Sunday, October 26, 2008

How to Solve It by G Polya

How to Solve It How to Solve It by George Pólya

My review

rating: 5 of 5 stars
This is a book I wish I had read at the beginning of grad school. How to Solve It is not as much about methods of solving mathematical problems as it is about various approaches to solving problems in general. The method he uses to teach problem solving is to apply the approaches to problems of geometry. This is actually in line with the ancient greek (Aristotle) opinion that the young should learn geometry first, then when they have learned logic and how to prove things with physical reality, then they can go on to things such as philosophy or politics.

The first part of How to Solve It are essays on how to teach and how to approach problems in general. His view on teaching is leading a student to think. Giving the student problems where the answer is not the goal, but the experience in seeing a new type of problem. This is contrasted with viewing teaching as a series of cookbook or algorithms to be taught. It also means the role of the teacher is to provide the problem, then give only what is necessary to nudge the student in the direction needed for the student to discover the method of solution. And presumably, to be able to develop methods for other problems the student has not seen before. Very much like what graduate school is supposed to be.

The bulk of How to Solve It describes a wide range of approaches to problem solving. Some are familiar to a variety of disciplines such as business, crisis management, or general analysis. Some are more familiar to those in sciences or mathematics. But the illustrations are understandable to anyone past a first or second year of high school mathematics, making them much more understandable then, say, a graduate course in real analysis.

If I was in the position of working with first year graduate students in anything, I would recommend this book as something to read before they arrive on campus. It provides a good first exposure to many problem-solving approaches and an exhortation on how to think logically and analytically, that will suit them well when they are faced with the complicated subject matter that is ahead of them.

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