Mathematical Models for Society and Biology, 2nd Ed.
Edward Beltrami, Academic Press, 2013. ISBN: 978-0-12-404624-5, xiii+266 pages, US$49.98
This 12-chapter text has the goal of showing how mathematics can illuminate fascinating problems drawn from society and biology. Each chapter takes a particular mathematical topic and applies it to one or more problems in society or biology. The text is written at the approximate level of a person who has completed sophomore mathematics and is familiar with items such as false positives and false negatives, probability, differential equations, etc. The text is not designed to be a classroom textbook but instead is recommended by this reviewer as a supplement to lectures in biology or applied mathematics or simply as an enjoyable read over a period of several afternoons at your leisure. For many readers, the mathematics in the chapters should be a review; however, a few chapters may cover topics that are not covered in undergraduate courses. Therefore, if needed, the appendices cover the normal density, Poisson events, nonlinear differential equations and oscillations, and conditional probability, and may be reviewed to aid understanding of a particular chapter topic.
Chapter 1 is titled “Crabs and Criminals.” The author discusses how hermit crabs occasionally upgrade the shells in which they live; this is compared to how people change positions in a corporation upon retirement of a higher officer, as well as to the real estate market for houses. This social mobility, especially with the crabs, leads naturally to a discussion of state transitions and Markov chains. From here, it is a brief step to a discussion of criminal behavior, the possible outcome states as a result of criminal behavior, and thus a discussion of recidivism.
Chapter 2, “It Isn’t Fair,” begins with an interesting discussion of the mechanics of scheduling trash pickup in New York City in a manner that is fair and equitable to the employees doing the job and optimal with respect to trash pickup scheduling based on the need for pickup. This then segues into a discussion of inheritance mathematics as mentioned in the Talmud and also the losses that occurred as a result of the infamous swindler Bernard Madoff.
In Chapter 3, “While the City Burns,” the Poisson distribution is used to analyze such items as firehouse response times and locations under the constraint of a city grid system. The remaining chapters cover various topics including street cleaning, colorectal screening, murderers, near coincidences, boom and bust, viral outbreaks, and more. Each chapter includes a nice mixture of mathematics and mathematical applications that explain details in relation to the events in the chapters. The writer did, however, miss one potential pun in the chapter on colorectal screening, to wit: “The colonoscopy example of Section 5.3 has an added twist in terms ofprior and posterior probabilities.”
This book is highly recommended.