# Understand Mathematics, Understand Computing

###### Arnold L. Rosenberg and Denis Trystram
Publisher:
Springer
Publication Date:
2020
Number of Pages:
577
Format:
Hardcover
Price:
99.99
ISBN:
978-3-030-58375-0
Category:
Textbook
[Reviewed by
Tom French
, on
10/3/2021
]
The knowledge and tools of the mid-20th century allowed for the development of the computing industries.  Early hardware and software designers developed tools and technologies to greatly enhance the speed and capabilities of computers. Our development tools for new systems have become increasingly sophisticated and complex in the past 50 years.  And, the foundations of all these advancements are discrete mathematics.

For many years, we have used these tools and technologies to assemble new and more complex systems, which, in many cases, we did not fully comprehend nor understand the mathematics and logic driving the system.  This obviously has led to many problems which affects all our lives. The authors Rosenberg and Trystram have put together a textbook to help system developers strive for understanding every system’s structure and function.  The purpose of this textbook is to promote the readers’ understanding of mathematics which will enable them to do mathematics.  The authors have done an admirable job in meeting this objective.

This book is suitable for a textbook or a supplementary textbook for a university course such as “Introduction to Discrete Mathematics” or as a text in wide variety of introductory mathematics courses.  The authors assembled two tables that describe which chapters and sections are suitable for eleven different courses in which this text might be used.  These tables are included in the book.

The vast array of topics covered in this book are too numerous to mention in a short review.  However, I will name a few to give the reader a taste of what one can expect in this text. One topic is mathematical induction. The authors not only demonstrate how to do proofs by using induction but also demonstrate how to use induction to go from simple to complex tasks. Another topic is the development of our number system which takes the reader from whole numbers through complex numbers.  The study of sets leads the reader into Boolean algebra and on to logic and truth tables culminating in Cook’s NP Theorem.  There are well developed discussions of graph theory, probability, and statistics using combinatorics.  The authors included a well-written discussion of the Fibonacci numbers which culminates in a discussion of how the multiplication of rabbits is related to Pascal’s Triangle and binomial coefficients.

The text is written in an easy to read format which generously incorporates narratives from the history of mathematics as well as rigorous proofs of the concepts presented. The appendices and references to other texts provide the reader with numerous sources of supplementary information for those wishing to delve into a subject at a deeper level than presented by the authors.

The chapters are organized and clearly labeled to express which sections are appropriate for a beginning learner, an intermediate learner, or the specialist.  Likewise, the exercises at the end of each chapter are organized according to difficulty.  The first few problems for each chapter can readily be resolved by following the text.  The next set of intermediate problems are supplied with hints for their resolution.  The more difficult problems have been resolved and solutions are available in the text.
Tom French has a B.S. and M.S. degree in Mathematics from Minnesota State University, Mankato.  He has 35 years of engineering and business experience with UNIVAC and its successor companies.  He was part of the design team that first implemented medium-scale and large-scale integrated circuits into computers.  Tom was the program manager for several large computer innovations and was one of the leaders who implemented the technology revolution into the banking system in the Russian Federation.  He has lectured on mathematics and computer systems throughout the world and has taught mathematics at a number of US colleges and universities.