- Paperback: 224 pages
- Publisher: John Wiley & Sons; 3rd Edition edition (10 Jun 2003)
- Language English
- ISBN-10: 0471453005
- ISBN-13: 978-0471453000
- Amazon Bestsellers Rank: 3,197,394 in Books (See Top 100 in Books)
- See Complete Table of Contents
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Product Description
Product Description
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.
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.
Inside This Book
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First Sentence
The objective of mathematicians is to discover and to communicate certain truths. Read the first page
Front Cover | Table of Contents | Excerpt | Index | Back Cover
The objective of mathematicians is to discover and to communicate certain truths. Read the first page
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Concordance
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Front Cover | Table of Contents | Excerpt | Index | Back Cover
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9 reviews
49 of 49 people found the following review helpful
An Excellent Rescource
29 Sep 2005
Format:Paperback
"How to Read and Do Proofs" is a magnificent introduction to mathematical thought processes. If you have always wanted to understand how to read and do your own proofs, this book will definitely provide you with the tools. This book is very thorough, and after having mastered it you will feel very comfortable about your abilities to read and construct proofs. Solow covers what he calls the "foward-backward" method first to give the reader a general understanding of how direct proof works. He then explains direct proof of existential quantifiers (there exists...), direct proof of universal quantifiers, proof by contradiction, proof by contrapositive, mathematical induction and more. He also has added 4 appendices pertaining to Modern Albebra, Analysis, Number Theory, and Linear Algebra. Many answers to exercises are provided either in the book or on-line. An excellent rescource for anyone wanting to learn the methods of mathematical proof.
36 of 37 people found the following review helpful
Outstanding math book, and great intro to proofs
30 Mar 2006
Format:Paperback
This is a great book, and one of my favorite math books. Like the other reviewer, I also wanted to learn how to read and write proofs. I am an engineer, (many years ago), and not a mathematician, (but really enjoy math). The author communicates clearly, and provides lots of good examples. But the heart of the book is the problem sets for each chapter. Most books on proofs spend way too much time on Logic, (or geometry), and not enough on "math" proofs. The book provides problems from a wide variety of math areas. The latest edition added a lot of new material. I struggled at times, since I went through the whole book without an instructor, and worked on all of the problems. So having most of the possible answers in the back of the book, or on the internet helped as a check on my understanding. This book would make a great gift.
11 of 12 people found the following review helpful
A MUST HAVE!!!!!
7 Nov 2006
Format:Paperback
I wish this book was out when I was an undergrad! It is clear and concise. It covers many of the basic areas of math and gives a tremendous amount of insight on which style of proof fits a particular situation. Every example is presented in a very clear way, which gave me confidence in my ability to write proofs. This book should be used by ALL professors who teach an introductory analysis course.
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