How to Solve It

How to Solve It

George Pólya's 1945 book "How to Solve It" is a small volume describing methods of problem solving.cite book
first = George
last = Pólya
author-link = George Pólya
title = How to Solve It
year = 1945
pages =
place =
publisher = Princeton University Press
url =
doi =
id =
isbn = 0-691-08097-6]

Overview

This book was published at Princeton University. It suggests the following steps when solving a mathematical problem:
# First, you have to "understand the problem".
# After understanding, then "make a plan".
# "Carry out the plan".
# "Look back" on your work. How could it be better?

If this technique fails, Pólya advises: "If you can't solve a problem, then there is an easier problem you can solve: find it." [ [http://www-groups.dcs.st-and.ac.uk/~history/Quotations/Polya.html Quotations by Polya ] ] Or: "If you cannot solve the proposed problem, try to solve first some related problem. Could you imagine a more accessible related problem?"

His book contains a dictionary-style set of heuristics, many of which have to do with generating a more accessible problem. For example:

The technique "have I used everything" is perhaps most applicable to formal educational examinations (e.g., "n" men digging "m" ditches) problems.

The book has achieved "classic" status because of its considerable influence (see the next section).

Other books on problem solving are often related to more creative and less concrete techniques. See lateral thinking, mind mapping and brainstorming.

Other Methods

There are other methods of problem solving:

Influence

* It has been translated into several languages and has sold over a million copies, and has been continuously in print since its first publication.
* Marvin Minsky said in his influential paper "Steps Toward Artificial Intelligence" that "everyone should know the work of George Pólya [87] on how to solve problems." [Citation
last = Minsky
first = Marvin
author-link = Marvin Minsky
title = Steps Toward Artificial Intelligence
journal =
volume =
issue =
pages =
date =
year =
url = http://web.media.mit.edu/~minsky/papers/steps.html
doi =
id = .]
* Pólya's book has had a large influence on mathematics textbooks as evidenced by the bibliographies for mathematics education. [cite journal
last = Schoenfeld
first = Alan H.
coauthors = D. Grouws (Ed.)
title = Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics
journal = Handbook for Research on Mathematics Teaching and Learning
publisher= MacMillan
location= New York
pages = pp. 334–370
date =
year = 1992
url = http://gse.berkeley.edu/faculty/ahschoenfeld/Schoenfeld_MathThinking.pdf
doi =
id = .]
* Russian physicist Zhores I. Alfyorov, (Nobel laureate in 2000) praised it, saying he was very pleased with Pólya's famous book.

Notes

See also

* Heuristic
* "How to Solve It By Computer"

External links

* [http://www.math.utah.edu/~alfeld/math/polya.html More information on Pólya can be found here.]
* [http://freefeel.org/wiki/SummaryHowToSolveIt#s-1 An uneven summary of the whole book.]


Wikimedia Foundation. 2010.

Игры ⚽ Нужно решить контрольную?

Look at other dictionaries:

  • How to Solve It By Computer — is a 1982 book by R. G. Dromey (Prentice Hall, ISBN 0 13 434001 9). It is an introduction to the why s of algorithms and data structures.Features of the book : #The design factors associated with problems #The creative process behind coming up… …   Wikipedia

  • how — 1. adverb /haʊ/ a) To what degree. How often do you practice? b) In what manner. How do you solve this puzzle? 2. adjective /haʊ/ …   Wiktionary

  • how — how1 /how/, adv. 1. in what way or manner; by what means?: How did the accident happen? 2. to what extent, degree, etc.?: How damaged is the car? 3. in what state or condition?: How are you? 4. for what reason; why?: How can you talk such… …   Universalium

  • how — [[t]haʊ[/t]] adv. 1) in what way or manner; by what means?: How did the fire start?[/ex] 2) to what extent, degree, etc.?: How difficult was the test?[/ex] 3) in what state or condition?: How is the baby?[/ex] 4) for what reason; why?: How can… …   From formal English to slang

  • solve — solve, *resolve, unfold, unravel, decipher can all mean to make clear or apparent or intelligible what is obscure or mysterious or incomprehensible. Solve is the most general in meaning and suggestion in this group; it implies the finding of a… …   New Dictionary of Synonyms

  • How to Read a Book — was written in 1940 by Mortimer Adler. He co authored a heavily revised edition in 1972 with Charles Van Doren. The book gives guidelines for critically reading what the authors consider to be the Western canon, which they refer to as the Great… …   Wikipedia

  • How Do You Solve a Problem Like Maria? — Infobox Television show name = How Do You Solve a Problem Like Maria? caption = format = Talent show picture format = PAL (576i), 16:9 runtime = 30–90mins creator = Andrew Lloyd Webber presenter = Graham Norton judges = Andrew Lloyd Webber David… …   Wikipedia

  • How Do You Solve a Problem Like Maria? (Canada) — Infobox Television show name = How Do You Solve a Problem Like Maria? (Canada) caption = How Do You Solve a Problem Like Maria? (CBC)‎ format = Talent competiton creator = Andrew Lloyd Webber starring = Gavin Crawford (Host) Simon Lee (Judge)… …   Wikipedia

  • How to Stop an Exploding Man — Infobox Television episode Caption= Peter and Sylar face off at Kirby Plaza. Title= How to Stop an Exploding Man Series=Heroes Season=1 Episode=23 Airdate= May 21, 2007 Production=123 Writer= Tim Kring Director= Allan Arkush Guests=Zachary Quinto …   Wikipedia

  • How Cleveland Got His Groove Back — Эпизод «Шоу Кливленда» «How Cleveland Got His Groove Back» Промо картинка …   Википедия

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”