Softcover ISBN: 978-1-4704-7493-5
Product Code: HMATH/48
History of Mathematics Volume: 48;
2025; Estimated: 260 pp
MSC: Primary 01; 14; 51; 54; 97; 00
This book 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. The work addresses institutional constraints and the pedagogical means through which students learned to do original mathematics in a time of limited professional opportunity.
The book rewards those interested in the disciplinary, epistemological, and material conditions of mathematical research. The technical content is within the reach of advanced undergraduate students. It is of particular value to historians of science, historians of gender, scholars of mathematics education, and practicing geometers and topologists curious about the histories of their fields.
Undergraduate and graduate students and researchers interested in questions of gender and inclusion within the profession; historical case studies in the practical constraints of organizing a math department; the role of visualization and the evolution of foundational principles in math education over the past century.
A Girton girl and the lady wrangler
Generals without armies: Mathematics at Cambridge beyond the Tripos
To organize a department of mathematics
Bryn Mawr in the mathematical landscape toward the end of the nineteenth century
Motivation: To trace an unsuspected connection
Theme: Distinguishing between appearance and reality
Technique: Curve tracing
“Better off in Noah’s Ark”: Bryn Mawr and professional mathematical societies
Pure imaginaries in the Mathematical Journal Club Notebook
Branches, knots, and topological research
The other half of the Bryn Mawr mathematics department
Readers, administrators, and professoresses
Remembering Bryn Mawr mathematics
Bibliography
Index
Softcover ISBN: 978-1-4704-7964-0
Expected availability date: October 17, 2025
Mathematical Surveys and Monographs Volume: 293;
2025; 398 pp
MSC: Primary 53; 58; 57
Ricci Solitons in Dimensions
and Higher 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
—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, the book is accessible to readers with a solid background in Riemannian geometry and partial differential equations. While self-contained in its core exposition, it serves as both a technical resource and an invitation to contribute to the study of Ricci flow in dimensions
and higher.
Graduate students and researchers interested in geometric flows and Ricci flow.
Chapters
Ricci solitons in the context of Ricci flow
Curvature estimates for 4-dimensional shrinking solitons
Counting ends of Ricci solitons
Asymptotically canonical shrinking solitons
Curvature and volume estimates for steady solitons
Conjugate heat kernel methods for steady solitons
Review of Riemannian orbifolds
Softcover ISBN: 978-1-4704-7784-4
Expected availability date: October 02, 2025
Contemporary Mathematics Volume: 825;
2025; 239 pp
MSC: Primary 26; 28; 37; 42; 11; 60
This volume contains the proceedings of the AMS Special Session on Fractal Geometry and Dynamical Systems, held at the Spring Eastern Virtual Sectional Meeting on April 1–2, 2023, and the virtual Conference on Functional Analysis and Fractals organized by the Indian Institute of Information Technology Allahabad (IIIT-A), India, on February 16–18, 2024.
Fifty years ago, Mandelbrot created a new type of geometry called fractal. One of the novelties of this new mathematics is a systematic qualitative and quantitative approach to the concepts of irregular shapes and roughness. Galileo said that the universe is written in mathematical language and its characters are triangles, circles, and “other” geometric figures. Mandelbrot masterly defined “other” geometric objects whose main property is the self-similarity and coined the term “fractal” for them. Such models fit better complex patterns such as the circulatory system, the coastline of a littoral country or a stock market chart. One way of quantifying the complexity of such structures is the computation of their fractal dimension.
This book presents modern advances in the concept of dimension and its related notion of fractal measure. The text is oriented to give insight into the current research in the area, and it contains novel contributions of important scientists in the field. The book deals with very diverse topics such as the Hausdorff dimension of a set of continued fractions, dimension theory of inhomogeneous attractors, ergodic conjecture of falling balls systems, or Hausdorff measures to represent uncertainty in neural networks.
Graduate students and research mathematicians interested in dynamical systems and the theory of fractals.
Articles
Ekta Agrawal and Saurabh Verma — Dimension preserving approximation and estimation: Fractal surfaces and Riemann-Liouville fractional integrals
Russel Cabasag, Samir Huq, Eric Mendoza and Mrinal Kanti Roychowdhury — Optimal quantization for nonuniform discrete distributions
Serena Doria — Coherent upper conditional previsions based on Hausdorff measures and its applications in Artificial Intelligence
Vasileios Drakopoulos and Song-Il Ri — Fractal interpolation surfaces generated by Rakotch type contraction mappings
Jonathan M. Fraser — Inhomogeneous attractors and box dimension
Palle E.T. Jorgensen and James Tian — Fractal Measures and their induced Gaussian Processes
María A. Navascués, R. Miculescu, B. C. Anghelina and Ram N. Mohapatra — Ćirić contractions and Banach-valued fractal interpolation functions
R. D. Nussbaum — Comparison of Hausdorff dimension of and for
Lars Olsen — Multifractal zeta-functions and multifractal prime counting formulas
Megala and Srijanani Anurag Prasad — Spectrality of certain self-affine measures
Tingting Wang, Bilel Selmi and Zhiming Li — General Hewitt-Stromberg Measures: Properties and Their Role in Multifractal Formalism
Nandor Simanyi — Proof of Wojtkowski’s Falling Particle Conjecture
Saurabh Verma and Amit Priyadarshi — Further analysis of Hausdorff dimension and separation conditions
Softcover ISBN: 978-1-4704-7763-9
Expected availability date: October 02, 2025
Contemporary Mathematics Volume: 826;
2025; Estimated: 441 pp
MSC: Primary 16; 11; 94
This volume contains the proceedings of two conferences: NonCommutative Rings and their Applications (NCRA, VIII) and Quadratic Forms, Rings and Codes (QFRC II) that were held in August 2023 at Artois University, Lens, France.
