to be accessible to those with just two years of university-level

mathematics as background. Third, it reflects on the historical development of the subject and

its significance for our understanding of what reality is and how we can know about the physical

universe. The book also takes note of historical prefigurations of relativity, such as Euler’s 1744

result that a particle moving on a surface and subject to no tangential acceleration will move

along a geodesic, and the work of Lorentz and Poincaré on space-time coordinate transformations

between two observers in motion at constant relative velocity.

The book is aimed at advanced undergraduate mathematics, science, and engineering majors

(and, of course, at any interested person who knows a little university-level mathematics). The

reader is assumed to know the rudiments of advanced calculus, a few techniques for solving

differential equations, some linear algebra, and basics of set theory and groups.

PUSHING LIMITS

From West Point to Berkeley & Beyond

Ted Hill

Apr 2017 334pp

9781470435844 Hardback £45.95 / €51.00

Pushing Limits: From West Point to Berkeley & Beyond challenges the myth that mathematicians lead

dull and ascetic lives. It recounts the unique odyssey of a noted mathematician who overcame

military hurdles at West Point, Army Ranger School and the Vietnam War, and survived many

civilian escapades - hitchhiking in third-world hotspots, fending off sharks in Bahamian reefs, and

camping deep behind the forbidding Iron Curtain. From ultra-conservative West Point in the ’60s

to ultra-radical Berkeley in the ’70s, and ultimately to genteel Georgia Tech in the ’80s, this is the

tale of an academic career as noteworthy for its offbeat adventures as for its teaching and research

accomplishments. It brings to life the struggles and risks underlying mathematical research, the

unparalleled thrill of making scientific breakthroughs, and the joy of sharing those discoveries

around the world. Hill’s book is packed with energy, humour, and suspense, both physical and

intellectual. Anyone who is curious about how a maverick mathematician thinks, who wants to

relive the zanier side of the ’60s and ’70s, who wants an armchair journey into the third world,

or who seeks an unconventional viewpoint about some of our more revered institutions, will be

drawn to this book.

…captivating memoir reveals an intriguing character who is part Renaissance Man, part Huckleberry

Finn.Fast-paced and often hilarious … provides some penetrating and impious insights into some of our

more revered institutions.

—Rick Atkinson, three-time Pulitzer Prize winner, author of The Long Gray Line

Thoughtful, funny, evocative, Ted Hill takes us through a life well-lived … an intensely personal story that

will appeal to every profession - and to every generation!

—General Wesley Clark, former NATO Supreme Commander

A co-publication of the AMS and Mathematical Association of America

2 HIGHLIGHTS

GAME THEORY, ALIVE AM

Anna R. Karlin & Yuval Peres

May 2017 396pp

9781470419820 Hardback £76.50 / €84.00

We live in a highly connected world with multiple self-interested agents interacting and

myriad opportunities for conflict and cooperation. The goal of game theory is to understand

these opportunities.

This book presents a rigorous introduction to the mathematics of game theory without

losing sight of the joy of the subject. This is done by focusing on theoretical highlights

(e.g., at least six Nobel Prize winning results are developed from scratch) and by presenting

exciting connections of game theory to other fields such as computer science (algorithmic game

theory), economics (auctions and matching markets), social choice (voting theory), biology

(signaling and evolutionary stability), and learning theory. Both classical topics, such as zero-

sum games, and modern topics, such as sponsored search auctions, are covered. Along the way,

beautiful mathematical tools used in game theory are introduced, including convexity, fixed-point

theorems, and probabilistic arguments.

The book is appropriate for a first course in game theory at either the undergraduate or graduate

level, whether in mathematics, economics, computer science, engineering, or statistics. The

importance of game-theoretic thinking transcends the academic setting - for every action

we take, we must consider not only its direct effects, but also how it influences the incentives

of others.

Game theory’s influence is felt in a wide range of disciplines, and the authors deliver masterfully on the

challenge of presenting both the breadth and coherence of its underlying world-view.The book achieves

a remarkable synthesis, introducing the reader to the blend of economic insight, mathematical elegance,

scientific impact, and counter-intuitive punch that characterizes game theory as a field.

—Jon Kleinberg, Cornell University, 2006 Nevanlinna Prize winner

A game theory textbook by people who love … games! It covers many classic as well as recent topics of

game theory.Its rigorous treatment, interspersed with illuminating examples, makes it a challenging

pleasure to read.

—Sergiu Hart, The Hebrew University of Jerusalem

GAME THEORY

A Playful Introduction

Matt DeVos & Deborah Kent

Jan 2017 360pp

9781470422103 Paperback £49.95 / €55.00

Student Mathematical Library, Vol. 80

Offers a gentle introduction to the mathematics of both sides of game theory: combinatorial and

classical. The combination allows for a dynamic and rich tour of the subject united by a common

theme of strategic reasoning.

The first four chapters develop combinatorial game theory, beginning with an introduction to

game trees and mathematical induction, then investigating the games of Nim and Hackenbush.

The analysis of these games concludes with the cornerstones of the Sprague-Grundy Theorem

and the Simplicity Principle.

The last eight chapters of the book offer a scenic journey through the mathematical highlights

of classical game theory. This contains a thorough treatment of zero-sum games and the von

Neumann Minimax Theorem, as well as a student-friendly development and proof of the Nash

Equilibrium Theorem. The Folk Theorem, Arrow's voting paradox, evolutionary biology,

cake-cutting, and other engaging auxiliary topics also appear.

The book is designed as a textbook for an undergraduate mathematics class. With ample material

and limited dependencies between the chapters, the book is adaptable to a variety of situations

and a range of audiences. Instructors, students, and independent readers alike will appreciate the

flexibility in content choices as well as the generous sets of exercises at various levels.

HIGHLIGHTS 3

LARGE DEVIATIONS

S.R.S. Varadhan

Dec 2016 104pp

9780821840863 Paperback £36.95 / €41.00

Courant Lecture Notes, Vol. 27

The theory of large deviations deals with rates at which probabilities of certain events decay as a

natural parameter in the problem varies. This book, which is based on a graduate course on large

deviations at the Courant Institute, focuses on three concrete sets of examples: (i) diffusions

with small noise and the exit problem, (ii) large time behavior of Markov processes and their

connection to the Feynman-Kac formula and the related large deviation behavior of the number

of distinct sites visited by a random walk, and (iii) interacting particle systems, their scaling limits,

and large deviations from their expected limits. For the most part the examples are worked out in

detail, and in the process the subject of large deviations is developed.

The book will give the reader a flavour of how large deviation theory can help in problems that are

not posed directly in terms of large deviations.

ORDERED GROUPS AND TOPOLOGY

Adam Clay & Dale Rolfsen

Dec 2016 154pp

9781470431068 Hardback £80.50 / €89.00

Graduate Studies in Mathematics, Vol. 176

Deals with the connections between topology and ordered groups. It begins with a self-contained

introduction to orderable groups and from there explores the interactions between orderability

and objects in low-dimensional topology, such as knot theory, braid groups, and 3-manifolds, as

well as groups of homeomorphisms and other topological structures. The book also addresses

recent applications of orderability in the studies of codimension-one foliations and

Heegaard-Floer homology. The use of topological methods in proving algebraic results is another

feature of the book.

The book was written to serve both as a textbook for graduate students, containing many

exercises, and as a reference for researchers in topology, algebra, and dynamical systems.

CARTAN FOR BEGINNERS

Differential Geometry via Moving Frames and

Exterior Differential Systems, Second Edition

Thomas A. Ivey & Joseph M. Landsberg

Jan 2017 455pp

9781470409869 Hardback £90.50 / €100.00

Graduate Studies in Mathematics, Vol. 175

Two central aspects of Cartan's approach to differential geometry are the theory of exterior

differential systems (EDS) and the method of moving frames. This book presents thorough

and modern treatments of both subjects, including their applications to both classic and

contemporary problems in geometry. It begins with the classical differential geometry of surfaces

and basic Riemannian geometry in the language of moving frames, along with an elementary

introduction to exterior differential systems. Key concepts are developed incrementally, with

motivating examples leading to definitions, theorems, and proofs.

Once the basics of the methods are established, the authors develop applications and advanced

topics. One notable application is to complex algebraic geometry, where they expand and update

important results from projective differential geometry. As well, the book features an introduction

to G-structures and a treatment of the theory of connections. The techniques of EDS are also

applied to obtain explicit solutions of PDEs via Darboux's method, the method of characteristics,

and Cartan's method of equivalence.

The second edition features three new chapters: on Riemannian geometry, emphasizing the use

of representation theory; on the latest developments in the study of Darboux-integrable systems;

and on conformal geometry, written in a manner to introduce readers to the related parabolic

geometry perspective.

4 HIGHLIGHTS

DIFFERENTIAL GALOIS THEORY THROUGH

RIEMANN-HILBERT CORRESPONDENCE

An Elementary Introduction

Jacques Sauloy

Jan 2017 279pp

9781470430955 Hardback £90.50 / €100.00

Graduate Studies in Mathematics, Vol. 177

Differential Galois theory is an important, fast developing area which appears more and more in

graduate courses since it mixes fundamental objects from many different areas of mathematics

in a stimulating context. For a long time, the dominant approach, usually called Picard-Vessiot

Theory, was purely algebraic. This approach has been extensively developed and is well covered in

the literature. An alternative approach consists in tagging algebraic objects with transcendental

information which enriches the understanding and brings not only new points of view but

also new solutions. It is very powerful and can be applied in situations where the Picard-Vessiot

approach is not easily extended. This book offers a hands-on transcendental approach to

differential Galois theory, based on the Riemann-Hilbert correspondence. Along the way, it

provides a smooth, down-to-earth introduction to algebraic geometry, category theory and

tannakian duality.

