MAA Press: An Imprint of the American Mathematical Society
Softcover ISBN: 978-1-4704-7587-1
Product Code: CLRM/77
Expected availability date: April 15, 2026
Classroom Resource Materials Volume: 77;
2026; 298 pp
MSC: Primary 00; 34
This book provides a collection of 130 fully solved problems, each derived from a mathematical model formulated in terms of an ordinary differential equation. As well as the problems, contextual descriptions are provided, grounding each model in its real-world setting. Applications to topics as diverse as physics, biology, engineering, and economics serve to underline the importance of differential equations in many areas of study.
The models are collected according to the underlying differential equation, making it a simple task to find the right model to implement within a class. The first chapter provides a catalog of first-order differential equations, which may be solved by elementary methods. The second chapter is concerned with models of exponential and logistic growth, including many models for population growth. Following this, there is a chapter on linear differential systems and equations. The book closes with a collection of problems arising from non-linear models. Here, qualitative methods such as phase portraits are emphasized.
The problems are designed for use in an undergraduate differential equations class. Knowledge of basic linear algebra and multivariable calculus is assumed, while an exposure to complex variables for some of the problems would be helpful, but not necessary.
Undergraduate and graduate students interested in learning and teaching ordinary differential equations and analysis of corresponding models of natural, technological, and social phenomena.
Requests
Diverse models described by first order ordinary differential equations
First order linear equations, second degree equations, and their applications
Models described by linear differential systems and equations
Nonlinear models. Qualitative analysis
Bibliography
Index
MAA Press: An Imprint of the American Mathematical Society
Softcover ISBN: 978-1-4704-7986-2
Product Code: CLRM/78
Expected availability date: April 15, 2026
Classroom Resource Materials Volume: 78;
2026; Estimated: 279 pp
MSC: Primary 34; 97; 00
Written by the founder of SIMIODE (Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations), this book provides a collection of resources that facilitate a modeling-first approach to teaching differential equations. Each of the forty-three chapters presents a unique, realistic, and classroom-tested modeling scenario, covering diverse topics such as chemical kinetics, stochastic processes, circuit tuning, and stadium design. The modules are standalone, meaning they can easily be introduced into an instructor’s differential equations course. Through these activities, students discover how differential equations arise naturally and appreciate their importance.
The material is presented in an informal style, taking the form of conversations between two colleagues discussing the underlying modeling scenarios. These colleagues share their methods, pedagogical approaches, and experiences, answering questions which arise about how to teach modeling. These dialogs also provide scaffolding, advice and reflections for faculty considering introducing active-learning opportunities into their classes.
Teaching Differential Equations with Modeling-First Scenarios offers a friendly introduction to modeling activities in the undergraduate classroom, with only prior exposure to derivatives being required. For the instructor, a desire to engender an attitude of experimentation, investigation, and excitement in their students is the most important prerequisite.
Materials supporting the scenarios will be available on the AMS Bookstore at www.ams.org/bookpages/clrm-78 after the book is published and on the SIMIODE webpage.
Undergraduate students interested in teaching differential equations using modeling activities.
Requests
Death and immigration
Falling column of water
Sublimation of dry ice
Slick oil slick modeling
Hang time
Deep well timing
Chord path time
Falling coffee filters
Intraocular surgery recovery
Evaporation
Cooling it
Building an ant tunnel
Chemical kinetics
Ramp bounce
Frequency response
LSD
Struggle for existence
Mystery circuit
Chemical optimization
Stochastic processes
Tuned mass dampers
Machine replacement
Guitar tuning
College savings
Dog drugs
Ice melt
Disease spread
Time of death
Water clock
Drug administration
Cloth dry
Rocket flight
Stadium design
Catapult launch
Falling in water
Circuit tuner
River crossing
Dialysis
Insect colony survival
Pursuit models
Acorns, rodents, and snakes
Lipoprotein modeling
Trig function approximation
Postlude–Make that prelude
Bibliography
Index
Softcover ISBN: 978-1-4704-7415-7
Product Code: CONM/834
Expected availability date: May 06, 2026
Contemporary Mathematics Volume: 834;
2026; Estimated: 182 pp
MSC: Primary 57; 41; 14; 81
This volume contains the proceedings of the AMS Special Session on Inverse Problems at the AMS Fall Western Sectional Meeting, held from October 22–23, 2022, at the University of Utah, Salt Lake City, Utah.
