AMS Spring 2026 Catalogue

Catalogue Spring 2026

AppliedMathematics

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Founded in 1888 to further mathematical research and scholarship, the American Mathematical Society fulfils its mission through programmes and services that promote mathematical research and its uses, strengthen mathematical education, and foster awareness and appreciation of mathematics and its connections to other disciplines and to everyday life.

ANILLUSTRATEDTHEORYOFNUMBERS

UpdatedEdition

Martin H. Weissman

An Illustrated Theory of Numbers gives a comprehensive introduction to number theory, with complete proofs, worked examples, and exercises. Its exposition reflects the most recent scholarship in mathematics and its history. Almost 500 sharp illustrations accompany elegant proofs, from prime decomposition through quadratic reciprocity. Geometric and dynamical arguments provide new insights and allow for a rigorous approach with less algebraic manipulation. The final chapters contain an extended treatment of binary quadratic forms, using Conway's topograph to solve quadratic Diophantine equations (e.g., Pell's equation) and to study reduction and the finiteness of class numbers.

Data visualizations introduce the reader to open questions and cutting-edge results in analytic number theory such as the Riemann hypothesis, boundedness of prime gaps, and the class number 1 problem. Accompanying each chapter, historical notes curate primary sources and secondary scholarship to trace the development of number theory within and outside the Western tradition. Requiring only high school algebra and geometry, this text is recommended for a first course in elementary number theory. It is also suitable for mathematicians seeking a fresh perspective on an ancient subject. In this updated edition, you will find a new chapter which brings the reader from undergraduate calculus into analytic number theory. A new section adds a second proof of quadratic reciprocity due to Gauss and Eisenstein. Hundreds of minor edits correct and improve the original edition.

RANDOMNESSANDTHERIEMANNHYPOTHESIS

Probability,Statistics,andthePrimes

Andrey Feuerverger & Greg Martin

Presents a rich, insightful exploration of the interplay between randomness, the Riemann Hypothesis, and analytic number theory. Written for readers with a moderate background in mathematics (preferably having some familiarity with probability theory and complex analysis), this book offers a deeper and more comprehensive account of the Riemann Hypothesis and its far-reaching consequences than is typically available in books aimed at general audiences.

The book takes a relaxed and engaging approach, highlighting the beauty and intuition behind the key ideas. Technical proofs are kept to a minimum, with accessible arguments presented fully, while deeper results are described in context and supported by historical background and comprehensive references. This combination allows readers to appreciate the elegance of the subject and to navigate their own path toward more advanced study.

Bringing together a wealth of material that is otherwise widely scattered across the literature, the book serves as an indispensable reference for researchers and enthusiasts alike. Throughout, it illuminates the crucial role that randomness plays in modern number theory - inspiring conjectures, guiding proofs, and opening new directions of inquiry. Six valuable appendices round out the volume, providing opportunities to review - or learn - essential background material across a range of mathematical topics. Jul 2026 446pp

BETWEENTWODISCIPLINES

B.L.vanderWaerdenandtheDevelopmentofQuantumMechanics

Martina R. Schneider

History of Mathematics, Vol. 49

Offers a historical analysis of Bartel Leendert van der Waerden's early contributions to quantum mechanics, focusing on his role in the development and application of group-theoretic methods around 1930. While van der Waerden is widely known for his modern algebra, his engagement with quantum theory has received little attention in the historical literature. Through careful study of published and archival sources, the author reconstructs the contexts in which van der Waerden worked, and examines his networks as well as his interactions with contemporaries such as Hermann Weyl, Eugene Wigner, Paul Ehrenfest, and John Slater. By comparing the different emerging approaches of adapting group-theoretic methods to problems in quantum mechanics, the author shows that van der Waerden stands out as a rather pragmatic and undogmatic thinker. Special attention is given to reconstructing a more nuanced picture of the arising controversy around the "group plague" in quantum mechanics.

Combining technical exposition with biographical and historical analysis, this book is intended for mathematicians, physicists, and historians of science. The reader is expected to have beginning, graduate-level knowledge of mathematics and, in particular, representation theory, as well as some background in quantum physics. This study sheds light on a complex and fascinating period in the development of mathematical physics, exploring the dynamics of the interactions between mathematics and physics, and thus contributes to ongoing discussions about mathematization processes in science in the twentieth century.

THEFLOERJUNGLE

ChartingtheDevelopmentofaTheory

Helmut Hofer & Siobhan Roberts

History of Mathematics, Vol. 51

The Floer Jungle traces the development of Floer theory while portraying the life of mathematician Andreas Floer (1956–1991), whose ideas transformed geometry and topology. Blending mathematical exposition with biography, it reconstructs the existing ideas, and introduces the main characters, describing their interactions, their judgements and attempts, wrong or right. Aimed at graduate students, researchers, and scientifically curious readers, it emphasizes examples over formalism and offers appendices and references for deeper study. The book is both an engaging introduction to sophisticated mathematics and an intimate portrait of the people who pursue it.

“The Floer Jungle is a first-hand account of the birth of a new mathematical field, and at the same time a touching memorial to its creator - both depicted with a richness and complexity that is far too often absent in our textbooks and papers”.

—Akshay Venkatesh, Institute for Advanced Study

Jul 2026, 230pp

9781470485146 Paperback £59.00 / US$69.00

INSTRUCTINGTHEMATHEMATICALIMAGINATION

CharlotteAngasScottandBrynMawrCollege,1880sto1920s

Jemma Lorenat

History of Mathematics, Vol. 48

Examines the creation and character of mathematical training at Bryn Mawr College between 1885 and 1926 under the leadership of Charlotte Angas Scott. Though designated as a college, Bryn Mawr boasted the world’s first graduate degree programs in which women taught women. Through detailed analysis of Scott’s publications, student dissertations, and institutional records - including the college’s Journal Club Notebooks - the author reconstructs how a sustained, collaborative, and visually grounded style of mathematics emerged in this setting. Rather than focusing on biographical exceptionalism, the study situates Scott and her students within broader shifts in the American mathematical community, including changing access to education, publication, and professional networks.

Following Scott’s own trajectory from England to the United States, the chapters explore the development of the mathematics department and trace themes such as algebraic representation in geometry, refined visual intuition, and early topology, addressing institutional constraints and the pedagogical means through which students learned to do original mathematics in a time of limited professional opportunity.

Dec 2025 260pp

9781470474935 Paperback £110.00 / US$129.00

SELECTEDCHAPTERSINNUMBERTHEORY

Hermann Minkowski

History of Mathematics, Vol. 50

Hermann Minkowski (1864-1909) was a prominent member of the famous golden epoch of mathematics at Göttingen University in Germany, which started with Karl Friedrich Gauss in 1807 and continued into the twentieth century until the beginning of World War II. Minkowski is well known for his foundational work introducing the "Minkowski spacetime" in special relativity. He made significant contributions to number theory, especially in geometry of numbers and other topics. Minkowski was also known as an excellent teacher.

The present book is an English translation of notes from the course on number theory taught by Hermann Minkowski in Winter 1907/08. The main topic of the course was the Fermat theorem and various methods used to prove it at that time. The book will be helpful and interesting to those studying number theory and to anyone interested in mathematics and its history.

THECALDERÓNPROBLEM

AnIntroduction

Joel Feldman, Mikko Salo & Gunther Uhlmann

Graduate Studies in Mathematics, Vol. 253

Inverse problems are those where, from "external" observations of a hidden "black box" system (a patient's body, nontransparent industrial object, interior of the Earth, etc.), one needs to recover the unknown parameters of the system. A prototypical example is the by now classical Calderón problem, forming the basis of Electrical Impedance Tomography (EIT). In EIT one attempts to determine the electrical conductivity of a medium by making voltage and current measurements at the boundary. EIT arises in several applications, including geophysical prospection and medical imaging. Since the original work of Calderón, there has been remarkable progress on this problem.

This textbook is an introduction to the mathematical theory of the Calderón problem. It includes a thorough account of many important developments and is intended for graduate students who are familiar with the basics of real, complex, and functional analysis. Basic properties of weak solutions of partial differential equations, of Sobolev spaces, and of Fourier transform are developed in the text and appendices.

Dec 2025

INTRODUCTIONTOLIEALGEBRAS

FiniteandInfiniteDimension

J. I. Hall

Graduate Studies in Mathematics, Vol. 248

Being both a beautiful theory and a valuable tool, Lie algebras form a very important area of mathematics. This modern introduction targets entry-level graduate students and might also be of interest to those wanting to refresh their knowledge of the area and be introduced to newer material. Infinite-dimensional algebras are treated extensively along with the finite-dimensional ones.

