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Concepts of Modern Mathematics (Dover Books on Mathematics) Paperback – February 1, 1995

ISBN-13: 978-0486284248 ISBN-10: 0486284247 Edition: 1st

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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 352 pages
  • Publisher: Dover Publications; 1 edition (February 1, 1995)
  • Language: English
  • ISBN-10: 0486284247
  • ISBN-13: 978-0486284248
  • Product Dimensions: 0.8 x 5 x 8.8 inches
  • Shipping Weight: 13.6 ounces (View shipping rates and policies)
  • Average Customer Review: 4.6 out of 5 stars  See all reviews (39 customer reviews)
  • Amazon Best Sellers Rank: #30,139 in Books (See Top 100 in Books)

Customer Reviews

I strongly recommend this book to anyone with a serious interest in mathematics.
Michael Vanier
I was not disappointed, but it was not until I settled down and read the whole book that I really got the point.
Randall Raus
I would recommend this book for anyone who's looking to get a better view of world of math.
N. Pinkston

Most Helpful Customer Reviews

157 of 158 people found the following review helpful By Michael Vanier on October 17, 2000
Format: Paperback
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!
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120 of 121 people found the following review helpful By Randall Raus on March 8, 2001
Format: Paperback
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.
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152 of 159 people found the following review helpful By D. C. Carrad on December 25, 1998
Format: Paperback Verified Purchase
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.
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61 of 62 people found the following review helpful By Ken Braithwaite on June 1, 2001
Format: Paperback
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.
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38 of 38 people found the following review helpful By Dylan on August 19, 2008
Format: Paperback
This book is by far the best book on mathematics I have ever read. It teaches the concepts in an intuitive, exciting way, and yet it is able to remain fun and engaging throughout. Technical material is tackled, in depth, without there seeming to be any work done. There are no exercises to be done, you simply follow Stewart along for a tour through modern mathematics. Ian Stewart's writing is flawless and almost turns this book into a thriller. I read this book in one night- I could not put it down! I stayed up until 4 in the morning reading and rereading passages; it is truly a masterpiece. The chapters are as follows:

Chapter 1- Mathematics in General: Here Stewart describes certain aspects of mathematics, and discusses their purpose and implications. He talks about abstractness and generality, intuition vs. formalism, and pure vs. applied mathematics. He tells the reader the importance of understanding WHY a theorem is true, not simply that it is. He ends with a collection of anecdotes.

Chapter 2- Motion without Motion: This is an example of thinking a bit outside the box. The chapter is devoted to overturning Euclid's proof that the base angles are congruent, and making a new one based on rigid motions. It doesn't sound too engaging, but, somehow, Stewart manages to make it quite exciting!

Chapter 3- Short Cuts in the Higher Arithmetic: A basic introduction to number theory- prime numbers, moduli, congruences, etc. The informal tone makes this the easiest and most understandable read on number theory I've yet encountered.

Chapter 4- The Language of Sets: Throughout the rest of the book, Stewart uses the language of set theory, so he introduces that here in an easy to understand way (using some imagery like bags of items, etc).
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57 of 66 people found the following review helpful By A Customer on April 2, 1999
Format: Paperback
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.
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Concepts of Modern Mathematics (Dover Books on Mathematics)
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