The book contains a few survey papers and many research articles. The latter have been written in an accessible style and should be of interest to specialists, researchers, and graduate students. The subjects cover classical ring theory (e.g. Baer rings, separativity problem, group algebras, quasi-duo) coding theory (MacWilliams identities, codes over Galois rings or from Lie algebras). Quadratic forms are also present in two important and nicely written papers. Finally, some papers offer new perspectives moving from classical ring theory to universal algebras and non-associative structures.
Graduate students and research mathematicians interested in ring theory and coding theory.
Articles
Tomasz Brzeziński and Krzysztof Radziszewski — On matrix Lie affgebras
Michela Ceria and Teo Mora — Gröbnerian and Gröbner free techniques on non-associative algebras
Soumitra Das, Yasser Ibrahim, Özgür Taşdemi̇r and Mohamed Yousif — Perspectively decomposable modules
Adam Chapman and Ilan Levin — Invariant for sets of Pfister forms
Joshua D. Carey and Steven T. Dougherty — Codes constructed from matrices associated with Lie algebras
Steven T. Dougherty, Navin Kashyap, Tania Sidana, Serap Şahinkaya and Deniz Ustun — Symplectically self-orthogonal additive codes and their applications to quantum stabilizer codes
Alberto Facchini and David Stanovský — Semidirect products in universal algebra
Septimiu Crivei, Derya Keski̇n Tütüncü and Rachid Tribak — On dual relative CS-Baer modules
Ahmed Laghribi and Diksha Mukhija — On the excellence for inseparable quartic extensions
S Launois and I Oppong — Is of type ?
Christian Lomp, Mohamed Yousif and Yiqiang Zhou — Essentially quasi-duo rings
Sergio R. López-Permouth and Ashley H. Pallone — Amenable bases for algebras of entangled polynomials
Nasibeh Aramideh and Ahmad Moussavi — Weakly right-Baer ring
Khaerudin Saleh, Intan Muchtadi-Alamsyah and Pudji Astuti — On the structure of a finitely generated module
Mohd Nazim, Nadeem ur Rehman, Nazim and Shabir Ahmad Mir — On the co-annihilating ideal graph of commutative rings
Mehrdad Nasernejad, Veronica Crispin Quiñonez and Jonathan Toledo — Normally torsion-freeness and normality criteria for monomial ideals
Pere Ara, Ken Goodearl, Pace P. Nielsen, Enrique Pardo and Francesc Perera — The separativity problem in terms of varieties and diagonal reduction
Frédérique Oggier — Revisiting constructions of codes over Galois rings through -ary lifts
A. Duarte and C. Polcino Milies — Twisted group algebras of Abelian groups: a survey
Louis H. Rowen — Residue structures
Jay A. Wood — Weights with maximal symmetry and failures of the MacWilliams identities
Hardcover ISBN: 978-1-4704-8108-7
Expected availability date: December 25, 2025
Graduate Studies in Mathematics Volume: 252;
2025; Estimated: 550 pp
MSC: Primary 62; 65; 68
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.
The 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. Part 1 is written for a general audience, including students in mathematics, statistics, computer science, data science, or engineering, while select chapters in Part 2 present more advanced mathematical theory requiring familiarity with analysis, probability, and stochastic processes. Together, they form an ideal foundation for an introductory course on the mathematics of deep learning.
Thoughtfully designed exercises and a companion website with code examples enhance both theoretical understanding and practical skills, preparing readers to engage more deeply with this fast-evolving field.
Graduate students and researchers interested in deep learning.
Introduction
Mathematical introduction to deep learning
Linear regression
Logistic regression
From perceptron to kernels to neural networks
Feed forward neural networks
Backpropagation
Basics on stochastic gradient descent
Stochastic gradient descent for multi-layer networks
Regularization and dropout
Batch normalization
Training, validation, and testing
Feature importance
Recurrent neural networks and sequential data
Convolution neural networks
Variational inference and generative models
Advanced topics and convergence results in deep learning
Transitioning from Part 1 to Part 2
Universal approximation theorems
Convergence analysis of gradient descent
Convergence analysis of stochastic gradient descent
The neural tangent kernel regime
Optimization in feature learning regime: Mean field scaling
Reinforcement learning
Neural differential equations
Distributed training
Automatic differentiation
Appendixes
Background material in probability
Background material in analysis
Bibliography
Index
Hardcover ISBN: 978-0-8218-9884-0
Expected availability date: December 07, 2025
Graduate Studies in Mathematics Volume: 253;
2025; Estimated: 466 pp
MSC: Primary 35; 30; 78; 81
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. The book is intended for graduate students who are familiar with basics of real, complex, and functional analysis. The text can be used for short or long graduate level courses on this topic. Basic properties of weak solutions of partial differential equations, of Sobolev spaces, and of Fourier transform are developed in the text and appendices. Comprehensive Notes sections with further references to the literature will be helpful for those readers who wish to study this topic further.
Graduate students and researchers interested in inverse problems and their applications
Introduction
Formulation of the Calderón problem
Boundary determination
The Calderón problem in dimensions
The Calderón problem in the plane
Partial data
Scattering theory
Functional analysis
The Fourier transform and tempered distributions
Sobolev spaces
Elliptic equations
Bibliography
Index