A co-publication of the AMS and Publish or Perish, Inc.
Hardcover
Hardcover ISBN: 978-0-8218-4313-0
Collected Works Volume: 19;
2025; 329 pp
This set is highly recommended to a broad mathematical audience, and, in particular, to young mathematicians who will certainly benefit from their acquaintance with Milnor's mode of thinking and writing. The volumes in this set have been organized by subject: Geometry (see MILNOR/1); The Fundamental Group; Differential Topology; Homotopy, Homology and Manifolds; Algebra; Dynamical Systems (1953-2000); and Dynamical Systems (1984-2012).
Readership
Graduate students and research mathematicians.
MILNOR/1
CWORKS/19.2
CWORKS/19.3
CWORKS/19.4
CWORKS/19.5
CWORKS/19.6
CWORKS/19.7
Softcover ISBN: 978-1-4704-8180-3
Product Code: SURV/294
Mathematical Surveys and Monographs Volume: 294;
2025; 268 pp
This book reveals how univalent functions appear in quantum probability theory. Building upon the recently established one-to-one correspondence between Loewner theory and the theory of non-commutative additive processes, the author invites readers to explore the interplay between complex analysis, classical probability theory, and quantum probability theory. Monotone independence and its relations to classical, free, and Boolean independence underpin the development of ideas.
Beginning with essential concepts from classical probability theory and complex analysis, the book goes on to define a quantum probability space and introduce five notions of independence. From this foundation, the central chapters explore convolutions and their respective central limit theorems; univalent functions; classical Loewner chains on the unit disk; slit mappings; and the relationship between free hemigroups, Loewner chains, and nonlinear resolvents. The final chapter offers an outlook on higher dimensional generalizations, including several open problems. Exercises with solutions invite readers to engage with the material throughout.
Univalent Functions in Quantum Probability Theory is an essential resource
at the intersection of previously distinct fields. Intended for graduate
students and researchers alike, it assumes a solid foundation in real and
complex analysis, with basic knowledge of classical probability theory
and Hilbert spaces
Graduate students and research mathematicians interested in the interplay between complex analysis, classical probability theory, and quantum probability theory.
Chapters
Introduction
Classical probability theory
The complex toolbox
Quantum probability theory
Convolutions and additive processes
Univalent functions
Radial Loewner chains revisited
Slit mappings
Free hemigroups, Loewner chains, and nonlinear resolvents
Graph products as quantum random walks
Outlook on higher dimensional generalizations
Compactness of the class
Continuous extension of univalent functions
For over fifty years, Boundary Value Problems and Partial Differential Equations, Seventh Edition has provided advanced students an accessible and practical introduction to deriving, solving, and interpreting explicit solutions involving partial differential equations with boundary and initial conditions. Fully revised and now in its Seventh Edition, this valued text aims to be comprehensive without affecting the accessibility and convenience of the original. The resource’s main tool is Fourier analysis, but the work covers other techniques, including Laplace transform, Fourier transform, numerical methods, characteristics, and separation of variables, as well, to provide well-rounded coverage. Mathematical modeling techniques are illustrated in derivations, which are widely used in engineering and science. In particular, this includes the modeling of heat distribution, a vibrating string or beam under various boundary conditions and constraints. New to this edition, the text also now uniquely discusses the beam equation. Throughout the text, examples and exercises have been included, pulled from the literature based on popular problems from engineering and science. These include some "outside-the-box" exercises at the end of each chapter, which provide challenging and thought-provoking practice that can also be used to promote classroom discussion. Chapters also include Projects, problems that synthesize or dig more deeply into the material that are slightly more involved than standard book exercises, and which are intended to support team solutions. Additional materials, exercises, animations, and more are also accessible to students via links and in-text QR codes to support practice and subject mastery.
1. Ordinary Differential Equations
2. Fourier Series and Integrals
3. The Heat Equation
4. The Wave Equation
5. The Potential Equation
6. Higher Dimensions and Other Coordinates
7. Transform Methods 8. Numerical Methods
Published: November 2025
Format: Paperback
ISBN: 9781009633536
This book provides a clear and accessible introduction to ring theory for undergraduate students. Aligned with standard curricula, it simplifies abstract concepts through structured explanations, practical examples, and real-world applications. Ideal for both students and instructors, it serves as a valuable resource for mastering fundamental concepts in ring theory with ease. The text begins with an introduction to rings and goes on to cover subrings, integral domains, ideals, and factor rings. It also discusses ring homomorphisms and polynomial rings. The book concludes with topics such as polynomial factorization and divisibility in integral domains. Each chapter is supplemented with solved examples to foster a deeper understanding of the subject. A set of practice questions is also provided to sharpen problem-solving skills.