After some motivation, the text gives a detailed and concise treatment of the Killing-Cartan classification of finite-dimensional semisimple algebras over algebraically closed fields of characteristic 0. Important constructions such as Chevalley bases follow. The second half of the book serves as a broad introduction to algebras of arbitrary dimension, including Kac-Moody (KM), loop, and affine KM algebras. Finite-dimensional semisimple algebras are viewed as KM algebras of finite dimension, their representation and character theory developed in terms of integrable representations. The text also covers triangular decomposition (after Moody and Pianzola) and the BGG category. Several applications to physics are touched on via differential equations, Lie groups, superalgebras, and vertex operator algebras. Each chapter concludes with a problem section and a section on context and history.

MATHEMATICALFOUNDATIONSOFDEEPLEARNING MODELSANDALGORITHMS

Konstantinos Spiliopoulos, Richard B. Sowers & Justin Sirignano Graduate Studies in Mathematics, Vol. 252

Deep learning uses multi-layer neural networks to model complex data patterns. Large models - with millions or even billions of parameters - are trained on massive datasets. This approach has produced revolutionary advances in image, text, and speech recognition and also has potential applications in a range of other fields such as engineering, finance, mathematics, and medicine. This book provides an introduction to the mathematical theory underpinning the recent advances in deep learning. Detailed derivations as well as mathematical proofs are presented for many of the models and optimization methods which are commonly used in machine learning and deep learning. Applications, code, and practical approaches to training models are also included.

This book is designed for advanced undergraduates, graduate students, practitioners, and researchers. Divided into two parts, it begins with mathematical foundations before tackling advanced topics in approximation, optimization, and neural network training.

Jan 2026 550pp

BILLIARDS,SURFACES,ANDGEOMETRY

AProblem-CenteredApproach

Diana Davis

Student Mathematical Library, Vol. 109

This richly illustrated text guides readers to discover the beautiful structure of mathematical billiards. Centered around expertly designed problem sets, this book incrementally builds up ideas through threads of related problems, fostering curiosity, exploration, and conversation. Working through the problems, the reader builds an understanding of foundational results, useful techniques, and key examples, all the way up to current research, while hands-on construction activities offer an opportunity to explore phenomena in three dimensions. Beginning with the square billiard table, the opening chapters explore periodic billiard paths in depth, including connections to continued fractions and symbolic dynamics. From this foundation, the book goes on to explore billiards in triangles and other polygons, flows on translation surfaces, interval exchange transformations, outer billiards and tiling billiards, billiards on the ellipse, and many other topics. Throughout, we meet contemporary mathematicians involved in the topics covered, showcasing the research achievements of the vibrant billiards community. Billiards, Surfaces, and Geometry offers a ground level, problem-centered entry point to this exciting field. Basic knowledge of geometry and matrix transformations is assumed, though the main prerequisite is a spirit of curiosity and exploration.

DEGREETHEORYANDSYMMETRICEQUATIONSASSISTEDBY GAPSYSTEM

WithaSpecialFocusonSystemswithHysteresis

Zalman Balanov et al

Mathematical Surveys and Monographs, Vol. 286

Symmetries are a common feature of real-world phenomena in many fields, including physics, biology, materials science, and engineering. They can help understand the behavior of a system and optimize engineering designs. Nonlinear effects such as delays, nonsmoothness, and hysteresis can have a significant impact on the dynamics and contribute to the increased complexity of symmetric systems. The goal of this book is to provide a complete theoretical and practical manual for studying a large class of dynamical problems with symmetries using degree theory methods. To study the impact of symmetries on the occurrence of periodic solutions in dynamical systems, special variants of the Brouwer degree, the Brouwer equivariant degree, and the twisted equivariant degree are developed to predict patterns, regularities, and symmetries of solutions. Applications to specific dynamical systems and examples are supported by a software package integrated with the GAP system, which provides assistance in the group-theoretic computations involved in equivariant analysis.

Mar 2025

THEGENIUSOFGAUDÍ

GeometryandArchitecture

Claudi Alsina & Roger B. Nelsen Spectrum, Vol. 106

Provides an exploration of the mathematics underlying the works of the Catalan architect Antoni Gaudí i Cornet (1852-1926). Illustrated by over 300 graphics and photographs, this text describes the applications of geometry that are found in Gaudí’s buildings. The narrative is further enhanced by numerous"MathMoments,"highlightingthemathematicsandmathematicians that come to mind when one observes Gaudí's creations.

After an opening chapter giving a pictorial overview of Gaudí's work, this book covers topics from two and three-dimensional geometry such as plane curves, ruled surfaces, ellipsoids, paraboloids, polygons, and polyhedra. Special attention is given throughout to Gaudí's magnum opus, the Basilica de la Sagrada Família.

Suitable for lovers of geometry or architecture, the modest prerequisites mean The Genius of Gaudí can also be used as a supplemental text for a geometry course at the high-school level and above, and may be enjoyed as a mathematical tour guide for anyone visiting the city of Barcelona.

AFIRSTCOURSEINTOPOLOGICALFIELDTHEORY

Jürgen Fuchs, Christoph Schweigert & Lukas Woike University Lecture Series, Vol. 80

Topological quantum field theories lie at the intersection of algebra, topology, and quantum field theory. The area is highly active, driven by recent developments in representation theory and topology, as well as developments in theoretical physics, including the study of topological phases of matter and topological symmetries. This book provides an accessible introduction to topological quantum field theories, along with basic notions of category theory - the natural mathematical setting for topological field theories - by describing these theories as a symmetric monoidal functor from a cobordism category to the category of vector spaces.

Using Dijkgraaf–Witten theories as a recurring example, the book introduces key tools such as category theory, Hopf algebras, and tensor categories, providing a solid foundation for students aiming to pursue a more advanced study in quantum topology and related areas. The book concludes with an outlook connecting the foundational theory to recent developments and current research directions

Jul 2026, 180pp 9781470485078 Paperback £59.00 / US$69.00

INTEGER-VALUEDPOLYNOMIALS

FromCombinatoricstoNumberTheory,��-adicAnalysis, CommutativeandNon-CommutativeAlgebra

Jean-Luc Chabert

Colloquium Publications, Vol. 69

Presents the theory of integer-valued polynomials, as transformed by the work of Manjul Bhargava in the late 1990s. Building from the core ideas in commutative algebra and number theory, the author weaves a panoramic perspective that encompasses results in combinatorics, ultrametric analysis, probability, dynamical systems, and non-commutative algebra. Whether already established in the area or just starting out, readers will find this deep and approachable treatment to be an essential companion to research.

Grouped into seven parts, this book begins with the preliminaries of integer-valued polynomials on Z and subsets of Z. Bhargava's revolutionary orderings and generalized factorials follow, laying the foundation for the modern perspective, before an interlude on algebraic number theory explores the Polya group. Connections between topology and multiplicative ideal theory return the focus to commutative algebra, providing tools for exploring Prufer domains. A part on ultrametric analysis ranges across ��-adic extensions of the Stone-Weierstrass theorem, new orderings, and dynamics. Chapters on asymptotic densities and polynomials in several variables precede the final part on non-commutative algebra. Exercises and historical remarks engage the reader throughout.

RICCISOLITONSINDIMENSIONS��ANDHIGHER

Bennett Chow, Brett Kotschwar & Ovidiu Munteanu

Mathematical Surveys and Monographs, Vol. 293

Offers a detailed account of recent developments of Ricci solitons –self-similar solutions to the Ricci flow equation which play a central role in modeling the formation of singularities of the flow. Building on the foundational work of Hamilton and Perelman and the recent advances of Bamler, Brendle, and others, this book focuses on the rich and technically demanding theory of these solutions. With special attention to dimension 4 where potential applications to the topology of smooth 4-manifolds are most promising, the authors present key results, open problems, and new perspectives on the structure and asymptotic behavior of complete noncompact solitons, the case of greatest significance to singularity analysis. The volume offers a systematic and research-oriented reference for ongoing work in geometric analysis, covering both foundational material and specialized topics.

Areas of focus include curvature growth and decay, bounds on the number of topological ends, asymptotically conical and asymptotically cylindrical solitons, volume growth, and applications of Bamler's theory. Written for graduate students and researchers in differential geometry, geometric analysis, and mathematical physics, this book is accessible to readers with a solid background in Riemannian geometry and partial differential equations.

