Picture of author.

George Pólya (1887–1985)

Forfatter af How to Solve It: A New Aspect of Mathematical Method

42+ Værker 3,009 Medlemmer 19 Anmeldelser 3 Favorited

Om forfatteren

Serier

Værker af George Pólya

How to Solve It: A New Aspect of Mathematical Method (1945) 1,991 eksemplarer, 15 anmeldelser
Induction and Analogy in Mathematics (1954) 255 eksemplarer, 1 anmeldelse
Patterns of Plausible Inference (1954) 204 eksemplarer, 1 anmeldelse
Mathematical Methods in Science (1984) 40 eksemplarer
Mathematical Discovery, Volume 2 (1962) 33 eksemplarer
Mathematical Discovery, Volume 1 (1962) 25 eksemplarer
Problems and theorems in analysis (1945) 13 eksemplarer
Complex Variables (1974) 13 eksemplarer
A Arte de Resolver Problemas (1978) 7 eksemplarer
Analysis 2 eksemplarer
Analysis I 2 eksemplarer
Inequalities 2 eksemplarer
A problémamegoldás iskolája (1979) 2 eksemplarer

Associated Works

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

Satte nøgleord på

Almen Viden

Kanonisk navn
Pólya, George
Fødselsdato
1887-12-13
Dødsdag
1985-09-07
Køn
male
Nationalitet
Hungary
Switzerland
USA
Fødested
Budapest, Austria-Hungary
Dødssted
Palo Alto, California, USA
Uddannelse
University of Budapest (Ph.D|1912)
Erhverv
professor (mathematics)
Relationer
Walter, Marion (student)
Organisationer
ETH Zurich
Stanford University
Priser og hædersbevisninger
American Academy of Arts and Sciences (1974)
National Academy of Sciences (1976)
Academie des Sciences
Hungarian Academy
Academie Internationale de Philosophie des Sciences
Kort biografi
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...]

Medlemmer

Anmeldelser

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.
… (mere)
 
Markeret
bnielsen | Apr 24, 2023 |
Indeholder "From the Preface to the First Printing", "From the Preface to the Seventh Printing", "Preface to the Second Edition", "'How to solve it' list", "Introduction", "Part I. In the classroom", " Purpose", " 1. Helping the student", " 2. Questions, recommendations, mental operations", " 3. Generality", " 4. Common sense", " 5. Teacher and student. Imitation and practice", " Main divisions, main questions", " 6. Four phases", " 7. Understanding the problem", " 8. Example", " 9. Devising a plan", " 10. Example", " 11. Carrying out the plan", " 12. Example", " 13. Looking back", " 14. Example", " 15. Various approaches", " 16. The teacher's method of questioning", " 17. Good questions and bad questions", " More examples", " 18. A problem of construction", " 19. A problem to prove", " 20. A rate problem", "Part II. How to solve it", " A dialogue", "Part III. Short Dictionary of Heuristic", " Analogy", " Auxiliary elements", " Auxiliary problem", " Bolzano", " Bright idea", " Can you check the result?", " Can you derive the result differently?", " Can you use the result?", " Carrying out", " Condition", " Contradictory", " Corollary", " Could you derive something useful from the data?", " Could you restate the problem?", " Decomposing and recombining", " Definition", " Descartes", " Determination, hope, success", " Diagnosis", " Did you use all the data?", " Do you know a related problem?", " Draw a figure", " Examine your guess", " Figures", " Generalization", " Have you seen it before?", " Here is a problem related to yours and solved before", " Heuristic", " Heuristic reasoning", " If you cannot solve the proposed problem", " Induction and mathematical induction", " Inventor's paradox", " Is it possible to satisfy the condition?", " Leibnitz", " Lemma", " Look at the unknown", " Modern heuristic", " Notation", " Pappus", " Pedantry and mastery", " Practical problems", " Problems to find, problems to prove", " Progress and achievement", " Puzzles", " Reductio ad absurdum and indirect proof", " Reductant", " Routine problem", " Rules of discovery", " Rules of style", " Rules of teaching", " Separate the various parts of the condition", " Setting up equations", " Signs of progress", " Specialization", " Subconscious work", " Symmetry", " Terms, old and new", " Test by dimension", " The future mathematician", " The intelligent problem-solver", " The intelligent reader", " The traditional mathematics professor", " Variation of the problem", " What is the unknown?", " Why proofs?", " Wisdom of proverbs", " Working backwards", "Part IV. Problems, Hints, Solutions", " Problems", " Hints", " Solutions".

En generel bog om at løse problemer. Dem er der ikke så mange af.
… (mere)
 
Markeret
bnielsen | 14 andre anmeldelser | Nov 27, 2016 |

Lister

Hæderspriser

Måske også interessante?

Associated Authors

Statistikker

Værker
42
Also by
3
Medlemmer
3,009
Popularitet
#8,478
Vurdering
4.0
Anmeldelser
19
ISBN
79
Sprog
10
Udvalgt
3

Diagrammer og grafer