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The Heart of Mathematics: An invitation to effective thinking (Textbooks in Mathematical Sciences) Hardcover – October 29, 1999

ISBN-13: 978-1559534079 ISBN-10: 1559534079 Edition: 1st

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Hardcover, October 29, 1999
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Product Details

  • Series: Textbooks in Mathematical Sciences
  • Hardcover: 646 pages
  • Publisher: Key College; 1 edition (October 29, 1999)
  • Language: English
  • ISBN-10: 1559534079
  • ISBN-13: 978-1559534079
  • Product Dimensions: 9.3 x 7.5 x 1.1 inches
  • Shipping Weight: 3.3 pounds
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (23 customer reviews)
  • Amazon Best Sellers Rank: #850,247 in Books (See Top 100 in Books)

Editorial Reviews


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)

--This text refers to an out of print or unavailable edition of this title.

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Customer Reviews

This book shows you how to have fun with math.
Ted R. Shoemaker
This is an excellent textbook in that its primary emphasis is on some of the great ideas in mathematics and effective thinking.
Mead C. Whorton Jr.
(Well, I realized this before start reading this book.
Rawitat Pulam

Most Helpful Customer Reviews

110 of 113 people found the following review helpful By -_Tim_- on July 21, 2002
Format: Hardcover Verified Purchase
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.
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70 of 71 people found the following review helpful By Ted R. Shoemaker on September 23, 2004
Format: Hardcover Verified Purchase
_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 different 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 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 any 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.
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102 of 107 people found the following review helpful By Rawitat Pulam on May 28, 2001
Format: 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.
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46 of 48 people found the following review helpful By Julie Brennan on July 29, 2004
Format: Hardcover Verified Purchase
The disturbing reviews indeed completely miss the point. The goal of this book is not to turn you into a mathematician. It is to help you appreciate what mathematics is.

I am planning on using this text for an adult self ed study group this fall. The goal is not to try to prove Cantor's method. You explore it and gain some understanding, but it isn't a mastery course that you come out of passing a test for, unless you are sitting in a classroom designed with that in mind, and the larger audience for this book is not in that narrow context. If you come out of it learning how to think mathematically, learning different ways to approach solving problems, learning that there is fun, beauty, art, order and sense to math, if you begin to *see* math in the world you live in, in nature, in ways you never noticed before - that is the goal. It is also threaded with history and the human drama that created math.

Both negative reviews were so poorly written and clearly missed the point that I dismissed them, but others I've recommended the book to have been confused, so I felt the need to respond.

I have also watched the video/DVD series these two authors put out through the Teaching Company, the Joy of Thinking, and I love what they are doing. Is every lecture perfect and resonating with everybody? No, but most resonate with most people. It certainly opened my eyes to things I never understood. Much of this book covers the same type of material.

Some people will find it more interesting than others, that is the nature of personal preference certainly. But the negative feedback indicates the book is flawed based on specific use in college classroom context, and it appears the reviewers did not understand the purpose of the book.

The four vs. five stars reflects the fact this is a first ed and could be just little more user friendly for lay people vs. college course users. I look forward to seeing the 2nd edition.
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