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

G. Polya , John H. Conway
4.5 out of 5 stars  See all reviews (67 customer reviews)

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Book Description

April 25, 2004 069111966X 978-0691119663 Princeton Science Library

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.

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How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library) + How to Prove It: A Structured Approach
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Editorial Reviews


"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 (1887-1985) was one of the most influential mathematicians of the twentieth century. His basic research contributions span complex analysis, mathematical physics, probability theory, geometry, and combinatorics. He was a teacher par excellence who maintained a strong interest in pedagogical matters throughout his long career. Even after his retirement from Stanford University in 1953, he continued to lead an active mathematical life. He taught his final course, on combinatorics, at the age of ninety. John H. Conway is professor emeritus of mathematics at Princeton University. He was awarded the London Mathematical Society's Polya Prize in 1987. Like Polya, he is interested in many branches of mathematics, and in particular, has invented a successor to Polya's notation for crystallographic groups. --This text refers to an alternate Paperback edition.

Product Details

  • Series: Princeton Science Library
  • Paperback: 288 pages
  • Publisher: Princeton University Press; Princeton Science Library edition (April 25, 2004)
  • Language: English
  • ISBN-10: 069111966X
  • ISBN-13: 978-0691119663
  • Product Dimensions: 7.9 x 5.1 x 0.6 inches
  • Shipping Weight: 10.6 ounces (View shipping rates and policies)
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (67 customer reviews)
  • Amazon Best Sellers Rank: #18,659 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews
93 of 94 people found the following review helpful
5.0 out of 5 stars A delightful and satisfying classic December 17, 2004
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.
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117 of 121 people found the following review helpful
5.0 out of 5 stars A Classic for Problem-Solvers September 16, 2001
By Phil
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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68 of 70 people found the following review helpful
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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29 of 29 people found the following review helpful
5.0 out of 5 stars A book that teaches Math and thinking at once December 28, 2005
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)
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Most Recent Customer Reviews
5.0 out of 5 stars Polya's Great Reference Book on Problem Solving
This is a classic math teacher's resource book; but could be read and enjoyed by countless math afficianados. Read more
Published 14 days ago by BEANIE
5.0 out of 5 stars Teaches you how to think and approach problems
Polya deserves an applause for the work that he has done teaching the masses how to approach problem solving. It is no wonder that this book has become a classic. Read more
Published 1 month ago by X Avatar
5.0 out of 5 stars Highly recommended
I haven't started the book, but my teacher highly recommended it to me. I can't wait to begin and become a better problem solver!
Published 1 month ago by Mike D
5.0 out of 5 stars Problem solving
I'd like this book, and very interesting for reading.

It has two parts. One is the problem solving methodology itself with an excellent detail and options in every step. Read more
Published 2 months ago by Alfredo Tassano
5.0 out of 5 stars How to Think
There are clearly a lot of in-depth reviews on this book, so I won't delve into the details. What I will say is that, as a non-math guy, I was very intimidated by this book. Read more
Published 6 months ago by Dan Bergevin
5.0 out of 5 stars Excellent overview of problem solving!
I originally encountered this book in the references of a few software books, and I was wondering why a book on software would take references from a book on Mathematics. Read more
Published 7 months ago by Satyanarayana Shanmugam
4.0 out of 5 stars An introduction to heuristic reasoning
This book is a gentle introduction to heuristic reasoning. It will very useful to mathematicians, physists, and engineering students, as well as professors in making. Read more
Published 8 months ago by Juan Rogelio
5.0 out of 5 stars A mandatory reading for any serious practitioner of mathematics or...
In retrospect, I regret very much not having read Polya's "How to solve it" before I went to grad school (or even better undergrad). Read more
Published 8 months ago by Dmitry Zinenko
5.0 out of 5 stars The book that gave me the impetus to major in Mathematics
I first read this book in 1957, as I entered the 11th Grade. Except for 10th grade Geometry, mathematical problem solving up to that point had been a mixture of about 90%... Read more
Published 10 months ago by Herbert L Calhoun
3.0 out of 5 stars How to Solve It: A New Aspect of Mathematical Method
Folks it was not what I remembered it to be. I lost or gave away my first copy and what I needed was not "G. Polya". Read more
Published 10 months ago by Dave Clingerman
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