MAA Press: An Imprint of the American Mathematical Society
Softcover ISBN: 978-1-4704-7934-3
Product Code: DOL/60
Expected availability date: October 25, 2026
Dolciani Mathematical Expositions Volume: 60;
2026; Estimated: 252 pp
MSC: Primary 68; 37; 20; 00
Beautiful self-similar patterns emerge when the entries of Pascal’s Triangle are reduced modulo a positive integer
. This book offers an engaging exploration of a natural extension of this idea: since the integers modulo
form a finite group, what happens when we construct Pascal-like triangles over other finite groups?
The book is organized into four parts. It begins with an introduction to the necessary background on Pascal’s Triangle, with a strong emphasis on its visual aspects. The second part builds on these visual phenomena—referred to as PascGalois triangles—to explore concepts from finite group theory, combining pattern recognition with underlying algebraic structure. In the third part, the PascGalois triangles are shown to be instances of cellular automata, opening the door to an investigation of discrete dynamical systems. The final part examines the emergence of self-similarity and fractal geometry from these automata.
Numerous student projects are included throughout to encourage further exploration, and the concluding chapter offers additional topics for extension. While much of the necessary background is developed within the text, readers will benefit from prior coursework in discrete mathematics and linear algebra, as well as some familiarity with mathematical proofs. No previous knowledge of group theory is assumed.
The PascGalois software and other resources can be found at the Project webpage: https://faculty.salisbury.edu/~despickler/pascgalois/.
Undergraduate students interested in groups, number theory, and cellular automata.
Abstracting a classic construction
Setting the stage
The patterns within
“Blaising” a new trail
Harmony with algebraic structure
The three little axioms
Hidden in plain sight
An alias for another
Dynamics in discrete space
Cells and evolution in a mathematical realm
When history must repeat itself
Fractals and beyond in a cellular world
Through the magnifying glass
Measuring a kaleidoscope
More fractals? Up to eleven then!
And then there were two
Bibliography
Index
*
Softcover ISBN: 978-1-4704-8576-4
Expected availability date: October 25, 2026
Mathematical Surveys and Monographs
Volume: 299; 2026; Estimated: 568 pp
MSC: Primary 32; Secondary 30; 46; 28
This monograph is a detailed development of geometric function theory in several complex variables from basic principles, focusing on the Euclidean unit ball as the domain. A thorough treatment covering decades of progress, the text presents subjects central to the field including the families of convex, starlike, and spirallike mappings, Loewner theory, and extension operators, as well as myriad additional topics such as linear invariance, Denjoy–Wolff theory, invariant metrics, holomorphic semigroups, the Andersén–Lempert theorem, Gromov hyperbolicity, and a Herglotz-type representation. Many results from the one-variable theory are found, often as consequences of higher-dimensional results.
All background needed beyond what is found in standard introductory graduate courses is provided, including introductory material on holomorphic mappings of several variables, ensuring the book is valuable to interested graduate students and experienced researchers alike.
Graduate students and researchers interested in geometric function theory.
Requests
Holomorphic mappings of domains in
Preliminaries for mappings in
Denjoy-Wolff theory
The generalized Carathéodory class
Cauchy problems and their solutions
Loewner chains
Geometric families arising from Loewner chains
Convex mappings
Extension operators
Linear-invariant families
Invariant mappings
Boundary behavior of convex mappings
Applications of Loewner theory
Appendix A. Convex sets in locally convex spaces
Appendix B. The Bochner integral
Bibliography
Index
Softcover ISBN: 978-1-4704-7942-8
Expected availability date: October 04, 2026
Contemporary Mathematics Volume: 846;
2026; 223 pp
MSC: Primary 57; 20; 37
This volume contains the proceedings of the Special Session on Knot Theory and Applications, which was held during the 2nd International AMS–UMI Joint Meeting, July 23–26, 2025, in Palermo, Italy.
Knots are ubiquitous—from closed loops of DNA and tangled polymers to the vortex filaments of turbulent fluids. Knot theory provides a language to understand these intricate patterns, and in recent years it has become one of the most dynamic branches of modern mathematics. This volume brings together an international group of leading researchers. The contributions in the volume concern the following topics: geometric insights into knots and links and novel approaches to braid theory and 4-manifolds, new diagrammatic invariants, and connections to physics and materials science. Alongside classical theory, readers will find generalizations such as pseudo-knots, welded knots, virtual knots, knotoids, and other structures that expand the boundaries of knot theory. Whether you are a specialist in topology or simply curious about how mathematics untangles complexity, this volume offers a window into the living landscape of knot theory today.
