How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library) [Paperback]

G. Polya (Author)

Book Description

ISBN-10: 069111966X | ISBN-13: 978-0691119663 | Publication Date: April 5, 2004

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."

Editorial Reviews

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

About the Author

George Polya was a Hungarian mathematician. Born in Budapest on 13 December 1887, his original name was Pólya Györg. He wrote this, perhaps the most famous book of mathematics ever written, second only to Euclid's “Elements”. In 1940 he came to America and spent the rest of his career as a Professor at Stanford University. --This text refers to an alternate Paperback edition.

Product Details

• Paperback: 288 pages
• Publisher: Princeton University Press (April 5, 2004)
• Language: English
• ISBN-10: 069111966X
• ISBN-13: 978-0691119663
• Product Dimensions: 7.8 x 5.3 x 0.6 inches
• Shipping Weight: 10.6 ounces (View shipping rates and policies)
• Average Customer Review: 4.3 out of 5 stars  See all reviews (24 customer reviews)
• Amazon Best Sellers Rank: #30,681 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

57 of 57 people found the following review helpful:

5.0 out of 5 stars A delightful and satisfying classic, December 17, 2004

By 

Sandra Feder "Author of Side Effect and One o... - See all my reviews
(REAL NAME)   

This review is from: How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library) (Paperback)

Are you like a dog with a bone when you're working on a brain teaser? After pages of scribbles, do you get a big grin on your face when you turn to the answers and say: "I'm right!" Then this book is for you.

And if you're not yet a die-hard problem-solver? You should step right up, too. You may get hooked.

G. Polya's book is based on the fact that, if we study how someone does something successfully, we can learn to do it successfully as well. How To Solve It is an application of 'heuristics' to solving problems.

There are certain mental operations useful in solving problems, any sorts of problems. Polya (who was an eminent mathematician and former Professor of Mathematics at Stanford University) describes and illustrates the most usual and useful of these operations, in a way that is irresistible and eye-opening.

These useful mental operations are organized according to when they come into play during the four steps to solving a problem. 1. You have to understand the problem. (Not as easy as it sounds.) 2. Find the connection between the data given and the unknown. Conceive the idea of a plan for the solution. 3. Carry out the plan. 4. Examine the solution obtained.

If you take some time and try to solve the problems selected to illustrate each mental operation, you will be well-rewarded. You will likely discover something surprising about your own problem-solving methods, and improve them in the process. You will definitely discover many new ideas and techniques to add to your arsenal.

For example, a first impulse when confronted with a problem is often to try to 'swallow it whole' -- to try to meet all of the conditions of the problem at once. G. Polya suggests keeping only part of the condition, and dropping the other part. This can lead you straight to a solution you might otherwise have completely missed.

His techniques help you to stand back and get to the heart of the problem, rather than getting lost in it.

Something else I liked very much about his book is his encouragement to guess, or to reason 'plausibly.' While the final proof must be strictly logical, "Anything is right that leads to the right idea." Problem-solving has every right to be fun, as well as purposeful.

20 of 20 people found the following review helpful:

5.0 out of 5 stars A book that teaches Math and thinking at once, December 28, 2005

By 

Marty Nickison II (Austintown, OH) - See all my reviews
(REAL NAME)   

This review is from: How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library) (Paperback)

Polya struck gold with this book! "How To Solve It" contains a simple, 5 step method for solving problems that's applicable in multitudes of disciplines. While the emphasis of this book is on story problems; Polya's method for problem solving is useful in areas such as computer programming, automotive troubleshooting, electronics repair, heating and cooling services, research writing, and much more.

I am constanly recommending this book to anyone in college. You can read the method and all the examples, or just read the method and a few examples. This book is easy to read, extremely relevant to today's promising careers, and can be understood in only 4 hours.


Marty A. Nickison II, BSCS Net+
author: Beyond the Books (Lulu)

16 of 16 people found the following review helpful:

4.0 out of 5 stars Excellent and useful book, December 22, 2005

By 

Dennis R. Mitton "tolstoy" (Eastern Washington, USA) - See all my reviews
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This review is from: How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library) (Paperback)

A really helpful book that goes way beyond math. In our hurry to get through algebra we almost completely sidestep problem solving in teaching. It's true that we have `story problems' but they're usually just applications that restate the chapter's contents. That's why so many people get to a class like physical chem in college and flounder: they've never really been taught how to solve a problem only to regurgitate what's been read. This book by Polya fills in that gap.

More than that, though, this book is useful for life in general. Much of life is a leap from one decision to another and this book will help in looking at all problems and decision from new angles. (See Polya's book "Plausible Thinking" for lots more detail on this subject.)

Like in his other books the author has a knack for making the difficult seem a whole lot easier but parts can still be heavy going. Well worth the trudge, though.