Softcover ISBN: 978-1-4704-7360-0
Product Code: PSPUM/111
Proceedings of Symposia in Pure Mathematics
Volume: 111; 2025; 364 pp
MSC: Primary 12; 13; 14; 52; 62; 65
Desrcription
This volume consists of surveys on topics to which Bernd Sturmfels has contributed over his mathematical career: invariant theory, Gröbner bases, toric ideals and varieties, algebraic methods in discrete and convex optimization, hypergeometric systems, algebraic statistics, likelihood geometry, tropical geometry, chemical reaction networks, numerical methods in algebraic geometry, sums of squares, tropical geometry, tensors, and algebraic vision. Each article gives a gentle introduction to the topic. Many contributions summarize the state of the art in each subject. The volume is perfect for anyone who wishes an entry point to any one of these diverse topics.
Readership
Graduate students and research mathematicians interested in combinatorial, computational, and applied algebraic geometry.
Table of Contents
Bernd Sturmfels — Adventures in mentoring
Gregor Kemper — Invariant theory: A third lease of life
Aldo Conca — A universal tale of determinants and Gröbner bases
Serkan Hoşten — An early history of toric ideals
Jesús A. De Loera — The nonlinear algebra view of discrete mathematics
Nobuki Takayama — Hypergeometric systems, statistics, and algorithms
Seth Sullivant — Bernd’s contributions to algebraic statistics
Carlos Améndola and Jose Israel Rodriguez — A primer in likelihood geometry
Michael Joswig — Developments in tropical convexity
Elisenda Feliu and Anne Shiu — From chemical reaction networks to algebraic and polyhedral geometry—and back again
Daniel J. Bates, Paul Breiding, Tianran Chen, Jonathan D. Hauenstein, Anton Leykin and Frank Sottile — Numerical nonlinear algebra
Grigoriy Blekherman — Sums of squares, spectrahedra, and Bernd
Kristian Ranestad — Algebraic degree in nonlinear models
Mateusz Michałek — Tensors: From complex problems to real applications
Joe Kileel and Kathlén Kohn — Snapshot of algebraic vision
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Softcover ISBN: 978-1-4704-7558-1
Product Code: CONM/827
Contemporary Mathematics
Volume: 827; 2025; 234 pp
MSC: Primary 57; 20
Desrcription
This volume contains the proceedings of the AMS Western Sectional Meeting on Algebraic Structures in Knot Theory held on May 6–7, 2023, at California State University, Fresno, California.
Modern knot theory includes the study of a diversity of different knotted
objects—classical knots, surface-links, knotoids, spatial graphs, and more.
Knot invariants are tools for probing the structure of these generalized
knots. Many of the most effective knot invariants take the form of algebraic
structures. In this volume we collect some recent work on algebraic structures
in knot theory, including topics such as braid groups, skein algebras,
Gram determinants, and categorifications such as Khovanov homology
Readership
Graduate students and researchers interested in various aspects of commutative algebra
Table of Contents
Rostislav Akhmechet and Melissa Zhang — On equivariant Khovanov homology
Christine Ruey Shan Lee — Computing Khovanov homology via categorified Jones-Wenzl projectors
Ioannis Diamantis — A survey on skein modules via braids
Blake Mellor and Robin Wilson — Topological symmetries of the Heawood family
Tonie Scroggin — On the cohomology of two stranded braid varieties
Kate Kearney — Symmetry of three component links
Paolo Cavicchioli and Sofia Lambropoulou — The mixed Hilden braid group and the plat equivalence in handlebodies
Jason Joseph and Puttipong Pongtanapaisan — Meridional rank, welded knots, and bridge trisections
Audrey Baumheckel, Carmen Caprau and Conor Righetti — On an invariant for colored classical and singular links
Dionne Ibarra and Gabriel Montoya-Vega — A study of Gram determinants in knot theory
Softcover ISBN: 978-1-4704-7462-1
Expected availability date: November 15, 2025
Contemporary Mathematics
Volume: 828; 2025; Estimated: 198 pp
MSC: Primary 28; 26; 35; 46; 05; 60
Desrcription
This volume contains the proceedings of the AMS-SMF-EMS Special Session on Fractal Geometry in Pure and Applied Mathematics, held from July 5–9, 2022, in Grenoble, France.
