Concepts of Modern Mathematics

by Ian Stewart

Book Overview

Some years ago, "new math" took the country's classrooms by storm. Based on the abstract, general style of mathematical exposition favored by research mathematicians, its goal was to teach students not just to manipulate numbers and formulas, but to grasp the underlying mathematical concepts. The result, at least at first, was a great deal of confusion among teachers, students, and parents. Since then, the negative aspects of "new math" have been...

• Format: Paperback
• Language: English
• ISBN: 0486284247
• ISBN13: 9780486284248
• Release Date: February 1995
• Publisher: Dover Publications
• Length: 368 Pages
• Weight: 0.89 lbs.
• Dimensions: 0.7" x 5.2" x 8.4"

Customer Reviews

for serious non-mathematicians

This is a serious book. Stewart explains clearly and concisely for a non-mathematician some of the central ideas of mathematics. Perfect for those willing to put in some thought. I'd also recommend it to anyone in first year pure math. And especially to anyone who teaches math.

A classic - the first version of this book appeared in 1975.

This charming book was written by a man who knows how to teach, and how to have fun. For example, as each successive topic is discussed, Mr. Stewart is careful to furnish the reader with an intuitive grasp of its main points. Only then, does he delve into the topic's details. However, what really makes this book readable is the author's wit, and sense of delight, as he illuminates--one-by-one--the abstract concepts of modern mathematics. Amazingly, this book can be read by almost anyone, and they will come away with an understanding of the why, and the wherefore, of modern math.In theory at least, having a degree in pure math meant that I had insights that most engineers don't have. In reality, it meant I was more aware of what I didn't understand. When I got this book, I went straight to the topics I'd never gotten the point of: set theory, topology, and hyperspace. I was not disappointed, but it was not until I settled down and read the whole book that I really got the point. Modern mathematics (modern meaning the late 1800s on) provides a framework for all math. That is why it is--of necessity--more abstract, generalized, and rigorous. Interestingly, the figures in this book are hand drawn. Perhaps its because this book has a way of transporting the reader to a university classroom - somewhere. It wouldn't have seemed right if the figures were anything but hand drawn.

outstanding guide to higher math for the layman

This book is very much in the same spirit as more recent books such as Keith Devlin's "Mathematics, the New Golden Age" (which I also recommend). It explains various subjects in pure mathematics in order to make them accessible and interesting to non-mathematicians. A great variety of subjects are covered, including abstract algebra, group theory, number theory, and especially topology, to which the author devotes several chapters. The links between different branches of mathematics (e.g. topology and group theory) are given special attention, and one of the central themes of the book is the fundamental unity of mathematics. I strongly recommend this book to anyone with a serious interest in mathematics. Plus, the price is definitely right!

One of the most lucid and enjoyable math books available

If you want great mathematical puzzles, you buy a Terry Stickels puzzle book. If you want to read about the universe from the world's best amateur mathematician and physicist, you read Martin Gardner. If you want a professional's point of view of all the above, you read anything by Ian Stewart. This is simply a must read for all clear thinking people.

Absolutely brilliant!

Deserves 10 stars. Here is an author who understands so many advanced concepts and who can write smoothly, clearly and convincingly, bearing the reader along with his keen and interesting mind. Convincingly demonstrates the interrelationships between different areas of modern mathematics. Great mathematics for the layman without being in the slightest bit condescending. I have had an amateur's interest in mathematics since high school but was never able to follow it up professionally. This book is the best I have read in the 30 years I have had this interest. A delight to read, educational and informative.