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How to Read and Do Proofs: An Introduction to Mathematical Thought Processes 3rd Edition

4.4 out of 5 stars 18 customer reviews
ISBN-13: 978-0471406471
ISBN-10: 0471406473
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Comment: Ex-library copy. Copyright 2002, 3rd edition, softcover. Shelf/use wears. Creased line on the front. Text pages are clean.
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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

LEARN HOW TO READ, UNDERSTAND, AND DO PROOFS!

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.

KEY FEATURES:

  • 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.
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Product Details

  • Paperback: 224 pages
  • Publisher: Wiley; 3 edition (July 6, 2001)
  • Language: English
  • ISBN-10: 0471406473
  • ISBN-13: 978-0471406471
  • Product Dimensions: 4.6 x 1.4 x 3.2 inches
  • Shipping Weight: 12.6 ounces
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (18 customer reviews)
  • Amazon Best Sellers Rank: #551,424 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

By Juan Gustavo Sanchez on September 27, 2011
Format: Paperback Verified Purchase
I'm an Electronic and Computer Systems Engineer, but in my spare time I like to do Mathematics, specially Real & Functional Analysis, I didn't go to any formal courses, but thanx to this book I had the possibility to learn these abstract subjects, now the part that I like most is to analyze proofs in any other subject of Mathematics dissecting their steps using what is taught in this book. I have, I thing, all the other books that talk about proofs, but for me this is the best.

P.S.:
This book works for Mathematicians too.

Recomendation:
Now you can have a Real Analysis Book that use the Dr. Solow Method of analyzing proofs, its name is: Introduction to Real Analysis by Michael J. Schramm
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Format: 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.
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By A Customer on February 14, 2002
Format: 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.
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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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I think this is the only book you should consider first when looking at how mathematical proofs are constructed and read. It is very clearly and fluently written. At the inner covers the various proof technique's main points are illustrated for quick reference, which comes very handy when you want to look up a proof techique without going into its details. This book contains all the important proof techniques you may require in your life as a student.
The main point of this book, of course, is to teach you how to write proofs by yourself by showing you how to construct and to disentangle dense written proofs. It is not enough to learn to write a proof, it also essential to know how to approach dense, compact wirtten proofs in order to learn from them. This one is the essential guide to mathematical proofs out there. I hope you enjoy it
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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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Nice, brief overview of math proof concepts and techniques. Focuses on understanding ideas rather than memorizing rules. Definitely worth triple what I paid for it.

One of my college math professors recommended this book as a study guide for a test to place out of a Mathematical Reasoning class (which the university requires for all 300+ level math classes). Two friends and I read through this book, and we all passed.
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Are you in an abstract algebra class or in a real analysis class? Are you having trouble with proofs? This is an excellent ancillary to your course textbook.
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