The volume includes papers on recent developments in fractal geometry and its applications, featuring both original research and expository summaries. Key topics include non-Brownian diffusion and randomized Dirichlet forms on Sierpinski gasket-type fractals, graph approximation of such fractals, heat diffusion across fractal boundaries and inverse problems on fractal domains. Some new results are also presented regarding Sobolev-type spaces on metric measure spaces, and function spaces related to iterated fractal drums like the Weierstrass curve.
Readership
Graduate students and researchers interested in fractal geometry and its applications.
Table of Contents
Raffaela Capitanelli — Time fractional equations on Sierpinski gasket like fractals
Gabriel Claret and Anna Rozanova-Pierrat — Existence of optimal shapes for heat diffusions across irregular interfaces
Simone Creo, Maria Rosaria Lancia, Gianluca Mola and Silvia Romanelli — Inverse problems in irregular domains: approximation via Mosco convergence
Claire David and Michel L. Lapidus — Iterated fractal drums
some new perspectives: Polyhedral measures, atomic decompositions and morse theory
Daniel Fontaine, Daniel J. Kelleher and Alexander Teplyaev — Green’s function and eigenfunctions on random Sierpinski gaskets
Brett Hungar, Gamal Mograby, Madison Phelps, Luke G. Rogers and Jonathan Wheeler — Spectra of three-peg Hanoi towers graphs
Nageswari Shanmugalingam — Homogeneous Newton-Sobolev spaces in metric measure spaces and their Banach space properties
Softcover ISBN: 978-1-4704-8202-2
Product Code: DOL/59
Expected availability date: December 17, 2025
Dolciani Mathematical Expositions
Volume: 59; 2025; Estimated: 187 pp
MSC: Primary 00; 53; 86
Desrcription
How are maps created? What is the process that enables a location on the Earth's surface to become a point on a sheet of paper? The answer lies in map projections. This book provides a highly readable account of the theory that underpins all major map projections, starting from the concept of map distortion, which all flat maps necessarily possess. The engaging exposition is enhanced by the extensive use of diagrams, including over sixty maps.
The opening chapters set the scene, covering the mathematical background, the notion of map distortion and the classification of map projections. The book then turns its attention to the different types of projection, including cylindrical, azimuthal, and conical projections. Following a modern analytic approach, the author uses the tools of multivariable calculus to derive the equations defining these map projections. The book ends with a chapter utilizing complex variables to study conformal projections, and a final summary chapter to wrap up the material. Each chapter is interwoven with a compelling historical narrative enriching the text.
A Mathematical Exploration of Map Projections assumes only a prior knowledge of elementary calculus, and is an excellent resource for anyone curious about the mathematics underlying map projections.
Readership
Students, mathematics professionals (teachers, academics, mathematicians in industry), and anyone with a basic knowledge of calculus who is curious about maps.
Table of Contents
Geometry and coordinates
Map distortion
Types of projection
Basic cylindrical projections
Psuedocylindrical projections
Oblique cylindrical projections
Azimuthal projections
Conic projections
Pseudoconic and polyconic projections
Other projections
Conformal projections using complex variables
Final thoughts
Trigonometric formulas
Bibliography
Index
Softcover ISBN: 978-1-4704-7524-6
Product Code: HMATH/47
Expected availability date: December 17, 2025
History of Mathematics Source Series
Volume: 47; 2025; 141 pp
MSC: Primary 01; Secondary 11
Desrcription
In mathematics, technical difficulties can spark groundbreaking ideas. This book explores one such challenge: a problem that arose
in the formative years of algebraic number theory and played a major role
in the early development of the field.
When nineteenth-century mathematicians set out to generalize E. E. Kummer's theory of ideal divisors in cyclotomic fields, they discovered that the existence of “common inessential discriminant divisors” blocked the obvious path. Through extensively annotated translations of key papers, this book traces how Richard Dedekind, Leopold Kronecker, and Kurt Hensel approached these divisors, using them to justify the need for entirely new mathematical ideas and to demonstrate their power.
Mathematicians interested in algebraic number theory will enjoy seeing what the field, which is still evolving today, looked like in its very early days. Historians of mathematics will find interesting questions for further study. Engaging and carefully researched, Common Inessential Discriminant Divisors is both a historical study and an invitation to experience mathematics as it was first discovered.
