Colin Adams, who writes the Mathematically Bent column for the Mathematical Intelligencer, has done about as much to inject humor into the study of calculus as any other person of whom I am aware. For example, together with his colleague Tom Garrity, he engaged in a humorous hour-long debate Derivative vs. Integral: Final Smackdown, currently available on youtube. I enjoyed this so much that, the last time I taught a calculus course, I told the students, as their Thanksgiving-vacation assignment, to watch the video and write a brief report on it; several students indicated they enjoyed it too. In addition, Adams is the co-author of How to Ace Calculus: A Streetwise Guide and How to Ace the Rest of Calculus: A Streetwise Guide, both of which teach calculus with considerable humor. And now, Adams has turned to zombies to help teach the subject. Even if I had not already had pleasant experiences with Adams’ previous work, the title of this book alone would have induced me to request it to review. (Amazingly enough, though, this is not the first book to bring zombies into a discussion of calculus; another of them, The Calculus Diaries: How Math Can Help You Lose Weight, Win in Vegas, and Survive a Zombie Apocalypse by Amy Ouellette, has even been reviewed in this column.)
This book (the main text of which is quite short, about 150 pages) is fiction, narrated by Craig Williams, who, like the author, is a professor of mathematics at a small liberal arts college in the Berkshires of western Massachusetts. As the book opens, he is standing at the blackboard lecturing in his first-semester calculus class, drawing pictures of curves and their tangent lines (which are reproduced in the book) when things start to go awry: he notices one of his students “shambling” towards class, and quickly realizes, after the student attacks others in the class, that the reason he was shambling is because he is now a zombie. The next 18 hours or so in the life of Professor Williams (along with a small group of other survivors he encounters along the way) are then recounted in the book, and it is surprising how much mathematics (and some physics and biology) gets discussed in that time.
For example, tossing a zombie over a bannister allows Williams to explain how integral calculus can be used to find the distance he (it?) falls; watching a zombie chase a dean provokes a discussion of tangent vectors and how, if the pursued is running in a straight line and the pursuer chooses a path so that at any point the pursuer’s tangent vector points toward the pursued, the pursuer’s path can be analyzed by differential equations.
Sometimes, in fact, as in the latter example above, the explanations are so involved that they are deferred to an appendix (entitled “Continuing the Conversations”). This is artfully done: the reader is given the option of immediately turning to the Appendix and reading the enlarged account (written so as to then allow seamless entry back into the main narrative) or skipping it and just continuing the text.
There are lots of other mathematical discussions that take place while Williams and his group attempt to survive the zombie onslaught, some with detailed diagrams that Williams is lucky enough to be able to draw on a blackboard in rooms where they happen to find themselves. Topics covered include: the logistic model of differential equations, the nonlinear differential equations resulting from an analysis of infection of brain cells, Newton’s law of cooling and the Volterra prey-predator equations.
Prerequisites for reading this book are fairly minimal. The author does include another Appendix, about thirty pages long, summarizing (in the form of a conversation between Williams’s two children) the basics of single and multivariable calculus, but I would think that at least some prior exposure to the subject would be advisable for really understanding the discussions in the book. Students who are, for example, concurrently taking a freshman first-semester calculus course would understand a lot of the book but may find some of the differential equations discussions a bit heavy going.
Of course, fans of science fiction or horror novels who are looking for a tense, exciting read should look elsewhere. This book only takes about three or four hours to read, its characters are two-dimensional, and the plot is thin, existing only as a clothesline on which to hang the mathematical discussions. (My apologies to Herbert Wilf, from whose book generatingfunctionology I stole this metaphor.)
The book elicits chuckles (quite a lot of them, actually), particularly when Adams is describing some academic types. His descriptions of the director of the Counseling Center and the student who, in the middle of the zombie attack, tries to hand in a late homework assignment, are priceless. There isn’t any sense of genuine suspense or dread. That’s not a criticism: the author didn’t intend to write a classic horror novel, he intended to write one that explained the ideas of calculus and differential equations (particularly the latter) in a humorous and unusual setting. He has succeeded admirably. This is a book that can be enjoyed by both students and by faculty members seeking a way to spice up their lectures.
Mark Hunacek (firstname.lastname@example.org) teaches mathematics at Iowa State University.