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
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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Most Helpful Customer Reviews
47 of 52 people found the following review helpful:
5.0 out of 5 stars
At the very root of mathematical discovery,
This review is from: Mathematics and Plausible Reasoning, Volume 1: Induction and Analogy in Mathematics (Paperback)
One of the most beautiful books on scientific discovery. Read this book and then keep it at bedside for sheer amusement. Analogies are frequently the key to a discovery, but it is rare that this essential step receives credit. Here there is a collection of them: some of the most beautiful. Perhaps the most famous is Bernoulli's solution of the brachistochrone problem, based on an analogy with the path of light in the atmosphere. But there are many others, with comments and analysis by Polya, who spent a life thinking at these things. It's a pity he didn't include Riemann's "proof" of the theorem of conformal representation, based on an analogy with the physics of electrical currents on a surface. The reader can find it beautifully described in Richard Courant's "Dirichlet Principle".
18 of 19 people found the following review helpful:
5.0 out of 5 stars
Be prepared to be amazed every few pages!,
By
This review is from: Mathematics and Plausible Reasoning, Volume 1: Induction and Analogy in Mathematics (Paperback)
This book shows you how simple concepts when applied properly can lead to ingenious solutions. For example, the author's proof of the Pythagorean Theorem will leave you shocked by its amazing elegance. And, there are several of these throughout the book.Read this book. It's money more than well spent.
14 of 14 people found the following review helpful:
4.0 out of 5 stars
Good writing - good reading,
By
This review is from: Mathematics and Plausible Reasoning, Volume 1: Induction and Analogy in Mathematics (Paperback)
The book delves deeply into logic and mathematical reasoning with quite a bit of intermediate math. While most of the chapters and concepts are mathematical Polya has skillfully made the reading easy and the concepts more universal. The book is really about thinking and looking at ideas with a clear light. Above all it's just good reading. Don't let the math scare you - there's lots of good stuff here.
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Inside This Book
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First Sentence:
1. Experience modifies human beliefs. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
shortest bisector, maximum area cut, isoperimetric theorem, perforated sphere, conjugate statements, most extraordinary law, isoperimetric quotient, tangent level line, leading special case, partial variation, optical interpretation, trihedral angle, extreme special case, minimum perimeter, double pyramid, same perimeter, traffic center, right prism, plausible reasoning, right generalization, right pyramid, inductive evidence, polyhedral surface, inductive phase, odd squares Key Phrases - Capitalized Phrases (CAPs): (learn more)
Jacques Bernoulli, Opera Omnia, Lord Rayleigh, Prove Proposition, Pure Mathematics New!
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Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
1. Experience modifies human beliefs. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
shortest bisector, maximum area cut, isoperimetric theorem, perforated sphere, conjugate statements, most extraordinary law, isoperimetric quotient, tangent level line, leading special case, partial variation, optical interpretation, trihedral angle, extreme special case, minimum perimeter, double pyramid, same perimeter, traffic center, right prism, plausible reasoning, right generalization, right pyramid, inductive evidence, polyhedral surface, inductive phase, odd squares Key Phrases - Capitalized Phrases (CAPs): (learn more)
Jacques Bernoulli, Opera Omnia, Lord Rayleigh, Prove Proposition, Pure Mathematics New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
Citations (learn more)
This book cites 8
books:
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100
books
cite this book:
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- Philosophy of the Inductive Sciences: Works in the Philosophy of Science 1830-1914 by William Whewell on page 205
- Jacob Steiner's Gesammelte Werke (AMS Chelsea Publishing) by Jacob Steiner on page 138
- Rules for the Direction of the Mind by Rene Descartes on page 168
- Gesammelte mathematische Abhandlungen (AMS Chelsea Publishing) by H. A. Schwarz on page 205
- How to Solve It: A New Aspect of Mathematical Method (Princeton Science Library) by G. Polya in Front Matter
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- 5th Conference on Automated Deduction: Les Arcs, France, July 8-11, 1980 (Lecture Notes in Computer Science) by W. Bibel on page 127, page 140, and page 142
- New Directions in the Philosophy of Mathematics by Thomas Tymoczko on page 97, page 98, and Back Matter
- Decouverte et justification en science: Kantisme, neo-positivisme et problematologie (Philosophia) (French Edition) by Michel Meyer on page 285, and Back Matter
- Structuralism and Structures (Series in Pure Mathematics) by Charles E. Rickart on page 122, and Back Matter
- A Priori Justification by Albert Casullo on page 116, and Back Matter
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