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Mathematics and Plausible Reasoning, Volume 1: Induction and Analogy in Mathematics (v. 1) Hardcover – October 1, 1954

by G. Polya (Author)

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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.

Mathematics and Plausible Reasoning, Volume 1: Induction and Analogy in Mathematics (v. 1)

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Product Details

Series: Mathematics and Plausible Reasoning
Hardcover: 296 pages
Publisher: Princeton University Press; 2d Ed edition (October 1, 1954)
Language: English
ISBN-10: 0691080054
ISBN-13: 978-0691080055
Product Dimensions: 0.8 x 6.2 x 9.5 inches
Shipping Weight: 1.3 pounds
Average Customer Review: 5.0 out of 5 stars See all reviews (4 customer reviews)
Amazon Best Sellers Rank: #3,239,280 in Books (See Top 100 in Books)
- #2237 in Books > Science & Math > Mathematics > History
- #2993 in Books > Politics & Social Sciences > Philosophy > Logic & Language

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3 of 3 people found the following review helpful

I bought this because I own volume 1

By travel light and smiling on December 12, 2012

Verified Purchase

The author of this work has a special relationship to math. As people were trying to forcefeed me the subject over 50 years ago, what I mostly got was pure math, with no intest in how or whether math had any true real-world connections. There was a heavy emphasis on deductive, Euclidian proof.

Polanyi is a breath of fresh air, because he is the first mathematician I have read who identifies insight and intuition as very important parts of math exploration. He identifies this element as guessing. Flat out.

Math and science do not begin with formalized statements which are then studied and tested. They begin with someone's sense that there is something interesting to look at, poking around some, and THEN seeing if you can come up with a rule which might help predict, or explain an outcome.. sort of. The analytical part-- E = MC squared, for example-- comes after the intuition and the poking.

What his work is about is getting better and the inductive part-- the improvement of guessing.

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3 of 3 people found the following review helpful

Great for aspiring Math researchers

By Abhi on February 17, 2013

Format: Paperback

This is a continuation of the first volume on the same topic. He talks about plausible reasoning and helps researchers very much. I was most interested in problem solving though. I am nevertheless giving 5 stars because he does a good job of explaining plausible reasoning. In the last chapter (no. 16), he talks about the 'Deus ex machina' where a step in the proof of a tough problem appears as if the step was pulled out of a hat the way magicians do. In section 6, he explains it for a specific case but nevertheless the book does not provide ample examples of how such critical steps were pulled out of a hat. I feel that today, the only way to acquire that skill is to obtain proper mentorship from someone like Arthur Engel or Titu Andrescu. If you wish to understand plausible reasoning in math research, this book is very helpful and very well written.

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1 of 1 people found the following review helpful

Excellent book!!

By vikash tiwari on May 25, 2013

Format: Hardcover Verified Purchase

Every maths lover most keep this !! It is a book which motivate us do research in a systematic way!! written in a lucid manner!! Interactive also!!

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Wonderful book; gave me tools to understand the process ...

By mike on August 15, 2014

Format: Paperback Verified Purchase

Wonderful book; gave me tools to understand the process of critical reasoning, so necessary with the flood of today's news. (News?) So many opinions are floated on the TV and internet, it is important to sort out fact from fiction.

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