The Mathematics that Power Our World: How is It Made?

The authors state in the preface that The Mathematics That Power Our World: How Is It Made? is an attempt at a mathematical version of the popular show How it’s Made intended to bridge the gap between two common (as defined by the authors) groups of mathematics students: the group that studies pure mathematics to further academic pursuits, and the group that views math simply as a tool or a means to an end. This reader is unconvinced as to how well the text does at bridging this supposed academic divide. Realistically, The Mathematics That Power Our World: How Is It Made? provides a simple but effective set of four case studies of widely used (and perhaps under-appreciated) computer-science based applications of mathematics. These case studies include an inspection of the mathematics behind basic calculators, the basics of data compression and the JPEG standard, the Global Positioning System (GPS), and the developing field of image processing and facial recognition applications.

The introductory chapters are readily approachable for students at the upper levels of high-school and beyond. Each of the case studies provides an introductory overview of the functionality and structure of the technologies explored before diving into a thorough, but approachable, exploration of the supporting mathematics. The cases unfold successively in a practical manner, starting with a foundational exploration of the development of binary and successively building through the computer science applications. As the book progresses into the algorithms utilized in the GPS system and beyond, a more stubborn interest in mathematics is required and the book ascends into a territory beyond its initial approachability.

The Mathematics That Power Our World can be read from cover to cover, although the steep ascension from basic to rather advanced explorations would likely either bore or bewilder the reader, depending upon his or her starting point. It appears the best use of the text to be as a resource for educators interested in providing individual case studies of applications of mathematics to their students while diving beyond the why and thoroughly into the how.

Kevin Tasley is an undergraduate student with an Economics/Finance major and Applied Mathematics minor at Southern New Hampshire University in Manchester, NH.