Mathematics and Plausible Reasoning, Volume 1: Induction and Analogy in Mathematics Reprint Edition

by G. Polya (Author)

9 customer reviews

ISBN-13: 978-0691025094

ISBN-10: 0691025096

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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

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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: 1.1 pounds (View shipping rates and policies)
Average Customer Review: 4.8 out of 5 stars See all reviews (9 customer reviews)
Amazon Best Sellers Rank: #779,190 in Books (See Top 100 in Books)
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- #6342 in Books > Textbooks > Science & Mathematics > Mathematics

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At the very root of mathematical discovery

Byhenrique flemingon 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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Good writing - good reading

ByDennis Mittonon 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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Be prepared to be amazed every few pages!

ByNihal Mehtaon January 13, 2003

Format: PaperbackVerified 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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Required Reading

ByStick-In-The-Mudon 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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Great insight into the art of "Guessing" in Math

ByAbhion December 13, 2012

Format: Paperback

I was looking for books to train myself for Math Olympiads. I always felt that there is more to it than "Just Practicing". To form conjectures or in other words, to make intelligent "Guesses", you need inductive reasoning. Deductive reasoning is the end where we present the proof formally and things appear very logical; however, that is the end result. The means to arrive at that is through inductive reasoning. This book and its second volume form a great source to learn to form intelligent conjectures which can be proved and then used to prove other problems. I am in the process of reading the book but I am very impressed so far. I highly recommend this book for anyone who is very interested in Olympiads, Putnams and in general, to become a great problem solver.

I also recommend Schoenfeld's Mathematical Problem Solving. There is a lot of information for people who wish to understand the psychology behind problem solving.

Finally, I wish make it clear that Polya's book is not a source to prepare for Olympiads. Perhaps Arthur Engel's book is the best book to start preparing for Olympiads. Polya's book provides an overview of how inductive reasoning is used to solve problems. It is NOT a source for training for the Olympiads. Arthur Engel's book or Titu Andreescu's book are the best sources for preparation for the Math Olympiad.

Added the following comments on 16th of Jan 2012: I must say that this is the only book which deals with conjecture making. There may be others but this is a very good book. Most of the problem solving that is needed for the Olympiads is done through practice and learning the tricks which can be used when a new problem is encountered. There are many instances when you run out of tricks. You get struck. What do you do then? Problem solvers who think originally do not always use one of the tricks from their bag of tricks all the time. Sometimes, they do think originally. Later on, while solving real math problems either in engineering or in math research, it is the inductive reasoning which comes to rescue and not the 'use one of the standard tricks' approach. This book is a must for anyone who is going to become a pure math major. I believe that high school kids will greatly benefit from this book as it will rescue them from becoming a 'standard trick user'. There is nothing wring with using standard tricks. You need to make sure that your main approach is that of an original thinker who uses inductive reasoning to arrive at the answer to tough problems.

Added the following comments on 3rd of Feb 2012: Completed reading this book. Honestly, I was not able to solve all the problems. But I solved most of them. Great book. Will surely help people aiming for a research career in math and I think that the second volume is more important for the aspiring researchers. I highly recommend this book to kids who wish to attempt Math Olympiad. This material may require maturity at times but it is nevertheless highly useful for problem solving. This material is seldom taught nor are such things discussed this systematically even in good math olympiad training camps.

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More Than A Math Book

Bymimozas_husbandon August 8, 2001

Format: Paperback

To follow the book you don't need to be a matematician but it helps to remember this and that about integrals and differentals.
However, the book is more than a guide to mathematical reasoning - you can look at it as a guide to problem solving orriented thinking. I work as a business consultant and I could resist constantly thinking about business decision-making in the context of the book. I strongly recommend it to anybody with interest in management decision-making.

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Format: HardcoverVerified Purchase

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Bymagnoliaon December 30, 2014

Format: PaperbackVerified Purchase

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Spock primer

If you have ever watched a star trek movie and seen Spock in action,then this is the book for you. Its all about logicical thinking when approaching problems in math.Excellent!

Published on June 10, 2007 by Larry A. Amati

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