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Mathematics and Plausible Reasoning, Volume 1: Induction and Analogy in Mathematics Paperback – August 23, 1990

ISBN-13: 978-0691025094 ISBN-10: 0691025096 Edition: Reprint
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Mathematics and Plausible Reasoning, Volume 1: Induction and Analogy in Mathematics + Mathematics and Plausible Reasoning: Vol. II: Patterns of Plausible Inference + Mathematical Discovery on Understanding, Learning, and Teaching Problem Solving, Volume II
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Editorial Reviews

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

About the Author

G. Polya (1887-1985) was Professor of Mathematics at Stanford University.
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Product Details

  • Paperback: 296 pages
  • Publisher: Princeton University Press; Reprint edition (August 3, 1990)
  • Language: English
  • ISBN-10: 0691025096
  • ISBN-13: 978-0691025094
  • Product Dimensions: 6 x 0.8 x 9 inches
  • Shipping Weight: 14.4 ounces (View shipping rates and policies)
  • Average Customer Review: 4.8 out of 5 stars  See all reviews (8 customer reviews)
  • Amazon Best Sellers Rank: #637,605 in Books (See Top 100 in Books)

Customer Reviews

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Most Helpful Customer Reviews

53 of 59 people found the following review helpful By henrique fleming on August 7, 1998
Format: 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".
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19 of 19 people found the following review helpful By Dennis Mitton on December 14, 2005
Format: 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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22 of 23 people found the following review helpful By Nihal Mehta on January 13, 2003
Format: Paperback Verified Purchase
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.
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6 of 6 people found the following review helpful By Stick-In-The-Mud on February 12, 2009
Format: Paperback
Though a math book, this is one of the best explanation of scientific reasoning ever written. I am amazed at the shoddy reasoning that now passes as 'scientific'. I assume that science majors are no longer expected to study more than basic calculus and probability unless they are physics majors. This is unfortunate. This book and its second volume would go a long way in clearing up sloppy thinking. Anyone interested in clear thinking, regardless of their interests and background, could do worse than study these books.
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Mathematics and Plausible Reasoning, Volume 1: Induction and Analogy in Mathematics
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