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How to Read and Do Proofs: An Introduction to Mathematical Thought Processes [Paperback]

Daniel Solow
4.1 out of 5 stars  See all reviews (10 customer reviews)

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How to Read and Do Proofs: An Introduction to Mathematical Thought Processes How to Read and Do Proofs: An Introduction to Mathematical Thought Processes
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Book Description

July 6, 2001 0471406473 978-0471406471 3
This book categorizes, identifies and explains the various techniques that are used repeatedly in all proofs and explains how to read proofs that arise in mathematical literature by understanding which techniques are used and how they are applied.

Editorial Reviews

From the Publisher

This straightforward guide describes the main methods used to prove mathematical theorems. Shows how and when to use each technique such as the contrapositive, induction and proof by contradiction. Each method is illustrated by step-by-step examples. The Second Edition features new chapters on nested quantifiers and proof by cases, and the number of exercises has been doubled with answers to odd-numbered exercises provided. This text will be useful as a supplement in mathematics and logic courses. Prerequisite is high-school algebra. --This text refers to an out of print or unavailable edition of this title.

From the Back Cover


Daniel Solow's new Third Edition of HOW TO READ AND DO PROOFS will help yopu master the basic techniques that are used in all proofs, regardless of the mathematical subject matter in which the proof arises. Once you have a firm grasp of the techniques, you'll be better equipped to read, understand and actually do proofs. You'll learn when each techniques is likely to be successful, based on the form of the theorem.
This edition present new material, examples and exercises that show you how to explain proofs in terms of the techniques discussed in the text, improved explanations, and a glossary of key terms for easy reference.


  • Shows how any proof can be understood as a sequence of techniques.
  • Covers the full range of techniques used in proofs, such as the contrapositive, induction, and proof by contradiction.
  • Explains how to identify which techniques are used and how they are applied in the specific problem.
  • Illustrates how to read written proofs with many step-by-step examples.
  • Requires no college-level math.
  • Uses ordinary language instead of symbolic logic to explain the nature of proofs.

Product Details

  • Paperback: 224 pages
  • Publisher: Wiley; 3 edition (July 6, 2001)
  • Language: English
  • ISBN-10: 0471406473
  • ISBN-13: 978-0471406471
  • Product Dimensions: 9.3 x 6.2 x 0.4 inches
  • Shipping Weight: 7.5 ounces
  • Average Customer Review: 4.1 out of 5 stars  See all reviews (10 customer reviews)
  • Amazon Best Sellers Rank: #436,227 in Books (See Top 100 in Books)

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Customer Reviews

4.1 out of 5 stars
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Most Helpful Customer Reviews
25 of 27 people found the following review helpful
4.0 out of 5 stars Basic proof techniques June 11, 2000
This book is the "magic decoder ring" for terse proofs. This book should be passed out to every undergraduate taking the first mathematical analysis course. Numerous examples and exercises are included. The typesetting and notation are very readable. The great strength of this book is that the proofs used for exercises are restricted to the level of algebra and set theory. This makes it easy to concentrate on the technique of proof rather than the specific results. Also check out Polya's book "How to Prove It" and Velleman's book of the same name.
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19 of 22 people found the following review helpful
5.0 out of 5 stars Big Improvement in Second Edition February 14, 2002
By A Customer
Contrary to the review by the person from Louisiana I feel the second edition is better than the first. The typesetting is greatly improved, and there are a few new tools for your toolbag in the second edition.
As to the criticism that the second edition only has solutions for the odd numbered problems, the reviewer failed to mention that there are twice as many problems in the new edition and that all the problems from the first edition were carried into the second (along with their solutions). I found it more satisfying working through the second edition knowing that the problems were correctly solved - not because the answer matches the back of the book - but because the arguments are compelling and demonstrably correct.
I heartily recommend this book to anyone who feels mystified at the process of writing proofs.
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27 of 33 people found the following review helpful
3.0 out of 5 stars The Velleman is better and costs less too December 10, 1999
By A Customer
One can learn to do proofs with this book but the examples and exercises seem to be geared for the average eighth grader. The reader would be better served with How to Prove It : A Structured Approach by Daniel J. Velleman, who's exercises are more similar to what one has to tackle in a normal college proof course. The only draw back of the Velleman is there are no solutions for the exercises.
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5.0 out of 5 stars The Nuts and Bolts of Math Proofs August 19, 2013
Format:Paperback|Verified Purchase
Without a doubt, the best self-help Math book I've ever purchased on AMAZON!
Actual techniques for working proofs are presented and they are fairly easy to understand.
The author provides some good foundational basics for understanding how proofs work
and the best approaches to use for arriving at conclusions! I would recommend this
book to any aspiring Mathematicians who want to learn to do proofs!
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5.0 out of 5 stars Classic book December 11, 2012
Format:Paperback|Verified Purchase
I enjoy handing out copies of this book to budding mathematicians. Proofs are useful in most any academic discipline including theatre such as figuring out how a character gets from the beginning to the end. That too is a deductive process.
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