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The Art and Craft of Problem Solving Paperback – 22 Sep 2006

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Product details

  • Paperback: 384 pages
  • Publisher: John Wiley & Sons; 2nd Edition edition (22 Sept. 2006)
  • Language: English
  • ISBN-10: 0471789011
  • ISBN-13: 978-0471789017
  • Product Dimensions: 19 x 2 x 23.5 cm
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Bestsellers Rank: 40,046 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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Product Description

From the Back Cover

You ve got a lot of problems. That s a good thing.

Across the country, people are joining math clubs, entering math contests, and training to compete in the International Mathematical Olympiad. What s the attraction? It s simple solving mathematical problems is exhilarating!

This new edition from a self–described "missionary for the problem solving culture" introduces you to the beauty and rewards of mathematical problem solving. Without requiring a deep background in math, it arms you with strategies and tactics for a no–holds–barred investigation of whatever mathematical problem you want to solve. You ll learn how to:

  • get started and orient yourself in any problem.
  • draw pictures and use other creative techniques to look at the problem in a new light.
  • successfully employ proven techniques, including The Pigeonhole Principle, The Extreme Principle, and more.
  • tap into the knowledge gained from folklore problems (such as Conway s Checker problem).
  • tackle problems in geometry, calculus, algebra, combinatorics, and number theory.

Whether you re training for the Mathematical Olympiad or you just enjoy mathematical problems, this book can help you become a master problem–solver!

About the Author

Paul Zeitz studied history at Harvard and received a Ph.D. in mathematics from the University of California, Berkeley. He 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 and helped train several American IMO teams, most notably the 1994 "Dream Team" which, for the first time in history, achieved a perfect score. In 2003, he received the Deborah Tepper Haimo award, a national teaching award for college and university math, given by the Math Association of America.

About the Author

Paul Zeitz studied history at Harvard and received a Ph.D. in mathematics from the University of California, Berkeley. He 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 and helped train several American IMO teams, most notably the 1994 "Dream Team" which, for the first time in history, achieved a perfect score. In 2003, he received the Deborah Tepper Haimo award, a national teaching award for college and university math, given by the Math Association of America.

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Most Helpful Customer Reviews

1 of 1 people found the following review helpful By george on 4 Aug. 2014
Format: Paperback
I am a physics PhD, and so my maths education was different from that of maths students. I read this book because I wanted to fill in some of the holes in my maths knowledge - number theory, graph theory, some combinatorics. I also like solving 'puzzle problems' (e.g. Project Euler problems) and many of the examples are 'Maths Olympiad' problems.

The book focuses on solving problems - concrete examples are always given, which suits my "physicist's style" of learning. Having read each chapter, I was smarter than when I started it - I knew new tools and techniques.

This isn't an easy maths book - I advise you to preview the first chapter, and check it matches your level. If it does, then read it all!
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Most Helpful Customer Reviews on Amazon.com (beta)

Amazon.com: 10 reviews
89 of 96 people found the following review helpful
Not ideal for self study 5 Oct. 2006
By Math Olympian - Published on Amazon.com
Format: Paperback
A primary group of people this book is aimed at is those preparing for Math contests such as the Olympiads. Many such people study the subject on their own. An important step in such preparation is solving a lot of problems. While it is important to try to solve the problems on one's own, it is equally important to be able to verify that one's solutions are correct. Unfortunately, this book does not provide solutions to the problems. Hence, it is not very helpful for those who are studying on their own. There are many other books in the market which are better from that point of view: For example, many books by Titu Andreescu, "Problem Solving Strategies" book by Arthur Engel are all good books that provide solutions as well. The "Art of Problem Solving" (Vol. 1 & Vol. 2) by Rusczyk et al. are also very good and have separate solution manuals available for purchase.
20 of 21 people found the following review helpful
Great 2nd edition; Would have liked more solved problems... 29 Dec. 2006
By smcheril - Published on Amazon.com
Format: Paperback
I recently got the 2nd edition and it seems to have some additional material compared to the first edition. There is a new chapter on Geometry and with expanded treatment of calculus. Seems like there are a few more problems in each chapter.

This is a must have book for those interested in competetive mathematics. The presentation is very good -- but since the material covered is rather complex, its not easy to do self-study with this book. The book doesn't have a solution manual -- I tried contacting the publisher to get access to their instructor site but was turned down saying that I needed to be an instructor using this as a textbook in class and so on to get access to the solutions manual. It kind of sucks when you are doing self-study to not have a way to get help. I wish Wiley will reconsider this and give folks like me who are engaged in self-study a chance to use this book effectively. It is some consolation that the books web site has a "students" section providing hints for some problems.

Overall, I would still give the book a 5 star rating because it is a class apart and covers a whole lot of ground. The first few chapters on strategies and tactics to solve problems are by themselves worth the price of the book. Definitely worth getting.
9 of 10 people found the following review helpful
Tough One 14 Aug. 2009
By Derek Premo - Published on Amazon.com
Format: Paperback Verified Purchase
This was a required purchase for a Graduate Level Math Problem Solving class. The text is really hard to read and understand, but covers a plethra of topics. There are no worked out solutions or an answer key which makes checking you work very difficult.
5 of 5 people found the following review helpful
Opens your mind 28 Dec. 2007
By Raymond Tay - Published on Amazon.com
Format: Paperback Verified Purchase
I have to admit i am not through reading this book but this book is what was and still is missing in my education :-)

Why?

Well, in my opinion the author understands why many people fear math - lack of proper method(s) + lack of confidence. And the author goes about tackling this problem by doing exactly that!

This book provides many "problems" - i love the way the author phrased the word "problem" - plus many words of encouragement to push its readers to attempt the problems to 3 goals:

1) Have the courage to think out-of-the-box when it comes to solving problems;
2) Have the confidence to tackle them;
2.1) Building this confidence by providing the methods + the reader's willingness to get "dirty"
3) Never give up (Take a rest if you must, but never ever give up).
4 of 4 people found the following review helpful
A treasure 15 Sept. 2010
By Nowell T. Teitelbaum - Published on Amazon.com
Format: Paperback Verified Purchase
A "cut to the chase" course in strategies for solving math problems of the kind found in the USAMO and IMO tests. The level of knowledge needed is up to a math major's sophomore year. I have yet to finish it but the book seems to offer an abundance of useful information along with example problems with step by step solutions. It would be nice, however, if access to solutions to the numerous problems and exercises was provided so people could check their work!
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