Dynamical Systems – Mathematical Association of America

Featured Resources

Complement (bottom-up) learning with top-down activities to develop mathematical thinking ability

By Keith Devlin @KeithDevlin@fediscience.org, @profkeithdevlin.bsky.social Sometime in the early 2000s, my primary care physician offered me the option of no longer having an annual health checkup in person. Rather, I could just call into my nearest walk-in testing lab and have a blood draw, followed up a few days later by a quick video-chat. (They also wanted...

Leveraging Data About Math Departments

By Dave Kung When I was department chair at St. Mary’s College of Maryland, we carefully tracked data about how we were serving students. Regularly updated spreadsheets showed how many students were in each course we offered and we used them to look for enrollment patterns and adjust our offerings as needed. We were particularly...

Differential Equations: A First Course on ODE and a Brief Introduction to PDE

This is the second edition of a book previously reviewed here. The preface to the new edition suggests that the first edition might have been rushed into publication because of the pandemic. The goals in the new edition include the usual correction of errors and misprints, as well as inclusion of new examples and exercises,...

Cover of "Differential Equations" by Antonio Ambrosetti and Shair Ahmad, 2nd edition, with abstract wave-like patterns.

Sharkovsky Ordering

This short book describes the role of Sharkovsky ordering in the theory of dynamical systems, and in particular the way Sharkovsky’s work opened the field of combinatorial dynamics. About ten years after Sharkovsky’s results, and apparently unaware of them, Li and Yorke published their famous ”Period Three Implies Chaos” paper. The book begins with the basic ideas and a proof of Shakovsky’s theorem. Then it goes...

Topics in Applied Mathematics and Modeling: Concise Theory with Case Studies

Subtitled “Concise Theory with Case Studies”, this book aims, according to the author, “… to provide a context for students to gain a deeper appreciation of mathematics and its connections with other disciplines.” It is intended for upper-level undergraduates in the mathematical and physical sciences and engineering who have a basic understanding of calculus, linear...

Book cover featuring the title "Topics in Applied Mathematics and Modeling" with a modern design and mathematical graphics.

Network Information Systems: A Dynamical Systems Approach

This monograph describes the development of a theoretical framework for analysis of network information systems using the theories of dynamical systems and control. Examples of network information systems include large-scale interconnected systems such as air traffic control, communications, power and energy grid operations as well as many kinds of biological networks. The authors describe a...

Braids and Dynamics

This short book considers an unusual combination of algebraic topology, dynamics and applications to the mixing of fluids. Probably not many mathematics texts use a taffy puller in a primary example. This one does, and it incorporates interesting connections to dynamics on surfaces, the algebraic topology of braids and applications to mixing. This book is...

Notes on Hamiltonian Dynamical Systems

The theory of Hamiltonian dynamical systems has a rich history, going back to at least the nineteenth century. Celestial mechanics provided a good deal of the original motivation, but the scope has expanded considerably since then. In this book the author provides a very complete development of the theory that is accessible to newcomers and...

An Introduction To Chaotic Dynamical Systems

This text on chaotic dynamics is the third edition of a book whose widely used second edition is thirty years old. This book, in contrast to another of Devaney’s well-known books (reviewed here), is aimed at graduate students and upper-level undergraduate students in mathematics. It is fully a mathematics book with careful definitions, theorems and...

Welcome to Real Analysis

In Welcome to Real Analysis, Benjamin B. Kennedy offers a complete and self-contained introduction to analysis that covers, and moves beyond, the foundational work of single-variable Calculus. Its subtitle, Continuity and Calculus, Distance and Dynamics reveals the author’s ambitions to explore topics across calculus and discrete dynamical systems. Kennedy’s aim is to ensure that a student’s first exposure...

Dynamics, Geometry, Number Theory

Gregory Margulis is a mathematician of incredible breadth and originality. His work in the early 1970's on discrete subgroups of semisimple Lie groups transformed the field and solved a number of important open problems that had long been considered out of reach. Around the same time he employed the representation theory of the group SL2(Zp) in order...

Discovering Dynamical Systems Through Experiment and Inquiry

Computer simulations give us a powerful new tool for approaching the teaching and learning the fundamentals of the theory of dynamical systems. The authors of the book under review take full advantage of that tool in this innovative book. The book is quite different from classical books on dynamical systems like Devaney’s A First Course in Chaotic Dynamical Systems:...

Cover of 'Discovering Dynamical Systems Through Experiment and Inquiry' by Thomas LoFaro and Jeff Ford, featuring a clean, academic design with the title and authors' names prominently displayed on a solid background.

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