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The Heart of Mathematics: An invitation to effective thinking 1st Edition

by Edward B. Burger (Author), Michael Starbird (Author)
4.1 4.1 out of 5 stars 56 ratings
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It is a rare mathematics book that can be called lucid, light-hearted, and profound, and yet these are the words that capture the spirit of The Heart of Mathematics. Using careful explanation, intriguing puzzles, and challenges, the authors invite readers to use open-ended thinking in discovering and constructing mathematical ideas. Throughout the book, the authors stress that mathematics is an analytical way of thinking, one that can be brought to bear on problem solving and effective thinking in any field of study.
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  1. ISBN-10
    1559534079
  2. ISBN-13
    978-1559534079
  3. Edition
    1st
  4. Publisher
    Key College
  5. Publication date
    October 29, 1999
  6. Language
    English
  7. Dimensions
    7.76 x 1.18 x 9.49 inches
  8. Print length
    672 pages
  9. See all details
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Product details

  • Publisher ‏ : ‎ Key College; 1st edition (October 29, 1999)
  • Language ‏ : ‎ English
  • Hardcover ‏ : ‎ 672 pages
  • ISBN-10 ‏ : ‎ 1559534079
  • ISBN-13 ‏ : ‎ 978-1559534079
  • Item Weight ‏ : ‎ 2.91 pounds
  • Dimensions ‏ : ‎ 7.76 x 1.18 x 9.49 inches
  • Customer Reviews:
    4.1 4.1 out of 5 stars 56 ratings

About the authors

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  1. Edward B. Burger

    Edward B. Burger

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    Edward Burger is the President of Southwestern University as well as an educational and business consultant. Most recently he was the Francis Christopher Oakley Third Century Professor of Mathematics at Williams College, and served as Vice Provost for Strategic Educational Initiatives at Baylor University. He is the author of over 60 research articles, books, and video series (starring in over 3,000 on-line videos). Burger was awarded the 2000 Northeastern Section of the Mathematical Association of America (MAA) Award for Distinguished Teaching and 2001 MAA Deborah and Franklin Tepper Haimo National Award for Distinguished Teaching of Mathematics. The MAA also named him their 2001-2003 Polya Lecturer. He was awarded the 2003 Residence Life Teaching Award from the University of Colorado at Boulder. In 2004 he was awarded Mathematical Association of America's Chauvenet Prize and in 2006 he was a recipient of the Lester R. Ford Prize. In 2007, 2008, and 2011 he received awards for his video work. In 2007 Williams College awarded him the Nelson Bushnell Prize for Scholarship and Teaching. Burger is an associate editor of the American Mathematical Monthly and Math Horizons Magazine and serves as a Trustee of the Kenan Institute for the Arts at the University of North Carolina School of the Arts. In 2006, Reader's Digest listed Burger in their annual "100 Best of America" as America's Best Math Teacher. In 2010 he was named the winner of the Robert Foster Cherry Award for Great Teaching---the largest and most prestigious prize in higher education teaching across all disciplines in the English speaking world. Also in 2010 he starred in a mathematics segment for NBC-TV on the Today Show and throughout the 2010 Winter Olympic coverage. That television appearance won him a 2010 Telly Award. The Huffington Post named him one of their 2010 Game Changers; "HuffPost's Game Changers salutes 100 innovators, visionaries, mavericks, and leaders who are reshaping their fields and changing the world." In 2012, Microsoft Worldwide Education selected him as one of their "Global Heroes in Education." In 2013 Burger was inducted as a Fellow of the American Mathematical Society.

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  2. Michael Starbird

    Michael Starbird

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    Michael Starbird is a University Distinguished Teaching Professor of Mathematics at The University of Texas at Austin. He has been at UT his whole career except for leaves, including as a Visiting Member of the Institute for Advanced Study in Princeton, New Jersey and a member of the technical staff of the Jet Propulsion Laboratory in Pasadena, California. He has received more than a dozen teaching awards including the Mathematical Association of America's 2007 national teaching award, the Texas statewide Minnie Stevens Piper Professor award, the UT Regents' Outstanding Teaching Award (in the inaugural year of the award), and most of the UT-wide teaching awards including the Jean Holloway Award for Excellence in Teaching, the Friar Centennial Teaching Fellowship, the Chad Oliver Plan II Teaching Award, the President's Associates Teaching Excellence Award, the Dad's Association Centennial Teaching Fellowship, the Eyes of Texas Excellence Award (twice), and others. He is a member of UT's Academy of Distinguished Teachers. He has produced DVD courses for The Teaching Company in the Great Courses Series on calculus, statistics, probability, geometry, and the joy of thinking and has given hundreds of lectures and workshops. He has co-authored several books including the innovative textbook for liberal arts students entitled "The Heart of Mathematics: An invitation to effective thinking." His new book with co-author Edward Burger is the general-audience book "The 5 Elements of Effective Thinking."

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4.1 out of 5 stars
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-_Tim_-
5.0 out of 5 stars An Unusual Book of Wide Interest
Reviewed in the United States on July 21, 2002
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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.
112 people found this helpful
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Ted R. Shoemaker
5.0 out of 5 stars Math Appreciation, not computation or rigor
Reviewed in the United States on September 23, 2004
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_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.
75 people found this helpful
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Julie Brennan
4.0 out of 5 stars Great adult self ed resource
Reviewed in the United States on July 29, 2004
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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.
50 people found this helpful
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T. Ostrowski
5.0 out of 5 stars Awesome!
Reviewed in the United States on August 18, 2013
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I used this book for a course to get my Masters degree. As a teacher of middle school mathematics I have referenced this text book many times with my students. The authors throw in a decent amount of humor and make it an easy read. Every math teacher should own this one!
One person found this helpful
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A. Williams
3.0 out of 5 stars Good for a math book
Reviewed in the United States on March 11, 2007
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It's filled with a lot of information and it seems the author was trying to make it more current... It's a math book, so it's really not all that interesting.
3 people found this helpful
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Nadiabihari
5.0 out of 5 stars An amazing book of mathematics
Reviewed in India on August 12, 2020
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Every school should adopt this book in their curriculum. The ways to understand some of the mathematical concepts presented here are phenomenal. If you are given any complicated problem, then try to simplify the problem without losing generality. If you fully understand the simpler version of the problem, try to put more details into the challenge and solve it again. Try to get some trends or ideas from solving the simpler one, then move to the original version.
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Ute Lehmann
5.0 out of 5 stars Difficult but excellent
Reviewed in Germany on January 11, 2016
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This book is very hard to think about. But this extreme thinking is good for your brain, for your knowledge and your maths abilities.
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boizette
5.0 out of 5 stars pour tout public
Reviewed in France on April 14, 2014
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Une invitation à la créativité. Nous permet de réconcilier avec les maths ceux d' entre nous que cette matière rebute
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A discerning reader
5.0 out of 5 stars The Heart of Maths
Reviewed in the United Kingdom on November 22, 2011
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It is a thoroughly interesting and enjoyable book. It introduces mathematical concepts in simple language. Very well presented with great illustrations
One person found this helpful
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Mr. James Tayamoi-moni
5.0 out of 5 stars Five Stars
Reviewed in the United Kingdom on August 13, 2015
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Imaginative.
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