The Heart of Mathematics: An invitation to effective thinking (Hardcover)

by Edward B. Burger (Author), Michael Starbird (Author) "We wrote this book to be read..." (more)
Key Phrases: sexiest rectangle, interest per interval, real number paired, Golden Rectangle, Julia Set, Developing Ideas (more...)

Editorial Reviews

Review

From the reviews of the second edition:

"In this book, the reader will see that mathematics is a network of intriguing ideas … . It is a really nice book. … This attractive book contains a lot of well-known and interesting problems … . It is really true that the ideas presented in this book are some of the most fascinating and beautiful ones around. … The reader will have something to explore, to learn, to think, to enjoy, and to add new aspects to his view of everything." (Valentina Dagienë, Zentralblatt MATH, Vol. 1065, 2005)

Product Description

The Heart of Mathematics addresses the big ideas of mathematics (many of which are cutting edge research topics) in a non-computational style intended to be both read and enjoyed by students and instructors, as well as by motivated general readers. It features an engaging, lively, humorous style full of surprises, games, mind-benders, and all without either sacrificing good mathematical thought or relying on mathematical computation or symbols.

The authors are award-winning authors, holding awards such as: Distinguished Teaching Award (Burger, from the Mathematical Association of America); Chauvenet Prize (the best expository mathematics writer in the world, Burger, from the MAA) and many others.

Product Details

• Hardcover: 760 pages
• Publisher: Key College Publishing; 2nd edition (2005)
• Language: English
• ISBN-10: 1931914419
• ISBN-13: 978-1931914413
• Product Dimensions: 9.4 x 7.6 x 1.4 inches
• Shipping Weight: 3.2 pounds
• Average Customer Review: 4.0 out of 5 stars See all reviews (18 customer reviews)
• Amazon.com Sales Rank: #41,469 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

87 of 87 people found the following review helpful:

5.0 out of 5 stars An Unusual Book of Wide Interest, July 21, 2002

By	-_Tim_- (The Western Hemisphere) - See all my reviews

This review is from: The Heart of Mathematics: An Invitation to Effective Thinking (Hardcover)

The Heart of Mathematics is an unconventional math survey aimed primarily at social science and humanities students. While students in "soft" majors are the primary intended audience, math majors and others who have already progressed beyond the introductory level are likely to find this book of great interest as well.

The book gives readers a good feel for the variety of problems that mathematicians tackle. In fact, one of the book's great strengths is the range of topics it covers, from number theory and games, to topology, to chaos and fractals. It does this with little use of conventional mathematical notation or jargon, and the level of presentation is so elementary that the book can be "read" just as any non-technical book can be read. At the same time, the authors go to great lengths to encourage reader participation. Many hands-on demonstrations and experiments are provided, and the end-of-chapter exercises ask readers to discuss the material with others and write about their experiences.

The topics presented are fascinating. I read this book on my vacation and found several passages to read to my wife and daughter almost every day. (This provided a lot of amusement for everyone when my 12-year-old daughter would solve problems in a few seconds that I had been pondering without much success.)

The book's subtitle is "An Invitation to Effective Thinking," and the authors present problem-solving strategies that can be applied to problems within and outside the field of mathematics. While readers will no doubt be familiar with many of them already, it is difficult for me to imagine anyone who would not benefit from at least some of the strategies presented.

The authors' writing is very informal with a lot of corny humor - possibly too much for a lot of people - but at the same time you do get a sense of the authors as good guys who know some important things and want to share the wealth.

In summary, this is a most unusual and stimulating book. Highly recommended.

84 of 88 people found the following review helpful:

5.0 out of 5 stars Without Any Doubt, One of the Best Math Books I've Ever Read, May 28, 2001

By	Rawitat Pulam (University of Tsukuba, Japan) - See all my reviews

This review is from: The Heart of Mathematics: An Invitation to Effective Thinking (Hardcover)

After browsing this book for a while in a book store somewhere near Tokyo station, I decided to buy it immediately, even it's price will about almost doubled the price I would get if I buy from internet. (I bought it for about $115).

But, it turned out to be one of the best decision I'd ever made in my life as a book-worm. (Well, I do love reading :-)

This book will change the way you look at the world, the way you look at yourself, the way you think, and so on. It is cleary one of the best books on Math I've ever read so far (I do love Math as well :)

Instead of throwing you the formulas, the authors lead you to the Mathematical Thinking. How to think this, how to solve that. What Mathematic really is and what are its applications, and why it had been used that way. All explained through simple but fun-to-think example/problems. Using non-technical language, and almost no formula(!). In fact, almost everyone with little math background can enjoy this book. It doesn't seem to require anything more than middle school math. So, you can really see the pictures, the very big pictures, clearly in your mind, which is really importand.

With the wide range of content, from Prime Numbers to Chaos, Fractals, Infinity, 4th Dimension, and more. The concept of each is well-explained, in a manner I mentioned earlier. This book will definitely help you to understand the making of "modern" science better.

One more thing is: Mathematic is not something that far from our everyday life as some might think. It's the alternative way to view our everyday life. The way with reason, pattern, logic, relation betweening things, and more. (Well, I realized this before start reading this book. But for those who haven't realize, this book will open the door for you).

Math can also be fun. (In fact, it IS .. That's why I love it :-)

And this book tell you why, and how to find and feel those "fun" and enjoy Math. Without any complicated computation, and limited only by your imagination.

49 of 50 people found the following review helpful:

5.0 out of 5 stars Math Appreciation, not computation or rigor, September 23, 2004

By	Ted R. Shoemaker (Madison, Wisconsin, USA) - See all my reviews (REAL NAME)

This review is from: The Heart of Mathematics: An Invitation to Effective Thinking (Hardcover)

_The_Heart_Of_Mathematics_ was never intended as a traditional textbook to teach you how to calculate. If that is what you are looking for, you need a diferent book. Its value -- and this is the best book of its kind that I have found -- is in helping the reader gain an appreciation for mathematics. Its title could well have been _Math_Appreciation_ . It was most likely intended as a way of satisfying the "math requirement" for non-math majors who feel allergic to math.

I have read comments from several people debating the merits of this book. Perhaps it would help to use inject an analogy into the conversation. Suppose you wanted to learn (or teach) music. One teacher chooses to teach her students how to play the piano;
another has her students listen to CDs of great performances; another teaches his students how to read music; and another teaches the biographies of Beethoven and Mozart. Which of these teachers is right? Which kind of music do you want to learn?

The question itself is mistaken, if you think that it has exactly one correct answer. The best answer is: ALL OF THEM. The problem here is not in what one of these approaches will teach, but in what it omits.

Now, translating back from the metaphor: I want my children to learn how to compute AND how to love math. Which is right? Both of them.

This book shows you how to have fun with math. If you or your students end up learning something, and wanting to learn more -- that's the idea.