The newly revised Second Edtion of this distinctive text uniquely blends interesting problems with strategies, tools, and techniques to develop mathematical skill and intuition necessary for problem solving. Readers are encouraged to do math rather than just study it. The author draws upon his experience as a coach for the International Mathematics Olympiad to give students an enhanced sense of mathematics and the ability to investigate and solve problems.
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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
68 of 71 people found the following review helpful:
3.0 out of 5 stars
Not ideal for self study,
By Math Olympian "Math Olympian" (California) - See all my reviews
This review is from: The Art and Craft of Problem Solving (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.
9 of 9 people found the following review helpful:
5.0 out of 5 stars
Great 2nd edition; Would have liked more solved problems...,
By smcheril (Memphis, TN) - See all my reviews
This review is from: The Art and Craft of Problem Solving (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.
6 of 7 people found the following review helpful:
3.0 out of 5 stars
Good but more advanced than the description would have you believing,
By math "mathmt" (NJ) - See all my reviews
This review is from: The Art and Craft of Problem Solving (Paperback)
This book is very useful for people who already know all the essentials but need to make the connections between various topics. I use it for math Olympiad prep for students with a lot of talent. Yet, they need help. It is much more advanced than the description says.
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Inside This Book
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Key Phrases - Statistically Improbable Phrases (SIPs):
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angle chasing, corner lattice points, wishful thinking strategy, orthic triangle, handshake numbers, locker problem, crux move, lattice point corners, medial triangle, alleged inequality, balanced wires, summation identity, phantom points, parity analysis, crux idea, pigeonhole principle, extreme principle, positive integer solutions, penultimate step Key Phrases - Capitalized Phrases (CAPs): (learn more)
Partial Solution, Bay Area Mathematical Olympiad, Pascal's Triangle, Leningrad Mathematical Olympiad, The Mathematical Association of America, Ptolemy's Theorem, George Pólya, Jim Propp, Pythagorean Theorem, Formal Solution, Affirmative Action, Use Problem, Fundamental Theorem of Algebra, The William Lowell Putnam Mathematical Competition, John Wiley, Crux Mathematicorum, Martin Gardner, Fermat's Last Theorem, Gauss's Lemma, Ravi Vakil, Centroid Theorem Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
angle chasing, corner lattice points, wishful thinking strategy, orthic triangle, handshake numbers, locker problem, crux move, lattice point corners, medial triangle, alleged inequality, balanced wires, summation identity, phantom points, parity analysis, crux idea, pigeonhole principle, extreme principle, positive integer solutions, penultimate step Key Phrases - Capitalized Phrases (CAPs): (learn more)
Partial Solution, Bay Area Mathematical Olympiad, Pascal's Triangle, Leningrad Mathematical Olympiad, The Mathematical Association of America, Ptolemy's Theorem, George Pólya, Jim Propp, Pythagorean Theorem, Formal Solution, Affirmative Action, Use Problem, Fundamental Theorem of Algebra, The William Lowell Putnam Mathematical Competition, John Wiley, Crux Mathematicorum, Martin Gardner, Fermat's Last Theorem, Gauss's Lemma, Ravi Vakil, Centroid Theorem Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
16
books
cite this book:
See all 16 books citing this book
- Count Down: Six Kids Vie for Glory at the World's Toughest Math Competition by Steve Olson on 4 pages
- Count Down: The Race for Beautiful Solutions at the International Mathematical Olympiad by Steve Olson on 4 pages
- Why Not?: How to Use Everyday Ingenuity to Solve Problems Big And Small by Barry Nalebuff on page 153, Back Matter (1), and Back Matter (2)
- Why Not? How to Use Everyday Ingenuity to Solve Problems Big and Small by Barry J. Nalebuff in Back Matter (1), and Back Matter (2)
- The IMO Compendium: A Collection of Problems Suggested for The International Mathematical Olympiads: 1959-2004 (Problem Books in Mathematics) by Duan Djuki in Back Matter
See all 16 books citing this book
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