In this book, the authors introduce some of the basic tenets of applied mathematics and the role they play in the discipline of machine learning. The text is intended for advanced undergraduates and succeeds in its primary goals of being imminently readable and accessible to students.

It consists of seven chapters, beginning with a treatment of the least squares approach in the context of datasets corresponding to the winning times in men’s and women’s 100-meter sprints during the Summer Olympics, starting with 1896. The authors do an excellent job of motivating many of the fundamental issues associated with linear and nonlinear regression by appealing to these two interesting datasets, setting the right tone for the topics in the remainder of the text, including the reasoning behind why we must consider the maximum likelihood and Bayesian approaches, which are addressed in the second and the third chapters. Bayesian inference, classification, and clustering are the foci of the following three chapters, in which some of the most common algorithms, including the Metropolis-Hastings algorithm, are presented in detail. The final chapter, dedicated to principal component analysis, continues the discussion of unsupervised methods with an eye toward data reduction--arguably one of the most intriguing current areas of research in applied mathematics and computer science, motivated by our desire to devise methods to enable us to project very high-dimensional datasets onto a smaller number of dimensions.

An important element that should contribute to this book’s adoption as a course text is the incorporation of MATLAB, which is present throughout the book. This feature is further enhanced by the availability of datasets for hands-on experimentation by students. On the whole, it is not difficult to imagine this book serving as an important resource for a senior-level elective course in several subdisciplines within mathematics or computer science. It should also serve as a valuable reference for those undergraduate students seeking a thesis topic in the critical discipline of machine learning.