Since the book studies only complex analytic linear differential equations, the main prerequisites

are complex function theory, linear algebra, and an elementary knowledge of groups and

of polynomials in many variables. A large variety of examples, exercises, and theoretical

constructions, often via explicit computations, offers first-year graduate students an accessible

entry into this exciting area.

QUIVER REPRESENTATIONS AND QUIVER VARIETIES

Alexander Kirillov, Jr.

Nov 2016 295pp

9781470423070 Hardback £90.50 / €100.00

Graduates Studies in Mathematics, Vol. 174

An introduction to the theory of quiver representations and quiver varieties, starting with basic

definitions and ending with Nakajima's work on quiver varieties and the geometric realization of

Kac–Moody Lie algebras.

The first part of the book is devoted to the classical theory of quivers of finite type. Here the

exposition is mostly self-contained and all important proofs are presented in detail. The second

part contains the more recent topics of quiver theory that are related to quivers of infinite type:

Coxeter functor, tame and wild quivers, McKay correspondence, and representations of Euclidean

quivers. In the third part, topics related to geometric aspects of quiver theory are discussed, such

as quiver varieties, Hilbert schemes, and the geometric realization of Kac–Moody algebras. Here

some of the more technical proofs are omitted; instead only the statements and some ideas of

the proofs are given, and the reader is referred to original papers for details. The exposition in the

book requires only a basic knowledge of algebraic geometry, differential geometry, and the theory

of Lie groups and Lie algebras. Some sections use the language of derived categories; however, the

use of this language is reduced to a minimum. The many examples make the book accessible to

graduate students who want to learn about quivers, their representations, and their relations to

algebraic geometry and Lie algebras.

HIGHLIGHTS 5

ALGEBRA IN ACTION

A Course in Groups, Rings, and Fields

Shahriar Shahriari

Apr 2017 655pp

9781470428495 Hardback £120.00 / €130.00

Pure and Applied Undergraduate Texts, Vol. 27

Based on the author’s popular courses at Pomona College, this text provides a readable,

student-friendly, and somewhat sophisticated introduction to abstract algebra. It is aimed at

sophomore or junior undergraduates who are seeing the material for the first time. In addition

to the usual definitions and theorems, there is ample discussion to help students build intuition

and learn how to think about the abstract concepts. The book has over 1300 exercises and

mini-projects of varying degrees of difficulty, and, to facilitate active learning and self-study, hints

and short answers for many of the problems are provided. There are full solutions to over 100

problems in order to augment the text and to model the writing of solutions. Lattice diagrams are

used throughout to visually demonstrate results and proof techniques. The book covers groups,

rings, and fields. In group theory, group actions are the unifying theme and are introduced early.

Ring theory is motivated by what is needed for solving Diophantine equations, and, in field theory,

Galois theory and the solvability of polynomials take center stage. In each area, the text goes deep

enough to demonstrate the power of abstract thinking and to convince the reader that the subject

is full of unexpected results.

THE TOOLS OF MATHEMATICAL REASONING

Tamara J. Lakins

Oct 2016 217pp

9781470428990 Hardback £70.50 / €77.00

Pure and Applied Undergraduate Texts, Vol. 26

This accessible textbook gives beginning undergraduate mathematics students a first exposure

to introductory logic, proofs, sets, functions, number theory, relations, finite and infinite sets, and

the foundations of analysis. The book provides students with a quick path to writing proofs and a

practical collection of tools that they can use in later mathematics courses such as abstract algebra

and analysis. The importance of the logical structure of a mathematical statement as a framework

for finding a proof of that statement, and the proper use of variables, is an early and consistent

theme used throughout the book.

MATHEMATICAL ANALYSIS AND ITS INHERENT NATURE

Hossein Hosseini Giv

Oct 2016 351pp

9781470428075 Hardback £90.50 / €100.00

Pure and Applied Undergraduate Texts, Vol. 25

Mathematical analysis is often referred to as generalized calculus. But it is much more than that.

This book has been written in the belief that emphasizing the inherent nature of a mathematical

discipline helps students to understand it better. With this in mind, and focusing on the essence

of analysis, the text is divided into two parts based on the way they are related to calculus:

completion and abstraction. The first part describes those aspects of analysis which complete

a corresponding area of calculus theoretically, while the second part concentrates on the way

analysis generalizes some aspects of calculus to a more general framework. Presenting the

contents in this way has an important advantage: students first learn the most important aspects

of analysis on the classical space R and then fill in the gaps of their calculus-based knowledge. Then

they proceed to a step-by-step development of an abstract theory, namely, the theory of metric

spaces which explores such crucial notions as limit, continuity, and convergence in a wider context.

The readers are assumed to have passed courses in one- and several-variable calculus and an

elementary course on the foundations of mathematics. A large variety of exercises and the

inclusion of informal interpretations of many results and examples will greatly facilitate the

reader's study of the subject.

6 HIGHLIGHTS

LECTURES ON CHEVALLEY GROUPS

Robert Steinberg

Feb 2017 157pp

9781470431051 Paperback £35.95 / €40.00

University Lecture Series, Vol. 66

Robert Steinberg’s Lectures on Chevalley Groups were delivered and written during the author’s

sabbatical visit to Yale University in the 1967–1968 academic year. The work presents the

status of the theory of Chevalley groups as it was in the mid-1960s. Much of this material was

instrumental in many areas of mathematics, in particular in the theory of algebraic groups and in

the subsequent classification of finite groups. This posthumous edition incorporates additions

and corrections prepared by the author during his retirement, including a new introductory

chapter. A bibliography and editorial notes have also been added.

This is a great unsurpassed introduction to the subject of Chevalley groups that influenced generations of

mathematicians.I would recommend it to anybody whose interests include group theory.

—Efin Zelmanov, University of California, Los Angeles

Robert Steinberg’s lectures on Chevalley groups were given at Yale University in 1967.The notes for the

lectures contain a wonderful exposition of the work of Chevalley, as well as important additions to that

work due to Steinberg himself.The theory of Chevalley groups is of central importance not only for group

theory, but also for number theory and theoretical physics, and is as relevant today as it was in 1967.The

publication of these lecture notes in book form is a very welcome addition to the literature.

—George Lusztig, Massachusetts Institute of Technology

ALGEBRAIC INEQUALITIES: NEW VISTAS

Titu Andreescu & Mark Saul

Dec 2016 126pp

9781470434649 Paperback £41.95 / €46.00

MSRI Mathematical Circles Library, Vol. 19

This book starts with simple arithmetic inequalities and builds to sophisticated inequality results

such as the Cauchy-Schwarz and Chebyshev inequalities. Nothing beyond high school algebra

is required of the student. The exposition is lean. Most of the learning occurs as the student

engages in the problems posed in each chapter. And the learning is not "linear''. The central topic

of inequalities is linked to others in mathematics. Often these topics relate to much more than

algebraic inequalities.

There are also "secret'' pathways through the book. Each chapter has a subtext, a theme which

prepares the student for learning other mathematical topics, concepts, or habits of mind. For

example, the early chapters on the arithmetic mean/geometric mean inequality show how very

simple observations can be leveraged to yield useful and interesting results. Later chapters give

examples of how one can generalize a mathematical statement. The chapter on the Cauchy-

Schwarz inequality provides an introduction to vectors as mathematical objects. And there are

many other secret pathways that the authors hope the reader will discover and follow.

In the interest of fostering a greater awareness and appreciation of mathematics and its

connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the

Mathematical Circles Library series as a service to young people, their parents and teachers, and the

mathematics profession.

A co-publication of the AMS and the Mathematical Sciences Research

HIGHLIGHTS 7

MOVING THINGS AROUND

Bowen Kerins et al

Nov 2016 152pp

9781470429263 Paperback £29.50 / €33.00

IAS/PCMI-The Teacher Program Series, Vol. 5

A carefully sequenced collection of problem sets designed to develop several interconnected

mathematical themes, and one of the goals of the problem sets is for readers to uncover these

themes for themselves. The goal of Moving Things Around is to help participants make what might

seem to be surprising connections among seemingly different areas: permutation groups, number

theory, and expansions for rational numbers in various bases, all starting from the analysis of card

shuffles. Another goal is to use these connections to bring some coherence to several ideas that

run throughout school mathematics-rational number arithmetic, different representations for

rational numbers, geometric transformations, and combinatorics. The theme of seeking structural

similarities is developed slowly, leading, near the end of the course, to an informal treatment

of isomorphism.

