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Rating: 
Summary: A delightful and satisfying classic
Review: 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. This can lead you straight to a solution you might otherwise have completely missed.
His techniques help you to stand back and get to the heart of the problem, rather than getting lost in it.
Something else I liked very much about his book is his encouragement to guess, or to reason 'plausibly.' While the final proof must be strictly logical, "Anything is right that leads to the right idea." Problem-solving has every right to be fun, as well as purposeful.
Rating: 
Summary: Resolute favorite: How to Solve It
Review: 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.
Rating:
Summary: Getting to Eureka
Review: 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.
Rating:
Summary: A Classic for Problem-Solvers
Review: 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.
Rating:
Summary: Very fresh for me!
Review: 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)
Rating:
Summary: Important classic
Review: 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."
Rating:
Summary: Very helpful to my programming work
Review: 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.
Rating:
Summary: Buy it!
Review: 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.
Rating:
Summary: For math thinkers maybe
Review: 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. I'm a philosophy PhD with an interest in "business strategy" (as they call it). The book's a little bit tough to move through, since he chose to write it as a glossary for the bulk of the text. That makes it boring. The more fundamental issue of course is that he's thinking about math when he gives his ideas for solving problems, and more specifically about TEACHING kids to solve math problems. Now, this is useful. And the general tenor is applicable to all kinds of problem solving. But I think it's not the holy grail it's meant to be -- there are other books on problem solving that make more practical sense if you are working on non-formal mathematical puzzles.
Rating:
Summary: Very basic book for one wants to solve problem.
Review: 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. Not in any University Library or in general. No way to be found in New Market. I asked some one will visit Calcutta, India. He was my teacher. He failed to bring it for me. At last, one of my friends at Toronto order the book for me, she got after 15 days and send it to me after 30 days through one of her relative. I felt I must read it. After having and reading, I found that the book is really a very basic book to open your mind for facing problems. Which helps to understand, think, analyze and solve problems. I'm a programmer in C. I love to think about problem.
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