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New and Noteworthy Titles on our Bookshelf

June/July 2024

A Brief History of Mathematics: A Promenade through the Civilizations of Our World

By Tianxin Cai

Birkhäuser, 2023, 344 pp.

When studying mathematics, one is often reminded of the historical context of the subject. From ancient civilizations to modern society, the study of mathematics and its applications is present. A Brief History of Mathematics takes the reader on a journey through the Middle East, Ancient Greece and China, India and Arabia, the European Renaissance and calculus, the Age of Analysis and the French Revolution, modern algebra and geometry, and the abstraction of mathematics. At 353 pages, this tome is hardly brief, yet perhaps it’s as brief as possible for the amount of material it covers.

If the author missed a contribution by a named historical figure, I wouldn’t know it. The history presented here is thorough and includes contributions from across the globe. This was intentional, as the author states, “this is a book that does not want to leave out any great mathematician or mathematical line of thought or to pass up any opportunity to investigate the interminglings of mathematics with all the other modes of culture and human activity.” I believe this book corroborates the notion that when we promote the sharing of ideas across cultures and distance, we have the chance to learn from each other and make significant contributions to mathematics. The book contains many illustrations and photographs, some taken by the author himself, that add meaningful enhancement to the accompanying descriptions of history and mathematics. You can use this book for a history of mathematics course or for your own edification, and if you are interested in including historical facts in any of your courses, papers, or expositions, you can find what you seek in this book.

book cover

Differential Equations: A Toolbox for Modeling the World

By Kurt Bryan

SIMIODE, 2022, 561 pp.

According to their website, SIMIODE (Systemic Initiative for Modeling Investigations & Opportunities with Differential Equations) is a “non-profit, open community of teachers and learners using modeling first to teach and learn differential equations in an original way.” This group runs an annual online conference and has organized paper sessions at in-person national mathematics conferences. Here I’d like to highlight one of SIMIODE’s initiatives: an undergraduate textbook. When I consider adopting a textbook, I look for readable prose, extensive examples, and exercises at a wide range of levels. The Differential Equations textbook from SIMIODE hits the mark for me. The book begins by motivating the study of differential equations through examples, such as a sprinter running the 100-meter dash, population growth, and intracochlear drug delivery. The book then progresses through first-order equations, numerical methods for ODEs, second-order equations, the Laplace transform, linear and nonlinear systems of differential equations, and partial differential equations. There is more than enough material for a one-semester undergraduate course in this book.

Each chapter ends with 3–6 modeling projects that not only walk students through the development of each differential equation but also include exercises and concept checks to be sure they are following along. Students could work on these projects as part of the course or as an independent study. I found this book to contain many desirable attributes: its low cost compared to other textbooks, availability in both paperback and pdf versions, and online resources accessible to students and instructors. If you want to refresh your undergraduate differential equations course and focus on modeling, this is a great book to consider.