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

G. Polya , John H. Conway
4.7 out of 5 stars  See all reviews (18 customer reviews)
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Book Description

April 25 2004 069111966X 978-0691119663 1

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 + How to Prove It: A Structured Approach + Concepts of Modern Mathematics
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"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

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Most helpful customer reviews
5.0 out of 5 stars Buy it! April 27 2004
By Manish
Format:Paperback
The issue is that solving problems is not made interesting and fulfilling experience.
This book beautifully explains the process of problem-solving. It starts from simple problems, lays down the fundamentals and leads to more complex problems.
One of the gems is the simple formula:
1. Understand the problem
2. Devise a plan (seeing how various items connect
3. Carry out the plan
4. Look back at the completed solution, review and discuss it.
It is also a good reference to teach kids how to approach problems.
Buy it and it will be a very handy reference.
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5.0 out of 5 stars Very helpful to my programming work Dec 30 2003
By Leo Lim
Format:Paperback
Polya prescribes different forms to approaching a problem through some guide questions that a solver should ask ("Is there a related problem"). The exposition is quite short, majority of the book is devoted to a glossary of heuristic terms which prove very helpful. Polya uses common problems in high school geometry to demonstrate his point which make it easily understandable.
I'm glad I have discovered an excellent book on problem solving which would prove indispensable in my programming career. Other programming books mainly demonstrate features of an OS or a computer language but this book goes into the heart of the computer science which is problem solving.
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4.0 out of 5 stars Getting to Eureka Jan. 2 2003
Format:Paperback
How does a teacher go about teaching? It is a hard trick. Written and published in the '40s, and then again subsequently Polya's "How to Solve It" is an attempt to describe the general paths to the student's Eureka! moments. As such it is also of interest to those who go about the task of discovery, and you must constantly rethink their strategies, in the face of a stubborn unknown.
Polya's consideration of the Various Approaches to problem solving hangs on several key structural bands that take the forms of a teacher's questions: Do you know any related problem? Do you know an analogous problem? [Parallelograms are considered.] Here is a problem related to yours and solved before. Can you use it? Should you introduce some auxiliary element in order to make its use possible?
These ring true to this recently mustered parental pedantic.
Polya's actual treatise is just 30 pages; the associated 'dictionary' definitions section is quite extended, actually, making up some 200 pages. He describes going back to first principles in problem solving. January 1, 2003 is a day perhaps to remember such back tracking is sometimes in order.
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4.0 out of 5 stars Resolute favorite: How to Solve It Jan. 1 2003
Format:Paperback
How does a teacher go about teaching? It is a hard trick. Written and published in the '40s, and then again subsequently Polya's "How to Solve It" is an attempt to describe the general paths to the student's Eureka! moments. As such it is also of interest to those who go about the task of discovery, and you must constantly rethink their strategies, in the face of a stubborn unknown.
Polya's consideration of the Various Approaches to problem solving hangs on several key structural bands that take the forms of a teacher's questions: Do you know any related problem? Do you know an analogous problem? [Parallelograms are considered.] Here is a problem related to yours and solved before. Can you use it? Should you introduce some auxiliary element in order to make its use possible?
These ring true to this recently mustered parental pedantic.
Polya's actual treatise is just 30 pages; the associated 'dictionary' definitions section is quite extended, actually, making up some 200 pages. He describes going back to first principles in problem solving. January 1, 2003 is a day perhaps to remember such back tracking is sometimes in order.
Was this review helpful to you?
5.0 out of 5 stars Very fresh for me! Sept. 2 2002
Format:Paperback
I got this book because I saw good reviews and heard that this was a classic...so I got it.
This is the first book that I ever encountered that teaches problem-solving. Further more, it teaches it through the use of heuristics(noun: A commonsense rule (or set of rules) intended to increase the probability of solving some problem). Half of the book cantains what the author calls The Dictionary - which contains a large number of heuristics that a problem-solver can use in his attempt to dissolve a problem. The author also describes in the first few chapters of the book on how to go about solving problems. Really gave me a new perspective on problem solving...Can't wait to apply what I have learned.
Buy it!(its cheap anyway...nothing to lose)
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5.0 out of 5 stars Important classic 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."
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Most recent customer reviews
4.0 out of 5 stars For math thinkers maybe
There seems to be a cultish following for Polya's book, so I decided to pick it up even though I'm not a mathematician. Read more
Published on July 19 2003 by Amol Sarva
5.0 out of 5 stars A Classic for Problem-Solvers
I found Pollya's "heuristic" approach to problem-solving applicable to both mathematical and non-mathematical problems. Read more
Published on Sept. 16 2001 by Phil
5.0 out of 5 stars Very basic book for one wants to solve problem.
You know? I was looking for the book for 6 months. It's a very old book(Second Edition 1956). I guess no one in Bangladesh have the book. Read more
Published on June 24 2001 by Zahid Hossain
5.0 out of 5 stars Thinking outside of the box
Critical thinking and problem solving are not stressed in any kind of modern education. Students tend to take a cookbook approach to problem solving and wonder how is it that some... Read more
Published on April 16 2001 by James E. Vancik
4.0 out of 5 stars ?
Yes, this is a classic. Yes, I refer back to it frequently and always find something new which informs my teaching. Read more
Published on Sept. 17 2000 by David E. Molnar
5.0 out of 5 stars An essential classic in the field of problem solving
Pardon the cliche, but: no home should be without this book. Polya's examples are mathematical, but the principles of heuristics and problem solving are universally applicable,... Read more
Published on Aug. 10 2000 by James Jones
5.0 out of 5 stars LONG LIVE POLYA!
i must say that this is one of the most interesting books i've ever read. it is a must for teachers of mathematics and the sciences. Read more
Published on July 13 2000
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