New and Noteworthy Titles on our Bookshelf

The Math You Need

A Comprehensive Survey of Undergraduate Mathematics

By Thomas Mack. The MIT Press, 2023, 496 pp., $55.

Courtesy of MIT Press.

The Math You Need is a collection of fundamental undergraduate topics in mathematics. I found it to be quite complete; it has chapters for group theory, commutative algebra, linear algebra, topology, real analysis, multivariable analysis, complex analysis, number theory, and probability. The text presents its contents using the traditional “Definition – Theorem – Proof” style of writing to which many mathematicians are accustomed. Since it does not contain excessive prose or many examples, I found the book well-suited to be a reference, likely useful for a graduate student who has already grappled with the ideas and proofs in an introductory course. It could be used as a textbook, however, as it contains exercises at the end of each of its nine chapters. While reading, I was reminded of many of the standard proof techniques of algebra, analysis, and topology that I saw in graduate school. I expect an advanced (and motivated!) undergraduate student could expand upon what they saw in their introductory courses and would appreciate what the book adds to their background.

I believe this book would be an excellent addition to the textbooks and reference books in the libraries of mathematics students, professors, and hobbyists. It might take you back to your graduate school days, as it did for me. I especially think a department could use it to add advanced topics to what is covered in their undergraduate courses or guide graduate students to the background material they will be expected to know as they take graduate courses or study for their preliminary exams.

Around the World in Eighty Games

From Tarot to Tic-Tac-Toe, Catan to Chutes and Ladders, A Mathematician Unlocks the Secrets of the World’s Greatest Games

By Marcus du Sautoy. Basic Books, 2023, 384 pp., $30.

Courtesy of Hachette Book Group.

As you might have guessed by its title, this book about games is playful and fun. In 80 vignettes, the author explores games from all over the globe. In interludes, he ponders aspects of a “game.” What are the qualities that turn an activity into a game? While he and others have tried to define it and we can certainly provide examples, the definition of a “game” is nearly impossible to pin down.

I found joy in reading about games familiar to me: backgammon, chess, Go, mancala, SET, and Nim. There were games that were new to me, such as Carrom from India, Hanafuda from Japan, and Truco from many countries in South America. The author turned the book into a game as well; he encourages a nonlinear reading of the text and suggests that the reader should roll a die to determine the next chapter to explore. He hypothesizes that games are popular in how they build community as well as offer a refuge from the complexities of daily life—they are rule-bound microcosms with a definite ending.

The book includes the general rules of each game, where it originated, and where mathematical concepts appear. The author also writes about parallels between games and mathematics. There are common traits of games across cultures as well as unique aspects provided by each. We often appreciate the aesthetics of a game and how simple rules give rise to complexity. They both offer a chance to overcome barriers to reach an end—a victory in a game or a QED in a proof. “The rules of the game are like the axioms of mathematics. Playing a game is like exploring the consequences of those axioms. Games for me are a way of playing mathematics.” This is a fun book about games and how math plays a role in them. Consider using it in a history of math course, as part of a math club, or for personal interest.