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George Pólya (1887–1985)

Teoksen Ratkaisemisen taito : kuinka lähestyä matemaattisia ongelmia tekijä

41+ teosta 3,016 jäsentä 19 arvostelua 3 Favorited

Tietoja tekijästä


Tekijän teokset

Patterns of Plausible Inference (1954) 204 kappaletta
Mathematical Methods in Science (1984) 40 kappaletta
Mathematical Discovery, Volume 2 (1962) 33 kappaletta
Mathematical Discovery, Volume 1 (1962) 25 kappaletta
Problems and theorems in analysis (1945) 13 kappaletta
Complex Variables (1974) 13 kappaletta
A Arte de Resolver Problemas (1978) 6 kappaletta
Analysis 2 kappaletta
Analysis I 2 kappaletta
Inequalities 2 kappaletta
A problémamegoldás iskolája (1979) 2 kappaletta

Associated Works

The World of Mathematics, Volume 3 (1955) — Avustaja — 117 kappaletta
New Directions in the Philosophy of Mathematics (1985) — Avustaja — 55 kappaletta
The Random Walks of George Pólya (2000) — Avustaja — 14 kappaletta

Merkitty avainsanalla


Kanoninen nimi
Pólya, George
Budapest, Austria-Hungary
Palo Alto, California, USA
University of Budapest (Ph.D|1912)
professor (mathematics)
Walter, Marion (student)
ETH Zurich
Stanford University
Palkinnot ja kunnianosoitukset
American Academy of Arts and Sciences (1974)
National Academy of Sciences (1976)
Academie des Sciences
Hungarian Academy
Academie Internationale de Philosophie des Sciences
Lyhyt elämäkerta
George Pólya (/ˈpoʊljə/; Hungarian: Pólya György [ˈpoːjɒ ˈɟørɟ]) (December 13, 1887 – September 7, 1985) was a Hungarian mathematician. He was a professor of mathematics from 1914 to 1940 at ETH Zürich and from 1940 to 1953 at Stanford University. He made fundamental contributions to combinatorics, number theory, numerical analysis and probability theory. He is also noted for his work in heuristics and mathematics education. He has been described as one of The Martians, a term used to refer to a group of prominent Jewish Hungarian scientists (mostly, but not exclusively, physicists and mathematicians) who emigrated to the United States in the early half of the 20th century [from Wikipedia: https://en.wikipedia.org/wiki/George_P...]