A co-publication of the AMS and IAS/Park City Mathematics Institute

SOME APPLICATIONS OF GEOMETRIC THINKING

Bowen Kerins et al

Nov 2016 222pp

9781470429256 Paperback £29.50 / €33.00

IAS/PCMI-The Teacher Program Series, Vol. 4

A carefully sequenced collection of problem sets designed to develop several interconnected

mathematical themes, and one of the goals of the problem sets is for readers to uncover these

themes for themselves. The goal of Some Applications of Geometric Thinking is to help teachers see

that geometric ideas can be used throughout the secondary school curriculum, both as a hub that

connects ideas from all parts of secondary school and beyond-algebra, number theory, arithmetic,

and data analysis-and as a locus for applications of results and methods from these fields.

A co-publication of the AMS and IAS/Park City Mathematics Institute

COLLECTED WORKS OF JOHN TATE

Edited by Barry Mazur & Jean-Pierre Serre

Part I (1951-1975)

Jan 2017 678pp

9780821890929 Hardback £155.00 / €170.00

Collected Works, Vol. 24.1

Part II (1976-2006)

Jan 2017 736pp

9780821890936 Hardback £155.00 / €170.00

Collected Works, Vol. 24.2

Parts I and II Save more than 10%

Jan 2017 1414pp

9780821890912 Hardback £270.00 / €300.00

Collected Works, Vol. 24

In these volumes, a reader will find all of John Tate's published mathematical papers - spanning

more than six decades - enriched by new comments made by the author. Included also is a

selection of his letters. His letters give us a close view of how he works and of his ideas in process

of formation.

8

ALGEBRA & ALGEBRAIC GEOMETRY

ALGEBRA IN ACTION ON GROUPS OF PL-HOMEOMORPHISMS OF

A Course in Groups, Rings, and Fields THE REAL LINE

Shahriar Shahriari Robert Bieri & Ralph Strebel

Dec 2016 174pp

See page 5 for details of this title 9781470429010 Hardback £115.00 / €125.00

Mathematical Surveys and Monographs, Vol. 215

COLLECTED WORKS OF JOHN TATE

Richard Thompson's famous group F has the striking property

Edited by Barry Mazur& Jean-Pierre Serre that it can be realized as a dense subgroup of the group of all

See page 7 for details of this title orientation-preserving homeomorphisms of the unit interval,

but it can also be given by a simple 2-generator-2-relator

DEVELOPMENT OF MODULI THEORY - AM presentation. This monograph studies a natural generalization

KYOTO 2013 of F that also includes Melanie Stein's generalized F-groups.

Edited by Osamu Fujino et al QUIVER REPRESENTATIONS AND

Nov 2016 537pp QUIVER VARIETIES

9784864970327 Hardback £175.00 / €195.00

Alexander Kirillov

Advanced Studies in Pure Mathematics, Vol. 69

See page 4 for details of this title

Contains the proceedings of the 6th Mathematical Society

of Japan Seasonal Institute Development of Moduli Theory, BESTSELLERS

which was held as the Seasonal Institute 2013, with support

from the A publication of the Mathematical Society of Japan ADVANCED MODERN ALGEBRA

and the 2013 Research Project of the Research Institute of Third Edition, Part I

Mathematical Science, Kyoto University. This volume consists

of five survey articles and eight research articles. Joseph J. Rotman

2015 709pp

A publication of the Mathematical Society of Japan 9781470415549 Hardback £90.50 / €105.00

Graduate Studies in Mathematics, Vol. 165

LECTURES ON CHEVALLEY GROUPS

This new edition has been significantly reorganised and many

Robert Steinberg sections have been rewritten. This first part consists of two

See page 6 for details of this title courses: Galois theory and Module theory.

MINIMAL MODELS AND EXTREMAL RAYS ALGEBRAIC CURVES AND

(KYOTO, 2011) RIEMANN SURFACES

Edited by János Kollár et al Rick Miranda

2016 420pp 1995 390pp

9784864970365 Hardback £155.00 / €170.00 9780821802687 Hardback £61.50 / €70.00

Graduate Studies in Mathematics, Vol. 5

Advanced Studies in Pure Mathematics, Vol. 70

Takes the approach that algebraic curves are best encountered

Since the appearance of extremal rays and the minimal model for the first time over the complex numbers, where the reader's

program in the early 1980s, we have seen the tremendous classical intuition about surfaces, integration, and other

development of algebraic geometry. With this in mind, the concepts can be brought into play.

conference on Minimal Models and Extremal Ray was held at

the Research Institute for Mathematical Sciences (RIMS) at ALGEBRAIC SPACES AND STACKS

Kyoto University in June 2011. The purpose of the conference

was to review the past, examine the present, and enjoy Martin Olsson

discussing the future. 2016 299pp

9781470427986 Hardback £105.00 / €115.00

This volume contains the proceedings of this conference Colloquium Publications, Vol. 62

and consists of one survey article on the mathematical work

of Shigefumi Mori, who turned sixty in 2011, and thirteen Provides an introduction to the theory of algebraic spaces

research papers presented by the authors. and stacks intended for graduate students and researchers

A publication of the Mathematical Society of Japan familiar with algebraic geometry at the level of a first-year

graduate course.

9

A N A LY S I S

COLORED OPERADS FINITE FRAME THEORY AM

A Complete Introduction to

Donald Yau Overcompleteness

2016 428pp

9781470427238 Hardback £90.50 / €105.00 Edited by Kasso A. Okoudjou

Graduate Studies in Mathematics, Vol. 170

2016 252pp

Explores the theory of operads and colored operads, sometimes

called symmetric multicategories. A (colored) operad is an 9781470420192 Hardback £105.00 / €115.00

abstract object which encodes operations with multiple inputs

and one output and relations between such operations. Proceedings of Symposia in Applied Mathematics, Vol. 73

GALOIS THEORIES OF LINEAR DIFFERENCE Mostly written in a tutorial style, the seven chapters in this

EQUATIONS: AN INTRODUCTION volume survey recent advances in the theory and applications

of finite frames. In particular, it presents state-of-the-

Charlotte Hardouin, Jacques Sauloy & Michael F. Singer art results on foundational frame problems, and on the

2016 171pp analysis and design of various frames, mostly motivated by

9781470426552 Hardback £115.00 / €130.00 specific applications.

Mathematical Surveys and Monographs, Vol. 211

FUNCTIONS WITH

Presents three introductory tutorials coming out of three DISCONNECTED SPECTRUM AM

courses given at the CIMPA Research School "Galois Theory of Sampling, Interpolation, Translates

Difference Equations" in 2012. The aim of these tutorials is to

introduce the reader to three Galois theories of linear difference Alexander M. Olevskii & Alexander Ulanovskii

equations and their interrelations. 2016 143pp

9781470428891 Paperback £44.95 / €50.00

LIE ALGEBRAS, LIE SUPERALGEBRAS, University Lecture Series, Vol. 65

VERTEX ALGEBRAS AND RELATED TOPICS

The classical sampling problem is to reconstruct entire

Edited by Kailash C. Misra, Daniel K. Nakano & Brian J. Parshall functions with given spectrum S from their values on a

2016 355pp discrete set L. From the geometric point of view, the possibility

9781470418441 Hardback £125.00 / €140.00 of such reconstruction is equivalent to determining for which

Proceedings of Symposia in Pure Mathematics, Vol. 92 sets L the exponential system with frequencies in L forms a

frame in the space L2(S). The book also treats the problem

Contains the proceedings of the 2012-2014 Southeastern of interpolation of discrete functions by analytic ones with

Lie Theory Workshop Series held between 2012 and spectrum in S.

2014. Some of the articles by experts in the field survey

recent developments while others include new results in MATHEMATICAL ANALYSIS AND ITS

representations of Lie algebras, and quantum groups, vertex

(operator) algebras and Lie superalgebras. INHERENT NATURE

MATRIX GROUPS FOR Hossein Hosseini Giv

UNDERGRADUATES

Second Edition See page 5 for details of this title

Kristopher Tapp SCHOOL ON REAL AND COMPLEX

2016 239pp SINGULARITIES IN SÃO CARLOS, 2012

9781470427221 Paperback £49.95 / €57.00

Student Mathematical Library, Vol. 79 Edited by Raimundo Nonato et al

Oct 2016 373pp

Matrix groups touch an enormous spectrum of the 9784864970303 Hardback £130.00 / €145.00

mathematical arena. This textbook brings them into the Advanced Studies in Pure Mathematics, Vol. 68

undergraduate curriculum. It is concrete and example-driven,

with geometric motivation and rigorous proofs. Topics treated in this volume cover a wide range, including

topology and geometry of real singularities, singularities of

holomorphic map-germs, singularities of complex algebraic

sets, algorithms of the computer algebra "SINGULAR",

singularities of maps and characteristic classes, and limit cycles

of systems of ordinary differential equations.

