# Zombies and Calculus

A calculus course is mandatory in many curriculums. The mathematics may not always be the most favourite material among the students, especially when their eventual ambition is not really mathematical. Many efforts have been undertaken by authors of popular math books to make the mathematics more attractive by applying them in all kinds of everyday situations as in Oscar Fernandez's Everyday Calculus. And when even this everyday situations are considered dull, they place the problems in a context that will hopefully be attractive to the young readers. That could be *labors of Hercules* as in Michael Huber's Mythematics, or *The Simpsons* in Simon Singh's *The Simpsons and Their Mathematical Secrets*, which also show up along with the *angry birds* in Tim Chartier's Math Bytes, or *science fiction* and *Harry Potter* in Charles Adler's Wizards, Aliens, and Starships, and even a full arithmetic course Egyptian style in David Reimer's Count Like an Egyptian, a detective story as in Arturo Sangalli's*Pythagoras**' revenge* or *The parrot's theorem* by Denis Guedj, etc. There is a very long list of them. Colin Adams is the humor columnist of *The Mathematical Intelligencer*. Some of his stories have been wrapped up in his *Riot at the Calc Exam*, and he has written other popularizing math books before. In this new book, he has cooked up the everyday math problems and the corresponding calculus course in the context of a zombie thriller.

When zombies start eating humans, infecting them to become zombies too, a pandemy has started. The story is about a math professor who tries to escape together with other survivors and save his family when the virus breaks loose. In the group of survivors is also a biology professor who explains for example how the zombie virus can spread like a kind of rabies. When it gets colder during the night, the zombies hibernate, which gives humans a chance to move around. It also shows that the only way to survive is to travel to Canada or Alaska and live there in trees since zombies are also unable to climb the ladders. Add a pinch of romance to all this terror and you have a perfect scenario for a frighteningly bloody apocalyptic horror story. There is obviously abundant violence by zombies, but also clubbing, and fighting by humans defending themselves. Skulls are cracked and brains are spattered around. Since indeed shooting a zombie is only a temporary relieve and so there are many zombies who get their head blown off by baseball bats and other blunt weapons. The "hero" is a math professor Craig Williams (Adams is professor of mathematics at Williams College, Williamstown, MA). Williams not only exercises brute force, but also uses his math skills to model the situation and to outwit the undead.

So this is where the calculus comes in. Craig Williams is teaching about the derivative when a zombiefied student arrives late and starts chewing a fellow student's neck. Just as zombies are not very commonly met in real life, it is neither very credible, that after a couple of bloody incidents and the general alarm, some people remain calmly discussing the exponential growth in the number of zombies, a function that solves the equation *Z' = rZ*. This model is later modified into a logistic one solving *Z' = k Z(P(0)-Z)*, as the the number of zombies increases together with the decrease in humans, and much later, near the end of the book, a predator-prey model is elaborated as the solution of a system of two differential equations. But several other problems are discussed as well. When a flail-like weapon is produced by putting a hard heavy object in a stocking, the model is first explained and the force that is inflicted on an aggressive zombie's head is meticulously computed. The cooling of a zombies body is modeled as well and the time it takes before it will hibernate is estimated. Plots and formulas are written on the blackboard to solve the pursuit problem with the intention of trapping the zombies in a circular motion by encircling them at a larger speed, etc. Thus, although this is an exiting story mostly told in the form of dialogs, there are a lot of plots and formulas in these conversations, which is very strange if you are used to the common way mathematics is presented in written format. To keep the story going and not to overdo the mathematical technicalities, part of these conversations are shifted to an appendix. That is, the reader can choose to take a shortcut and read on skipping the appendix, or the particular appendix can be interlaced, which seamlessly continues the conversation, and at the end it fits perfectly with the continuation of the story. There is no discontinuity in the conversation whether or not the appendix is included. Even, a brief review of calculus (derivatives and integrals) is brought as an extra appendix but it is again told by Craig's son who explains to his younger sister what this mathematics is that their father is always talking about.

The examples I gave in the beginning of this review show that mathematics can be combined with all kinds of realistic or fictitious situations. However it is usually the author as an outsider who discusses the mathematical problems, their modeling and their solution. In this book, unlike any other, it is not the author, but it are the characters of the story who are discussing the models and their mathematical solutions. I have never met a novel in which the hero is actually teaching calculus to the ones he just rescued in between blowing out the little bit of brains from zombie heads, and smashing cars with a snow plough. Quite a reading experience. I only hope that the youngsters for which this book is intended, associate the mathematics with the hero and do not project the horror of the zombie story onto the mathematics needed to survive the Z virus.

**Submitted by Adhemar Bultheel |

**5 / Oct / 2014