Mathematics and plausible reasoning. / by G. Polya.

Format:

Book

Author/Creator:

Pólya, George, 1887-1985, author.

Language:

English

Subjects (All):

Logic, Symbolic and mathematical.

Mathematics--Philosophy.

Mathematics.

Physical Description:

1 online resource (300 pages) : illustrations

Place of Publication:

Princeton, New Jersey : Princeton University Press, 1990.

Summary:

A guide to the practical art of plausible reasoning, this book has relevance in every field of intellectual activity. Professor Polya, a world-famous mathematician from Stanford University, uses mathematics to show how hunches and guesses play an important part in even the most rigorously deductive science. He explains how solutions to problems can be guessed at; good guessing is often more important than rigorous deduction in finding correct solutions. Vol. I, on Induction and Analogy in Mathematics, covers a wide variety of mathematical problems, revealing the trains of thought that lead to solutions, pointing out false bypaths, discussing techniques of searching for proofs. Problems and examples challenge curiosity, judgment, and power of invention.

Contents:

Frontmatter

PREFACE

HINTS TO THE READER

CONTENTS

Volume I. Induction and Analogy in Mathematics

CHAPTER I. INDUCTION

CHAPTER II. GENERALIZATION, SPECIALIZATION, ANALOGY

CHAPTER III. INDUCTION IN SOLID GEOMETRY

CHAPTER IV. INDUCTION IN THE THEORY OF NUMBERS

CHAPTER V. MISCELLANEOUS EXAMPLES OF INDUCTION

CHAPTER VI. A MORE GENERAL STATEMENT

CHAPTER VII. MATHEMATICAL INDUCTION

CHAPTER VIII. MAXIMA AND MINIMA

CHAPTER IX. PHYSICAL MATHEMATICS

CHAPTER X. THE ISOPERIMETRIC PROBLEM

CHAPTER XI. FURTHER KINDS OF PLAUSIBLE REASONS

FINAL REMARK

SOLUTIONS TO PROBLEMS

BIBLIOGRAPHY

Notes:

Description based on print version record.

Includes bibliographical references (pages [279]-280) and index.

ISBN:

9780691086408

0691086400

9780691218304

0691218307