A publication of the Mathematical Society of Japan

10 ANALYSIS

BESTSELLERS FOURIER ANALYSIS AND

ITS APPLICATIONS

ADVANCED CALCULUS

Gerald B. Folland

Second Edition 2009 433pp

9780821847909 Hardback £77.50 / €89.00

Patrick M. Fitzpatrick Pure and Applied Undergraduate Texts, Vol. 4

2009 590pp Presents the theory and applications of Fourier series and

integrals, eigenfunction expansions, and related topics, on a

9780821847916 Hardback £88.50 / €105.00 level suitable for advanced undergraduates.

Pure and Applied Undergraduate Texts, Vol. 5

Suitable as a text for courses that furnish the backbone of the AN INTRODUCTION TO CLASSICAL

student's undergraduate education in mathematical analysis, REAL ANALYSIS

this book intends to present the fundamental concepts within

the context of examples and exercises. Karl R. Stromberg

2016 575pp

ANALYSIS 9781470425449 Hardback £50.95 / €58.00

Elliott H. Lieb & Michael Loss AMS Chelsea Publishing, Vol. 376

2001 348pp

9780821827833 Hardback £48.95 / €56.00 This classic book is a text for a standard introductory course

Graduate Studies in Mathematics, Vol. 14 in real analysis, covering sequences and series, limits and

continuity, differentiation, elementary transcendental

Presents the concepts and tools to solve problems of analysis, functions, integration, infinite series and products, and

and shows how to apply these concepts to research in a variety trigonometric series. The author has avoided any presumption

of areas. that the reader has knowledge of mathematical concepts until

they are presented in the book.

A COMPREHENSIVE COURSE IN

ANALYSIS, FIVE-VOLUME SET AN INTRODUCTION TO

MEASURE THEORY

Barry Simon

Terence Tao

2016 2011 206pp

9780821869192 Hardback £56.95 / €65.00

Part 1: Real Analysis

Graduate Studies in Mathematics, Vol. 126

789pp 9781470410995 Hardback £85.00 / €105.00

Introduces the fundamentals of measure theory and

Part 2A: Basic Complex Analysis integration theory. It focuses first on the concrete setting of

Lebesgue measure and the Lebesgue integral, before moving

641pp 9781470411008 Hardback £85.00 / €105.00 on to abstract measure and integration theory, including the

standard convergence theorems, Fubini's theorem, and the

Part 2B: Advanced Complex Analysis Caratheodory extension theorem. Classical differentiation

theorems are also covered, as are connections with

321pp 9781470411015 Hardback £85.00 / €105.00 probability theory.

Part 3: Harmonic Analysis

759pp 9781470411022 Hardback £85.00 / €105.00

Part 4: Operator Theory

749pp 9781470411039 Hardback £85.00 / €105.00

Five Volume Set Save more than 25% MATHEMATICS++

Selected Topics Beyond the

3259pp 9781470410988 Hardback £315.00 / €390.00 Basic Courses AM

Written by Poincaré Prize winner Barry Simon, this is a Ida Kantor, Jiri Matousek & Robert Samal

five-volume set that can serve as a graduate-level analysis 2015 353pp

textbook with a lot of additional bonus information, including

hundreds of problems and numerous notes that extend the 9781470422615 Paperback £49.95 / €57.00

text and provide important historical background.

Student Mathematical Library, Vol. 75

Offers a concise introduction to six areas of 20th century

mathematics - measure theory, high-dimensional geometry,

Fourier analysis, representations of groups, multivariate

polynomials, and topology - providing numerous modern

mathematical tools used in contemporary research in computer

science, engineering, and other fields.

11

APPLIED MATHEMATICS

PROBLEMS IN REAL AND BESTSELLERS

FUNCTIONAL ANALYSIS

LECTURES AND PROBLEMS

Alberto Torchinsky A Gift to Young Mathematicians

2016 467pp

9781470420574 Hardback £80.50 / €92.00 V. I. Arnold

Graduate Studies in Mathematics, Vol. 166 Translated by Dmitry Fuchs & Mark Saul

2015 176pp

The purpose of this book is to complement the existing 9781470422592 Paperback £29.50 / €34.00

literature in introductory real and functional analysis at the MSRI Mathematical Circles Library, Vol. 17

graduate level with a variety of conceptual problems (1,457

in total), ranging from easily accessible to thought provoking, Vladimir Arnold (1937-2010) was one of the great

mixing the practical and the theoretical. mathematical minds of the late 20th century. He did significant

work in many areas of the field. On another level, he was

A USER-FRIENDLY INTRODUCTION TO keeping with a strong tradition in Russian mathematics to

LEBESGUE MEASURE AND INTEGRATION write for and to directly teach younger students interested in

mathematics. This book contains some examples of Arnold's

Gail S. Nelson contributions to the genre.

2015 221pp A co-publication of the AMS and the Mathematical

9781470421991 Paperback £49.95 / €57.00 Sciences Research Institute

Student Mathematical Library, Vol. 78

MATHEMATICAL MODELS IN

Provides a bridge between an undergraduate course in Real DEVELOPMENTAL BIOLOGY

Analysis and a first graduate-level course in Measure Theory

and Integration. The main goal of this book is to prepare Jerome K. Percus & Stephen Childress

students for what they may encounter in graduate school, but 2015 249pp

will be useful for many beginning graduate students as well. 9781470410803 Paperback £44.95 / €52.00

Courant Lecture Notes, Vol. 26

WINDING AROUND

The Winding Number in Topology, Introduces an interleaved set of mathematical models

Geometry, and Analysis representative of research in the last few decades, as well as the

techniques that have been developed for their solution. Such

John Roe models offer an effective way of incorporating reliable data in

2015 269pp a concise form, provide an approach complementary to the

9781470421984 Paperback £49.95 / €57.00 techniques of molecular biology, and help to inform and direct

Student Mathematical Library, Vol. 76 future research.

A co-publication of the AMS and the Courant Institute

Explores how the winding number can help us show that every of Mathematical Sciences at New York University

polynomial equation has a root, guarantee a fair division of

three objects in space by a single planar cut, explain why every THE MATHEMATICS OF ENCRYPTION

simple closed curve has an inside and an outside, relate calculus An Elementary Introduction

to curvature and the singularities of vector fields, and allow one

to subtract infinity from infinity and get a finite answer. Margaret Cozzens & Steven J. Miller

2013 348pp

9780821883211 Paperback £49.95 / €57.00

Mathematical World, Vol. 29

Provides a historical and mathematical tour of cryptography,

from classical ciphers to quantum cryptography. The authors

introduce just enough mathematics to explore modern

encryption methods, with nothing more than basic algebra and

some elementary number theory being necessary. Complete

expositions are given of the classical ciphers and the attacks

on them, along with a detailed description of the famous

Enigma system.

12 APPLIED MATHEMATICS

MIRROR SYMMETRY AND QUANTUM FIELDS AND STRINGS,

ALGEBRAIC GEOMETRY VOLUME 1

A Course for Mathematicians

David A. Cox & Sheldon Katz

1999 469pp Edited by Pierre Deligne et al

9780821821275 Paperback £61.50 / €70.00 2000 723pp

9780821820124 Paperback £36.95 / €42.00

Mathematical Surveys and Monographs, Vol. 68

Ideas from quantum field theory and string theory have had

Mirror symmetry began when theoretical physicists made considerable impact on mathematics. In 1996-97 the Institute

some astonishing predictions about rational curves on quintic for Advanced Study (Princeton, NJ) organized a special year-

hypersurfaces in four-dimensional projective space. This book long program designed to teach mathematicians the basic

presents a comprehensive monograph on mirror symmetry, physical ideas which underlie the mathematical applications.

covering the original observations by the physicists. These volumes are a written record of the program.

NUMERICAL ANALYSIS QUANTUM FIELD THEORY

Mathematics of Scientific Computing, A Tourist Guide for Mathematicians

Third Edition

Gerald B. Folland

David Kincaid & Ward Cheney 2008 325pp

2009 788pp 9780821847053 Hardback £98.95 / €115.00

9780821847886 Hardback £95.50 / €110.00 Mathematical Surveys and Monographs, Vol. 149

Pure and Applied Undergraduate Texts, Vol. 2 Presents the elements of quantum field theory, with the goal of

understanding the behavior of elementary particles rather than

Introduces students with diverse backgrounds to various building formal mathematical structures.

types of mathematical analysis that are commonly needed in

scientific computing. This title treats the subject of numerical QUANTUM MECHANICS

analysis from a mathematical point of view, offering an FOR MATHEMATICIANS

analysis of methods for scientific computing with appropriate

motivations and proofs. Leon A. Takhtajan

2008 387pp

ORIGAMI6 9780821846308 Hardback £76.50 / €87.00

Graduate Studies in Mathematics, Vol. 95

Edited by Koryo Miura et al

Presents a comprehensive treatment of quantum mechanics

I. Mathematics from a mathematics perspective. Including traditional topics,

like classical mechanics, mathematical foundations of quantum

2016 368pp mechanics, quantization, and the Schrödinger equation, this

book gives a mathematical treatment of systems of identical

9781470418755 Paperback £80.50 / €92.00 particles with spin.

II. Technology, Art, Education SAGE FOR UNDERGRADUATES

Gregory V. Bard

2016 368pp

2015 362pp

9781470418762 Paperback £80.50 / €92.00 9781470411114 Paperback £29.50 / €34.00

Two-Volume Set Save more than 15% An introduction to Sage for undergraduate students toward

the end of Calculus II or higher-level course work. The audience

2016 736pp of the book is not only math majors, but also physics,

engineering, finance, statistics, chemistry, and computer

9781470418748 Paperback £135.00 / €155.00 science majors.

This unique collection of papers illustrates the connections

between origami and a wide range of fields. The papers

compiled in this two-part set display the creative melding of

origami (or, more broadly, folding) with fields ranging from cell

biology to space exploration, from education to kinematics,

from abstract mathematical laws to the artistic and aesthetics

of sculptural design.