Mar 2025 398pp

9781470479640 Paperback £116.00 / US$135.00

COMBINATORIAL,COMPUTATIONAL, ANDAPPLIEDALGEBRAICGEOMETRY

ATributetoBerndSturmfels

Edited by Serkan Hosten, Diane Maclagan & Frank Sottile

Proceedings of Symposia in Pure Mathematics, Vol. 111

A collection of surveys that traverse rich mathematical landscapes from invariant theory, Grobner bases, and toric ideals to discrete and convex optimization, hypergeometric systems, algebraic statistics, and tropical geometry. Each article in this book offers an inviting introduction and modern overview of key topics.

Oct 2025 354pp 9781470473600 Paperback £116.00 / US$139.00

INEQUALITIESINMATRIXALGEBRAS

Eric Carlen

Graduate Studies in Mathematics, Vol. 251

Examines the mathematical theory that supports quantum mechanics and computing, delving into positive and completely positive maps, entropy inequalities, and entanglement. This book blends finite system analysis with fundamentals from linear algebra, analysis, and probability, charting decades of refined progress.

Sep 2025 458pp

INTEGER-VALUEDPOLYNOMIALS

FromCombinatoricstoNumberTheory,��-adicAnalysis, CommutativeandNon-CommutativeAlgebra

Jean-Luc Chabert

See page 9 for details of this title.

INTRODUCTIONTOLIEALGEBRAS

FiniteandInfiniteDimension

J. I. Hall

See page 6 for details of this title.

IWASAWATHEORYANDITSPERSPECTIVE

Tadashi Ochai

Tracing Iwasawa theory’s journey from the study of ideal class groups to its expansion into elliptic curves and modular forms, these volumes examine algebraic and analytic methods, coveringp-adic L-functions, cyclotomicp-adic Galois representations, and deformations, reshaping traditional views.

Volume1

Mathematical Surveys and Monographs, Vol. 272

2023 154pp

9781470456726 Paperback £110.00 / US$129.00

Volume2

Mathematical Surveys and Monographs, Vol. 280

2024 211pp

9781470456733 Paperback £116.00 / US$135.00

Volume3

Mathematical Surveys and Monographs, Vol. 291

Jul 2025 110pp

9781470477325 Paperback £103.00 / US$120.00

Volumes1-3

Mathematical Surveys and Monographs, Vol. 272

Aug 2025

9781470481773489ppPaperback

£299.00 / US$350.00

BESTSELLERS

ALGEBRA:CHAPTER0

Paolo Aluffi

Graduate Studies in Mathematics, Vol. 104

Offers an introduction to the main topics of algebra, including approximately 1,000 exercises that provide practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics.

2009 713pp 9781470465711 Paperback £76.00 / US$89.00

APPLIEDLINEARALGEBRA

TheDecouplingPrinciple,SecondEdition

Lorenzo Sadun

Linear algebra permeates mathematics, as well as physics and engineering. In this text for junior and senior undergraduates, the author treats diagonalization as a central tool in solving complicated problems in these subjects by reducing coupled linear evolution problems to a sequence of simpler decoupled problems.

2008 371pp 9781470470043 Paperback £59.00 / US$69.00

BASICMODERNTHEORYOFLINEARCOMPLEX ANALYTIC��-DIFFERENCEEQUATIONS

Jacques Sauloy

Mathematical Surveys and Monographs, Vol. 287

Based on early ideas by Birkhoff, this book re-examines q-difference equations through a fusion of algebraic and analytic methods, moving from elementary q-calculus and scalar challenges to transforming systems, ultimately addressing Fuchsian versus irregular cases with Riemann-Hilbert and Galois theory.

2024 680pp 9781470478407 Paperback £116.00 / US$135.00

LINEARALGEBRA: GATEWAYTOMATHEMATICS

SecondEdition

Robert Messer

AMS/MAA Textbooks, Vol. 66

Uses linear algebra as a vehicle to introduce students to the inner workings of mathematics. The structures and techniques of mathematics in turn provide an accessible framework to illustrate the powerful and beautiful results about vector spaces and linear transformations.

2021 434pp

9781470462956 Paperback £76.00 / US$89.00

MAA Press

THEPRACTICEOFALGEBRAICCURVES

ASecondCourseinAlgebraicGeometry

David Eisenbud & Joe Harris

Graduate Studies in Mathematics, Vol. 250

Explores modern theory of complex projective algebraic curves with vivid examples linking classical geometry, commutative algebra and moduli theory. Beginning with key ideas like projective maps, invertible sheaves and the Riemann–Roch theorem, this book advances to topics such as Jacobians and Hilbert schemes.

Feb 2025 413pp

9781470479435 Paperback £76.00 / US$89.00

9781470476373 Hardback £116.00 / US$135.00

VISUALGROUPTHEORY

Nathan Carter

Classroom Resource Materials, Vol. 32

With more than 300 illustrations, this book brings groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups to advanced structural concepts.

2009 295pp

9781470464332 Paperback £68.00 / US$79.00

MAA Press

ANALYSIS

DEGREETHEORYANDSYMMETRICEQUATIONSASSISTEDBY GAPSYSTEM

WithaSpecialFocusonSystemswithHysteresis

Zalman Balanov et al

See page 7 for details of this title.

ERGODICTHEORY

Simon Rubinstein-Salzedo

The Carus Mathematical Monographs, Vol. 38

An engaging exploration of ergodic theory leading readers through dynamical systems using measure theory and the Lebesgue integral. Invariant measures, recurrence theorems, mixing, and entropy bridge classical foundations with modern applications in number theory and combinatorics, supported by diverse exercises and open problems.

Jun 2025 228pp

9781470479206 Paperback £68.00 / US$79.00

MAA Press

THEHEISENBERGGROUP

ASurvey

Gerald B. Folland

Colloquium Publications, Vol. 68

Explores the multifaceted influence of the Heisenberg group on group representation theory, mathematical physics, complex analysis, partial differential equations, and differential geometry.

Jun 2025 233pp

MATHEMATICALFOUNDATIONSOFDEEPLEARNINGMODELS ANDALGORITHMS

Konstantinos Spiliopoulos, Richard B. Sowers & Justin Sirignano

See page 6 for details of this title.

RICCISOLITONSINDIMENSIONS��ANDHIGHER

Bennett Chow, Brett Kotschwar & Ovidiu Munteanu

See page 9 for details of this title.

STABILITYOFNONLINEARWAVESIN HAMILTONIANDYNAMIALSYSTEMS

AM

Anna Geyer & Dmitry E. Pelinovsky

Mathematical Surveys and Monographs, Vol. 288

Delves into the rigorous study of stability in nonlinear waves within Hamiltonian systems, bridging classical equilibrium analysis with modern methods for infinitedimensional dispersive equations.

Sep 2025 380pp

9781470475529 Paperback £116.00 / US$135.00

UNIVALENTFUNCTIONSINQUANTUM PROBABILITYTHEORY

Sebastian Schlessinger

Mathematical Surveys and Monographs, Vol. 294

Considers the interplay between complex analysis and quantum probability theory, bridging classical concepts with non-commutative processes.

Dec 2025

9781470481803268ppPaperback £116.00 / US$135.00

BESTSELLERS

COMPLEX

ANALYSIS

AnIntroductiontotheTheoryofAnalytic FunctionsofOneComplexVariable,ThirdEdition

Lars Ahlfors

Chelsea Publications, Vol. 385

Offers a rigorous introduction on an elementary level to the theory of analytic functions of one complex variable. This book covers standard topics in an introductory complex analysis course. The presentation is slanted toward the geometric approach to complex analysis.

2022 331pp 9781470467678 Paperback

AMSChelseaPublishing

DISCRETEANALOGUESINHARMONICANALYSIS

Bourgain,Stein,andBeyond

Ben Krause

Graduate Studies in Mathematics, Vol. 224

Discrete harmonic analysis is a rapidly developing field of mathematics that fuses together classical Fourier analysis, probability theory, ergodic theory, analytic number theory, and additive combinatorics in new and interesting ways. This timely book explores certain modern topics and connections at the interface of harmonic analysis, ergodic theory, number theory, and additive combinatorics.

2023 542pp

FractalDimensions,Self-Similarity,andFractalCurves

Michel L. Lapidus & Goran Radunović

Graduate Studies in Mathematics, Vol. 247

Exploring fractal geometry in depth, this resource explains self-similarity, fractal curves, and various fractal dimensions through rigorous proofs and diverse exercises, introducing classical examples like the Cantor set, Sierpinski gasket, and Koch snowflake, paving the way for advanced studies in fractals.