Indeholder "Preface", "Preface to the second edition", "Hints to the reader", "Chapter XII. Some Conspicuous Patterns", " 1. Verification of a consequence", " 2. Successive verification of several consequences", " 3. Verification of an improbable consequence", " 4. Inference from analogy", " 5. Deepening the analogy", " 6. Shaded analogical inference", " Examples and Comments on Chapter XII, 1-14", " 14. Inductive conclusion from fruitless efforts", "Chapter XIII. Further Patterns and First Links", " 1. Examining a consequence", " 2. Examining a possible ground", " 3. Examining a conflicting conjecture", " 4. Logical terms", " 5. Logical links between patterns of plausible inference", " 6. Shaded inference", " 7. A table", " 8. Combination of simple patterns", " 9. On inference from analogy", " 10. Qualified inference", " 11. On successive verifications", " 12. The influence of rival conjectures", " 13. On judicial proof", " Examples and Comments on Chapter XIII, 1-20", " First Part 1-10. Second Part 11-20", " 9. On inductive research in mathematics and in the physical sciences", " 10. Tentative general formulations", " 11. More personal, more complex", " 12. There is a straight line that joins two given points", " 13. There is a straight line with a given direction through a given point. Drawing a parallel", " 14. The most obvious case may be the only possible case", " 15. Setting the fashion. The power of words", " 16. This is too improbable to be a mere coincidence", " 17. Perfecting the analogy", " 18. A new conjecture", " 19. Another new conjecture", " 20. What is typical?", "Chapter XIV. Chance, the Ever-present Rival Conjecture", " 1. Random mass phenomena", " 2. The concept of probability", " 3. Using the bag and the balls", " 4. The calculus of probability. Statistical hypotheses", " 5. Straightforward prediction of frequencies", " 6. Explanation of phenomena", " 7. Judging statistical hypotheses", " 8. Choosing between statistical hypotheses", " 9. Judging non-statistical conjectures", " Examples and Comments on Chapter XIV, 1-33", " First Part 1-18. Second Part 19-33", " 19. On the concept of probability", " 20. How not to interpret the frequency concept of probability", " 24. Probability and the solution of problems", " 25. Regular and Irregular", " 26. The fundamental rules of the Calculus of Probability", " 27. Independence", " 30. Permutations from probability", " 31. Combinations from probability", " 32. The choice of a rival statistical conjecture: an example", " 33. The choice of a rival statistical conjecture: general remarks", "Chapter XV. The Calculus of Probability and the Logic of Plausible Reasoning", " 1. Rules of plausible reasoning?", " 2. An aspect of demonstrative reasoning", " 3. A corresponding aspect of plausible reasoning", " 4. An aspect of the calculus of probability. Difficulties", " 5. An aspect of the calculus of probability. An attempt", " 6. Examining a consequence", " 7. Examining a possible ground", " 8. Examining a conflicting conjecture", " 9. Examining several consequences in succession", " 10. On circumstantial evidence", " Examples and Comments on Chapter XV, 1-9", " 4. Probability and credibility", " 5. Likelihood and credibility", " 6. Laplace's attempt to link induction with probability", " 7. Why not quantitative?", " 8. Infinitesimal credibilities?", " 9. Rules of admissibility", "Chapter XVI. Plausible Reasoning in Invention and Instruction", " 1. Object of the present chapter", " 2. The story of a little discovery", " 3. The process of solution", " 4. Deus ex machina", " 5. Heuristic justification", " 6. The story of another discovery", " 7. Some typical indications", " 8. Induction in invention", " 9. A few words to the teacher", " Examples and Comments on Chapter XVI. 1-13", " 1. To the teacher: some types of problems", " 7. qui nimium probat nihil probat", " 8. Proximity and credibility", " 9. Numerical computation and plausible reasoning", " 13. Formal demonstration and plausible reasoning", "Solutions to problems", "Bibliography", "Appendix", " I. Heuristic Reasoning in the Theory of Numbers", " II. Additional Comments, Problems, and Solutions".

George Polya tænkte meget over det at tænke og hvordan man får ideer, når man ikke er Gearløs og har en tænkehat. Han nævner en conjecture af Euler om at tal af formen 8n+3 kan skrives som et kvadrattal + det dobbelte af et primtal. Barry Mazur skrev i 2012 at det stadig hverken er bevist eller modbevist. Euler var interesseret i at vise det, for så kunne han skrive alle tal som summen af tre trekanttal. Det har Gauss senere bevist i 1796 i Disquisitiones Arithmeticae.
… (lisätietoja)
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bnielsen | Apr 24, 2023 |
Polya was more general than I would have liked, without a lot of examples that related to what I was trying to learn.
The best lesson i learned from this work was to first try to understand the problem before slogging into it with some random sort of method.
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mykl-s | 14 muuta kirja-arvostelua | Apr 23, 2023 |
Not for the general reader (one star). This mostly about induction, mathematical and logical. Useful as an introduction to a limited readership interested in science with a strong leaning toward Mathematics. Valuable mostly in pointing out inductive fallacies. That is worth the third star.

Probably suited best to high school math whizzes and college undergrads majoring or minoring in Mathematics or a closely related field such as Physics.

I have a math degree (48 years ago) and found that the most interesting parts were stuff I already knew, and most of the rest not especially engaging. I did enjoy Euler's discovery of a pattern in the primes, which was new to me. It would seem that has deep implications for group theory, but this was only hinted at and not explored. Also enjoyed some of Archimedes's proofs.… (lisätietoja)
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KENNERLYDAN | Jul 11, 2021 |
I'm conflicted about this book. There is a lot of good advice around the art of problem solving, but my god is there a lot of shit too. The layout is mostly a big alphabetical glossary of _math things_ --- everything from leading questions to notions of symmetry to anecdotes about absentminded professors --- and the layout doesn't particularly help. It's not organized by topic or ordered by first things first, it's just plopped down alphabetically. As such, it's hard to get into the flow.

This book however is lacking primarily in that it deals with how to solve "well-posed questions," which is to say, toy problems. There is very little about conducting your own open-ended research, and about how to turn wisps of ideas into well-posed ones.… (lisätietoja)
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isovector | 14 muuta kirja-arvostelua | Dec 13, 2020 |



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