Special Note to AMS Members

AMS members qualify for a discount on the price of AMS

publications. Please provide your membership number

when making your purchase.

13

DHIFGFHELRIEGNHTTISAL EQUATIONS

DIFFERENTIABLE DYNAMICAL SYSTEMS A FIRST COURSE IN THE AM

An Introduction to Structural Stability CALCULUS OF VARIATIONS

and Hyperbolicity

Mark Kot

Lan Wen 2014 298pp

2016 199pp 9781470414955 Paperback £50.95 / €58.00

9781470427993 Hardback £80.50 / €89.00

Graduate Studies in Mathematics, Vol. 173 Student Mathematical Library, Vol. 72

This is a graduate text in differentiable dynamical systems. This book is intended for a first course in the calculus of

It focuses on structural stability and hyperbolicity, a topic variations, at the senior or beginning graduate level. The reader

that is central to the field. Starting with the basic concepts of will learn methods for finding functions that maximize or

dynamical systems, analysing the historic systems of the Smale minimize integrals.

horseshoe, Anosov toral automorphisms, and the solenoid

attractor, the book develops the hyperbolic theory first for AN INTRODUCTION TO

hyperbolic fixed points and then for general hyperbolic sets. DYNAMICAL SYSTEMS

Continuous and Discrete, Second Edition

DIFFERENTIAL GALOIS THEORY THROUGH

RIEMANN-HILBERT CORRESPONDENCE R. Clark Robinson

An Elementary Introduction 2016 733pp

9780821891353 Hardback £94.50 / €110.00

Jacques Sauloy

Pure and Applied Undergraduate Texts, Vol. 19

See page 4 for details of this title

Provides a mathematical treatment of the introduction to

SHOCK FORMATION IN SMALL-DATA qualitative differential equations and discrete dynamical

SOLUTIONS TO 3D QUASILINEAR systems.

WAVE EQUATIONS

NONLINEAR ELLIPTIC EQUATIONS

Jared Speck OF THE SECOND ORDER

Dec 2016 518pp

9781470428570 Hardback £115.00 / €125.00 Qing Han

Mathematical Surveys and Monographs, Vol. 214 2016 368pp

9781470426071 Hardback £90.50 / €105.00

Serge Alinhac's groundbreaking work on wave equations in Graduate Studies in Mathematics, Vol. 171

the late 1990s was the first to treat more than one spatial

dimension. In 2007, for the compressible Euler equations in Provides a detailed discussion of the Dirichlet problems for

vorticity-free regions, Demetrios Christodoulou remarkably quasilinear and fully nonlinear elliptic differential equations

sharpened Alinhac's results. In this monograph, Christodoulou's of the second order with an emphasis on mean curvature

framework is extended to two classes of wave equations in equations and on Monge-Ampere equations.

three spatial dimensions.

ORDINARY DIFFERENTIAL EQUATIONS

BESTSELLERS AND DYNAMICAL SYSTEMS

CLASSICAL MECHANICS WITH AM Gerald Teschl

CALCULUS OF VARIATIONS AND 2012 356pp

OPTIMAL CONTROL 9780821883280 Hardback £65.50 / €75.00

An Intuitive Introduction Graduate Studies in Mathematics, Vol. 140

Mark Levi Provides a self-contained introduction to ordinary differential

equations and dynamical systems suitable for beginning

2014 316pp graduate students.

9780821891384 Paperback £42.95 / €49.00

Student Mathematical Library, Vol. 69

An intuitively motivated presentation of many topics in

classical mechanics and related areas of control theory and

calculus of variations.

14

DISCRETE MATHEMATICS &

COMBINATORICS

KEY BESTSELLER GAME THEORY AM

A Playful Introduction

PARTIAL

DIFFERENTIAL Matt DeVos & Deborah Kent

EQUATIONS

Second Edition See page 2 for details of this title

Lawrence C. Evans GAME THEORY, ALIVE

2010 749pp Anna R. Karlin & Yuval Peres

See page 2 for details of this title

9780821849743 Hardback

THE MATHEMATICAL LEGACY OF

£94.50 / €110.00 RICHARD P. STANLEY

Graduate Studies in Edited by Patricia Hersh et al

Mathematics, Vol. 19 Jan 2017 352pp

9781470427245 Hardback £59.95 / €66.00

The definitive text

on partial differential Richard Stanley's work in combinatorics revolutionized

equations (PDE). It and reshaped the subject, inspiring a generation of

offers a comprehensive survey of modern techniques in researchers. In this volume, these researchers explain how

the theoretical study of PDE with particular emphasis on Stanley's vision and insights influenced and guided their

nonlinear equations. Its wide scope and clear exposition own perspectives on the subject. As a bonus, the book

make it a great text for a graduate course in PDE. This contains a collection of Stanley's short comments on each

revised edition incoporates numerous changes, including of his papers.

a new chapter on nonlinear wave equations, more than

80 new exercises, several new sections, and a significantly SELECTED WORKS OF

expanded bibliography. RICHARD P. STANLEY

WEAK CONVERGENCE METHODS Edited by Patricia Hersh et al

FOR NONLINEAR PARTIAL May 2017 783pp

DIFFERENTIAL EQUATIONS 9781470416829 Hardback £165.00 / €180.00

Collected Works, Vol. 25

Lawrence C. Evans

1990 82pp In addition to collecting several of Stanley's most

9780821807248 Paperback £20.50 / €24.00 influential papers, this volume also includes his own short

reminiscences on his early years, and on his celebrated proof

CBMS Regional Conference Series in Mathematics, Vol. 74 of The Upper Bound Theorem.

The purpose of this book is to explain systematically and

clearly many of the most important techniques set forth in

recent years for using weak convergence methods to study

nonlinear partial differential equations.

PARTIAL DIFFERENTIAL EQUATIONS AM POLYNOMIAL METHODS

An Accessible Route through Theory IN COMBINATORICS

and Applications

Larry Guth

András Vasy 2016 273pp

2016 280pp 9781470428907 Paperback £48.95 / €54.00

9781470418816 Hardback £70.50 / €81.00 University Lecture Series, Vol. 64

Graduate Studies in Mathematics, Vol. 169 Explains some recent applications of the theory of polynomials

and algebraic geometry to combinatorics and other areas of

This text on partial differential equations is intended for readers mathematics. One of the first results in this story is a short

who want to understand the theoretical underpinnings of elegant solution of the Kakeya problem for finite fields. The

modern PDEs in settings that are important for the applications author also discusses in detail various problems in incidence

without using extensive analytic tools required by most geometry associated to Paul Erdös's distinct distances problem

advanced texts. in the plane from the 1940s.

DISCRETE MATHEMATICS & COMBINATORICS 15

BESTSELLERS THE KNOT BOOK

An Elementary Introduction to the

COMBINATORICS AND RANDOM Mathematical Theory of Knots

MATRIX THEORY

Colin Adams

Jinho Baik, Percy Deift & Toufic Suidan 2004 277pp

2016 461pp 9780821836781 Paperback £34.95 / €40.00

9780821848418 Hardback £90.50 / €100.00

Knots are familiar objects. Yet the mathematical theory of knots

Graduate Studies in Mathematics, Vol. 172 quickly leads to deep results in topology and geometry. This

work offers an introduction to this theory, starting with our

The goal of this book is to analyse in detail Ulam's problem for understanding of knots. It presents the applications of knot

increasing subsequences of random permutations, and domino theory to modern chemistry, biology and physics.

tilings of the Aztec diamond. Other examples are also described

along the way, but in less detail. The book is self-contained, and POINCARÉ'S LEGACIES, PART I

develops enough of the theory from each area that a general pages from year two of a mathematical blog

reader can learn the subject directly from the text.

Terence Tao

COMPLEX GRAPHS AND NETWORKS 2009 293pp

9780821848838 Paperback £41.95 / €48.00

Fan R. K. Chung & Linyuan Lu

2006 264pp Focuses on ergodic theory, combinatorics, and number

9780821836576 Paperback £57.95 / €67.00 theory. This book discusses a variety of topics, ranging from

CBMS Regional Conference Series in Mathematics, Vol. 107 developments in additive prime number theory to expository

articles on individual mathematical topics such as the law of

Based on lectures given at the CBMS Workshop on the large numbers and the Lucas-Lehmer test for Mersenne primes.

Combinatorics of Large Sparse Graphs, this work presents

fresh perspectives in graph theory and helps to contribute to a RAMSEY THEORY FOR PRODUCT SPACES

sound scientific foundation for our understanding of discrete

networks that permeate the information age. Pandelis Dodos & Vassilis Kanellopoulos

A co-publication of the AMS and CBMS 2016 245pp

9781470428082 Hardback £115.00 / €130.00

EXPERIMENTAL MATHEMATICS

Mathematical Surveys and Monographs, Vol. 212

V.I. Arnold

Translated by Dmitry Fuchs & Mark Saul This book is devoted to one of the most important areas of

2015 158pp Ramsey theory - the Ramsey theory of product spaces. It is a

9780821894163 Paperback £29.50 / €34.00 culmination of a series of recent breakthroughs by the two

authors and their students who were able to lift this theory

MSRI Mathematical Circles Library, Vol. 16 to the infinite-dimensional case. The book presents major

results and methods in the area, such as Szemeredi's regularity

Presents several new directions of mathematical research. All of method and the hypergraph removal lemma.

these directions are based on numerical experiments conducted

by the author, which led to new hypotheses that currently RAMSEY THEORY ON THE INTEGERS AM

remain open. The hypotheses range from geometry and Second Edition

topology to combinatorics to algebra and number theory.

