You are here

How to Derive a Formula

Alexei A Kornyshev and Dominic O'Lee
World Scientific Publishing
Publication Date: 
Number of Pages: 
[Reviewed by
Andrzej Sokolowski
, on
The book How to Derive a Formula, Volume 1: Basic Analytical Skills and Methods for Physical Scientists presents mathematical theorems as essential tools to understand the laws of nature. It is the first volume of a series about intertwining abstract mathematical apparatus with scientific inquiry at an undergraduate level. The authors, theoretical physicists, guide the readers on uncovering scientific meanings stored in algebraic entanglements. The volume, consisting of two parts, introduces mathematical concepts initiating the journey from analyzing polynomial functions and concluding with Euler gamma and complex logarithmic functions. Such sequencing allows the reader to absorb presented knowledge in a very accessible manner. The authors also considered consistency in the chapter's design by first introducing mathematical laws or concepts followed by corresponding scientific applications. Such integration is unique, and it certainly presents the book as an outstanding and valuable resource for scientists seeking to master their skills in mathematizing natural phenomena. In addition, the book offers mathematical exercises accompanied by narratively presented detailed solutions and critical points that summarize each chapter's significant pieces of information. The book is highly recommended for undergraduate STEM students.
There is no doubt that the side by side presentation of algebraic structures and their applications in science in conducted a very thoughtful way yet, some minor suggestions emerged that could perhaps strengthen the value of the volume:
  • (a) The book is titled How to Derive a Formula, and as such, it suggests that the reader will learn how to construct scientific formulas by, for instance, applying hypothetical deductive mathematical thought processes or by possessing empirical pieces of evidence in the form of data. The reader will realize that the book offers analyses of already assembled or existing formulas whose structures parallel to reviewed mathematical law on-site. Such presentation is productive, however including examples that guide the readers through nuances of enacting new or existing formulas from scratch would gravitate more toward the book’s objective.
  • (b) The book chapters introduce mathematical laws and then immerse the readers into their applications; however, discussing the formulation of new mathematical laws based on a need to describe a given phenomenon quantitatively would perhaps present the math-science interface more comprehensively. The history of scientific discovery provides many such examples.
  • (c) It seems that the idea of function differentiability and continuity, albeit very significant in calculus and their interpretations, remain silent in the book. While the concept of limit is discussed and applied, extending its applicability to areas not yet explored could perhaps serve as an inspiration for the readers to undertake their investigations and research. 

The book series is very desirable and will surely be appreciated by the scientific community and STEM students.  It is certain that after immersing in the book's first volume, the reader will look forward to its subsequent volumes.

Andrzej Sokolowski, Ph.D., authored several books and research papers on developing students' mathematical reasoning skills to improve physics understanding. He is also a mathematics and physics professor at Lone Star College, TX, USA.