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

Daniel Solow (Author)

Book Description

ISBN-10: 0471510041 | ISBN-13: 978-0471510048 | Publication Date: March 1990 | Edition: 2

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.

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.

From the Back Cover

How to Read and Do Proofs Describes All of the Fundamental Techniques used in mathematical proofs and illustrates each with an example requiring only high school mathematics Simplifies Complex Proofs by showing how a complicated proof can be understood as a sequence of applications of the individual techniques Unravels the Mystery of "Condensed" Proofs that are found in textbooks and journal articles by teaching you to identify which techniques are being used and how they are being applied in the particular proof Gets You Started in the right direction by showing how the form of the problem under consideration can often be used to choose a successful proof technique

Product Details

• Paperback: 264 pages
• Publisher: Wiley; 2 edition (March 1990)
• Language: English
• ISBN-10: 0471510041
• ISBN-13: 978-0471510048
• Product Dimensions: 8.9 x 5.9 x 0.6 inches
• Shipping Weight: 12.8 ounces
• Average Customer Review: 3.9 out of 5 stars  See all reviews (7 customer reviews)
• Amazon Best Sellers Rank: #1,157,434 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

23 of 25 people found the following review helpful:

4.0 out of 5 stars Basic proof techniques, June 11, 2000

By 

UNPINGCO (Los Angeles, CA) - See all my reviews

This review is from: How to Read and Do Proofs: An Introduction to Mathematical Thought Processes (Paperback)

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.

27 of 31 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

This review is from: How to Read and Do Proofs: An Introduction to Mathematical Thought Processes (Paperback)

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.

18 of 21 people found the following review helpful:

5.0 out of 5 stars Big Improvement in Second Edition, February 14, 2002

By A Customer

This review is from: How to Read and Do Proofs: An Introduction to Mathematical Thought Processes (Paperback)

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.