- Paperback: 384 pages
- Publisher: Wiley; 2 edition (August 18, 2006)
- Language: English
- ISBN-10: 0471789011
- ISBN-13: 978-0471789017
- Product Dimensions: 7.3 x 0.9 x 9.2 inches
- Shipping Weight: 15.2 ounces (View shipping rates and policies)
- Average Customer Review: 27 customer reviews
- Amazon Best Sellers Rank: #196,029 in Books (See Top 100 in Books)
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The Art and Craft of Problem Solving 2nd Edition
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"Overall, The Art and Craft of Problem Solving is an excellent gateway to the culture of problem solving. It is challenging and rewarding. Zeitz’s book shines a new light on mathematics and engages readers with its wonderful insights and problems." (Mathematical Association of America 2016)
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.
Top customer reviews
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).
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. Anyone with a good dose of intelligence and motivation will benefit.
For an additional problem book, check out Mathematical Olympiad Challenges by Andreescu and Gelca. For purely Putnam treatment, there are several volumes written by Kedlaya. And if you're a CS student, looking for honing those CS math skills to be razor sharp, you should definitely look into Concrete Mathematics by Graham, Knuth, and Patashnik.
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.
Most recent customer reviews
Today, I solved my first Geometry IMO problem (1st problem of IMO 1998).Read more