One of my all-time favorite books on solving math problems. "Polya has become the Marx and Lenin of mathematical problem solving; a few words of obeisance need to be offered in his name before an author can get down to the topic at hand."
[How to solve math problems -- 10/9/07]

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Product Description

A perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight.

In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed, brilliant--instructions on stripping away irrelevancies and going straight to the heart of the problem.

In this best-selling classic, George Pólya revealed how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out--from building a bridge to winning a game of anagrams. Generations of readers have relished Pólya's deft instructions on stripping away irrelevancies and going straight to the heart of a problem. How to Solve It popularized heuristics, the art and science of discovery and invention. It has been in print continuously since 1945 and has been translated into twenty-three different languages.

Pólya was one of the most influential mathematicians of the twentieth century. He made important contributions to a great variety of mathematical research: from complex analysis to mathematical physics, number theory, probability, geometry, astronomy, and combinatorics. He was also an extraordinary teacher--he taught until he was ninety--and maintained a strong interest in pedagogical matters throughout his long career. In addition to How to Solve It, he published a two-volume work on the topic of problem solving, Mathematics of Plausible Reasoning, also with Princeton.

Pólya is one of the most frequently quoted mathematicians, and the following statements from How to Solve It make clear why: "My method to overcome a difficulty is to go around it." "Geometry is the science of correct reasoning on incorrect figures." "In order to solve this differential equation you look at it till a solution occurs to you."

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Product Details

• Amazon Sales Rank: #11519 in Books
• Published on: 2004-04-05
• Number of items: 1
• Binding: Paperback
• 288 pages

Review
Every prospective teacher should read it. In particular, graduate students will find it invaluable. The traditional mathematics professor who reads a paper before one of the Mathematical Societies might also learn something from the book: 'He writes a, he says b, he means c; but it should be d.'
(E. T. Bell Mathematical Monthly )

[This] elementary textbook on heuristic reasoning, shows anew how keen its author is on questions of method and the formulation of methodological principles. Exposition and illustrative material are of a disarmingly elementary character, but very carefully thought out and selected.
(Herman Weyl Mathematical Review )

I recommend it highly to any person who is seriously interested in finding out methods of solving problems, and who does not object to being entertained while he does it.
(Scientific Monthly )

Any young person seeking a career in the sciences would do well to ponder this important contribution to the teacher's art.
(A. C. Schaeffer American Journal of Psychology )

Every mathematics student should experience and live this book
(Mathematics Magazine )

Review
Any young person seeking a career in the sciences would do well to ponder this important contribution to the teacher's art.

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Customer Reviews

How To Solve It, Polya
Very interesting book on how to solve problems, which can be applied to both mathematical and real-life problems. It contains general themes of problem-solving, attitudes one should have towards problems, and detailed methods of how to go about solving problems. It also discusses the optimal teacher-student relationship in the context of problem-solving.

Problem Solving Methods - Excellent Book on Heuristics
Every teacher and parent should read this book. Every person interested in problem solving should also read it.

This book is not just about mathematical methods, mathematical problem solving, or teaching mathematics. It is about solving problems. It presents concrete methods (or heuristics) and illustrates by guiding the reader using these methods through clear and cogent examples.

The problem solving insight this book provides is extremely useful. It is about how to go about solving a problem. There are many different ways to approach a difficult problem and often in complex problem solving one does not know where to begin to even think about the problem.

I recall Andrew Wiles, the mathematician who proved Fermat's Last Theorem (a very famous, long-lasting, and seemingly unproven theorem - unproven for centuries), discussed how during his initial work on the problem, work which ultimately took Wiles about seven years to figure out how to prove, and then to go ahead and prove the theorem, had to study problem solving methodologies just to know how to approach the problem. He needed to learn how to attack the problem - where to begin.

This book is great for learning the different approaches to problem solving. One method discussed in detail is to work similar problems or simpler problems that are similar to the main problem. This allows one to start gauge the issues surrounding the problem and the assist the mind in thinking about the problem and its boundaries.

Anyone interested in becoming a better problem solver, a better teacher, or a parent trying to teach or help their children learn mathematics or science (or to help them with their homework - but to do so by teaching advanced problem solving methods implicitly), then this book is for you. It is not a difficult book and you do not have to be an expert in mathematics or mathematically inclined.

Not just for academics
There is a reason that this book has been in print for decades. It should be required reading for teachers, students, and anybody interested in thinking. Problem-solving is a useful skill that can be learned. Polya does the teaching.