Here the author of How to Solve It explains how to become a "good guesser." Marked by G. Polya's simple, energetic prose and use of clever examples from a wide range of human activities, this two-volume work explores techniques of guessing, inductive reasoning, and reasoning by analogy, and the role they play in the most rigorous of deductive disciplines.
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Polya . . . does a masterful job of showing just how plausible reasoning is used in mathematics. . . . The material in both volumes is fresh and highly original; the presentation is stimulating, informal, and occasionally humorous; examples from science, legal reasoning, and daily life make the arguments clear even to a nonspecialist. Polya's book is a rare event. . . . -- Morris Kline, Scientific American
Professor Polya's beautifully written hook has become a classic. . . . -- -A. 0. L. Atkin, The Mathematical Gazette
Professor Polya . . . is interested in problem solving and the psychological aspects of mathematical discovery. . . . [These books] should provide many entertaining hours for anyone who cares to pick up the challenge. -- Carl Hammer, Journal of the Franklin Institute
Professor Polya presents a forceful argument for the teaching of intelligent guessing as well as proving. . . . There are also very readable and enjoyable discussions of such concepts as the isoperimetric problem and 'chance, the ever-present rival of conjecture.' -- Bruce E. Meserve, The Mathematics Teacher
About the Author
G. Polya (1887-1985) was Professor of Mathematics at Stanford University.
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First Sentence:
In the first volume of this work on Induction and Analogy in Mathematics we found some opportunity to familiarize ourselves with the practice of plausible reasoning. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
fundamental inductive pattern, random mass phenomenon, two rival conjectures, random mass phenomena, long range relative frequency, demonstrative pattern, tetrahedron collapses, isoperimetric theorem, heuristic pattern, plausible reasoning, verified consequences, principal frequency, proposed conjecture, rainless days, principal chord, statistical hypothesis, demonstrative inference, inductive investigation, plausible inference, demonstrative reasoning, virtual mass, fair dice Key Phrases - Capitalized Phrases (CAPs): (learn more)
Daniel Bernoulli, United States, Boulevard Raspail New!
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Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
In the first volume of this work on Induction and Analogy in Mathematics we found some opportunity to familiarize ourselves with the practice of plausible reasoning. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
fundamental inductive pattern, random mass phenomenon, two rival conjectures, random mass phenomena, long range relative frequency, demonstrative pattern, tetrahedron collapses, isoperimetric theorem, heuristic pattern, plausible reasoning, verified consequences, principal frequency, proposed conjecture, rainless days, principal chord, statistical hypothesis, demonstrative inference, inductive investigation, plausible inference, demonstrative reasoning, virtual mass, fair dice Key Phrases - Capitalized Phrases (CAPs): (learn more)
Daniel Bernoulli, United States, Boulevard Raspail New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
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- An Introduction to the Theory of Numbers (Oxford Science Publications) by G. H. Hardy in Back Matter
- Mathematics and Plausible Reasoning, Volume 1: Induction and Analogy in Mathematics by G. Polya in Front Matter
- How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library) by G. Polya in Front Matter
- Mathematical Discovery, Volume II, On Understanding, Learning, and Teaching Problem Solving by George Polya in Back Matter
- Rules for the Direction of the Mind by Rene Descartes on page 167
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- The Science of Conjecture: Evidence and Probability before Pascal by Professor James Franklin on 4 pages
- New Directions in the Philosophy of Mathematics by Thomas Tymoczko on page 97, page 98, and Back Matter
- A Priori Justification by Albert Casullo on page 116, and Back Matter
- What Is Mathematics, Really? by Reuben Hersh on page 215, and Back Matter
- Euclid in the Rainforest: Discovering Universal Truth in Logic and Math by Joseph Mazur in Back Matter (1), and Back Matter (2)
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