NIGELKALTON'SLECTURESINNONLINEAR FUNCTIONALANALYSIS

Adam Bowers

University Lecture Series, Vol. 79

Delves into the nonlinear geometry of Banach spaces and its central challenges in nonlinear functional analysis. Based on graduate lectures from 2008, this book connects theoretical computer science, noncommutative geometry, and geometric group theory while presenting fresh insights alongside recent, unpublished results.

2024

ONE-DIMENSIONALERGODIC SCHRÖDINGEROPERATORS

I.GeneralTheory

David Damanik & Jake Fillman

Graduate Studies in Mathematics, Vol. 221

Beginning with a refresher on key topics in spectral theory, this volume presents the basic theory of discrete one-dimensional Schrödinger operators with dynamically defined potentials, including a self-contained introduction to the relevant aspects of ergodic theory and topological dynamics.

2022

ONE-DIMENSIONALERGODIC SCHRÖDINGEROPERATORS

II.SpecificClasses

David Damanik & Jake Fillman

Graduate Studies in Mathematics, Vol. 249

Integratingdynamicalsystems,topology,andanalysis,this bookexaminesone-dimensionalergodicoperatorsthat capturephenomenaincrystals,disorderedmedia,and quasicrystals.Highlightingrandomandalmost-periodic cases,itoffersaself-containedintroductionforaspiring researchersandgradstudents.

2025 627pp

EXPERIMENTALMATHEMATICS

A

ComputationalPerspective

Matthew P. Richey & Matthew L. Wright

AMS/MAA Textbooks, Vol. 74

Explores computational mathematics where experiments illuminate theoretical concepts. Rich examples drawn from number theory, complex analysis and probability inspire discovery. Over 450 problems and exercises foster both mathematical reasoning and practical programming skills.

Aug 2025

MAA Press

MATHEMATICALANDCOMPUTATIONAL METHODSFORCOMPLEXSOCIALSYSTEMS

Edited by Heather Z. Brooks et al

Proceedings of Symposia in Applied Mathematics, Vol. 80

Delves into the intricacies of societal phenomena such as meme diffusion, urban gentrification, and voter dynamics, while examining how individual interactions shape collective behavior. This collection intertwines mathematical modeling, data analysis, network science, and geometry to unveil the dynamics of complex social systems. Jun

AMATHEMATICALEXPLORATIONOFMAP PROJECTIONS

C.M. Linton

Dolciani Mathematical Expositions, Vol. 59

Explores the captivating mechanics behind transforming Earth's surface into an accurate flat representation. This book unravels the mathematical ideas of map distortion through diagrams, multivariable calculus, and complex variables while following a rich historical narrative that illuminates cylindrical, azimuthal, and conical projections.

Dec 2025 187pp

MAA Press

OPTIMALCONTROL

ADifferentialEquationsApproach

Stewart Johnson

AMS/MAA Textbooks, Vol. 75

Explores the dynamics of controlled systems to optimize outcomes using differential equations. The text presents core techniques, Pontryagin’s method, linear-quadratic models, and higher-dimensional challenges, while also addressing bang-bang controls, differential games, and Euler-Lagrange theory alongside practical exercises. Dec 2025

MAA Press

BESTSELLERS

3DPRINTINGINMATHEMATICS

Edited by Maria Trnkova & Andrew Yarmola

Proceedings of Symposia in Applied Mathematics, Vol. 79

Focuses on the process and applications of 3D printing for mathematical education, research, and visualization, and discusses the challenges and open mathematical problems that arise in the design and algorithmic aspects of 3D printing.

2024 226pp 9781470469160 Paperback

APPLIEDASYMPTOTICANALYSIS

Peter D. Miller

Graduate Studies in Mathematics, Vol. 75

A survey of asymptotic methods set in the applied research context of wave propagation. This work stresses rigorous analysis in addition to formal manipulations and is suitable for a beginning graduate course on asymptotic analysis in applied mathematics, aimed at students of pure and applied mathematics as well as science and engineering.

2006 467pp

9780821840788 Hardback £116.00 / US$135.00

LARGENETWORKSANDGRAPHLIMITS

László Lovász

Colloquium Publications, Vol. 60

Describes one recent approach to the limit theory of graphs which has emerged over the last decade. This theory has rich connections with other approaches to the study of large networks and this work explains many of these connections, first at an informal level to emphasise the need to apply more advanced mathematical methods, and then as an exact development of the theory of the algebraic theory of graph homomorphisms and of the analytic theory of graph limits.

2013 475pp

9780821890851 Hardback £85.00 / US$99.00

MATHEMATICALINTERESTTHEORY

ThirdEdition

Leslie Jane Federer Vaaler, Shinko Kojima Harper & James W. Daniel

AMS/MAA Textbooks, Vol. 57

Provides an introduction to how investments grow over time in a mathematically precise manner. The emphasis is on practical applications that give the reader a concrete understanding of why the various relationships should be true.

2019 581pp 9781470465681 Paperback £90.00 / US$105.00

MAA Press

NUMERICALANALYSIS

MathematicsofScientificComputing, ThirdEdition

David Kincaid & Ward Cheney

Pure and Applied Undergraduate Texts, Vol. 2

Introduces students with diverse backgrounds to various types of mathematical analysis that are commonly needed in scientific computing. This book treats the subject of numerical analysis from a mathematical point of view, offering an analysis of methods for scientific computing with appropriate motivations and proofs.

2009 788pp

9780821847886 Hardback £86.00 / US$100.00

QUANTUMCOMPUTATIONAND QUANTUMINFORMATION

AMathematicalPerspective

J. M. Landsberg

Graduate Studies in Mathematics, Vol. 243

Delves into the mathematical transition from classical computation to quantum mechanics, where probability gives way to quantum postulates. Key algorithms alongside Shannon’s theory adapted to quantum settings are rigorously examined, while representation theory reveals the origins of entropy inequalities.

2024 204pp

9781470477776 Paperback £76.00 / US$89.00

BESTSELLERS

APPROXIMATELYCALCULUS

Shahriar Shahriari

Calculus is a powerful tool because it allows us to approximate complicated functions with simpler ones. Indeed, replacing a function locally with a linear - or higher order - approximation is at the heart of calculus. Emphasizing the role of approximations in calculus, this book addresses topics such as derivatives, integrals, and sequences.

2006 292pp

CALCULUSIN

3D

Geometry,Vectors,andMultivariateCalculus

Zbigniew Nitecki

AMS/MAA Textbooks, Vol. 40

An accessible, well-written textbook for an honours course in multivariable calculus for mathematically strong first or second-year university students. This treatment carefully balances theoretical rigour, the development of student facility in the procedures and algorithms, and inculcating intuition into underlying geometric principles.

2018 405pp

MAA Press

GLOBALCALCULUS

S. Ramanan

Graduate Studies in Mathematics, Vol. 65

Suitable for a first year graduate course on global analysis, this title proves the basics of Fourier transforms, Sobolev theory and interior regularity at the same time as symbol calculus, culminating in beautiful results in global analysis, real and complex.

2004 316pp 9780821837023 Hardback £85.00 / US$99.00 ��, ∏,��, & ��

David Perkins

Spectrum, Vol. 96

Certain constants occupy precise balancing points in the cosmos of number, like habitable planets sprinkled throughout our galaxy at just the right distances from their suns. This book introduces and connects four of these constants (��, ∏,��,&��). The authors discuss their properties, as a group, at a level appropriate for an audience armed only with the tools of elementary calculus.

2020 176pp 9781470447991 Paperback £56.00 / US$65.00

MAA Press

BiologyEdition

THESIXPILLARSOFCALCULUS

Lorenzo Sadun

Offers a conceptual and practical introduction to differential and integral calculus for use in a one or two-semester course. By boiling calculus down to six common-sense ideas, this text invites students to make calculus an integral part of how they view the world. Each pillar is introduced by tackling and solving a challenging, realistic problem.

Pure and Applied Undergraduate Texts, Vol. 60

2023 383pp

9781470469962 Paperback £85.00 / US$99.00

BusinessEdition

Pure and Applied Undergraduate Texts, Vol. 56

2023 381pp

9781470469955 Paperback £85.00 / US$99.00

DIFFERENTIAL EQUATIONS

THECALDERÓNPROBLEM

AnIntroduction

Joel Feldman, Mikko Salo & Gunther Uhlmann

See page 5 for details of this title.

BESTSELLERS

ANALYSISOFMONGE-AMPÈRE EQUATIONS

Nam Q. Le

Graduate Studies in Mathematics, Vol. 240

PresentsasystematicanalysisoftheMonge-Ampère equation,thelinearizedMonge-Ampèreequation, and their applications, with emphasis on interior and boundary theories. Thisbookgivesanextensive surveyoffundamentalresults,essentialtechniques, andintriguingphenomenainthesolvability,geometry, andregularityofMonge-Ampèreequations.