Bruce M. Landman & Aaron Robertson

THE GAME OF COPS AND ROBBERS AM 2014 396pp

ON GRAPHS

9780821898673 Paperback £62.50 / €71.00

Anthony Bonato & Richard J. Nowakowski

2011 276pp Student Mathematical Library, Vol. 73

9780821853474 Paperback £48.95 / €56.00

Ramsey theory is the study of the structure of mathematical

Student Mathematical Library, Vol. 61 objects that is preserved under partitions. In its full generality,

Ramsey theory is quite powerful, but can quickly become

This book is the first to examine the topic of Cops and Robbers complicated. By limiting the focus of this book to Ramsey

games, and more generally, the field of vertex pursuit games on theory applied to the set of integers, the authors have

graphs. One of its main goals is to bring together the key results produced a gentle, but meaningful, introduction to an

in the field; as such, it presents structural, probabilistic, and important and enticing branch of modern mathematics.

algorithmic results on Cops and Robbers games.

16

GENERAL INTEREST

RUDIMENTS OF RAMSEY THEORY GALLERY OF THE INFINITE

Second Edition

Richard Evan Schwartz

Ron Graham & Steve Butler Dec 2016 187pp

2015 82pp 9781470425579 Paperback £24.95 / €29.00

9780821841563 Paperback £29.50 / €34.00

Gallery of the Infinite is a mathematician's unique view of

CBMS Regional Conference Series in Mathematics, Vol. 123 the infinitely many sizes of infinity. Written in a playful yet

informative style, it introduces important concepts from set

In every sufficiently large structure which has been partitioned theory (including the Cantor Diagonalization Method and

there will always be some well-behaved structure in one of the Cantor-Bernstein Theorem) using colourful pictures,

the parts. This takes many forms. For example, colourings with little text and almost no formulas.

of the integers by finitely many colours must have long

monochromatic arithmetic progressions; and colourings of the BESTSELLER

edges of large graphs must have monochromatic subgraphs

of a specified type. This book explores the basic results and REALLY BIG NUMBERS

variations of this theory.

Richard Evan Schwartz

STABLE MARRIAGE AND ITS AM 2014 192pp

RELATION TO OTHER 9781470414252 Paperback £19.95 / €24.00

COMBINATORIAL PROBLEMS

In the American Mathematical Society's first-ever book

Donald E. Knuth for kids (and kids at heart), mathematician and author

1996 74pp Richard Evan Schwartz leads math lovers of all ages on an

innovative and strikingly illustrated journey through the

9780821806036 Paperback £25.50 / €29.00 infinite number system. By means of engaging, imaginative

visuals and endearing narration, Schwartz manages the

CRM Proceedings & Lecture Notes, Vol. 10 monumental task of presenting the complex concept of Big

Numbers in fresh and relatable ways.

Uses the theory of stable marriage to introduce and illustrate

a variety of important concepts and techniques of computer BESTSELLER

science and mathematics: data structures, control structures,

combinatorics, probability, analysis, algebra, and especially the YOU CAN COUNT ON MONSTERS

analysis of algorithms. The First 100 Numbers and Their Characters

A co-publication of the AMS and Centre de Recherches Richard Evan Schwartz

Mathématiques 2015 242pp

9781470422097 Paperback £19.95 / €24.00

If you are a teaching academic or course

leader you may request up to three titles A unique teaching tool that takes math lovers on a journey

as FREE inspection copies (especially those designed to motivate kids (and kids at heart) to learn the

marked with the textbook icon) to consider as fun of factoring and prime numbers. This volume visually

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For further details please visit: composite numbers. The playful and colourful monsters

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REALLY BIG NUMBERS AND YOU CAN

COUNT ON MONSTERS Save 20%

Two-Volume Set

2015 436pp

9781470422943 Paperback £32.50 / €39.00

PUSHING LIMITS

From West Point to Berkeley and Beyond

Ted Hill

See page 1 for details of this title

17

GEOMETRY & TOPOLOGY

BESTSELLERS CARTAN FOR BEGINNERS

Differential Geometry via Moving Frames and

THE CASE OF ACADEMICIAN NIKOLAI Exterior Differential Systems, Second Edition

NIKOLAEVICH LUZIN

Thomas A. Ivey & Joseph M. Landsberg

Edited by Sergei S. Demidov & Boris V. Levshin See page 3 for details of this title

2016 386pp

9781470426088 Hardback £59.95 / €69.00 ORDERED GROUPS AND TOPOLOGY

History of Mathematics, Vol. 43

Adam Clay & Dale Rolfsen

A campaign to ‘Sovietize' all sciences in the USSR took aim at See page 3 for details of this title

Nikolai Nikolaevich Luzin, the leader of the Soviet school of

mathematics, with an accusatory article published in Pravda. BESTSELLERS

This book contains the transcripts of the five 1936 meetings of

the commission of the Academy of Sciences who were charged COMPUTATIONAL TOPOLOGY AM

with investigating the accusations against Luzin. An Introduction

JOHN VON NEUMANN Herbert Edelsbrunner & John L. Harer

The Scientific Genius Who Pioneered the

Modern Computer, Game Theory, Nuclear 2010 241pp

Deterrence, and Much More

9780821849255 Hardback £63.50 / €72.00

Norman Macrae

1999 406pp Combining concepts from topology and algorithms, this book

9780821826768 Paperback £36.95 / €42.00 delivers what its title promises: an introduction to the field of

computational topology.

Presents the biography of John von Neumann, one of the

greatest scientists of the century after Einstein. This book DIFFERENTIAL GEOMETRY

discusses von Neumann's work in areas such as game theory, Curves - Surfaces - Manifolds,

mathematics, physics, and meteorology which formed Third Edition

the building blocks for the most important discoveries of

the century: the modern computer, game theory, and the Wolfgang Kuhnel

atom bomb. 2016 412pp

9781470423209 Paperback £49.95 / €57.00

WHAT'S HAPPENING IN THE

MATHEMATICAL SCIENCES, VOLUME 10 Student Mathematical Library, Vol. 77

Dana Mackenzie & Barry Cipra Offers an introduction to the beautiful ideas and results of

2015 111pp differential geometry. The first half covers the geometry of

9781470422042 Paperback £22.50 / €29.00 curves and surfaces, which provide much of the motivation

and intuition for the general theory. The second part studies

Offers a collection of articles highlighting some of the most the geometry of general manifolds, with particular emphasis

recent developments in mathematics. Articles include "Prime on connections and curvature. The text is illustrated with many

Clusters and Gaps: Out-Experting the Experts", and "The figures and examples.

Kadison-Singer Problem: A Fine Balance"; "Climate Past,

Present, and Future" and "The Truth Shall Set Your Fee". GEOMETRY AND THE IMAGINATION

D. Hilbert & S. Cohn-Vossen

1952 357pp

9780821819982 Hardback £46.95 / €54.00

AMS Chelsea Publishing, Vol. 87

Suitable for beginners and experienced mathematicians, this

book begins with examples of the simplest curves and surfaces,

including thread constructions of certain quadrics and other

surfaces. It offers a discussion of linkages and the geometry

of configurations of points and rods that are connected and,

perhaps, constrained in some way.

18

LOGIC & FOUNDATIONS

GRID HOMOLOGY FOR KNOTS AND LINKS THE TOOLS OF

MATHEMATICAL REASONING

Peter S. Ozsvath, Andras I. Stipsicz & Zoltan Szabo

2015 410pp Tamara J. Lakins

9781470417376 Hardback £115.00 / €130.00

Mathematical Surveys and Monographs, Vol. 208 See page 5 for details of this title

Starting from the combinatorial point of view on knots using BESTSELLERS

their grid diagrams, this book serves as an introduction to

knot theory.

KNOTS, MOLECULES, AND AM BASIC SET THEORY

THE UNIVERSE

An Introduction to Topology A. Shen & N.K. Vereshchagin

2002 128pp

Erica Flapan 9780821827314 Paperback £26.50 / €31.00

Student Mathematical Library, Vol. 17

2015 386pp

Suitable for undergraduate students as well as professional

9781470425357 Hardback £70.50 / €81.00 mathematicians who want to finally find out what transfinite

induction is and why it is always replaced by Zorn's Lemma, this

Provides an elementary introduction to geometric topology text introduces the main subjects of 'naive' (nonaxiomatic) set

and its applications to chemistry, molecular biology, and theory: functions, cardinalities, ordered and well-ordered sets,

cosmology. It does not assume any mathematical or and operations on ordinals.

scientific background, sophistication, or even motivation to

study mathematics.

