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The Art and Craft of Problem Solving (Paperback) (Paperback)
by Paul Zeit
| Category:
Self help, Personal improvement, Problem solving, Mathematics |
| Market price: ¥ 498.00
MSL price:
¥ 438.00
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| Stock:
Pre-order item, lead time 3-7 weeks upon payment [ COD term does not apply to pre-order items ] |
MSL rating:
 Good for Gifts |
| MSL Pointer Review:
This book uniquely blends interesting problems with strategies, tools, and techniques to develop mathematical skill and intuition necessary for problem solving. |
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Author: Paul Zeit
Publisher: Wiley
Pub. in: August, 2006
ISBN: 0471789011
Pages: 384
Measurements: 9.1 x 7.5 x 0.7 inches
Origin of product: USA
Order code: BA01034
Other information: 2 edition
ISBN-13: 978-0471789017
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- MSL Picks -
The Art and Craft of Problem Solving is an excellent book that covers the essentials of Algebra, Combinatorics, Number Theory, and even Calculus from a problem-solving point of view.
This is a must have book for those interested in competetive mathematics. The presentation is very good. 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.
Target readers:
General readers.
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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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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:
1. get started and orient yourself in any problem.
2. draw pictures and use other creative techniques to look at the problem in a new light.
3. successfully employ proven techniques, including The Pigeonhole Principle, The Extreme Principle, and more.
4. tap into the knowledge gained from folklore problems (such as Conway's Checker problem).
5. 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!
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Sen Peng Eu (MSL quote), Taiwan
<2007-07-04 00:00>
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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A reader (MSL quote), USA
<2007-07-04 00:00>
Paul Zeitz has himself a masterpiece of a book in THE ART AND CRAFT OF PROBLEM SOLVING. As a student who was bored by the conventional curriculum in high school, I was interested in a more theoretical and challenging approach to mathematics. I was not disappointed. While this book does not go into considerable depth, it covers almost all major areas needed for an introduction to problem-solving. The examples he chooses are excellent and sometimes awe-inspiring-- everything from John Conway's amazing solution of the checkers problem to some fascinating proofs of common theorems.
Everything from algebraic combinatorics, probability, methods of proof, overarching mathematical ideas, problem-solving strategies, and more specific techniques are introduced. Zeitz explains everything in an understandable yet informed manner. If you ever wonder how some mathematicians manage to do what they do, look no further than this book.
A warning to the impatient: this book is not for you. If you can't stand thinking for longer than 5 minutes about a problem, DO NOT BUY THIS BOOK. You will be frustrated by many of the problems (not exercises, as Zeitz poignantly points out) presented at the end of each chapter. There are hints in the back, but no full solutions.
This book is also pretty good for those wanting to do well in math competitions. A lot of the problems come from national high school/college exams, and the all the ideas he presents are very relevant to solving those kinds of problems.
In summary, I would definitely recommend purchasing this book if you are an aspiring mathematician or just someone who likes problem-solving.
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Robert Pisani (MSL quote), USA
<2007-07-04 00:00>
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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Aditya Prasad (MSL quote), USA
<2007-07-04 00:00>
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. 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.
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