Follow the Authors
The Heart of Mathematics: An invitation to effective thinking 2nd Edition
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.
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)
- Publisher : Key College Publishing; 2nd edition (January 1, 2005)
- Language : English
- Hardcover : 760 pages
- ISBN-10 : 1931914419
- ISBN-13 : 978-1931914413
- Item Weight : 3.04 pounds
- Dimensions : 7.5 x 1.5 x 9.25 inches
- Best Sellers Rank: #428,990 in Books (See Top 100 in Books)
- Customer Reviews:
About the authors
Top reviews from the United States
There was a problem filtering reviews right now. Please try again later.
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.
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.
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.