Book Reviews

If you are teaching a course (or otherwise looking for a text) in the techniques and applications of mathematical modeling, or mathematical approaches that analyze or solve those equations, you may find one of the reviews in this issue's collection interesting. Our featured review was written by Shawn Ryan, on the book Mathematical Modeling in Biology: A Research Methods Approach, by Shandelle M. Henson and James L. Hayward. Ryan's favorite part of the book is the authors' use of the technique of “proposing logical alternative models and then using mathematical or statistical approaches to rule them out.” Even though he found the book to contain less mathematical rigor and theory development compared to a couple of existing math biology texts, Ryan thought that it has accomplished its goal of encouraging “students to think deeply about how mathematics can provide a useful tool in science.” Flour beetles make an appearance in Chapter 6. Our next book, reviewed by Sascha Desmettre, is A First Course in Options Pricing Theory, written by Simone Cologero. A particularly notable recent application of stochastic processes is arguably in the mathematical theory of finance. This book focuses on the part of stochastic finance pertaining to option pricing theory, omitting (important but less out-of-scope) topics as futures and term-structure. Desmettre listed a number of strengths of the book, including “clear motivation from the real world with the help of real data,” and recommended the book to those wishing to take the first steps in the field of option pricing. The next book is about mathematical tools that can be used to model biological systems, the stock market, and various other applications. Sarah Iams and Margo Levine reviewed Differential Equations: A Toolbox for Modelling the World, by Kurt Bryan. This book is published by SIMIODE (Systemic Initiative for Modeling Investigations & Opportunities with Differential Equations) and describes itself as modeling-first. Iams and Levine praised its framing of the content in terms of modeling and data as “refreshing.” They also considered this book perhaps “the best resource [they] have encountered” for use in differential equations courses. That said, there are apparently formatting and language issues that make the book less accessible than a typical textbook, according to Iams and Levine. I will let you read the review to get the complete picture. Next in the collection is Bayesian Models of Perception and Action: An Introduction, by Wei Ji Ma, Konrad Paul Kording, and Daniel Goldreich. The review was written by one of our associate editors, Kres̆imir Josić. As noted by Josić, this is not a book about Bayesian statistics, which the authors only briefly discuss in the context of analyzing experimental data. Rather, the authors focus on perceptual inference and describe “how to develop models of the computations that our brain performs when making decisions based on prior information and sensory evidence.” Philipp Öffner reviewed Property-Preserving Numerical Schemes for Conservation Laws, authored by Dmitri Kuzmin and Hennes Hajduk, who based the book on lecture notes written for an advanced graduate-level course. Our reviewers typically say positive things about the books, but Öffner seemed to really like this book, saying that it is “a comprehensive and lucid summary of current research in limiters,” the “writing is superb.” And he commends the authors for “creating what could be considered a contemporary classic on limiting strategies.” We wrap up with a review by Jean Vélin, on Linear and Convex Optimization: A Mathematical Approach, by Michael H. Veatch. This book contains, as its title suggests, a mathematical approach to linear and nonlinear optimization problems. Vélin gave a summary of each of the fifteen chapters, and concluded that the book is well written and easy to read, with examples that help deepen the reader's understanding of the material. I hope you find something that interests you.