Graduate students and research mathematicians interested in knot theory.
Articles
Colin Adams, Francisco Gomez-Paz, Jiachen Kang, Lukas Krause, Gregory Li, Reyna Li, Chloe Marple and Ziwei Tan — Hyperbolicity and volumes of bongles
Maria Rita Casali and Paola Cristofori — Kirby diagrams, trisections, and gems of PL 4-manifolds: Relationships, results, and open problems
Paolo Bellingeri, Celeste Damiani, Oscar Ocampo and Charalampos Stylianakis — Powers of half-twists and congruence subgroups of braid groups
Anastasios Kokkinakis — Framed braid equivalences
Alessia Cattabriga, Paolo Cavicchioli, Rama Mishra and Visakh Narayanan — Knots and non-orientable surfaces in 3-manifolds
Neslihan Gügümcü and Louis H. Kauffman — State summation invariants for knots, links, knotoids, and linkoids
Tumpa Mahato, Rama Mishra and Sahil Joshi — Non-triviality of welded knots and ribbon torus-knots
Ioannis Diamantis, Sofia Lambropoulou and Sonia Mahmoudi — The theory of doubly periodic pseudo tangles
Ioannis Diamantis, Sofia Lambropoulou and Sonia Mahmoudi — From planar to annular to toroidal bracket polynomials for pseudo knots and links
Renzo L. Ricca and Samuele Faglioni — Field-line helicity and adapted polynomials in vortex knots dynamics
Softcover ISBN: 978-1-4704-8033-2
Expected availability date: October 04, 2026
Contemporary Mathematics Volume: 847;
2026; 337 pp
MSC: Primary 37; 70; 39; 17; 14; 34; 33
This volume is a collection of six lecture notes from the Abecedarian School of SIDE15 (ASIDE15-Milano-Italy), held before the 15th International Conference on Symmetries and Integrability of Difference Equations (SIDE15-Sirmione-Italy), in 2025.
This book introduces contemporary research topics in discrete integrable systems, including applications of classical algebraic geometry, classical and modified Yang-Baxter equations,
-matrices, Fermi-Pasta-Ulam-Tsingou-type models, Hamiltonian approaches to differential-difference equations, and orthogonal polynomials with connections to discrete Painlevé equations. The focus lies on providing clear, self-contained expositions of both foundational and advanced ideas. The chapters explain key theoretical frameworks, give practical computational techniques, and emphasize important examples. Exercises are also included in some chapters. The book offers a wide range of perspectives for anyone seeking to learn or expand their research in discrete integrable systems and related fields. This book features both introductory and advanced topics, accessible exposition, and numerous insights into current research trends. It will be beneficial for graduate students and experienced mathematicians.
Graduate students and research mathematicians interested in integrability and symmetries.
Articles
Gessica Alecci, Michele Graffeo and Alexander Stokes — Classical algebraic geometry and discrete integrable systems
Jaume Alonso — From 3D QRT to discrete Painlevé equations
Marta Dell’Atti —
-matrices for integrable systems
Matteo Gallone — The role of integrability in Fermi-Pasta-Ulam-Tsingou-like models
Edoardo Peroni and Matteo Casati — Hamiltonian operators for integrable differential-difference equations
Sofia Tarricone — Orthogonal polynomials and discrete Painlevé equations: theory and applications
Softcover ISBN: 978-1-4704-7595-6
Expected availability date: October 25, 2026
Contemporary Mathematics, Volume: 848;
2026; 191 pp
MSC: Primary 53; 37; 57
This volume stems from the AMS Special Session “Qualitative and Quantitative Aspects of Symplectic Topology”, held in Cincinnati, Ohio, April 15–16, 2023, and it features contributions from leading researchers in the field.
This volume collects recent advances at the interface of symplectic geometry, topology, and dynamics, emphasizing quantitative and computational methods. Topics include symplectic embedding problems, symplectomorphism groups, Hamiltonian dynamics, Floer and Gromov–Witten theory, and new developments in quantitative symplectic invariants. Several papers introduce refined tools for measuring symplectic rigidity and flexibility, while others explore algorithmic or formal aspects that connect symplectic topology to computation and mirror symmetry.
The book provides a coherent snapshot of current trends and methodologies shaping the subject, making it an essential reference for both established researchers and graduate students interested in modern approaches to symplectic topology.
Graduate students and research mathematicians interested in symplectic topology.