PERSISTENCE THEORY: FROM COMPUTABILITY THEORY AM

QUIVER REPRESENTATIONS TO

DATA ANALYSIS AM Rebecca Weber

2012 206pp

Steve Y. Oudot 9780821873922 Paperback £37.95 / €43.00

2015 218pp

Student Mathematical Library, Vol. 62

9781470425456 Hardback £115.00 / €130.00

Gives the reader a firm grounding in the fundamentals

Mathematical Surveys and Monographs, Vol. 209 of computability theory and an overview of currently

active areas of research, such as reverse mathematics and

Persistence theory emerged in the early 2000s as a new theory algorithmic randomness.

in the area of applied and computational topology. This book

provides a broad and modern view of persistence theory, PRINCIPLES OF MATHEMATICAL LOGIC

including its algebraic, topological, and algorithmic aspects. It

also elaborates on applications in data analysis. D. Hilbert & W. Ackermann

1950 172pp

QUANDLES AM 9780821820247 Hardback £34.95 / €40.00

An Introduction to the Algebra of Knots AMS Chelsea Publishing, Vol. 69

Mohamed Elhamdadi & Sam Nelson David Hilbert was particularly interested in the foundations

2015 248pp of mathematics. Among many other things, he is famous for

his attempt to axiomatize mathematics. This text presents his

9781470422134 Paperback £49.95 / €57.00 treatment of symbolic logic. It lays the groundwork for his later

work with Bernays.

Student Mathematical Library, Vol. 74

Provides an accessible introduction to quandle theory for SET THEORY

readers with a background in linear algebra. Important concepts

from topology and abstract algebra motivated by quandle Felix Hausdorff

theory are introduced along the way. Includes elementary 1957 352pp

self-contained treatments of topics such as group theory, 9780821838358 Hardback £46.95 / €54.00

cohomology, knotted surfaces and more. AMS Chelsea Publishing, Vol. 119

Presents various theorems of the theory of sets along with

complete proofs. This book discusses strengthening of

theorems, the simplification of proofs, and the removal of

unnecessary hypotheses.

19

MATHEMATICAL PHYSICS

IT’S ABOUT TIME MATHEMATICAL UNDERSTANDING AM

Elementary Mathematical Aspects of Relativity OF NATURE

Essays on Amazing Physical Phenomena and

Roger Cooke their Understanding by Mathematicians

See page 1 for details of this title V. I. Arnold

2014 167pp

BESTSELLERS 9781470417017 Paperback £29.50 / €34.00

COLLECTED PAPERS ON WAVE MECHANICS This collection of 39 short stories gives the reader a unique

Third Edition opportunity to take a look at the scientific philosophy of

Vladimir Arnold. Topics of the stories included range from

Erwin Schrödinger astronomy, to mirages, to motion of glaciers, to geometry of

1982 208pp mirrors and beyond.

9780821835241 Hardback £40.95 / €47.00

NAVIER-STOKES EQUATIONS

AMS Chelsea Publishing, Vol. 302 Theory and Numerical Analysis

The famous equation that bears Erwin Schrödinger's name Roger Temam

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mechanics using wave mechanics. This third, augmented 9780821827376 Hardback £69.50 / €79.00

edition of his papers on the topic contains the six original, AMS Chelsea Publishing, Vol. 343

famous papers in which Schrödinger created and developed the

subject of wave mechanics as published in the original edition. Presents a systematic treatment of results on the theory and

numerical analysis of the Navier-Stokes equations for viscous

MATHEMATICAL METHODS IN AM incompressible fluids.

QUANTUM MECHANICS

With Applications to Schrödinger Operators, PROBABILITY AND STATISTICAL PHYSICS

Second Edition IN ST. PETERSBURG

Gerald Teschl Edited by V. Sidoravicius & S. Smirnov

2016 478pp

2014 356pp 9781470422486 Hardback £125.00 / €140.00

9781470417048 Hardback £68.50 / €78.00 Proceedings of Symposia in Pure Mathematics, Vol. 91

Graduate Studies in Mathematics, Vol. 157 Brings the reader to the cutting edge of several important

directions of the contemporary probability theory. The authors

A brief, but self-contained, introduction to the mathematical are leading experts in the field and provide a panorama of

methods of quantum mechanics, with a view towards the field from the point of view of scientists who played, and

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MATHEMATICAL METHODS OF AM analysis, and conformal field theory.

ELECTROMAGNETIC THEORY

QUANTUM FIELDS AND STRINGS

Kurt O. Friedrichs A Course for Mathematicians, Two-Volume Set

2014 145pp

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1999 1501pp

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Provides a mathematically precise but intuitive introduction to Ideas from quantum field theory and string theory have had

classical electromagnetic theory and wave propagation, with a considerable impact on mathematics. In 1996-97 the Institute

brief introduction to special relativity. for Advanced Study (Princeton, NJ) organized a special year-

long program designed to teach mathematicians the basic

A co-publication of the AMS and the Courant Institute physical ideas which underlie the mathematical applications.

of Mathematical Sciences at New York These volumes are a written record of the program.

Special Note to AMS Members

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20

MATHEMATICS EDUCATION

RANDOM OPERATORS AM TEACHING

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Spectra and Dynamics MATHEMATICS:

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2016 320pp Hung-Hsi Wu

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Graduate Studies in Mathematics, Vol. 168

A systematic exposition

Provides an introduction to the mathematical theory of of introductory school

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STRING-MATH 2012 teachers. The emphasis of

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Proceedings of Symposia in Pure Mathematics, Vol. 90

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Proceedings of Symposia in Pure Mathematics, Vol. 93 TEACHING SCHOOL MATHEMATICS:

The conference String-Math 2014 was held from June 9-13, FROM PRE-ALGEBRA

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was the first to include satellite workshops: "String-Math TO ALGEBRA

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UNDERSTANDING NUMBERS

IN ELEMENTARY SCHOOL

MATHEMATICS

Hung-Hsi Wu

2011 551pp

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A textbook for pre-service elementary school teachers

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MATHEMATICS EDUCATION 21

ALGEBRAIC INEQUALITIES: NEW VISTAS GEOMETRY IN PROBLEMS

Titu Andreescu & Mark Saul Alexander Shen

2016 232pp

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MSRI Mathematical Circles Library, Vol. 18

MOVING THINGS AROUND

Classical Euclidean geometry, with all its triangles, circles, and

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school mathematics students. This book contains more than

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geometry and solutions for most of them, as well as additional

SOME APPLICATIONS OF problems for self-study. Each chapter also provides concise

GEOMETRIC THINKING reminders of basic notions used in the chapter.

A co-publication of the AMS and the Mathematical

Bowen Kerins et al Sciences Research Institute

See page 7 for details of this title HOW TO TEACH MATHEMATICS

Third Edition

BESTSELLERS

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The American Experience, Volume I

This third edition is a lively and provocative tract on how to

Edited by Zvezdelina Stankova & Tom Rike teach mathematics in today's new world of online learning

2009 326pp tools and innovative teaching devices. The author guides the

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A co-publication of the AMS and the Mathematical 2014 163pp

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MSRI Mathematical Circles Library, Vol. 13

A DECADE OF THE BERKELEY

MATH CIRCLE Introduces the basics of many important areas of modern

The American Experience, Volume II mathematics, including logic, symmetry, probability theory,

knot theory, cryptography, fractals, and number theory.

Edited by Zvezdelina Stankova & Tom Rike A co-publication of the AMS and the Mathematical

2015 364pp Sciences Research Institute

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MSRI Mathematical Circles Library, Vol. 14

The Berkeley Math Circle (BMC) started in 1998 as one of

the very first maths circles in the US. Over the last decade

and a half, 100 instructors have shared their passion for

mathematics by delivering over 800 BMC sessions. This

second volume is based on a dozen of these sessions,

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A co-publication of the AMS and the Mathematical

Sciences Research Institute

22 NUMBER THEORY

MATH FROM THREE TO SEVEN BEURLING GENERALIZED NUMBERS

The Story of a Mathematical Circle

for Preschoolers Harold G. Diamond & Wen-Bin Zhang

Oct 2016 244pp

Alexander Zvonkin 9781470430450 Hardback £115.00 / €125.00

2011 300pp Mathematical Surveys and Monographs, Vol. 213

9780821868737 Paperback £25.50 / €29.00

MSRI Mathematical Circles Library, Vol. 5 Using both analytic and elementary methods, this book

presents many old and new theorems, including several of the

Provides a captivating account of a professional authors' results, and many examples of extremal behaviour of

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mathematical education for little kids is a real mystery. This is a needed for proving the Riemann hypothesis.

narrative about what he did, what he tried, what worked, what

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A co-publication of the AMS and the Mathematical

Sciences Research Institute A COURSE IN ANALYTIC AM

NUMBER THEORY

A MOSCOW MATH CIRCLE

Week-by-week Problem Sets Marius Overholt

2015 371pp

Sergey Dorichenko 9781470417062 Hardback £80.50 / €92.00

2012 354pp

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MSRI Mathematical Circles Library, Vol. 8

Offers an introduction to analytic number theory suitable for

Presents materials used during the course of one year in a beginning graduate students. It covers everything one expects

math circle organised by mathematics faculty at Moscow State in a first course in this field, such as growth of arithmetic

University, and also used at the mathematics magnet school functions, existence of primes in arithmetic progressions, and

known as Moscow School Number 57. the Prime Number Theorem.

