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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 Polya 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 Polya'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. Polya 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. Polya 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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最も参考になったカスタマーレビュー
2 人中、1人の方が、｢このレビューが参考になった｣と投票しています。
形式:ペーパーバック|Amazonが確認した購入
数学の問題を解く方法が、学生を指導する、という視点で体系的に述べられています。 解答を導き出すための学生への質問集も用意されています。 考え方にびっくりするほどの斬新さは感じられませんが、数学教師や数学を志す人には役立つと思います。 では数学以外の一般的問題解決やプロジェクトなどの問題分析に役立つかというと、そこまでの応用力を求めるのは無理かな、と感じました。 文章は簡潔で英語は読みやすいです。 今まで馴染みのなかった数学英語に接することも出来ました。また、錆付いた数学知識を（ある程度）思い出すきっかけになったと思います。 ガリレオ時代のフランスの学者 Descartes,Reneが引用されていたりもします。
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102 人中、100人の方が、｢このレビューが参考になった｣と投票しています。
A Classic for Problem-Solvers
2001/9/17
形式:ペーパーバック
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.
63 人中、63人の方が、｢このレビューが参考になった｣と投票しています。
Indispensable for anyone who solves problems professionally.
1996/7/8
形式:ハードカバー
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.
62 人中、62人の方が、｢このレビューが参考になった｣と投票しています。
A delightful and satisfying classic
2004/12/18
形式:ペーパーバック
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.
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.
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