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How to Read and Do Proofs: An Introduction to Mathematical Thought Processes Paperback – 21 Jun 1990

by
Daniel Solow (Author)
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How to Read and Do Proofs: An Introduction to Mathematical Thought Processes
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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

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Amazon.com: 4.4 out of 5 stars 18 reviews
26 of 28 people found the following review helpful
4.0 out of 5 stars Basic proof techniques 12 Jun. 2000
By UNPINGCO - Published on Amazon.com
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.
16 of 16 people found the following review helpful
5.0 out of 5 stars Like it says for Engineers... 27 Sept. 2011
By Juan Gustavo Sanchez - Published on Amazon.com
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
28 of 34 people found the following review helpful
3.0 out of 5 stars The Velleman is better and costs less too 10 Dec. 1999
By A Customer - Published on Amazon.com
Format: 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.
20 of 24 people found the following review helpful
5.0 out of 5 stars Big Improvement in Second Edition 15 Feb. 2002
By A Customer - Published on Amazon.com
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.
4 of 5 people found the following review helpful
5.0 out of 5 stars The definite guide to mathematical proofs. 10 Dec. 2013
By Burak Selcuk Soyer - Published on Amazon.com
Format: Paperback Verified Purchase
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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