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How to Solve It: A New Aspect of Mathematical Method
 
 
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How to Solve It: A New Aspect of Mathematical Method [Paperback]

G. Polya (Author)
4.8 out of 5 stars  See all reviews (20 customer reviews)


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How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library) How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library) 4.3 out of 5 stars (24)
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Book Description

0691023565 978-0691023564 1971 2nd
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.



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 )

Product Details

  • Paperback: 224 pages
  • Publisher: Princeton University Press; 2nd edition (1971)
  • Language: English
  • ISBN-10: 0691023565
  • ISBN-13: 978-0691023564
  • Product Dimensions: 7.9 x 5 x 0.7 inches
  • Shipping Weight: 12.8 ounces
  • Average Customer Review: 4.8 out of 5 stars  See all reviews (20 customer reviews)
  • Amazon Best Sellers Rank: #176,846 in Books (See Top 100 in Books)

 

Customer Reviews

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4.8 out of 5 stars (20 customer reviews)
 
 
 
 
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98 of 99 people found the following review helpful:
5.0 out of 5 stars A Classic for Problem-Solvers, September 16, 2001
By 
This review is from: How to Solve It: A New Aspect of Mathematical Method (Paperback)
I found Pollya's "heuristic" approach to problem-solving applicable to both mathematical and non-mathematical problems. The goal of the heuristic approach is to study (and use!) the methods and rules of discovery and invention.

Here are just some of the questions that Pollya teaches as tools:

1. What is the unknown? What is the data? What conditions does the solution need to satisfy?
2. Do you know a related problem? Look at the unknown and try to think of a familiar problem having the same or a similar unknown.
3. Can you restate the problem? Can you solve a part of the problem.
4. Can you think of other data appropriate to determine the unknown?
5. Can you check the result?
6. Can you look back and use the result or the method for some other problem?

Overall, the author provides a systematic way to creatively solve problems. This volume has withstood the test of time for nearly 50 years. I recommend it highly.

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61 of 61 people found the following review helpful:
5.0 out of 5 stars Indispensable for anyone who solves problems professionally., July 7, 1996
By A Customer

How to Solve It is the most significant contribution to heuristic since Descartes' Discourse on Method. The title is accurate enough, but the subtitle is far too modest: the examples are drawn mostly from elementary math, but the method applies to nearly every problem one might encounter. (Microsoft, for instance, used to and may still give this book to all of its new programmers.) Polya divides the problem-solving process into four stages--Understanding the Problem, Devising a Plan, Carrying out the Plan, and Looking Back--and supplies for each stage a series of questions that the solver cycles through until the problem is solved. The questions--what is the unknown? what are the data? what is the condition? is the condition sufficient? redundant? contradictory? could you restate the problem? is there a related problem that has been solved before?--have become classics; as a computer programmer I ask them on the job every day.

The book is short, 250 large-print pages in the paperback. Its style is clear, brilliant and does not lack in humor. Here is Polya's description of the traditional mathematics professor: "He usually appears in public with a lost umbrella in each hand. He prefers to face the blackboard and turn his back on the class. He writes A; he says B; he means C; but it should be D." Behind the humor, though, lurks a serious complaint about mathematical pedagogy. Fifty years ago, when Polya was writing, and today still, mathematics was presented to the student, under the tyranny of Euclid, as a magnificent but frozen edifice, a series of inexorable deductions. Even the student who could follow the deductions was left with no idea how they were arrived at. How to Solve It was the first and best attempt to demystify math, by concentrating on the process, not the result. Polya himself taught mathematics at Stanford for many years, and one can only envy his students. But the next best thing is to read his book.

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31 of 32 people found the following review helpful:
5.0 out of 5 stars Important classic, June 30, 2002
This review is from: How to Solve It: A New Aspect of Mathematical Method (Paperback)
It's delightful to see this book is still in bookstores after 60 years, and I can still remember how much fun it was to read it 30 years ago. I came across it recently in a local bookstore, and after poring over it again, I was inspired to write a little review about it.

The most important thing about the book is Polya's little heuristic method for breaking down math problems and guiding you thru the process of solving them. Try to visualize the problem as a whole. Diagram it at first, even if you don't have all the details. Just initially try to get the most important parts of the problem down. Then try to get some sense of the relationship of the parts to the whole. Then tackle each of the component parts. If you get stuck, ask yourself if you could approach it another way, what could be missing, and so on. To this end, the questions at the back of the book are worth their weight in gold.

Polya's little heuristic and methods book is a timeless classic. This and Lancelot Hogben's "Mathematics for the Millions" have done more good for suffering math students than all the the dry textbooks put together that really don't teach you "how to solve it."

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Inside This Book (learn more)
First Sentence:
Helping the student. Read the first page
Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
heuristic syllogism, accessible related problem, proposed problem try, simpler analogous problem, drop the other part, account all essential notions, introduce suitable notation, auxiliary problem, similar unknown, ambitious problem, auxiliary elements, incomplete proofs, familiar theorem, proposed theorem, heuristic reasoning, derive something, same unknown, whole hypothesis, rectangular parallelepiped
Key Phrases - Capitalized Phrases (CAPs): (learn more)
Euclid's Elements, John Jones, Director Brown, North Pole
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