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Posts Tagged ‘G. Polya’

Solve It

Posted by heyrandy on June 10, 2008

How to Solve It, G. Polya. Princeton University Press, Princeton, 1957 (1985).  253pp. footnotes, no index

Troubled by some intractable puzzle?  Mystified by a quandry?  Then this is the book for you.  Polya (1887-1985), Professor of Mathematics at Stanford University, has written a book to help you figure it out.

Do not be afraid of Polya job description.  The mathematically underequipped will not be overwhelmed by a barrage of numbers and symbols.  There are numbers and symbols in the book, but there are also examples of non-mathematical problems such a crossword puzzle clues and the color of bears.

Polya begins the book with a detailed outline of the system he sets forth.  The text of the book is exposition and application of the outline’s details.  Along the way Polya gives some instruction to teachers on how to help the less than bright student.

Polya’s method is spelled out in four steps: Understand the problem, Devise a plan, Carry out the plan, and Test the solution.  These all seem so self-evident that you may wonder why a book had to be written to explain them and why such a book would become a classic.  The answer is that we are all a little dumb and often more than a little lazy.

Even those exceptional people that were born with the brains I lack need to have their minds trained to make maximum use of what God gave them.  The book is a manual for such training.  Work through some of his examples and you may call it a manual for rigorous training.

The book is an example of heuristic thinking.  Heuristic thinking is not as exact as what Polya call rigorous proof, but it is what is often need to get the problem solving process started and what is required step into the more rigorous methods.  Polya states that he wrote this book to revive heuristic thinking.

Polya’s work is not one of profound research; he give few footnotes.  It is a work that will enable you to be equipped to do profound research.  Learning usually does not come easy.  It takes work.  Usually lots of hard work.  Polya gives a method that will make that work effective and effecient.

The book ends with a set of sample problems, along with hints and the solutions.  So you will have some practice using his teachings.  I have worked though some of the samples, and I find them a challenge.  But this is what you get in life, except for the explicit hints and easy answers.

Read this book, and then you can SOLVE IT.

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