Monograph – Mathematical Association of America

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There and Back Again: Why I’m Finally Trying Alternative Grading

Three years ago, in the early months after ChatGPT arrived, I predicted that “Alternative Grading in the Age of AI” would be the next best selling book on the faculty development circuit. Here we are three years later, and while this text has yet to materialize, I’m finally ready to dip my Hobbit-like toes into...

It was thirty years ago today …

By Keith Devlin @KeithDevlin@fediscience.org, @profkeithdevlin.bsky.social This month marks the 30th anniversary of the MAA website you are looking at, which back then was a new members-service medium called MAA Online. “Devlin’s Angle” was one of the regular features from the getgo. Out of curiosity, when I was deciding what to write about for January 2026, I looked...

Metabolic Networks, Elementary Flux Modes, and Polyhedral Cones

This monograph describes a mathematical model for the metabolic networks that are present in every living organism. The authors pursue a surprising connection between metabolic networks and the geometry of polyhedral cones. The notion of a connection like that is relatively new, but it is proving to be of real value. Metabolism, the collection of...

Control Problems for Conservation Laws with Traffic Applications

Control theory develops analyses, creates models, and produces designs that enable dynamical systems to achieve certain desirable behaviors using feedback and control methods. It has a strong theoretical basis in mathematics, and it is widely used in several engineering disciplines. This book is aimed at graduate students. The authors suggest that it is also accessible...

Ergodic Theory

Ergodic theory is a branch of dynamical systems theory that deals with measure-theoretic andstatistical properties of dynamical systems. Some of the big theorems in the subject giveconditions for when an average over time and an average over space for trajectories of adynamical system time agree. This book offers a solid introduction and explores some of...

Cover of the book Ergodic Theory by Simon Rubinstein-Salzedo, published as Volume 38 in The Carus Mathematical Monographs series by AMS/MAA Press. The cover features a central mathematical equation representing the ergodic theorem. The background has a dark gradient with a subtle abstract texture. Logos for MAA Press and the American Mathematical Society appear at the bottom.

Topics in Cyclic Theory

In various lecture courses given at Oxford University, Quillen introduces and develops cyclic cohomology and its many applications. His presentation emphasizes analysis and differential geometry – a companion volume Topology and K-Theory: Lectures by Daniel Quillen edited by Robert Penner focuses on topology and homological algebra. The editor of this volume, Gordon Blower, has brought together several...

Book cover of Topics in Cyclic Theory by Daniel G. Quillen and Gordon Blower. The cover is a solid blue cover with the title in white.

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...

The Logical Syntax of Greek Mathematics

This book is an English version, with expansions and improvements, of the author’s La sintassi logica della matematica greca (2011, published online). Since this earlier work has received too little attention—perhaps partly for linguistic reasons—an English version is a welcome contribution to scholarship. That said, this book is still written for the specialist. It is directed to...

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...

Essays in Constructive Mathematics

This is the second edition of Harold Edwards' Essays in Constructive Mathematics. See Bonnie Shulman's review of the first edition. In the preface to the first edition, Edwards writes that the 1880's marked a turning point in mathematics. It was then that mathematicians like Cantor, Dedekind, and Weierstrass began employing and advocating the acceptance of transfinite constructions such...

Recovery Methodologies: Regularization and Sampling

Recovery questions arise in applied mathematics when one needs to recover something- a function, a signal, or an image – from partial or incomplete information. Such problems, often described as inverse problems, are usually ill-posed and often difficult to resolve. This book offers an approach that describes methods to use regularization and sampling to find...

Geometric Structures on Manifolds

Geometric Structures on Manifolds is an accessible, sophisticated, modern, and grounded introduction to the theory of (G,X)-structures on manifolds, which standardize the notion of spaces locally modeled on manifolds with geometry, aimed at a graduate level audience and above. Themselves modeled after the atlas definition of a differentiable manifold, (G,X)-structures consist of atlases of charts valued...

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