The Art and Craft of Problem Solving 1st Edition

17 customer reviews
ISBN-13: 978-0471135715
ISBN-10: 0471135712
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Editorial Reviews

From the Back Cover

Are you up for the challenge? "This is the only book I know that can be used as a source of problems (as opposed to exercises), provides strategies and intuition into problem solving, and also provides tools and techniques for solving problems. The integration of these three areas is extremely distinctive and highly commendable." Jeffery Bergen, DePaul University In many ways, solving a mathematical problem is as challenging and exhilarating as reaching the peak of a majestic mountain. Like the climber, the problem solver sets out on a journey where getting lost and finding one’s way are part of the fun. The solution may be elusive, but creative investigation and an adventurous spirit often bring it within grasp. The challenge is waiting for you inside this exciting text!

About the Author

About the Author Paul Zeitz studied history at Harvard and received a Ph.D. in mathematics from the University of California, Berkeley. He taught high school math in San Francisco and Colorado and currently is an associate professor at the University of San Francisco. He won the USA Mathematical Olympiad (USAMO) and was a member of the first American team to participate in the International Mathematical Olympiad (IMO) in 1974. Since 1985, he has composed and edited problems for several national math contests, including the USAMO. He has helped train several American IMO teams, most notably the 1994 "Dream Team" which, for the first time in history, achieved a perfect score.
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Product Details

  • Hardcover: 352 pages
  • Publisher: John Wiley and Sons; 1 edition (February 23, 1999)
  • Language: English
  • ISBN-10: 0471135712
  • ISBN-13: 978-0471135715
  • Product Dimensions: 7.7 x 0.7 x 9.5 inches
  • Shipping Weight: 1.5 pounds
  • Average Customer Review: 4.6 out of 5 stars  See all reviews (17 customer reviews)
  • Amazon Best Sellers Rank: #603,857 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

87 of 92 people found the following review helpful By Bob Lugoi on January 12, 2000
Format: Hardcover
Sometimes a piece of music or a painting or a film just leaves me speechless. Sometimes it is a book, and this is such a book. When I first saw this book, I looked at no more than a handful of pages and bought it instantly. This book is truly thrilling, certainly for young and beginning mathematicians but even for mature ones. Every new page I read is full of thought and insight and elegance (both in the mathematical sense and otherwise). I don't know of any other book in its class. I honed my problem solving skills on the classics by Polya, but Polya did not cover this turf in even nearly the comprehensive way and the full and extensive detail of this book by Paul Zeitz. I wish I had had this extraordinary book when I was in high school -- I think it would have changed my life -- but I am so pleased that I at least have it now. Polya's books are of course classics in this area, but this book takes its place clearly beside them. It is destined to become a classic itself. In my eyes, it already has.
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39 of 40 people found the following review helpful By Mark McDonald on May 7, 2004
Format: Hardcover
When I was in high school, I placed second in the Alabama State Mathematics Contest and won many others. However, I might could have been competitive with the IMO style problems had I had this book and would be much better off today had I seen this book earlier.
This book is for the exceptionally brilliant and the mentally tough. It is absolutely necessary to approach this book in a different way from a standard math textbook. You MUST attempt the examples BEFORE looking at the example solutions, NO MATTER HOW DIFFICULT OR FRUSTRATING. You may be bamboozled by the problems, but even trying to understand the problems before looking at the solutions and thinking about how a solution might proceed will pay huge dividends in the long run.
For example, in the first chapter Zeitz presents an example asking the reader to prove that the product of four consecutive integers cannot be a perfect square. The solution involves some clever algebraic trickery not visible to the inexperienced, but persistence and getting your hands dirty is key.
If you persist in spite of the considerable difficulty, you will find that you get better very, very quickly. You will also notice that it isn't just contest problems it helps you solve. I have found that I have solved my homework sets in the Berkeley graduate engineering program much more easily since working these problems. You will start to see creative and clever solutions where they exist in everything problem oriented.
PATIENCE PATIENCE PATIENCE!
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29 of 31 people found the following review helpful By Aditya K. Prasad on June 13, 2004
Format: Hardcover Verified Purchase
I join the ranks of previous reviewers here who honestly feel that having read this book in high school would have almost certainly changed my life. I, too, did very well in high school math competitions, but the maturity I am gleaning from this gem may have vaulted me into a different league.

It contains hundreds of problems from various levels of competition, from AIME problems all the way through some of the toughest Putnam problems (which, if you know anything about the Putnam, are about as hard as competition problems come). But the biggest help are the vital insights and exciting ways of looking at these problems. Don't take my word for it--many past IMO contestants have suggested this book too.

Particularly helpful is the way the author divides the book into sections based on often-used concepts and techniques. For example, you will see applications of the pigeonhole principle from the most basic (e.g. "In a drawer with socks of 2 colors, show that after picking any 3 socks, we must have a pair of same-colored socks.") through some rather difficult ones (1994 Putnam A4, an Erdos problem, and more).

The same goes for a multitude of others--the invariants section includes both the classic chocolate bar-cutting problem and Conway's rather difficult checker problem. Then, not only does he solve the latter beautifully, but incorporates nontrivial questions that ensure the reader has completely understood the solution (e.g., "Could we have replaced lambda with an arbitrary integer? Why not?").

You don't have to be a math competition buff to gain from this book, however. If you're simply interested in mathematical puzzles and problems, and are looking to expand your repertoire, this book will help you.
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52 of 59 people found the following review helpful By Sen Peng Eu on October 30, 2001
Format: Hardcover Verified Purchase
This book is indeed one of the best problem-solving textbook so far. As a frequent lecturer of Taiwan IMO team, I have many many MO books. Most of the books available are well-written by professionals and excellent mathematicians. However, since IMO does really prevail in recent years, these authors could not be the participants themselves (^^). Furthermore, usually these books (except those are merely problems collections) contains a good proportion of "harder" and beautiful problems, and the easier and basic training problems are relatively few. It often get the beginners frustrate.
Now this maybe is the first book written by a member of former MO team, and now a training lecturer. (The author himself won the USAMO and IMO in 1974, and helped train several USA IMO teams, including the 1994 "perfect score team"). So here is the precious experience! Besides, the ratio between the harder problems and the easier problems is really good. In my opinion this is an excellent textbook for ambitious beginners (both teachers and students), for self-studys and problem-solving fans. Highly recommended.
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