2024 227pp

9781470476250 Paperback £76.00 / US$89.00

9781470474201 Hardback £116.00 / US$135.00

BIFURCATIONTHEORY

Ale Jan Homburg & Jurgen Knobloch

Graduate Studies in Mathematics, Vol. 246

Explores bifurcation theory with a rigorous treatment of classical and advanced phenomena. This text navigates local, nonlocal, and global bifurcations using geometric and analytic methods - normalformreductions,centermanifold techniques, and more - supported by full proofs to deepen understanding in dynamical systems.

Jan 2025 646pp

9781470478803

ELLIPTICPARTIAL DIFFERENTIAL EQUATIONS

SecondEdition

Qing Han & Fanghua Lin

Courant Lecture Notes, Vol. 1

Presents basic methods for obtaining various a priori estimates for second-order equations of elliptic type with a particular emphasis on maximal principles, Harnack inequalities, and their applications. The equations considered in this book are linear, but the presented methods also apply to nonlinear problems.

2011 147pp

THEMATHEMATICALANALYSIS OFTHEINCOMPRESSIBLEEULER ANDNAVIER-STOKESEQUATIONS

AnIntroduction

Jacob Bedrossian & Vlad Vicol

Graduate Studies in Mathematics, Vol. 225

PARTIAL DIFFERENTIAL EQUATIONS

SecondEdition

Lawrence C. Evans

Graduate Studies in Mathematics, Vol. 19

The definitive text on partial differential equations (PDEs), offering a comprehensive survey of modern techniques in the theoretical study of PDEs with particular emphasis on nonlinear equations.

2010 662pp

Provides graduate students with exposure to the mathematical analysis of the incompressible Euler and Navier-Stokes equations. This book gives a concise introduction to the fundamental results in the well-posedness theory of these PDEs, leaving aside some of the technical challenges presented by bounded domains or by intricate functional spaces.

2022 218pp

/ US$99.00

STURM-LIOUVILLE OPERATORS,THEIR SPECTRALTHEORY,AND SOMEAPPLICATIONS

Fritz Gesztesy, Roger Nichols & Maxim Zinchenko

Colloquium Publications, Vol. 67

Offers an in-depth exploration of modern Sturm-Liouville theory, this book examines Weyl–Titchmarsh and oscillation theories, boundary data maps, and operators with singular potentials, showcasing diverse examples from Floquet theory to scattering, and providing essential appendices on spectral theory and operator extensions.

2024 927pp

/ US$135.00

HANDS-ONCOMBINATORICS

BuildingColorfulTrainstoManifestPascal's Triangle,FibonacciNumbers,andMuchMore

Brian Hopkins

Classroom Resource Materials, Vol. 74

Experience an engaging exploration of combinatorial reasoning through interactive challenges, vivid illustrations, and train-themed proofs. The narrative unfolds from a student’s perspective while detailed instructor guidance supports learners at diverse levels, bridging theory and hands-on discovery.

Mar 2025 196pp

MAA

MILESTONESINGRAPHTHEORY ACenturyofProgress

Lowell W. Beineke, Bjarne Toft & Robin J. Wilson

Spectrum, Vol. 108

Graph theory evolved from early challenges to a central role in modern mathematics, charting a course through rapid growth in the 1960s and 1970s. Organized into themed chapters, this study highlights milestones in map colorings, planarity, Hamiltonian graphs, matchings, and complexity with extensive notes. Aug

BESTSELLERS

COMBINATORICS:THEARTOFCOUNTING

Bruce E. Sagan

Graduate Studies in Mathematics, Vol. 210

Offers a gentle introduction to the enumerative part of combinatorics. In addition to covering all the standard techniques for counting combinatorial objects, the text contains material from the research literature such as the use of quotient posets to study the Möbius function and characteristic polynomial of a partially ordered set.

2021 304pp

9781470460327 Paperback £76.00 / US$89.00

DISCRETEMATHEMATICS

Martin Aigner

The advent of fast computers and the search for efficient algorithms revolutionized combinatorics and brought about the field of discrete mathematics. This book provides an introduction to the main ideas and results of discrete mathematics, with an emphasis on algorithms.

2007 388pp

9781470470630 Paperback £64.00 / US$75.00

GAMETHEORY,ALIVE

Anna R. Karlin & Yuval Peres

Presents a rigorous introduction to the mathematics of game theory, focusing on theoretical highlights and presenting exciting connections of game theory to other fields such as computer science, economics, social choice, biology, and learning theory. Both classical topics and modern topics are covered.

2017 372pp

9781470419820 Hardback £68.00 / US$79.00 AM

INTRODUCTIONTO QUANTUMALGORITHMS

Johannes A. Buchmann

Pure and Applied Undergraduate Texts, Vol. 64

The theory of quantum algorithms is based on advanced concepts from computer science, mathematics, and physics. This book offers a mathematically precise exploration of these concepts, accessible to those with a basic mathematical university education, while also catering to more experienced readers.

2024 371pp 9781470473983 Paperback £76.00 / US$89.00

OPENPROBLEMSINALGEBRAIC COMBINATORICS

Edited by Christine Berkesch et al

Proceedings of Symposia in Pure Mathematics, Vol. 110

Focusing on exact results, this collection unites algebraic combinatorics with algebra, topology, geometry, and physics. Drawing on talks from the 2022 conference, this work highlights remarkable research and intriguing open problems, sparking exchanges of innovative ideas and promising new directions.

2024 371pp

9781470473334 Paperback £119.00 / US$139.00

POLYNOMIALMETHODSINCOMBINATORICS

Larry Guth

University Lecture Series, Vol. 64

Explains some recent applications of the theory of polynomials and algebraic geometry to combinatorics and other areas of mathematics, discussing in detail various problems in incidence geometry associated to Paul Erdos's distinct distances problem in the plane from the 1940s.

2016 273pp 9781470428907 Paperback £59.00 / US$69.00

GENERAL INTEREST

BETWEENTWODISCIPLINES

B.L.vanderWaerdenandtheDevelopmentofQuantum Mechanics

Martina R. Schneider

See page 3 for details of this title.

THEFLOERJUNGLE

ChartingtheDevelopmentofaTheory

Helmut Hofer & Siobhan Roberts

See page 4 for details of this title

INSTRUCTINGTHEMATHEMATICALIMAGINATION

CharlotteAngasScottandBrynMawrCollege,1880sto1920s

Jemma Lorenat

See page 4 for details of this title.

BESTSELLERS

THEMATHEMATICSOFSHUFFLINGCARDS

Persi Diaconis & Jason Fulman

Miscellaneous Book Series, Vol. 146

Provides a lively development of the mathematics needed to answer the question, ‘How many times should a deck of cards be shuffled to mix it up?’ The shuffles studied are the usual ones that real people use: riffle, overhand, and smooshing cards around on the table.

2023 346pp

Paperback £68.00 / US$79.00

MAXDEHN

PolyphonicPortrait

Edited by Jemma Lorenat et al

Explores the multifaceted legacy of mathematician Max Dehn, traversing his early years as a brilliant student of Hilbert, a period leading a dedicated circle in Frankfurt, and a daring escape from Nazi Germany. The essays uncover his innovations, his life’s journey, and his devotion to history and the arts.

2024 290pp

9781470461065 Paperback £107.00 / US$125.00

REALLYBIGNUMBERS

Richard Evan Schwartz

TASTYJAPANESEMORSELSINRECREATIONAL MATHEMATICS

Yoshiyuki Kotani

Edited by Toshiro Kawamata et al

Spectrum, Vol. 105

AcharmingcollectionofpuzzlescreatedbyYoshiyukiKotani, oneofthefoundingmembersoftheAcademyofRecreational Mathematics, Japan. Kotani has selected some of his favourite puzzles from over 40 years of puzzle setting, most of which have never appeared in western literature.

2024 262pp

9781470476786 Paperback £34.00 / US$39.00

MAA Press

YOUCANCOUNTONMONSTERS

TheFirst100NumbersandTheir Characters

Richard Evan Schwartz 2015 242pp

Paperback £20.99 / US$25.00

REALLYBIGNUMBERSandYOUCANCOUNTON MONSTERS,2-VOLUMESET

Richard Evan Schwartz

Monograph Books

In Really Big Numbers, mathematician and author, Richard Evan Schwartz, leads math lovers of all ages on an innovative and strikingly illustrated journey through the infinite number system.

You Can Count on Monsters is a unique teaching tool that takes maths lovers on a journey designed to motivate kids to learn the fun of factoring and prime numbers.

