Mathematical modeling can be described as the process of converting a qualitative or quantitative description of some phenomenon into the more formal language of mathematics in such a way that the mathematics can then be used to provide greater insight into the nature of that phenomenon. Mathematical modeling has proven essential in progressing our understanding of the world around us. As a result, there are a large variety of books and courses that expound one or more of the numerous aspects of mathematical modeling. *The Calculus of Happiness* is essentially a book on mathematical modeling. It is different both in scope and in content, however, from many of the other currently available books on mathematical modeling. Before describing how Fernandez’s book is different, we take a short digression to look at a simple example of mathematical modeling.

Suppose that for a simple projectile we record its position in space at a number of distinct time points. Listing the time and position values in a table, or plotting the position values versus the time points, provides a quantitative description of the phenomenon of the motion of the projectile. Perhaps the simplest approach to the mathematical modeling of this phenomenon is to construct a mathematical function \(y = f(t)\), giving the position \(y\) of the projectile as it depends on the time \(t\), that reasonably closely reproduces the observed position values at the observed time points. A more sophisticated approach to the mathematical modeling of this projectile problem would be to apply Newton’s laws of motion to derive a differential equation whose solution would determine the projectile’s position as a function of time. Either way, mathematical functions have an important role to play in mathematical modeling.

*The Calculus of Happiness* fully embraces this approach. It is all about using mathematical functions to mathematically model phenomena that many of us experience on a day to day basis, and which have major impact on our health, finances, and personal lives. For example, the book gives the function \(\text{MHR} = 192 - 0.007 a^2\), which describes one’s maximum heart rate \(\text{MHR}\) as a function of one’s age \(a\). This function can be used to help you determine an appropriate exercise routine to lead a healthy life. Other examples of functions relevant to one’s health, wealth and happiness to be found in *The Calculus of Happiness* are a function for monthly loan payments that can be used to get out of debt, and functions that help one to understand decisions that lead to a successful relationship.

It is the fact that the book focuses on modeling topics that are of personal interest that makes it distinct from a lot of other books on mathematical modeling. In addition, the book is short, accessible and engaging. Thus, it is appropriate for a wide audience of readers. Since Fernandez takes great care in explaining mathematical concepts and notation, if you have the background obtained after a year of high school algebra, then *The Calculus of Happiness* should be highly readable. In fact, it could serve as a great supplement to material for courses on college algebra or precalculus. Readers are sure to get a sense of how content from algebra and precalculus can help inform us about important decisions that are almost universally relevant.

Jason M. Graham is an assistant professor in the department of mathematics at the University of Scranton, Scranton, Pennsylvania. His current professional interests are in teaching applied mathematics and mathematical biology, and collaborating with biologists specializing in the collective behavior of groups of organisms.