Problem Book – Mathematical Association of America

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Pop Culture as a Gateway to Research: Expanding Belonging in Mathematics

By Qianyi Jiang, Niharika Nirankari, Monica Morales Hernandez Undergraduate students often experience mathematics as a sequence of courses centered on technique, correctness, and speed. Research, when it appears at all, usually shows up later — after students have racked up enough credentials to be granted permission to ask questions. This structure privileges speed, prior access,...

Furnishing the Hobbit-Hole

By Lew Ludwig Markdown, project setup, and what to do when AI gives you garbage: this month, the tools. "If I didn't know any better, I'd assume you joined last week's department meeting. Did you hide in the back corner when these conversations took place?" That came in last month, after "I Worry." Blake, a...

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...

100+1 Problems in Advanced Calculus

The book 100+1 Problems in Advanced Calculus by P.Toni, D. Lamberti, and G. Drago provides one-hundred problems on various calculus topics. It consists of eight chapters whose content complexity gradually increases following, to a certain extent, a sequence of a traditional textbook for an undergraduate calculus course. From this standpoint, this book can be used as a...

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...

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