2015 436pp 9781470422943 Set £34.00 / US$39.00

WHAT'SHAPPENINGINTHEMATHEMATICAL SCIENCES

Volume13

Dana Mackenzie & Leila Sloman

Exploring topics ranging from artificial intelligence to non-Euclidean geometry, the 13th volume of What's Happening in the Mathematical Sciences by Dana Mackenzie and Leila Sloman is an exquisitely crafted and skillfully authored examination of cutting-edge advancements in mathematics.

2024 132pp

9781470474904 Paperback £24.99 / US$29.00

GEOMETRY & TOPOLOGY

BILLIARDS,SURFACES,ANDGEOMETRY

AProblem-CenteredApproach

Diana Davis

See page 7 for details of this title.

COMPARISONTHEOREMSINRIEMANNIAN

GEOMETRY

Jeff Cheeger & David G. Ebin

Chelsea Publications, Vol. 365

Explores the intricate interplay between curvature, topology, and global geometry in complete Riemannian manifolds. Early chapters introduce foundational aspects like Riemannian geometry, Toponogov's theorem, homogeneous spaces, and Morse theory, while later sections analyze rigidity phenomena and pivotal results from 1959–1974.

Aug 2025

9781470481117161ppPaperback

£59.00 / US$69.00

AMS Chelsea Publishing

THEGENIUSOFGAUDÍ

GeometryandArchitecture

Claudi Alsina & Roger B. Nelsen

See page 8 for details of title.

MORSEINDEXOFMINIMALSUBMANIFOLDS

Francisco Urbano

Mathematical Surveys and Monographs, Vol. 292

A systematic treatment of the Morse index for minimal submanifolds in Riemannian manifolds, with essential background information, a survey of key properties, and diverse examples with calculated indices. Detailed analyses in Euclidean, spherical, and projective settings highlight open problems and inspire further research in geometric analysis.

BESTSELLERS

FOUNDATIONSOFMECHANICS

SecondEdition

Ralph Abraham & Jerrold E. Marsden

Chelsea Publications, Vol. 364

For many years, this book has been viewed as a classic treatment of geometric mechanics, known for its broad exposition of the subject, with many features that cannot be found elsewhere. This book is recommended as a textbookandasabasicreferenceworkforthefoundations of differentiable and Hamiltonian dynamics.

2008 826pp

9780821844380

AMS Chelsea Publishing

FRONTIERSINGEOMETRYANDTOPOLOGY

Paul M. N. Feehan, Lenhard L. Ng & Peter S. Ozsvath

Proceedings of Symposia in Pure Mathematics, Vol. 109

Proceedings stemming from an influential summer school and research conference capture the vibrant interplay among analysis, geometry, and topology during a milestone celebration in which scholars delved into knot theory, manifold topology, various homology theories, and pseudoholomorphic curve methods, uniting diverse mathematical ideas.

2024 284pp

INTRODUCTIONTOCOMPLEXMANIFOLDS

John M. Lee

Graduate Studies in Mathematics, Vol. 244

Complex manifolds are smooth manifolds endowed with coordinate charts that overlap holomorphically. They have deep and beautiful applications in many areas of mathematics. This book is an introduction to the concepts, techniques, and main results about complex manifolds.

2024 361pp

INTRODUCTIONTOTHE��-PRINCIPLE

SecondEdition

K. Cieliebak, Y. Eliashberg & N. Mishachev

Graduate Studies in Mathematics, Vol. 239

Covers two main methods for proving the h-principle: holonomic approximation and convex integration. Special emphasis is placed on applications to symplectic and contact geometry. This book is the first broadly accessible exposition of the theory and its applications.

LECTURESONDIFFERENTIALGEOMETRY

Bennett Chow & Yutze Chow

Graduate Studies in Mathematics, Vol. 245

Vertically integrated coverage unfolds across three sections, from Euclidean submanifolds and smooth manifoldstoRiemanniantheoryandadvancedgeometric analysis. This book explores bundles, curvature, Ricci flow, harmonic functions, eigenvalue problems, and minimal surfaces to pave the path toward deeper study.

TREESOFHYPERBOLICSPACES

Michael Kapovich & Pranab Sardar

Mathematical Surveys and Monographs, Vol. 282

OfferinganalternativeproofoftheBestvina-Feighntheorem fortreesofhyperbolicspaces,thisworkdefinesuniform quasigeodesicsanddemonstratesCannon-Thurstonmaps for subtrees and relatively hyperbolic spaces. It probes laminations and discusses key group-theoretic outcomes.

2024 278pp 9781470474256 Paperback £116.00 /

BESTSELLERS

ABRIDGETOADVANCEDMATHEMATICS

FromNaturaltoComplexNumbers

Sebastian M. Cioabă & Werner Linde

Pure and Applied Undergraduate Texts, Vol. 58

Most introduction to proofs textbooks focus on the structure of rigorous mathematical language and only use mathematical topics incidentally as illustrations and exercises. In contrast, this book gives students practice in proof writing while simultaneously providing a rigorous introduction to number systems and their properties.

2023 525pp

9781470471484 Paperback £76.00 / US$89.00

AFIRSTJOURNEYTHROUGHLOGIC

Martin Hils & François Loeser

Student Mathematical Library, Vol. 89

Presents mathematical logic to students who are interested in what this field is but have no intention of specializing in it. The point of view is to treat logic on an equal footing to any other topic in the mathematical curriculum.

2019 195pp

9781470452728 Paperback £51.00 / US$59.00

RESIDUATEDSTRUCTURESINALGEBRA ANDLOGIC

George Metcalfe, Francesco Paoli & Constantine Tsinakis

Mathematical Surveys and Monographs, Vol. 277

An introduction to residuated structures, a common thread binding together algebra and logic, designed to serve the purposes of novices and experts alike. The first three chapters provide a gentle introduction to the subject, while subsequent chapters provide a state-ofthe-art account of recent developments in the field.

2023 265pp

9781470469856 Paperback £110.00 / US$129.00

SETTHEORY

Felix Hausdorff

Chelsea Publications, 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.

1957 352pp

9781470464943 Paperback £59.00 / US$69.00

AMS Chelsea Publishing

THETOOLSOFMATHEMATICALREASONING

Tamara J. Lakins

Pure and Applied Undergraduate Texts, Vol. 26

Offers 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. This 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.

2016 217pp

9781470428990 Hardback £76.00 / US$85.00

ULTRAFILTERSTHROUGHOUTMATHEMATICS

Isaac Goldbring

Graduate Studies in Mathematics, Vol. 220

Presents the basic facts about ultrafilters and ultraproducts to readers with no prior knowledge of the subject. These techniques are then applied to a wide variety of topics. The first part of the book deals solely with ultrafilters, and the second part presents the classical ultraproduct construction.

2022 408pp

9781470469610 Paperback £76.00 / US$85.00

MATHEMATICAL PHYSICS

AFIRSTCOURSEINTOPOLOGICALFIELDTHEORY

Jurgen Fuchs, Christoph Schweigert & Lukas Woike

See page 8 for this title.

BESTSELLERS

LATTICEMODELSANDCONFORMALFIELDTHEORY

Franck Gabriel, Clement Hongler & Francesco Spadaro

Courant Lecture Notes, Vol. 32

Mathematical ideas unite Statistical Mechanics and Conformal Field Theory by charting a path from two-dimensional lattice models and phase transitions to the emergence of 2D CFT, focusing on Unitary Minimal Models. In this book, scaling assumptions and probabilistic definitions are explored, offering guided examples for researchers and grad students.

2024 205pp

MATHEMATICALUNDERSTANDINGOFNATURE

EssaysonAmazingPhysicalPhenomenaandtheir UnderstandingbyMathematicians

V. I. Arnold

A collection of 39 short stories giving the reader a unique opportunity to take a look at the scientific philosophy of Vladimir Arnold. Topics of the stories included range from astronomy, to mirages, to motion of glaciers, to geometry of mirrors and beyond. In each case Arnold's explanation is both deep and simple, which makes the book interesting and accessible to an extremely broad readership.

2014 167pp

Paperback £34.00 / US$39.00

QUANTUMFIELDTHEORY

ATouristGuideforMathematicians

Gerald B. Folland

Mathematical Surveys and Monographs, Vol. 149

Presents the elements of quantum field theory, with the goal of understanding the behaviour of elementary particles rather than building formal mathematical structures, in a form that will be comprehensible to mathematicians. Rigorous definitions and arguments are presented as far as they are available, but the text proceeds on a more informal level when necessary, with due care in identifying the difficulties.

