The Art and Craft of Problem Solving 1st Edition

This book is great for helping you learn how to solve math problems. It gives a lot of techniques and strategies that are used again and again and after reading this book you'll start to recognize them in your math courses. I think it's helpful for anyone who is studying for a math intensive major. It's definitely not a math textbook though. It's more of a supplement or a fun read for a hobby problem-solver.

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.

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.

My brother loved it

good product

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. However, there are very few solved problems. I strongly recommend this book, but also suggest that the student study other books as well, books with many more solved examples, because this book alone does not provide enough experience in putting the concepts into practice.

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.

If you are ever called upon to teach a general problem solving class, this is the resource you want.