This book presents a wide variety of high-quality research in Reshetikhin–Turaev invariants, Khovanov homology, quantum groups, topological quantum field theories over algebraic number fields, nonreductive geometric invariant theory, Chebyshev polynomials, oriented bundles over oriented surfaces, and entanglement topology and tensor networks. The book may be useful for both junior and senior researchers and mathematicians in low-dimensional topology, mathematical physics, and algebraic geometry.
Graduate students and research mathematicians interested in inverse problems, geometric and topological aspects of representation theory and low-dimensional topology.
Nathan Geer, Adam Robertson, Jan-Luca Spellmann, and Matthew B. Young — Renormalized Reshetikhin–Turaev invariants for the unrolled quantum group of
Fabian Espinoza, Mee Seong Im, and Mikhail Khovanov — Two-dimensional topological quantum field theories of rank two over Dedekind domains
Mee Seong Im and Meral Tosun — Towards the affine and geometric invariant theory quotients of the Borel moment map
Louis H. Kauffman — ER=EPR, entanglement topology and tensor networks
Gabriel Montoya-Vega — On the Khovanov homology of via long exact sequence
Dionne Ibarra, Alex Landry, Gabriel Montoya-Vega, and Józef H. Przytycki — Exploring unimodality of the plucking polynomial with delay function
Anthony Christiana, Huizheng Guo, and Józef H. Przytycki — Using Fibonacci numbers and Chebyshev polynomials to express Fox coloring groups and Alexander–Burau–Fox modules of diagrams of wheel graphs
Mieczyslaw K. Dabkowski and Sushmita Sinha Roy — Isotopies of links in oriented
-bundles over surfaces
Robert Owczarek — Are Sławianowski and Kijowski theories good models for TQFTs of Schwarz type?
Softcover ISBN: 978-1-4704-7686-1
Product Code: CONM/835
Expected availability date: May 06, 2026
Contemporary Mathematics Volume: 835;
2026; 294 pp
MSC: Primary 15; 62; 14; 32; 68; 94; 11
This volume contains the proceedings of the 2024 Spring Central Sectional Meeting, held at the University of Wisconsin-Milwaukee, Milwaukee, WI, on April 20–21, 2024.
Our motivation for this volume is to fill the void of mathematical literature in the current developments of artificial intelligence, machine learning, deep learning, geometric deep learning, geometric information theory, etc. While there are some excellent mathematical ideas in such developments, the literature is flooded by papers and books written by computer scientists and engineers that lightly touch upon these subjects, thereby missing deep mathematical understanding. This makes it difficult for anyone who wants to enter such areas of research. What is missing in the literature is exactly the theoretical mathematical background in artificial intelligence and machine learning.
Graduate students and research mathematicians interested in artificial intelligence and mathematics research.
Articles
Tony Shaska — Artificial neural networks on graded vector spaces
Mee Seong Im and Venkat R. Dasari — Computational complexity reduction of deep neural networks
Carl Henrik Ek, Oisin Kim and Challenger Mishra — Calabi–Yau metrics through Grassmannian learning and Donaldson’s algorithm
José Luis Crespo, Jaime Gutierrez and Angel Valle — Neural network design options for RNG’s verification
Mee Seong Im, Clement Kam and Caden Pici — Diagrammatics of information
Ilias Kotsireas and Tony Shaska — A neurosymbolic framework for geometric reduction of binary forms
Yuta Kambe, Yota Maeda and Tristan Vaccon — Geometric generality of Transformer-based Gröbner basis computation
Mee Seong Im — Semi-invariants of filtered quiver representations with at most two pathways
Elira Curri and Tony Shaska — Polynomials, Galois groups, and database-driven arithmetic
A publication of the Société Mathématique de France
Softcover ISBN: 978-2-37905-222-4
Product Code: PASY/65
Expected availability date: March 05, 2026
Panoramas et Synthèses Volume: 65;
2025; 63 pp
MSC: Primary 35; 82
This volume covers subjects related to the mini-courses delivered during the winter school held at CIRM, Marseille-Luminy, France, from January 18–22, 2021. It formed part of the extensive program “Kinetic Theory: Analysis, Computation and Applications” organized at CIRM from January to June 2021, with Shi Jin as the Jean-Morlet Chair and Mihai Bostan as the Local Project Leader.
