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Mathematics and Plausible Reasoning: Vol. II: Patterns of Plausible Inference

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George Polya (Author)
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5 out of 5 stars 4 customer reviews
ISBN-13: 978-4871878340
ISBN-10: 4871878341
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  • Mathematics and Plausible Reasoning: Vol. II: Patterns of Plausible Inference
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  • Mathematics and Plausible Reasoning, Volume 1: Induction and Analogy in Mathematics
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Product Details

  • Paperback: 202 pages
  • Publisher: Ishi Press (July 13, 2009)
  • Language: English
  • ISBN-10: 4871878341
  • ISBN-13: 978-4871878340
  • Product Dimensions: 6 x 0.5 x 9 inches
  • Shipping Weight: 12.8 ounces (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (4 customer reviews)
  • Amazon Best Sellers Rank: #1,487,851 in Books (See Top 100 in Books)

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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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