The Art and Craft of Problem Solving 1st Edition

by Paul Zeitz (Author)

17 customer reviews

ISBN-13: 978-0471135715

ISBN-10: 0471135712

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This text on mathematical problem solving provides a comprehensive outline of "problemsolving-ology," concentrating on strategy and tactics. It discusses a number of standard mathematical subjects such as combinatorics and calculus from a problem solver's perspective.

The Art and Craft of Problem Solving [International Edition]

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Product Details

Hardcover: 352 pages
Publisher: John Wiley and Sons; 1 edition (February 23, 1999)
Language: English
ISBN-10: 0471135712
ISBN-13: 978-0471135715
Product Dimensions: 7.7 x 0.7 x 9.5 inches
Shipping Weight: 1.5 pounds
Average Customer Review: 4.6 out of 5 stars See all reviews (17 customer reviews)
Amazon Best Sellers Rank: #384,971 in Books (See Top 100 in Books)
- #131 in Books > Science & Math > Mathematics > Pure Mathematics > Logic
- #200 in Books > Science & Math > Mathematics > Mathematical Analysis
- #2564 in Books > Textbooks > Science & Mathematics > Mathematics

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Customer Reviews

4.6 out of 5 stars

5 star		88%
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2 star		6%
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Most Helpful Customer Reviews

87 of 92 people found the following review helpful

Extraordinary

By Bob Lugoi on January 12, 2000

Format: Hardcover

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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39 of 40 people found the following review helpful

The Book I wish I had in High School

By Mark McDonald on May 7, 2004

Format: Hardcover

When I was in high school, I placed second in the Alabama State Mathematics Contest and won many others. However, I might could have been competitive with the IMO style problems had I had this book and would be much better off today had I seen this book earlier.
This book is for the exceptionally brilliant and the mentally tough. It is absolutely necessary to approach this book in a different way from a standard math textbook. You MUST attempt the examples BEFORE looking at the example solutions, NO MATTER HOW DIFFICULT OR FRUSTRATING. You may be bamboozled by the problems, but even trying to understand the problems before looking at the solutions and thinking about how a solution might proceed will pay huge dividends in the long run.
For example, in the first chapter Zeitz presents an example asking the reader to prove that the product of four consecutive integers cannot be a perfect square. The solution involves some clever algebraic trickery not visible to the inexperienced, but persistence and getting your hands dirty is key.
If you persist in spite of the considerable difficulty, you will find that you get better very, very quickly. You will also notice that it isn't just contest problems it helps you solve. I have found that I have solved my homework sets in the Berkeley graduate engineering program much more easily since working these problems. You will start to see creative and clever solutions where they exist in everything problem oriented.
PATIENCE PATIENCE PATIENCE!

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29 of 31 people found the following review helpful

Essential for budding (and experienced) problem-solvers

By Aditya K. Prasad on June 13, 2004

Format: Hardcover Verified Purchase

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.Read more ›

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52 of 59 people found the following review helpful

One of the best

By Sen Peng Eu on October 30, 2001

Format: Hardcover Verified Purchase

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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Most Recent Customer Reviews

Problem Solving Strategies

Probably one of the best books for learning how to solve a math problem. It really flexes your mind. I still have a bunch of problems in there I have no idea how to do. Read more

Published on September 23, 2007 by Mikhail Shklyar

Outstanding, but you will need other sources

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... Read more

Published on October 4, 2005 by Chess Maniac

a marvelous introduction to problem solving

this is one of the rare books which truly

give us a glimpse into the beauty of mathematics,

I recommend it to every person which want

to enhance... Read more

Published on August 25, 2005 by Shimon Kogan

Brilliant

As a high school student that is essentially bored with the regular, ho-hum classes that my school offers, this book is perfect. Read more

Published on February 21, 2004

Amazing

this book is what a beginner needs.
if u like to know how to solve problems and u want to know these "beautiful ideas"... Read more

Published on July 26, 2003 by Fatma

Almost silly!

I just can't understand what all the hype is about! The book is almost silly. The book is too chatty, costly, many of the problems are boring, there are many typos, it gives little... Read more

Published on June 9, 2003

The Beauty of Mathematics

I happened to come across this book in my universities' used book store last summer. As a read and worked through the problems in this book I realized that this type of mathematics... Read more

Published on December 22, 2002

This book is fantastic!

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... Read more

Published on September 22, 2002 by Amazon Customer

save your money

This combines two undesirable features of a
textbook, namely numerous problems without
solutions and a high price. Read more

Published on March 16, 2002

General Problem Solving Strategies.

Perfect match for all math problem solvers.
Wonderful Book with around 660 problems.
Level National Math competition, IMO, Putnam. Read more

Published on December 19, 2001 by Julio Cesar De Yncera