The Art and Craft of Problem Solving [Hardcover]

Paul Zeitz (Author)

Book Description

ISBN-10: 0471135712 | ISBN-13: 978-0471135715 | Publication Date: February 9, 1999 | Edition: 1

This text on mathematical problem solving provides a comprehensive outline of "problemsolving-ology," concentrating on strategy and tactics. It discusses a number of standard mathematical subjects such as combinatorics and calculus from a problem solver's perspective.

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.

Product Details

• Hardcover: 352 pages
• Publisher: Wiley; 1 edition (February 9, 1999)
• Language: English
• ISBN-10: 0471135712
• ISBN-13: 978-0471135715
• Product Dimensions: 9.6 x 7.5 x 0.8 inches
• Shipping Weight: 1.7 pounds
• Average Customer Review: 4.6 out of 5 stars  See all reviews (17 customer reviews)
• Amazon Best Sellers Rank: #474,307 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

83 of 88 people found the following review helpful:

5.0 out of 5 stars Extraordinary, January 12, 2000

By 

Bob Pisani (Boulder, Colorado) - See all my reviews

This review is from: The Art and Craft of Problem Solving (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.

38 of 39 people found the following review helpful:

5.0 out of 5 stars The Book I wish I had in High School, May 7, 2004

By 

Mark McDonald (Berkeley, CA United States) - See all my reviews
(REAL NAME)   

This review is from: The Art and Craft of Problem Solving (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!

51 of 57 people found the following review helpful:

5.0 out of 5 stars One of the best, October 30, 2001

By 

Sen Peng Eu "ESP=Math+Music+Literature" (Kaohsiung, Taiwan) - See all my reviews
(REAL NAME)   

Amazon Verified Purchase

This review is from: The Art and Craft of Problem Solving (Hardcover)

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.