How To Solve It: A New Aspect of Mathematical Method

89 customer reviews
ISBN-13: 978-4871878302
ISBN-10: 4871878309
Why is ISBN important?
ISBN
This bar-code number lets you verify that you're getting exactly the right version or edition of a book. The 13-digit and 10-digit formats both work.
Scan an ISBN with your phone
Use the Amazon App to scan ISBNs and compare prices.
Sell yours for a Gift Card
We'll buy it for $3.48
Learn More
Trade in now
Have one to sell? Sell on Amazon
Buy used
$14.05
Buy new
$24.95
Amazon Price New from Used from
eTextbook
"Please retry"
Hardcover
"Please retry"
Paperback, June 26, 2009
"Please retry"
$24.95
$19.99 $14.05
Mass Market Paperback
"Please retry"
$5.26
Unknown Binding
"Please retry"
$28.00
More Buying Choices
20 New from $19.99 20 Used from $14.05
Free Two-Day Shipping for College Students with Amazon Student Free%20Two-Day%20Shipping%20for%20College%20Students%20with%20Amazon%20Student


InterDesign Brand Store Awareness Rent Textbooks
$24.95 FREE Shipping on orders over $35. In Stock. Ships from and sold by Amazon.com. Gift-wrap available.

Frequently Bought Together

How To Solve It: A New Aspect of Mathematical Method + How to Prove It: A Structured Approach, 2nd Edition
Price for both: $53.55

Buy the selected items together

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



"In an age that all solutions should be provided with the least possible effort, this book brings a very important message: mathematics and problem solving in general needs a lot of practice and experience obtained by challenging creative thinking, and certainly not by copying predefined recipes provided by others. Let's hope this classic will remain a source of inspiration for several generations to come."--A. Bultheel, European Mathematical Society

--This text refers to an out of print or unavailable edition of this title.

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.
NO_CONTENT_IN_FEATURE


Best Books of the Month
Best Books of the Month
Want to know our Editors' picks for the best books of the month? Browse Best Books of the Month, featuring our favorite new books in more than a dozen categories.

Product Details

  • Paperback: 280 pages
  • Publisher: Ishi Press (June 26, 2009)
  • Language: English
  • ISBN-10: 4871878309
  • ISBN-13: 978-4871878302
  • Product Dimensions: 5.5 x 0.6 x 8.5 inches
  • Shipping Weight: 1 pounds (View shipping rates and policies)
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (89 customer reviews)
  • Amazon Best Sellers Rank: #189,312 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews

127 of 132 people found the following review helpful By Phil on September 16, 2001
Format: 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.
1 Comment Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback. If this review is inappropriate, please let us know.
Sorry, we failed to record your vote. Please try again
107 of 111 people found the following review helpful By Sandra Feder on December 17, 2004
Format: 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.
Read more ›
1 Comment Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback. If this review is inappropriate, please let us know.
Sorry, we failed to record your vote. Please try again
75 of 80 people found the following review helpful By A Customer on July 7, 1996
Format: Hardcover
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.
1 Comment Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback. If this review is inappropriate, please let us know.
Sorry, we failed to record your vote. Please try again
35 of 37 people found the following review helpful By Magellan HALL OF FAMETOP 1000 REVIEWER on June 30, 2002
Format: 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."
Comment Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback. If this review is inappropriate, please let us know.
Sorry, we failed to record your vote. Please try again

Most Recent Customer Reviews

Set up an Amazon Giveaway

Amazon Giveaway allows you to run promotional giveaways in order to create buzz, reward your audience, and attract new followers and customers. Learn more
How To Solve It: A New Aspect of Mathematical Method
This item: How To Solve It: A New Aspect of Mathematical Method
Price: $24.95
Ships from and sold by Amazon.com