Articles
Joseph Palmer — Integrable systems with symmetries: Toric, semitoric, and beyond
Tian-Jun Li and Shuo Zhang — Lagrangian torus fibrations and visible non-orientable Lagrangians in rational surfaces
Yichen Liu — A lower bound of the Hofer-Zehnder capacity via Delzant polytopes
Olguta Buse and Jun Li — Symplectic inflation techniques and applications to embeddings, topological stability, and cones
Jie Min and Shengzhen Ning — Almost complex geometry of symplectic log Calabi-Yau pairs with applications to almost toric fibrations
Jonghyeon Ahn and Ely Kerman — On the symplectic capacity and mean width of convex bodies
MAA Press: An Imprint of the American Mathematical Society
Softcover ISBN: 978-1-4704-7795-0
Expected availability date: November 11, 2026
Classroom Resource Materials Volume: 80;
2026; Estimated: 158 pp
MSC: Primary 97; 62; 68
Motivated by the rapid growth of interest in data science in recent years, many faculty are seeking ways to incorporate data-related concepts into their existing curricula. This book presents a collection of classroom-tested activities that enable instructors to integrate meaningful, data-rich experiences into their mathematics courses. Each module has been carefully designed for seamless incorporation into courses such as finite mathematics, calculus, and linear algebra. Through these activities, students encounter mathematical concepts in authentic, data-driven contexts.
Many of the featured scenarios are inspired by real-world problems, such as determining optimal locations for concession stands in a theme park or analyzing the fairness of NFL overtime rules. Each chapter discusses the motivation and structure of the activity, the tools and techniques used to address the problem, and pedagogical considerations for implementation. In addition, every module includes guidance on locating or generating the relevant datasets. Quickstart boxes at the beginning of each chapter make it easy to identify the key ideas and essential components of each module at a glance.
To maximize flexibility, student prerequisites have been intentionally kept to a minimum. Instructors are not required to have prior experience or training in data science.
Supplementary materials will be available at www.ams.org/bookpages/clrm-80 after the book is published.
Undergraduate instructors interested in introducing data science concepts into mathematics courses.
Elizabeth L. Bouzarth and Kevin R. Hutson — Introducing
-means clustering through a real-world theme park example
Nora Gilbertson, Jake Price, and Jeremy Upsal — Predicting movie preferences using the
-nearest neighbors algorithm
Boyan Kostadinov — From Kepler to code: Data science lessons inspired by physics
Russell E. Goodman — A geospatial data science lesson...inspired by a comedian!
Nicholas Gorgievski and Megan Powell — Analyzing first-possession advantage in NFL overtime using Markov chains
Haiyan Su — Data-driven problem-solving through partnerships with business and industry in a mathematics topic course
Mutiara Sonjaja — Numbers to knowledge: A hands-on modeling module for quantitative reasoning
R. N. Uma, Adrienne A. Smith, Rebecca A. Zulli Lowe, and Alade O. Tokuta — Data science for social justice
Daniel T. Kaplan — Linear algebra in introductory calculus
Bibliography
Index
MAA Press: An Imprint of the American Mathematical Society
Softcover ISBN: 978-1-4704-8493-4
Expected availability date: November 29, 2026
AMS/MAA Textbooks
Volume: 76; 2026; Estimated: 442 pp
MSC: Primary 00
Engages readers through open-ended exercises focused on reasoning, trends, and real-world events
Explores data and estimation visually using charts and graphs
Navigates personal finance through practical exercises and web resources
New edition features full-color examples, updated exercises, and a refreshed instructor guide
Common Sense Mathematics is a textbook designed for a one-semester, college-level course in quantitative literacy. It draws on examples from current events and the media to promote common sense, estimation, straightforward mathematics, and accessible software as tools for analyzing practical questions.
After the book is published, an instructor's guide, solutions manual, and additional teaching materials will be available at www.ams.org/publications/authors/books/postpub/text-76.
Undergraduate students interested in learning quantitative reasoning and being comfortable with everyday data.
Calculating on the back of an envelope
Units and unit conversions
Percentages, sales tax and discounts
Inflation
Average values
Income distribution–Spreadasheets, charts, and statistics
Electricity bills and income taxes–Linear functions
Climate change–Linear models
Compound interest–Exponential growth
Money matters
Probability–Counting, betting, insurance
Break the bank–Independent events
How good is that test?
