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Mathematics and Plausible Reasoning, Volume 1
Induction and Analogy in Mathematics
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Sprache:
Englisch
Veröffentlicht/Copyright:
2020
Über dieses Buch
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.
Information zu Autoren / Herausgebern
G. Polya (1887-1985) was Professor of Mathematics at Stanford University.
Rezensionen
"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
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"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
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"Professor Polya's beautifully written hook has become a classic."----A. 0. L. Atkin, The Mathematical Gazette
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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
Fachgebiete
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Frontmatter
i -
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PREFACE
v -
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HINTS TO THE READER
xi -
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CONTENTS
xiii - Volume I. Induction and Analogy in Mathematics
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CHAPTER I. INDUCTION
1 -
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CHAPTER II. GENERALIZATION, SPECIALIZATION, ANALOGY
12 -
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CHAPTER III. INDUCTION IN SOLID GEOMETRY
35 -
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CHAPTER IV. INDUCTION IN THE THEORY OF NUMBERS
59 -
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CHAPTER V. MISCELLANEOUS EXAMPLES OF INDUCTION
76 -
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CHAPTER VI. A MORE GENERAL STATEMENT
90 -
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CHAPTER VII. MATHEMATICAL INDUCTION
108 -
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CHAPTER VIII. MAXIMA AND MINIMA
121 -
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CHAPTER IX. PHYSICAL MATHEMATICS
142 -
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CHAPTER X. THE ISOPERIMETRIC PROBLEM
168 -
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CHAPTER XI. FURTHER KINDS OF PLAUSIBLE REASONS
190 -
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FINAL REMARK
210 -
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SOLUTIONS TO PROBLEMS
213 -
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BIBLIOGRAPHY
279
Informationen zur Veröffentlichung
Seiten und Bilder/Illustrationen im Buch
eBook veröffentlicht am:
11. Februar 2021
eBook ISBN:
9780691218304
Seiten und Bilder/Illustrationen im Buch
eBook ISBN:
9780691218304
Schlagwörter für dieses Buch
Conjecture; Theorem; Analogy; Mathematical induction; Mathematics; Parity (mathematics); Summation; Sign (mathematics); Physical mathematics; Special case; Variable (mathematics); Proportionality (mathematics); Prime number; Number theory; Plausible reasoning; Mathematical proof; Mathematical problem; Degeneracy (mathematics); Mathematician; Quantity; Series (mathematics); Isoperimetric problem; Right triangle; Equation; Pure mathematics; Mathematical sciences; Euler's theorem; Projection (linear algebra); Limit (mathematics); Elementary proof; Regular polygon; Harmonic series (mathematics); Pythagorean theorem; Integer; Maxima and minima; Cauchy's theorem (geometry); A Course of Pure Mathematics; Mathematical fallacy; Geometry; Commutative property; Result; E6 (mathematics); Inductive reasoning; Numbering (computability theory); Intersection (set theory); Mathematical beauty; Traditional mathematics; Ball (mathematics); Solid geometry; Applied mathematics; Calculus of variations; Tetrahedron; Euclidean geometry; Scientific notation; Rectangle; Mathematical physics; Isoperimetric inequality; Explicit formulae (L-function); Axiom; Geometric mean; Goldbach's conjecture; Rational number; Numerical analysis; Analytic geometry; Polyhedron; Euler's formula; Simultaneous equations; Similarity (geometry); Natural number; Computation
Zielgruppe(n) für dieses Buch
For an expert adult audience, including professional development and academic research
