The Calculus Diaries by Jennifer Ouellette

I finished Jennifer Ouellette’s new book a few weeks ago, shortly after my trip to Alabama, but it’s taken me a long time to get around to reviewing it due to a combination of too much work and being a Bad Person. There’s finally a tiny break in the storm of work, though, so here’s a slightly belated review.

The Calculus Diaries is not a book that will teach you how to do math. There aren’t worked examples, detailed derivations, or homework problems in the main text. It might, however, teach you not to fear math, as it provides a witty and accessible explanation of the key concepts behind calculus, and how those ideas show up in everyday life.

For all its fearsome reputation, calculus is really very simple in concept: it’s a mathematical toolbox for dealing with change. Differential calculus (derivatives) is the study of individual small changes– how mathematical functions change when you change their inputs– and integral calculus is the study of the cumulative effect of lots of little changes. Those core concepts can get lost in a haze of calculation when you first encounter the subject in school, but in the end, everything flows from those two ideas.

In this book, Ouellette spells those concepts out very clearly, and explains how they apply to a wide range of real-life situations: amusement park rides, games of chance, population biology. OK, that’s “real-life” for values of real life that include zombie apocalypses, but the point is, there are lots of engaging examples drawn from everyday experience and pop culture. Each example in the book includes a clear explanation of how it can be understood in terms of individual changes or cumulative effects, setting out the essential relationships in words, not equations, and explaining the important properties of the solution. As a bonus, it also includes some of the many colorful historical anecdotes about the development of key ideas in mathematics.

I’m not really the target market for this, in a lot of ways– I’d probably be happier with the equations written out in mathematical notation– but I know enough about the target market to recognize it as something that is pitched to the right level for the audience that needs this book. The idea of integrals as the sum of a lot of little steps is something that we spend a lot of time banging on in the introductory physics curriculum, and for many of these students, it would probably be more effective to explain it first without equations, and come back to the math later (insert obligatory grumble about our too-short academic terms).

(There is an appendix with all the mathematical equations and functions spelled out. I’m obscurely proud to say that I was the second great big dork to point out that there’s a typo in one of the equations…)

This is a fast-moving and engagingly written book about what math means. It won’t teach you how to calculate anything, but if you’re not already mathematically inclined, it’s a good way to get a sense of the attraction of math for those who are.