A co-publication of the AMS and the Mathematical

Sciences Research Institute FERMAT'S LAST THEOREM

Basic Tools

PROBABILITY THROUGH ALGEBRA

Takeshi Saito

Bowen Kerins et al 2013 277pp

2015 176pp

9781470419257 Paperback £29.50 / €34.00 9780821898482 Paperback £49.95 / €57.00.

IAS/PCMI-The Teacher Program Series, Vol. 1

Translations of Mathematical Monographs. Vol. 243

Consists of a carefully sequenced collection of problem sets

designed to develop several interconnected mathematical The Proof

themes. The specific themes developed is to introduce readers

to the algebraic properties of expected value and variance 2015 234pp

through analysis of games, and to the use of generating 9780821898499 Paperback £54.95 / €63.00

functions and formal algebra as combinatorial tools.

A co-publication of the AMS and IAS/Park City Translations of Mathematical Monographs, Vol. 245

Mathematics Institute

Two-Volume Set Save more than 15%

2015 34pp

9781470422165 Paperback £86.50 / €99.00

Translations of Mathematical Monographs Vols. 243/245

Presents in full detail the proof of Fermat's Last Theorem

given by Wiles and Taylor. With these two books, the

reader will be able to see the whole picture of the proof to

appreciate one of the deepest achievements in the history

of mathematics.

23

PROBABILITY & STATISTICS

INTRODUCTION TO ANALYTIC AND LARGE DEVIATIONS

PROBABILISTIC NUMBER THEORY

Third Edition S.R.S. Varadhan

Gérald Tenenbaum See page 3 for details of this title

2015 641pp

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Graduate Studies in Mathematics, Vol. 163

ASYMPTOPIA

Provides a self contained, thorough introduction to the analytic

and probabilistic methods of number theory. The prerequisites Joel Spencer

being reduced to classical contents of undergraduate courses, with Laura Florescu

it offers to students and young researchers a systematic and 2014 195pp

consistent account on the subject. 9781470409043 Paperback £39.95 / €46.00

Student Mathematical Library, Vol. 71

LECTURES ON THE RIEMANN

ZETA FUNCTION Asymptotics in one form or another are part of the landscape

for every mathematician. The objective of this book is to

H. Iwaniec present the ideas of how to approach asymptotic problems

2014 119pp that arise in discrete mathematics, analysis of algorithms, and

9781470418519 Paperback £40.95 / €47.00 number theory. A broad range of topics is covered, including

University Lecture Series, Vol. 62 distribution of prime integers, Erdős Magic, random graphs,

Ramsey numbers, and asymptotic geometry.

The famous Riemann Hypothesis, asserting that all of the non-

trivial zeros of zeta are on a critical line in the complex plane,

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distribution of prime numbers.

RAMANUJAN

Twelve Lectures on Subjects Suggested by His

Life and Work

G.H. Hardy

1991 254pp

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AMS Chelsea Publishing, Vol. 136

Ramanujan occupies a unique place in analytic number theory.

His formulas, identities, and calculations are still amazing three-

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seem to have appeared as if from the ether. The author

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THE ULTIMATE CHALLENGE

The 3x+1 Problem

Edited by Jeffrey C. Lagarias

2011 344pp

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Reports on what is known on this problem. It begins with two

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related questions.

24 PROBABILITY & STATISTICS

CONTINUOUS TIME MARKOV PROCESSES AN INTRODUCTION TO AM

An Introduction STOCHASTIC DIFFERENTIAL

EQUATIONS

Thomas M. Liggett

2010 271pp Lawrence C. Evans

9780821849491 Hardback £58.95 / €68.00

Graduate Studies in Mathematics, Vol. 113 2014 151pp

Markov processes are among the most important stochastic 9781470410544 Hardback £34.95 / €40.00

processes for both theory and applications. This book develops

the general theory of these processes, and applies this theory to Provides a quick, but very readable introduction to stochastic

various special examples. differential equations - that is, to differential equations subject

to additive "white noise" and related random disturbances.

A COURSE ON LARGE DEVIATIONS WITH The exposition is strongly focused upon the interplay between

AN INTRODUCTION TO GIBBS MEASURES probabilistic intuition and mathematical rigour.

Firas Rassoul-Agha & Timo Seppalainen MARKOV CHAINS AND

2015 314pp MIXING TIMES

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Graduate Studies in Mathematics, Vol. 162 David A. Levin, Yuval Peres & Elizabeth L. Wilmer

2009 371pp

Presents an introductory course on the methods of computing 9780821847398 Hardback £72.50 / €83.00

asymptotics of probabilities of rare events: the theory of large

deviations. The book combines large deviation theory with Presents an introduction to the modern approach to the theory

basic statistical mechanics, namely Gibbs measures with their of Markov chains. This book intends to determine the rate of

variational characterization and the phase transition of the Ising convergence of a Markov chain to the stationary distribution as

model, in a text intended for a one semester or quarter course. a function of the size and geometry of the state space.

FOKKER-PLANCK-KOLMOGOROV PROBABILITY THEORY

EQUATIONS S.R.S Varadhan

Vladimir I. Bogachev et al 2001 167pp

2016 489pp 9780821828526 Paperback £28.50 / €33.00

9781470425586 Hardback £115.00 / €130.00 Courant Lecture Notes, Vol. 7

Mathematical Surveys and Monographs, Vol. 207

Presents topics in probability theory covered during a first-year

Gives an exposition of the principal concepts and results related graduate course given at the Courant Institute of Mathematical

to second order elliptic and parabolic equations for measures, Sciences, USA. The necessary background material in measure

the main examples of which are Fokker-Planck-Kolmogorov theory is developed, including all the standard topics.

equations for stationary and transition probabilities of diffusion A co-publication of the AMS and the Courant Institute

processes. Existence and uniqueness of solutions are studied of Mathematical Sciences at New York University

along with existence and Sobolev regularity of their densities

and upper and lower bounds for the latter. TOPICS IN RANDOM MATRIX THEORY

Terence Tao

2012 291pp

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Graduate Studies in Mathematics, Vol. 132

The field of random matrix theory has seen an explosion of

activity in recent years, with connections to many areas of

mathematics and physics. This graduate text focuses on one

specific sector of the field, namely the spectral distribution

of random Wigner matrix ensembles, as well as iid matrix

ensembles. The text is largely self-contained and starts with

a review of relevant aspects of probability theory and linear

algebra. It includes over 200 exercises.

25

CONTEMPORARY MATHEMATICS

Algebra & Algebraic Geometry CATEGORIFICATION IN RECENT PROGRESS ON

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RECENT DEVELOPMENTS IN AND PHYSICS APPROXIMATION IN SPACES

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26 CONTEMPORARY MATHEMATICS

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27

MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY

Algebra & Algebraic Geometry IMAGINARY RECTIFIABLE MEASURES,

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Society, Vol. 245, No. 1161

SALES REPRESENTATIVES & CONTACTS

EUROPE, MIDDLE EAST & AFRICA MIDDLE EAST ASIA-PACIFIC

UK & REPUBLIC OF IRELAND Bahrain, Iran, Iraq, Israel, Jordan, CENTRAL ASIA

Kuwait, Lebanon, Oman, Palestine,

UK & Republic of Ireland Qatar, Saudi Arabia, Syria, Turkey, Afghanistan, Kazakhstan, Kyrgyzstan,

Michelle Zappa United Arab Emirates, Yemen Tajikistan, Turkmenistan, Uzbekistan

[email protected] David Atiyah Marc Bedwell

[email protected] [email protected]

London

Darryl Richards AFRICA SOUTH ASIA

[email protected]

Algeria, Egypt, Libya, Morocco, Tunisia Bangladesh, Bhutan, Maldives, Nepal,

CONTINENTAL EUROPE David Atiyah Sri Lanka

[email protected] Vinod Vasishtha

Denmark, Finland, Iceland, [email protected]

Norway, Sweden Angola, Ghana, Kenya, Nigeria, Sudan,

David Towle Uganda, Zambia, Zimbabwe SOUTH EAST ASIA

[email protected] Guy Simpson

[email protected] Brunei, Malaysia, Singapore

Bosnia Herzegovina, Bulgaria, Croatia, Raymond Lim

Czech Republic, Estonia, Georgia, Botswana, Namibia, Lesotho, South [email protected]

Hungary, Latvia, Lithuania, Poland, Africa, Swaziland Cambodia, East Timor, Indonesia,

Romania, Russia, Serbia, Slovakia, Chris Reinders Laos, Philippines, Thailand, Vietnam

Slovenia, Ukraine [email protected] Melvin Choo

László Horváth [email protected]

[email protected]

AUSTRALASIA & OCEANIA

Austria, Belgium, France, Germany,

Italy, Luxembourg, Netherlands, Australia, New Zealand, Oceania

Portugal, Spain, Switzerland Emma White

Michelle Zappa [email protected]

[email protected]

Greece

Charles Gibbes

[email protected]

All other European countries

Michelle Zappa

[email protected]

Due to currency fluctuations and publisher price changes, prices charged may vary from those listed. AMMPB0117

CUSTOMER SERVICES DESPATCH INFORMATION OTHER ENQUIRIES

Tel: +44 (0)1767 604972 Standard delivery per order - Tel: +44 (0)20 7240 0856

Fax: +44 (0)1767 601640 UK £3.50 Fax: +44 (0)20 7379 0609

[email protected] Continental Europe €6.00 [email protected]

Africa US$15.00 3 Henrietta Street

Middle East US$15.00 Covent Garden

Asia-Pacific US$15.00 London WC2E 8LU, UK

Faster delivery options available on request.

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