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# How to Solve It: A New Aspect of Mathematical Method

by
George Pólya

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. Gener
...more

Paperback, 288 pages

Published
April 25th 2004
by Princeton University Press
(first published November 30th 1944)

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What this books is, is a systematic and incredibly instructive overview of guidelines in mathematical problem solving, which are, as the author put it - "natural, simple, obvious, and proceed from plain common sense."

If you've ever put yourself against a serious problem which you really, really, really wanted to have solved ...more

Still, the way I went at the book is that I skimmed thro ...more

Jun 15, 2012
Jessica
added it

Geometry and Discrete Math are the only high school math classes I aced. Likely, it had to do with some teaching and presenting, as well as the interest I mustered not being totally repelled by them in the hoisting of what curriculum mandates must-be-learned.

This book takes a simple, interesting approach and though it's written in the 40s, many benefits remain to-be-had from popularity outside its field. For me, beginning this book, I recalled how as an undergrad tutor for ESL students, our cla ...more

This book takes a simple, interesting approach and though it's written in the 40s, many benefits remain to-be-had from popularity outside its field. For me, beginning this book, I recalled how as an undergrad tutor for ESL students, our cla ...more

But one of the big takeaways is that problems are only as hard as they are unresolved. Not only does Polya give excellent ideas for solving problems: creating auxiliary problems, using heuristics, working backwards.

Each example that Polya gives takes concentration and critical analysis. But when yo ...more

Oct 26, 2008
Louis
rated it
5 of 5 stars
·
review of another edition

Recommends it for:
Anyone who has to analyze situations not seen before

Shelves:
math-stats

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, t ...more
Aug 09, 2007
Ari
rated it
5 of 5 stars
·
review of another edition

Recommends it for:
everyone

Shelves:
owned

I don't remember when I first encountered this book -- I think it was early in my time at Cornell. It's had a great deal of influence on how I approach math. It's one of the best math books I've ever read, and quite possibly the best book on mathematical problem solving ever written.

There are two copies of it floating around my lab at Berkeley, evidence, i think, that I'm not the only one who appreciates it.

Polya was a first rate mathematician, and his book is devoted to explaining simply and u ...more

There are two copies of it floating around my lab at Berkeley, evidence, i think, that I'm not the only one who appreciates it.

Polya was a first rate mathematician, and his book is devoted to explaining simply and u ...more

Unfortunately, almost everything gets repeated numerous times, and as a whole the books ends up being thoroughly redundant. You don't really need to read beyond the first 36 pages (the rest of the book consists of a 'problem solving dictionary', and here's where the redundancy begins).

The ...more

It teaches solving mathematical problems. It is mostly focused on high-school problems, but it is applicable to most types of mathematical problems out there. The author has developed a nice heuristic framework for tackling problems and has done a wonderful job of explaining it. It's not just the methods – exposition is also a great takeaway from this read.

On the downside, the book was written in 1945 and sometime it shows. It's more cute than a nuisance, though :)

Dec 08, 2014
Andrew
rated it
4 of 5 stars
·
review of another edition

Shelves:
math-statistics,
owned

Here's how you solve it:

...moreFirst.

You have tounderstandthe problem.

UNDERSTANDING THE PROBLEMWhat is the unknown? What are the data? What is the condition?

Is it possible to satisfy the condition? Is the condition sufficient to determine the unknown? Or is it insufficient? Or redundant? Or contradictory?

Draw a figure. Introduce suitable notation.

Separate the various parts of the condition. Can you write them down?Second.

Find the connection between the data and the unknown.

You may be obliged to consi

The thing that makes this book unusual is that it's about the ...more

- Know the purpose in each step of your problem-solving

- If you can't solve a problem, solve a different problem that is similar enough to help you

- Account for all the data

- Can you check the result?

- Can you derive it differently?

I also really enjoyed the section on proverbs (p. 221):

Who understands ill, answer ill.

A fool looks to the beginning, a wise man reg ...more

I'm giving this three stars ...more

This book is unique in that it describes the actual method of problem solving, and walks through generic techniques that apply strongly, not just in mathematics, but anywhere.

This book is a foundation in my reasoning through problems at work. I've lent out multiple copies, never seen them again, and it makes me happy.

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