I never thought I would read, nevertheless enjoy, a book on math. This book is unquestionably one of the best works I have ever read on the sciences. Devlin writes in an uncannily concise and proficient style that actually makes the topic of math interesting and understandable to a lay person. Devlin intricately weaves history, mathematical concepts, and complex theories into a very readable text. (I did not think it could be done.) 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, in my opinion, 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 my favorite chapter. For once, someone has the insight to simply state that gambling and insurance are derived from the same origins. The chapter is an excellent treatment of regressions, means, and other "statistical" math. Chapter 8 reminds me of Michiu Kaku. It takes many of the mathematical theories and information presented and applies it to modern scientific pursuits like gravity, relativity, and space time.
What I liked about this book is that Devlin explained mathematical proofs and methods using plain language, covering topics as diverse as Euclid's geometry, non-Euclidean geometry, manifolds, tessellations, calculus, probability, knot theory, Maxwell's equations, Einstein's theories of relativity and quantum mechanics, though he only touches on these last three at the end of the book.
In particular, I liked his explanation of Bayesian probabilities using 2 real-world examples, his explanation of fields and groups (including Evariste Galois' seminal discovery) and his explanation of the fundamentals of calculus. I never knew that integration actually evolved independently of Newton's and Leibniz's differential calculus, originating with a student of Archimedes, Eudoxus, and the discovery that they were inverse functions of each other was a serendipitous surprise.
Although I'm well read in science and mathematics, this book gave expositions that had previously eluded me, and it will open the eyes of people who think mathematics is an elitist sect.
This is a brilliant exposition of some key areas of maths. Devlin writes in a way which is intelligible to readers with little mathematical background, and succeeds in conveying some complex maths in an easily-understood fashion. The historical background is well set out. Do not worry if you were bored or confused by maths at school: this book is truly fascinating. If you want to gain an insight into the way maths works, why maths matters, and the excitement mathematicians can feel, get this book.
I agree with the other reviews, this is an excellent book. Even if you have no understanding of maths you will have a good grasp by the time you get to the end. If you want you can skip the working out details and just read the text, and you will still understand it.
This book gives a fantastic overview of many, admittedly not all, areas of Mathematics - covering many topics in University Level depth. That may put some people off, but the author writes in a way that makes everything interesting and engaging.
A fantastic read for a Mathematics Student in particular as it gives an appreciation of the subject that isn't readily observable in daily life without some prior knowledge.
Keith Devlin has the ability to explain mathmatical concepts. This is the first time have truely understood what calculus, sets & number theorey are all about. Most popular maths books just tantalise with the final conclusion -leaving the reader deeply unsatisfied because they cannot understand how it was reached. Most instructional maths books start very simply then completely lose the student as they shortcut into assumed knowledge and half explanations. Either is probably OK for the mathmatically gifted or knowledgeable. But for most of us it is very frustrating. Prof Devlins book is different. He manages to see things from the students point of view consistantly and communicate that. He is very frank about unexpected findings in Maths (Like the power of integration). The fundamental theorems (Of arithmatic, calculsu and algebra) actually mean smetthing after he has finishce explaining and putting them in context. This book would be aa brilliant primer for an pre university student but can be understood at any age - schoolchild or pensioner (Like me).
this book is a fascinating book and deserves no less than a five star rating, because of the way it is written it tells you the history of mathematics as well as, at the same time the useful formulaes and explains them. This book is not simple, you really have to concentrate to understand most of it but if you think this kind of book is only for people with a massive vocabulary you are right. So keep a dictionary next to you. Overall once you get to understand the book you will enjoy it thoroughly. That is if you want to. gsandhu