This volume is one of an informal sequence of works within the History of Mathematics series. Volumes in this subset, “Sources”, are classical mathematical works that served as cornerstones for modern mathematical thought.
Readership
Research mathematicians interested in a particular problem in the early history of algebraic number theory.
Table of Contents
Setting the stage
An outlines of the problem
Dedekind’s Anzeige, 1871
Dedekind on higher congruences
Kronecker on CIDDs
Hensel’s 1894 paper on Common Inessential Discriminant Divisors
The rock in the middle of the road
Bibliography
Index
Softcover ISBN: 978-1-4704-7783-7
Product Code: TEXT/75
Expected availability date: December 18, 2025
AMS/MAA Textbooks
Volume: 75; 2025; 225 pp
MSC: Primary 49; 34; 35; 37
Desrcription
Optimal control theory concerns the study of dynamical systems where one operates a control parameter with the goal of optimizing a given payoff function. This textbook provides an accessible, examples-led approach to the subject. The text focuses on systems modeled by differential equations, with applications drawn from a wide range of topics, including engineering, economics, finance, and game theory. Each topic is complemented by carefully prepared exercises to enhance understanding.
The book begins with introductory chapters giving an overview of the subject and covering the necessary optimization techniques from calculus. After this, Pontryagin’s method is developed for control problems on one-dimensional state spaces, culminating in the study of linear-quadratic systems. The core material is rounded out by the consideration of higher-dimensional systems. The text concludes with more advanced topics such as bang-bang controls and differential game theory. A final chapter examines the calculus of variations, giving a brief overview of the Euler-Lagrange theory and general isoperimetric problems.
Designed for undergraduates in mathematics, physics, or economics, Optimal Control Theory can be used in a structured course or for self-study. The treatment is highly accessible and only requires a familiarity with multivariable calculus, differential equations, and basic matrix algebra.
Readership
Undergraduate students interested in optimization problems, control theory, and applications.
Table of Contents
Getting started
Static optimization
Control: A discrete start
First principle
Unpacking Pontryagin
Easing the restrictions
Linear-quadratic systems
Two dimensions
Targets
Switching controls and stationarity
Time, value, and Hamilton-Jacobi-Bellman equation
Differential games
Calculus of variations
Table of principles
Two-dimensional linear systems
Hints
Solutions
Bibliography
Index
Hardcover ISBN: 978-1-4704-8206-0
Product Code: COLL/69
Expected availability date: January 10, 2026
Colloquium Publications
Volume: 69; 2025; Estimated: 314 pp
MSC: Primary 13; 12; Secondary 11; 41
Desrcription
This book 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, the book begins with the preliminaries of integer-valued polynomials on
and subsets of
. Bhargava’s revolutionary orderings and generalized factorials follow, laying the foundation for the modern perspective, before an interlude on algebraic number theory explores the Pólya group. Connections between topology and multiplicative ideal theory return the focus to commutative algebra, providing tools for exploring Prüfer 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.
A thoroughly modern sequel to the author’s 1997 Integer-Valued Polynomials with Paul-Jean Cahen, this book welcomes readers with a grounding in commutative algebra and number theory at the level of Dedekind domains. No specialist knowledge of probability, dynamics, or non-commutative algebra is required.
Readership
Graduate students and research mathematicians interested in integer-valued polynomials occurring in combinatorics, number theory, commutative algebra, topology, dynamics, and non-commutative algebra.
Table of Contents
The paradigmatic example:
Combinatorics
Integer-valued polynomials on a subset of
Bhargava’s orderings and generalized factorials
Number theory
Algebraic number theory: The Pólya group of Galois extensions
Examples of Pólya fields (Galois extensions of small degrees)
Class field theory: The Pólya group of non-Galois extensions
Commutative algebra
Topology: The polynomial closure
Algebra and ultrafilters: The Prüfer properties
Commutative ring theory: More algebraic properties
Ultrametric analysis
More about orderings in valued fields
Orthonormal bases of spaces of smooth functions
Dynamics: Valuative capacity and successor function
More about I. V. P.–Asymptotic densities several variables
Probabilistic number theory–Using Kempner-Bhargava’s formula
Several indeterminates
Non-commutative algebra
I. V. P. on non-commutative algebras–The case of matrices
I. V. P. on division algebras–The case of quaternions
To go further–Other possible themes around I. V. P.
Bibliography
Index