Kinetic equations play an indispensable role in bridging the microscopic scales at the molecular level with the macroscopic scales at the continuum level. Macroscopic fluid flow equations can be derived from mesoscopic kinetic equations or even from microscopic interacting particle systems. This is one of the core areas of partial differential equations and mathematical physics, with a wide range of applications in astronautics, astrophysics, plasma physics, biology, and even the social sciences.
This book provides a comprehensive overview of current activity in some of the most important topics of investigation in the field, including collective dynamics, fluid-dynamic limits, mean-field limits, and multiscale numerical methods.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Graduate students and research mathematicians.
ISBN: 978-981-98-2369-7 (hardcover)
This book is based on the lecture notes for the TCC (Taught Course Centre for graduates) course given by the author in Trinity Terms of 2009–2011 at the Mathematical Institute of Oxford University. It provides an accessible yet rigorous introduction to the mathematical theory of the Navier–Stokes equations, including both classical PDE theory and modern regularity results developed in the style of the St Petersburg school. The book covers fundamental concepts from basic theory to state-of-the-art results, with a focus on the interplay between regularity and well-posedness — a central theme in the study of the Navier–Stokes equations and one of the Millennium Prize Problems.
The second edition introduces major new material that extends the scope of the original text. Chapter 8 explores the regularity of axially symmetric solutions and examines Type I and Type II blowup in suitable weak solutions, offering insights into possible singularity formation and the broader global regularity problem. In addition, Appendix C provides detailed proofs of key results, enhancing the mathematical rigor and connecting the material to ongoing research and open problems in fluid dynamics.
Together, the comprehensive coverage of classical and modern theory, enriched with these new contributions, makes this edition a valuable resource for graduate students, researchers, and anyone interested in the analytical foundations of fluid dynamics.
Foreword
Foreword 2
Preliminaries
Linear Stationary Problem
Non-Linear Stationary Problem
Linear Non-Stationary Problem
Non-Linear Non-Stationary Problem
Local Regularity Theory for Non-Stationary Navier–Stokes Equations
Behaviour of L3-Norm
Further Analysis of Potential Blowups of Suitable Weak Solutions
Appendix A: Backward Uniqueness and Unique Continuation
Appendix B: Lemarie-Riesset Local Energy Solutions
Appendix C: Proof of Lemma 2.2 of Chapter 8
Bibliography
Index
Undergraduate and graduate students in differential equations and fluid mechanics.
Pages: 172
ISBN: 978-981-98-1593-7 (hardcover)
This volume presents the combined proceedings of two major conferences in mathematical logic — the 16th Asian Logic Conference (ALC) and the 14th International Conference on Computability, Complexity and Randomness (CCR) — held at Nazarbayev University, Astana, Kazakhstan, from 17–21 June 2019 and 23–25 June 2019, respectively. ALC is a prominent international event promoting research and collaboration in logic across the Asia–Pacific region, featuring developments in mathematical logic, logic in computer science, and philosophical logic. CCR focuses on algorithmic information theory, Kolmogorov complexity, and their intersections with computability, complexity theory, and reverse mathematics.
This collection brings together leading voices in the field, offering fresh perspectives and state-of-the-art research in logic, computability, set theory, and model theory. It is an essential resource for researchers, scholars, and students interested in contemporary developments in mathematical logic and its applications.
Comparing the isomorphism types of equivalence structures and preorders
Comparing the Isomorphism Types of Equivalence Structures and Preorders (N Bazhenov and L San Mauro)
Rogers Semilattices in the Analytical Hierarchy: The Case of Finite Families (N Bazhenov and M Mustafa)
Some Notes on the wtt-Jump (K Ambos-Spies, R Downey and M Monath)
E-Combinations and Closures of Quite O-Minimal Theories (B Sh Kulpeshov and S V Sudoplatov)
Geology of Symmetric Grounds (T Usuba)
Strong Downward Löwenheim-Skolem Theorems for Stationary Logics, III — Mixed Support Iteration (S Fuchino, A O M Rodrigues and H Sakai)
On Interior of Definable Subsets of Ordered O-ω-Stable Fields (V V Verbovskiy)
On Diophantine Equations over ℤ[i] with 52 Unknowns (Y Matiyasevich and Z-W Sun)
Advanced undergraduate students, graduate students, and researchers interested in logic, computability theory, set theory, and model theory.