2008 325pp

/ US$127.00

QUANTUMFIELDSANDSTRINGS

ACourseforMathematicians,Volume1&2

Edited by Pierre Deligne et al

Ideas from quantum field theory and string theory have had a considerable impact on mathematics. In 1996-97 the Institute for Advanced Study (Princeton, NJ) organized a special year-long program designed to teach mathematicians the basic physical ideas which underlie the mathematical applications. These volumes are a written record of the program.

1999 1,501pp 9780821820148 Paperback £107.00 / US$124.00

STRING-MATH2022

Edited by Ron Donagi et al

Proceedings of Symposia in Pure Mathematics, Vol. 107

Contains the proceedings from the String-Math conference which took place at the University of Warsaw in 2022. This proceedings volume contains articles summarizing 14 conference lectures devoted to several research areas actively being developed.

2024 296pp

9781470472405 Paperback £119.00 / US$137.00

MATHEMATICS EDUCATION

EXPLORINGMATH

NineHands-on,Eye-openingLabProjects

Edited by Marco Abrate et al

Classroom Resource Materials, Vol. 75

Engaging classroom projects promote active learning in high schools and universities with nine hands-on labs solving real-world challenges. This book covers topics from origami and mapping to bridge design and search algorithms, blending practical activities with essential math, inspiring collaborative exploration across diverse disciplines.

Jun 2025 158pp 9781470477035 Paperback £51.00 / US$59.00

MAA Press

AMATHEMATICIAN'SANGLEONSCHOOLMATH

EssaysfromtheFirst25YearsoftheMAAOnline

Column,Devlin'sAngle,1996-2020

Keith Devlin

Spectrum, Vol. 107

Gathering 46 engaging posts from a celebrated online series spanning 25 years, this collection explores K–12 math instruction through nine themed chapters, offering lively perspectives on topics like multiplication, conceptual understanding, and creativity, with insights that also resonate in college-level teaching.

Aug 2025 272pp

9781470479336 Paperback £34.00 / US$39.00

MAA Press

BESTSELLERS

EUCLIDEANGEOMETRYINMATHEMATICALOLYMPIADS

Evan Chen

Problem Books, Vol. 27

A challenging problem-solving book in Euclidean geometry, assuming nothing of the reader other than a good deal of courage. Topics covered include cyclic quadrilaterals, power of a point, and homothety; along the way the reader will meet such classical gems as the nine-point circle, the Simson line, and the symmedian and the mixtilinear incircle. 2016

MAA Press

MATHCIRCLEBYTHEBAY

TopicsforGrades1-5

Laura Givental, Maria Nemirovskaya & Ilya Zakharevich

MSRI Mathematical Circles Library, Vol. 21

Introduces children to combinatorics, Fibonacci numbers, Pascal's triangle, and the notion of area, among other things. The authors choose topics with deep mathematical context that are part of the continuously developing stream of mathematical thought.

2019 179pp

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

MATHFROMTHREETOSEVEN

TheStoryofaMathematical

CircleforPreschoolers

Alexander Zvonkin

MSRI Mathematical Circles Library, Vol. 5

Provides a captivating account of a professional mathematician's experiences conducting a math circle for preschoolers in his apartment in Moscow in the 1980s. As anyone who has taught or raised young children knows, mathematical education for kids is a real mystery. This is a narrative about what he did, what he tried, what worked, what failed, but most important, what the children experienced.

2011 300pp

9780821868737 Paperback £29.99 / US$35.00

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

AMOSCOWMATHCIRCLE

Week-by-weekProblemSets

Sergey Dorichenko

MSRI Mathematical Circles Library, Vol. 8

Presents materials used during the course of one year in a math circle organised by mathematics faculty at Moscow State University. Each problem set has a similar structure, combining review material with a new topic, offering problems in a range of difficulty levels. This time-tested pattern has proved its effectiveness in engaging all students and helping them master new material while building on earlier knowledge.

2012 240pp

9780821868744 Paperback £29.99 / US$35.00

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

NAVIGATINGTHEMATHMAJOR ChartingYourCourse

Carrie Diaz Eaton et al

Classroom Resource Materials, Vol. 73

Designed for students at any point in their mathematical journey, this guide mixes interactive exercises, course previews, and realistic strategies to overcome setbacks, offering study tips, extracurricular ideas, and career as well as graduate program insights, illuminating a clear path forward.

2024 172pp

9781470475833 Paperback £56.00 / US$65.00

MAA Press

TRANSFORMATIONALCHANGEEFFORTS

StudentEngagementinMathematicsthroughan InstitutionalNetworkforActiveLearning

Edited by Wendy M. Smith et al

The purpose of this handbook is to help launch institutional transformations in mathematics departments to improve student success. The authors report findings from the Student Engagement in Mathematics through an Institutional Network for Active Learning (SEMINAL) study.

2021 348pp

9781470463779 Paperback £68.00 / US$79.00

This book is published in cooperation with CBMS

NUMBER THEORY

ANALYTICNUMBERTHEORYREVEALED

AFirstGuidetoPrimeNumbers

Andrew Granville

By blending classical results with current perspectives, this book prepares advanced undergraduates and beginning graduate students to not just learn analytic number theory, but to acquire contemporary ways of thinking about the subject.

Oct 2025 292pp

9781470481520 Paperback £68.00 / US$79.00

COMMONINESSENTIALDISCRIMINANTDIVISORS

ScenesfromtheEarlyHistoryofAlgebraicNumberTheory

Fernando Q. Gouvea & Jonathan Webster

History of Mathematics, Vol. 47

Mathematical challenges spurred nineteenth-century experts to rethink algebraic number theory when inessential discriminant divisors impeded conventional methods. Annotated key papers showcase how Dedekind, Kronecker, and Hensel turned obstacles into catalysts, reshaping the discipline with fresh insights.

Dec 2025 141pp

9781470475246 Paperback £81.00 / US$95.00

ANILLUSTRATEDTHEORYOFNUMBERS

Martin H. Weissman

See page 1 for details of this title.

NUMBERTHEORYINFORMEDBYCOMPUTATION

Edited by Jennifer S. Balakrishnan, Bjorn Poonen & Akshay Venkatesh

A collection of lecture notes from the Graduate Summer School “Number Theory Informed by Computation” held at the IAS/Park City Mathematics Institute 2022, addressing topics at the interface between number theory and computation, both terms interpreted broadly. This volume is aimed at students with a background in graduate level number theory.

Jan 2026

9781470461249325ppPaperback

£107.00 / US$125.00

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

THELANGLANDSPROGRAM

Edited by Pierre-Henri Chaudouard et al

These three volumes comprise the proceedings of a summer school on the Langlands Program held at the Institut des Hautes Études Scientifiques during the three weeks of July 11–29, 2022.

I.Representations,Shimura Varieties,andShtukas

Proceedings of Symposia in Pure Mathematics, Vol. 112.1

Jan 2026 557pp

9781470474379 Paperback

£119.00 / US$139.00

II.GeometrizationoftheLanglandsCorrespondence

Proceedings of Symposia in Pure Mathematics, Vol. 112.2

Jan 2026 551pp

9781470474386 Paperback £119.00 / US$139.00

III.Periods,L-Functions,andtheRelativeTraceFormula

Proceedings of Symposia in Pure Mathematics, Vol. 112.3

Jan 2026 425pp

9781470474393 Paperback £119.00 / US$139.00

TheSet(VolumesI,II,andIII)

Proceedings of Symposia in Pure Mathematics, Vol. 112

Jan 2026

97814704694671,533ppPaperback

£299.00 / US$350.00

RANDOMNESSANDTHERIEMANNHYPOTHESIS

Probability,Statistics,andthePrimes

Andrey Feuerverger & Greg Martin

See page 2 for details of this title

SELECTEDCHAPTERSINNUMBERTHEORY

Hermann Minkowski

See page 5 for details of this title.

BESTSELLERS

ANALYTICNUMBERTHEORY

Henryk Iwaniec & Emmanuel Kowalski

Colloquium Publications, Vol. 53

Shows the scope of analytic number theory, both in classical and modern directions, and exhibits its wealth and prospects, its beautiful theorems and powerful techniques. This book distinguishes itself by the variety of tools it uses to establish results, many of which belong to the mainstream of arithmetic.

ANALYTICNUMBERTHEORYFORBEGINNERS

SecondEdition

Prapanpong Pongsriiam

Student Mathematical Library, Vol. 103

Presents a friendly introduction to analytic number theory for both advanced undergraduate and beginning graduate students, offering a comfortable transition between the two levels. Each chapter provides examples and exercises of varying difficulty and ends with a section of notes.