Focused approach tailored to the latest National Educational Policy guidelines
Simplified exposition of abstract concepts
Connection of theoretical concepts to practical scenarios
Preface
Preliminaries
Chapter 1. Introduction to Rings
Chapter 2. Subrings
Chapter 3. Integral Domains
Chapter 4. Ideals
Chapter 5. Ring Homomorphisms
Chapter 6. Polynomial Rings
Chapter 7. Factorization of Polynomials Chapter 8. Divisibility in Integral Domains
Index.
Series: Encyclopedia of Mathematics and its Applications
Published: January 2026
Format: Hardback
ISBN: 9781009699983
A valuable resource for researchers in discrete and combinatorial geometry, this book offers comprehensive coverage of several modern developments on algebraic and combinatorial properties of polytopes. The introductory chapters provide a new approach to the basic properties of convex polyhedra and how they are connected; for instance, fibre operations are treated early on. Finite tilings and polyhedral convex functions play an important role, and lead to the new technique of tiling diagrams. Special classes of polytopes such as zonotopes also have corresponding diagrams. A central result is the complete characterization of the possible face-numbers of simple polytopes. Tools used for this are representations and the weight algebra of mixed volumes. An unexpected consequence of the proof is an algebraic treatment of Brunn–Minkowski theory as applied to polytopes. Valuations also provide a thread running through the book, and the abstract theory and related tensor algebras are treated in detail.
A unique and comprehensive approach to the basic properties of convex polyhedra, using only straightforward techniques
Offers a full treatment of results in context, particularly their interconnexions
Builds up to treatment of several deep results in the theory without relying on external knowledge or concepts
Algebra
1. Polyhedra
2. Linear systems
3. Representations
4. Polyhedral functions
5. Finite tilings
6. Polytopes
7. Refinements in polytopes
8. Numbers of faces
9. Polytopes with symmetry
10. Zonotopes
11. Infinite tilings
12. Volume and its relatives
13. Scalar weight algebra
14. Simple polytopes
15. Brunn–Minkowski theory
16. Algebra of polyhedra
17. Polytope ring
18. Polytope algebra
19. Tensor weights
20. Fibre algebra
21. Lattice polytopes and valuations
Afterword
References
Notation index
Author index
Subject index.
Series: Cambridge Monographs on Mathematical Physics
Published: April 2026
Format: Hardback
ISBN: 9781009664813
The Bethe Ansatz is a powerful method in the theory of quantum integrable models, essential for determining the energy spectrum of dynamical systems - from spin chains in magnetism to models in high-energy physics. This book provides a comprehensive introduction to the Bethe ansatz, from its historical roots to modern developments. First introduced by Hans Bethe in 1931, the method has evolved into a universal framework encompassing algebraic, analytic, thermodynamic, and functional forms. The book explores various Bethe ansatz techniques and their interrelations, covering both coordinate and algebraic versions, with particular attention to nested structures and functional relations involving transfer matrices. Advanced tools such as the separation of variables method are presented in detail. With a wealth of worked examples and precise calculations, this volume serves as an accessible and rigorous reference for graduate students and researchers in mathematical physics and integrable systems.
Offers an in-depth introduction to the coordinate Bethe ansatz that will be accessible to readers without prior specialization in the subject
Includes detailed exposition of both classical and modern techniques, connecting foundational insights with recent developments in integrable systems
Uses an extensive collection of worked examples and explicit calculations to equip readers with practical tools and operational understanding
Preface
1. Classical integrable systems
2. Bethe wave function and S-matrix
3. Coordinate Bethe Ansatz
4. Transfer matrix method
5. Nested coordinate Bethe Ansatz
6. Algebraic approach to factorized scattering
7. Algebraic Bethe Ansatz
8. Functional methods
9. Separation of variables.
Published: April 2026
Format: Paperback
ISBN: 9781009344371
Over the past few decades, graph theory has developed into one of the central areas of modern mathematics, with close (and growing) connections to areas of pure mathematics such as number theory, probability theory, algebra and geometry, as well as to applied areas such as the theory of networks, machine learning, statistical physics, and biology. It is a young and vibrant area, with several major breakthroughs having occurred in just the past few years. This book offers the reader a gentle introduction to the fundamental concepts and techniques of graph theory, covering classical topics such as matchings, colourings and connectivity, alongside the modern and vibrant areas of extremal graph theory, Ramsey theory, and random graphs. The focus throughout is on beautiful questions, ideas and proofs, and on illustrating simple but powerful techniques, such as the probabilistic method, that should be part of every young mathematician's toolkit.
Focuses on the modern areas of extremal graph theory, Ramsey theory, and random graphs, whilst also covering more classical topics
Written in a gentle style that makes the more advanced material easier to understand and more fun to read than existing textbooks
Includes nearly 200 carefully chosen exercises, as well as solutions (and additional discussion) for instructors
Introduction
1. Basic graph theory
2. Extremal graph theory
3. Classical graph theory
4. Ramsey theory
5. Random graphs.