Problem Book – Mathematical Association of America

Featured Resources

When Water Isn’t Really Water

By Lew Ludwig The hamburger graph has become my unexpected companion this summer. It first appeared in a workshop I was co-facilitating, comparing the water usage of AI prompts to beef production. Then it surfaced again a few weeks later - and that's when I realized we weren't really arguing about water at all. The first...

Where do our numbers come from?

By Keith Devlin @KeithDevlin@fediscience.org, @profkeithdevlin.bsky.social The numbers we use every day are so familiar, and so much a part of life, it’s easy to forget that they are a recent invention, having been introduced in the late nineteenth and early twentieth centuries. Sure, humanity has had some form of numbers for at least ten thousand years, and...

Mathematical Reflections – Two Lockdown Years

Although the authors primarily see this book, “encouraged by appreciative and constructive feedback from faithful readers, as a compilation and revision of the 2020 and 2021 volumes of the online journal, Mathematical Reflections", this reviewer would emphasize two other aspects of the book: i) a multi-national statement of human resilience in response to the pandemic, and ii) a collection of 16 beautiful...

Ten Themes in Algebra for Mathematics Competitions

This book reviews ten major techniques useful in solving mathematical problems. It should be of use to mathematics competition candidates, problem writers, problem solvers, and researchers. The book form facilitates mastery of these techniques: The first 40% of the book presents brief but concise exposition of theory accompanied by practice problems while the last 60%...

Selected Exercises in Algebra: Volume 2

Also see our review of Volume 1. These two volumes are translations of two Italian-language volumes, Esercizi scelti di Algebra, published in this same series in 2017 and 2018. The exercises are exam questions from the undergraduate program at the University of Pisa. The background and intentions of the book are described in detail in the Preface. In particular they note (p. ix):...

Mathematics via Problems: Part 2: Geometry

Zaslavsky and Skopenkov’s Mathematics via Problems Part 2: Geometry is not your average textbook. Though it touches upon most high school geometry topics, it does go beyond the level required by the standards. In fact, it is not an instructive book for students’ first time engaging with relevant geometry content; rather, it is a collection of relevant...

A Festival of Mathematics: A Source Book

There are a number of books available with intriguing problems for students (and others) to puzzle over, but you will want to make room in your bookshelf for one more. This collection, the 28th volume from MSRI’s Mathematical Circles Library, provides a unique set of resources for use in mathematical circles and similar formal and...

120 Awesome Algebra Problems

This book, employing a problem-solving approach, reviews useful algebraic techniques that many of us don’t think of initially. Therefore, this book should be of interest to those who prepare for Olympiad competitions, to mathematics researchers including student researchers, as well as to those who enjoy recreationally reading a good collection of problems solved by ingenious methods. This book...

Disciplinary Literacy and Gamified Learning in Elementary Classrooms

In this text, Drs. Haas, Metzger, and Tussey provide eight chapters of quests about three elementary-aged siblings who travel via a lava lamp to different thrilling locations, such as Stonehenge, Machu Picchu, and The Great Wall of China. The children complete various discipline-specific tasks at each destination. For each chapter, there are three elementary-themed quests:...

Conversational Problem Solving

Although this book is based on material accumulated while teaching the M.I.T. freshman problem solving seminar focused on the Putnam competition, it is not the usual collection of topics and tricks that constitute many “competition math” books. This book consists of a series of dialogues between a teacher (“Professor Mortimer Ignatius Blakely”) and the participants...

Sharpening Mathematical Analysis Skills

This book is a book of problems and worked out solutions covering all areas of real analysis. It should be of use to a variety of readers including, those teaching the traditional Calculus sequence, researchers who routinely deal with series, and mathematical laypeople who wish to enjoy some punchy, beautiful identities and revel at some...

Recurrent Sequences

What a delightful, current, compactly written book. This book could serve as a stand-alone text i) for an advanced, undergraduate, second-term, Discrete-Mathematics course, ii) for a first, or preferably, second-year stand-alone text for graduate students specializing in dynamical systems, combinatorics, or discrete systems, or iii) for researchers in these areas. The prerequisites for reading the book ...

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