Книга: George Polya «George Polya Collected Papers Location of Zeros V 2»
Производитель: "Неизвестный" George Polya Collected Papers Location of Zeros V 2 ISBN:9780262661690 Издательство: "Неизвестный" (2003)
ISBN: 9780262661690 |
George Pólya
George Pólya (b.
Life and works
He was born as "Pólya György" in
In "How to Solve It", Pólya provides general
In 1976 The Mathematical Association of America established the George Pólya award "for articles of expository excellence published in the College Mathematics Journal."
Quotes
*To be a good mathematician, or a good gambler, or good at anything, you must be a good guesser.
*Observe also (what modern writers almost forgot, but some older writers, such as
*How I need a drink, alcoholic of course, after the heavy chapters involving
*If you can't solve a problem, then there is an easier problem you can solve: find it.
*Wishful thinking is imagining good things you don't have... [It] may be bad as too much salt is bad in the soup and even a little garlic is bad in the chocolate pudding. I mean, wishful thinking may be bad if there is too much of it or in the wrong place, but it is good in itself and may be a great help in life and in problem solving.
*He was the only student that ever scared me (in reference to
*Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive equipment.
*A Great discovery solves a great problem but there is a grain of discovery in the solution of any problem. Your problem may be modest; but if it brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery (from "Faces of Mathematics", page 3, Robert, A. W.,
*To conjecture and not to test is the mark of a savage.
*A drunk man will eventually return home but a drunk bird will lose its way in space. (In reference to random walks in dimension 2 and 3).
Pólya's four principles
First principle: Understand the problem
This seems so obvious that it is often not even mentioned, yet students are often stymied in their efforts to solve problems simply because they don't understand it fully, or even in part. Pólya taught teachers to ask students questions such as:
* Do you understand all the words used in stating the problem?
* What are you asked to find or show?
* Can you restate the problem in your own words?
* Can you think of a picture or a diagram that might help you understand the problem?
* Is there enough information to enable you to find a solution?
* Do you need to ask a question to get the answer?
Second principle: Devise a plan
Pólya mentions (1957) that there are many reasonable ways to solve problems. The skill at choosing an appropriate strategy is best learned by solving many problems. You will find choosing a strategy increasingly easy. A partial list of strategies is included:
* Guess and check
* Make an orderly list
* Eliminate possibilities
* Use symmetry
* Consider special cases
* Use direct reasoning
* Solve an equation
Also suggested:
* Look for a pattern
* Draw a picture
* Solve a simpler problem
* Use a model
* Work backward
* Use a formula
* Be creative
* Use your head
Third principle: Carry out the plan
This step is usually easier than devising the plan. In general (1957), all you need is care and patience, given that you have the necessary skills. Persist with the plan that you have chosen. If it continues not to work discard it and choose another. Don't be misled, this is how mathematics is done, even by professionals.
Fourth principle: Review/extend
Pólya mentions (1957) that much can be gained by taking the time to reflect and look back at what you have done, what worked and what didn't. Doing this will enable you to predict what strategy to use to solve future problems, if these relate to the original problem.
See also
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References
External links
* [http://www.maa.org/Awards/polya.html The George Pólya Award]
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* [http://www.geocities.com/polyapower/ PolyaPower -- an introduction to Polya's Heuristics]
* [http://wik.ed.uiuc.edu/index.php/P%C3%B3lya%2C_George George Pólya on UIUC's WikEd]
* [http://histsoc.stanford.edu/pdfmem/PolyaG.pdf Memorial Resolution]
Источник: George Pólya
См. также в других словарях:
George Polya — George Pólya, ca 1973 George (György) Pólya (* 13. Dezember 1887 in Budapest, † 7. September 1985 in Palo Alto) war ein amerikanischer Mathematiker ungarischer Herkunft. Seine Arbeitsgebiete waren insbesondere Wahrscheinlichkeitstheorie,… … Deutsch Wikipedia
George Pólya — George Pólya. George Pólya (13 de diciembre de 1887 – 7 de septiembre de 1985, Pólya György en húngaro) fue un matemático que nació en Budapest, Hungría y murió en Palo Alto, EUA. Trabajó en una gran variedad de temas matemáticos, incluidas las… … Wikipedia Español
George Pólya — (b. December 13, 1887 ndash; d. September 7, 1985, in Hungarian Pólya György ) was a Hungarian mathematician.Life and worksHe was born as Pólya György in Budapest, Hungary, and died in Palo Alto, California, USA. He was a professor of mathematics … Wikipedia
George Pólya — George Pólya, ca. 1973 George (György) Pólya (* 13. Dezember 1887 in Budapest; † 7. September 1985 in Palo Alto) war ein ungarischer Mathematiker. Seine Arbeitsgebiete waren insbesondere Wahrscheinlichkeitstheorie, Kombinatorik und Zahlentheorie … Deutsch Wikipedia
George Polya — George Pólya George Pólya vers 1973 George (György) Pólya, né à Budapest (Hongrie) le 13 décembre 1887 et mort à Palo Alto (États Unis le 7 septembre 1985, est un mathématicien américain d origine hongroise … Wikipédia en Français
George Pólya — vers 1973 George (György) Pólya, né à Budapest (Hongrie) le 13 décembre 1887 et mort à Palo Alto (États Unis) le 7 septembre 1985, est un mathématicien américain d origine hongroise. Après des études secondaires classiqu … Wikipédia en Français