How to Read and Do Proofs

An Introduction to Mathematical Thought Processes

Daniel Solow

202 pages, parution le 07/12/2001 (3^eme édition)

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Résumé

How to Read and Do Proofs has been teaching students how to do proofs for over 20 years!

This text provides a systematic approach for teaching undergraduate and graduate students how to read, understand, think about, and do proofs. The approach is to catagorize, identify, and explain (at the student's level) the various techniques that are used repeatedly in all proofs, regardless of the subject in which the proofs arise. How to Read and Do Proofs 3/e also explains when each technique is likely to be used, based on certain key words that appear in the problem under consideration. Doing so enables students to choose a technique consciously, based on the form of the problem. Students are taught how to read proofs that arise in textbooks and other mathematical literature by understanding which techniques are used and how they are applied. It shows how any proof can be understood as a sequence of the individual techniques. The goal is to enable students to learn advanced mathematics on their own. This book is suitable as: (1) a text for a transition-to-advanced-math course, (2) a supplement to any course involving proofs, and (3) self-guided teaching.

Contents

The Truth of It All
The Forward-Backward Method
On Definitions and Mathematical Terminology
Quantifiers I: The Construction Method
Quantifiers II: The Choose Method
Quantifiers III: Specialization
Quantifiers IV: Nested Quantifiers
The Contradiction Method
The Contrapositive Method
Nots of Nots Lead to Knots
Uniqueness Methods and Induction
Either/Or and Max/Min Methods
Summary
Appendix A: Putting It All Together: Part I
Appendix B: Putting It All Together: Part II
Solutions to Selected Exercises (includes answers to those exercises marked with a B)
Glossary
References
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Wiley
Auteur(s)	Daniel Solow
Parution	07/12/2001
Édition	3^eme édition
Nb. de pages	202
Format	15,5 x 23,5
Couverture	Broché
Poids	300g
Intérieur	Noir et Blanc
EAN13	9780471406471
ISBN13	978-0-471-40647-1