Mathematics Rebooted: A Fresh Approach to Understanding

This is an interesting take on the popular math book. It is aimed at people who liked math at one point in school, but then fell behind or got turned off for some reason and stopped studying it. The aim is to rekindle their interest in the subject. It is not for people who are terrified of math: the book is full of formulas, diagrams, and calculations. The author’s specialty is math education and she works specifically in math thinking and learning. She won the 2012 Annie and John Selden Prize for Research in Undergraduate Mathematics Education.

The emphasis in the book is really on mathematical reasoning rather than mathematical results. The book differs from most popular math books in that it says very little about the triumphs of modern mathematics. It takes a number of very tangible problems, such as tilings (tessellations) and shows how we can figure out things by reasoning. There’s a good balance of geometric and numeric work.

The book has a strong discovery flavor, in that it works through many examples of the thing we are interested in, with lots of trial and error, before guessing or deducing a general rule. Everything is elementary. I thought the chapter on graphing (Cartesian and polar coordinates) was especially interesting, because it focuses on practical applications of graphs rather than graphing techniques.

Very Good Feature: an excellent index. There’s also a good list of follow-on books for people of various interests, including teachers and psychologists, and a roughly 125-item scholarly bibliography.

I think this book is very well done, but I’m not sure how large the audience is. We run across lots of people who say they never understood math in school, but not many who say they would like to have understood it better. A good second book for those who like this book is Courant & Robbins’s What is Mathematics? It’s a much harder book, but it too tries to lead the reader through the reasoning that produced these results, rather than just displaying them for our admiration.

Allen Stenger is a math hobbyist and retired software developer. He is an editor of the Missouri Journal of Mathematical Sciences. His personal web page is allenstenger.com. His mathematical interests are number theory and classical analysis.