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The Art and Craft of Problem Solving 1st Edition
- ISBN-100471135712
- ISBN-13978-0471135715
- Edition1st
- PublisherJohn Wiley and Sons
- Publication dateFebruary 23, 1999
- LanguageEnglish
- Dimensions7.72 x 0.72 x 9.47 inches
- Print length352 pages
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- Publisher : John Wiley and Sons; 1st edition (February 23, 1999)
- Language : English
- Hardcover : 352 pages
- ISBN-10 : 0471135712
- ISBN-13 : 978-0471135715
- Item Weight : 1.5 pounds
- Dimensions : 7.72 x 0.72 x 9.47 inches
- Best Sellers Rank: #1,909,617 in Books (See Top 100 in Books)
- #884 in Mathematical Logic
- #6,743 in Mathematics (Books)
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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.
Happy solving.
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.