AUTOMORPHICFORMSBEYOND������

Lecturesfromthe2022ArizonaWinterSchool

Ellen Elizabeth Eischen et al

Mathematical Surveys and Monographs, Vol. 279

The Langlands program has been a very active and central field in mathematics ever since its conception over 50 years ago. This book features expository accounts of several topics on automorphic forms on higher rank groups, including rationality questions on unitary group, theta lifts and their applications to Arthur's conjectures, and more.

2024 187pp

THEDISTRIBUTIONOFPRIMENUMBERS

Dimitris Koukoulopoulos

Graduate Studies in Mathematics, Vol. 203

Prime numbers have fascinated mathematicians since the time of Euclid. This book presents some of the best tools to capture the properties of these fundamental objects, beginning with the most basic notions of asymptotic estimates and arriving at the forefront of mathematical research.

2020 356pp 9781470462857 Paperback £76.00 / US$89.00

PRIMESOFTHEFORM

Fermat,ClassFieldTheory,andComplex Multiplication,ThirdEditionwithSolutions

David A. Cox

Chelsea Publications, Vol. 387

Examines when a prime p can be written in the form ����+������. This book begins at an elementary level with results of Fermat and Euler and then discusses the work of Lagrange, Legendre and Gauss on quadratic reciprocity and the genus theory of quadratic forms.

2022 542pp 9781470470289 Paperback £56.00 / US$65.00

AMS Chelsea Publishing

PROBABILITY & STATISTICS

BESTSELLERS

APPLIEDSTOCHASTICANALYSIS

Miranda Holmes-Cerfon

Courant Lecture Notes, Vol. 33

Stochastic analysis tackles randomness in physical systems by blending simulation methods with hands-on problem-solving strategies. This book examines key concepts like Markov chains, Gaussian processes, Ito calculus and stochastic differential equations, building intuition for modeling evolving, time-dependent phenomena.

2024 244pp

9781470478391 Paperback £51.00 / US$59.00

AFIRSTCOURSEINSTOCHASTICCALCULUS

Louis-Pierre Arguin

Pure and Applied Undergraduate Texts, Vol. 53

A complete guide for advanced undergraduate students to take the next step in exploring probability theory and for master's students in mathematical finance who would like to build an intuitive and theoretical understanding of stochastic processes.

2022 270pp

9781470464882 Paperback £73.00 / US$85.00

INTRODUCTIONTOPROBABILITY

SecondEdition

Charles M. Grinstead & J. Laurie Snell

Designed for an introductory probability course at the university level for sophomores, juniors, and seniors in mathematics, physical and social sciences, engineering, and computer science. This book presents a thorough treatment of ideas and techniques necessary for a firm understanding of the subject.

2012 510pp

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Provides a quick, but very readable introduction to stochastic differential equations - that is, to differential equations subject to additive “white noise" and related random disturbances. This exposition is strongly focused upon the interplay between probabilistic intuition and mathematical rigour.

2014 151pp

9781470410544 Hardback £39.00 / US$45.00

MARKOVCHAINS

ANDMIXINGTIMES

SecondEdition

David A. Levin & Yuval Peres

Offers an introduction to the modern theory of Markov chains, whose goal is to determine the rate of convergence to the stationary distribution as a function of state space size and geometry. This topic has important connections to combinatorics, statistical physics, and theoretical computer science. Many of the techniques presented originate in these disciplines.

2017 447pp

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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 book focuses on one specific sector of the field, namely the spectral distribution of random Wigner matrix ensembles, as well as iid matrix ensembles. With over 200 exercises, this book is suitable as an introductory text for beginning graduate students seeking to enter the field.

2012 282pp

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Contemporary Mathematics, Vol. 813

Apr 2025

9781470473617351ppPaperback £116.00 / US$135.00

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9781470473624 Paperback £116.00 / US$135.00

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Contemporary Mathematics, Vol. 815

Jun 2025

9781470471897159ppPaperback

£116.00 / US$135.00

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9781470474966 Paperback £116.00 / US$135.00

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9781470476205 Paperback £116.00 / US$135.00

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9781470478384 Paperback £116.00 / US$135.00

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9781470476533 Paperback £116.00 / US$135.00

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9781470476540 Paperback £116.00 / US$135.00

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Aug 2025

9781470476342225ppPaperback

£116.00 / US$135.00

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Nov 2025

9781470474621198ppPaperback £116.00 / US$135.00

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Mar 2025

9781470473013146ppPaperback

£116.00 / US$135.00

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Mar 2025

9781470473389308ppPaperback £116.00 / US$135.00

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Contemporary Mathematics, Vol. 811

Mar 2025

9781470472153287ppPaperback

£116.00 / US$135.00

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Contemporary Mathematics, Vol. 812

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9781470475260 Paperback £116.00 / US$135.00

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9781470475581234ppPaperback £116.00 / US$135.00

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9781470471811166ppPaperback

£73.00 / US$85.00

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9781470473310124ppPaperback

£73.00 / US$85.00

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Memoirs of the American Mathematical Society, Vol. 305, No. 1539

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9781470470548 Paperback

£73.00 / US$85.00

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Memoirs of the American Mathematical Society, Vol. 308, No. 1558

Aug 2025

9781470473181114ppPaperback

£73.00 / US$85.00

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Memoirs of the American Mathematical Society, Vol. 310, No. 1566

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9781470475307 Paperback

£73.00 / US$85.00

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DifferentialEquations

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£73.00 / US$85.00

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£73.00 / US$85.00

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9781470475321152ppPaperback

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Yakir Forman & Tom VandenBoom

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9781470476472 Paperback

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DiscreteMathematics&Combinatorics

CATALAND

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May 2025

9781470463144143ppPaperback

£73.00 / US$85.00

FOUNDATIONSOFMATROIDS,PART1

MatroidswithoutLargeUniformMinors

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Geometry&Topology

EQUIVARIANTINFINITELOOPSPACETHEORY

TheSpaceLevelStory

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Memoirs of the American Mathematical Society, Vol. 305, No. 1540

May 2025

9781470472481136ppPaperback

£73.00 / US$85.00

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CENTRALIZERSOFHAMILTONIANCIRCLEACTIONSON RATIONALRULEDSURFACES

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Memoirs of the American Mathematical Society, Vol. 309, No. 1560

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WEINSTEINHANDLEBODIESFORCOMPLEMENTSOFSMOOTHED TORICDIVISORS

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9781470472702 Paperback

£73.00 / US$85.00

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£73.00 / US$85.00

WEAKLAPLACIANBOUNDSANDMINIMALBOUNDARIES INNON-SMOOTHSPACESWITHRICCICURVATURE LOWERBOUNDS

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9781470474171117ppPaperback

£73.00 / US$85.00

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£73.00 / US$85.00

SHARPBOUNDONABELIANAUTOMORPHISMGROUPSOF SURFACESOFGENERALTYPE

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9781470475291105ppPaperback

£73.00 / US$85.00

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9781470475338 Paperback

£73.00 / US$85.00

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9781470475796168ppPaperback

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Aug 2025 88pp

9781470475888 Paperback

£73.00 / US$85.00

����0(��,��+��)-MAXIMALREPRESENTATIONSANDHYPERBOLIC SURFACES

Filippo Mazzoli & Gabriele Viaggi

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THICKHYPERBOLIC3-MANIFOLDSWITHBOUNDEDRANK

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Memoirs of the American Mathematical Society, Vol. 317, No. 1613

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9781470478063 Paperback £73.00 / US$85.00

Logic&Foundations

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9781470472696176ppPaperback

£73.00 / US$85.00

STRONGLYMINIMALSETSANDCATEGORICITYIN CONTINUOUSLOGIC

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Aug 2025 88pp

9781470475017 Paperback

£73.00 / US$85.00

NumberTheory

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9781470472733122ppPaperback

£73.00 / US$85.00

MODULIOFFONTAINE-LAFFAILLEREPRESENTATIONSANDA MOD-PLOCAL-GLOBALCOMPATIBILITYRESULT

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Aug 2025 191pp

9781470475826 Paperback

£73.00 / US$85.00

Probability&Statistics

SPATIALPOPULATIONSWITHSEED-BANK:RENORMALISATION

ONTHEHIERARCHICALGROUP

Andreas Greven, Frank den Hollander & Margriet Oomen

Memoirs of the American Mathematical Society, Vol. 307, No. 1553

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9781470473150207ppPaperback

£73.00 / US$85.00

THECRITICALLENGTHFORGROWINGADROPLET

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Aug 2025 180pp

9781470474874 Paperback

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