Mathematics and Plausible Reasoning: Vol. II: Patterns of Plausible Inference - Softcover

Polya, George

Softcover

ISBN 10: 4871878341 ISBN 13: 9784871878340

Publisher: Ishi Press, 2009

Synopsis

This is a guide to the practical art of plausible reasoning, particularly in mathematics but also in every field of human activity. Using mathematics as the example par excellence, Professor Polya shows how even that most rigorous deductive discipline is heavily dependent on techniques of guessing, inductive reasoning, and reasoning by analogy. In solving a problem, the answer must be guessed at before a proof can even begin, and guesses are usually made from a knowledge of facts, experience, and hunches. The truly creative mathematician must be a good guesser first and a good prover afterward; many important theorems have been guessed but not proved until much later. In the same way, solutions to problems can be guessed, and a good guesser is much more likely to find a correct solution. This work might have been called "How to Become a Good Guesser." Professor Polya's deep understanding of the psychology of creative mathematics enables him to show the reader how to attack a new problem, how to get at the heart of it, what trains of thought may lead to a solution. There is no magic formula here, but there is much practical wisdom. Volumes I and II together make a coherent work on Mathematics and Plausible Reasoning. Volume I on Induction and Analogy stands by itself as an essential book for anyone interested in mathematical reasoning. Volume II on Patterns o f Plausible Inference builds on the examples of Volume I but is not otherwise dependent on it. A more sophisticated reader with some mathematical experience will have no difficulty in reading Volume II independently, though he will probably want to read Volume I afterward. Professor Polya's earlier more elementary book How to Solve It was closely related to Mathematics and Plausible Reasoning and furnished some background for it.

About this title

About the Author

George Polya was a Hungarian mathematician. Born in Budapest on 13 December 1887, his original name was Pólya Györg. He wrote “How to Solve It”, perhaps the most famous book of mathematics ever written, second only to Euclid's “Elements”. George Polya continued to work on mathematics, even past age 90. He died in Palo Alto, California on September 7, 1985, at age 97.

Review

"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

Edition details

• Publisher: Ishi Press
• Publication date: 2009
• Language: English
• ISBN 10: 4871878341
• ISBN 13: 9784871878340
• Binding: Paperback
• Number of pages: 202