Hints
References
Index
Softcover ISBN: 978-1-4704-8553-5
Expected availability date: November 11, 2026
Contemporary Mathematics Centre de Recherches Mathématiques Proceedings Volume: 849;
2026; Estimated: 317 pp
MSC: Primary 11; 14
This volume contains the detailed exposition of virtual lectures on the theme “Modularity and Generalized Fermat’s Equation”, which were delivered in January–April 2022 during the program organized by the Bhaskaracharya Pratishthan Research Institute in Mathematics, Pune, India.
Modularity of elliptic curves over the field of rational numbers plays a central role in the proof of the celebrated Fermat’s Last Theorem (FLT) by Wiles and Taylor–Wiles in 1995. Around the same time Henri Darmon and his collaborators initiated the study of Generalized Fermat Equations (GFE) in a series of papers. This work leads to an ambitious program to study the generalized Fermat equation
using the modularity of abelian varieties of
-type over totally real fields. This volume covers some of the background material and presents the current state of the art in this area.
Graduate students and research mathematicians interested in algebraic number theory
Requests
B. Sury — The role of elliptic curves and modular forms in Fermat’s last theorem: A beginner’s guide
Philippe Michaud-Jacobs — Mazur’s isogeny theorem
Barinder S. Banwait — Modularity of
implies modularity over
Mihir Sheth — The Eichler-Shimura relation
Ehsan Shahoseini — Deformation theory of Galois representations and the Taylor-Wiles method
Subham Bhakta, Srilakshmi Krishnamoorthy, and Sunil Kumar Pasupulati — Modular degree and a conjecture of Watkins
Pilar Bayer — Exploring Shimura curves through algorithmic methods
Ajith Nair and Ajmain Yamin — Hilbert modular forms and Galois representations
Nicolas Billerey — Introduction to the modular method
Maleeha Khawaja and Samir Siksek — The modular approach to Diophantine equations over totally real fields
William Y. Chen — Noncongruence modular curves as Hurwitz spaces
Imin Chen and Angelos Koutsianas — Darmon’s program: A survey
Anand Deopurkar — The arithmetic and geometry of branched coverings: Theorems of Belyi and Darmon–Granville
Expected availability date: December 05, 2026
History of Mathematics Volume: 52;
2026; Estimated: 268 pp
MSC: Primary 01
This book is the first intellectual biography of Colin Maclaurin to appear in English. It traces the development of his mathematical thought through three major phases of his career: an early period shaped primarily by geometry, a second period centered on algebraic methods, and a final period of synthesis in which he engaged deeply with Newton's method of fluxions and fluents.
Maclaurin's scientific work was closely intertwined with the social and intellectual life of eighteenth-century Scotland and Great Britain. Through both his mathematical achievements and his extensive network of personal and scholarly connections, he actively promoted a practical and dynamic form of Newtonianism closely linked to the advancement of his country.
At the same time, Maclaurin was far more than a mere follower of Newton. This book shows how he emerged as one of the most important interpreters and defenders of Newtonian science while also transforming and extending it.
The book will appeal both to readers interested in the intellectual and cultural history of science and to those curious about the mathematics itself. While the historical and biographical discussions are accessible to any interested reader, the mathematical passages can be appreciated with no more than a high-school background in mathematics.
Undergraduate and graduate students and researchers interested in Colin Maclaurin.
Requests
Introduction
Maclaurin studies
Geometria Organica: His first major work
De Linearum Geometricarum Proprietatibus Generalibus Tractatus: An extension of the Geometria Organica?
The prize by the Royal Academy of Sciences in Paris on the Collision of Bodies of 1724
Maclaurin’s Tour de France and his election as professor in Edinburgh: A key moment for his career
The Treatise of Algebra: A combination of commentaries on Newton’s Arithmetica Universalis and original results
The George Campbell–Maclaurin controversy: A debate on algebra
The account of Sir Isaac Newton’s philosophical discoveries: A posthumous tribute to Newton and an insightful commentary on Newton’s Principia
Maclaurin’s living conditions and his marriage to Anne Stewart
Memorial to the Commissioners of Excise Concerning the Mensuruation of Tuns or Backs: An example of Maclaurin’s social commitment
The creation of the Philosophical Society of Edinburgh: Maclaurin as a driving force in Scotland’s scientific life
His magnum opus: The Treatise of Fluxions
The Scheme for Providing an Annuity to Ministers’ Widows and a Stock for their Children: Maclaurin as scientific guarantor
The defense of Edinburgh and Maclaurin’s death
Epilogue
Archival sources
Bibliography
Index