The Language of Mathematics is Devlin’s second iteration of the approach he used in Mathematics: The Science of Patterns. It covers all the same ground (and uses many of the same words) as the latter, but with fewer glossy pictures, sidebars, and references. Devlin has also added chapters on statistics and on mathematical patterns in nature.
Keith Devlin is trying to be the Carl Sagan of mathematics, and he is succeeding. He writes: “Though the structures and patterns of mathematics reflect the structure of, and resonate in, the human mind every bit as much as do the structures and patterns of music, human beings have developed no mathematical equivalent of a pair of ears. Mathematics can be seen only with the eyes of the mind”. All of his books are attempts to get around this problem, to “try to communicate to others some sense of what it is we experience–some sense of the simplicity, the precision, the purity, and the elegance that give the patterns of mathematics their aesthetic value”.
The text is divided into eight sections ranging from numbers to astrophysics. While the book does build on the information offered in each chapter, it is not necessary to read the book in a linear fashion. Devlin makes it very easy to choose chapters of interest.
The first chapter deals with numbers. Ironically, we assume a lot about numbers when considering math. Devlin does an excellent job of defining what numbers are apart from the symbols we ascribe to them.
The second chapter provides a concise explanation of mathematical proofs, reason and logic. Using his unique style, Devlin is able to cover this chapter with examples from classic math (algebra) to modern linguistic analysis. The latter is an excellent example of how Devlin applies math theories presented to natural real world examples.
Chapter 3 deals with the calculus. If you have ever asked: what is calculus used for, there is finally a concise, understandable presentation available in this chapter.
Chapter 4 refers to geometries. Devlin traces the evolution of geometries and provides a good introduction to dimensions beyond the third dimension. (These ideas are continued in Chapters 6 and 8.)
Chapter 5 is rather odd but seems to build on analyzing patterns in geometries. It treats topics like packing objects and snowflake patterns.
Chapter 6 is the most difficult chapter, but also the most rewarding. This chapter alone is well worth the book. If you ever wanted to understand donuts, coffee cups, manifolds, strings, and knots, this is an excellent chapter.
Chapter 7 is an excellent treatment of regressions, means, and other “statistical” math.
Chapter 8 takes many of the mathematical theories and information presented and applies it to modern scientific pursuits like gravity, relativity, and space time.
Related Books:
- The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics : Clifford A. Pickover
- Single Variable Calculus: Early Transcendentals – By James Stewart
- Elementary and Middle School Mathmatics: Teaching Developmentally (Paperback)- By John A. Van De Walle
- Linear Algebra and Its Applications, 3rd Updated Edition (Book & CD-ROM) : By David C. Lay
- Algebra and Trigonometry : By Michael Sullivan
- Math Doesn’t Suck: How to Survive Middle School Math Without Losing Your Mind or Breaking a Nail – By Danica McKellar
- Policy Paradox: The Art of Political Decision Making, Revised Edition – Deborah Stone
- Computer Networking: A Top-Down Approach (5th Edition) : James F. Kurose, Keith W. Ross
