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Review
[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
Book Description
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."
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Most helpful customer reviews
5.0 out of 5 stars
Buy it!,
By Manish (NJ, USA) - See all my reviews
This review is from: How to Solve It: A New Aspect of Mathematical Method (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: It is also a good reference to teach kids how to approach problems. Buy it and it will be a very handy reference.
5.0 out of 5 stars
Very helpful to my programming work,
By
This review is from: How to Solve It: A New Aspect of Mathematical Method (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.
4.0 out of 5 stars
Getting to Eureka,
By
This review is from: How to Solve It: A New Aspect of Mathematical Method (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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