How to read and do proofs : an introduction to mathematical thought processes / Daniel Solow (Department of Operations, Weatherhead School of Management, Case Western Reserve University, Cleveland, OH 44106, e-mail daniel.solow@case.edu, web http://weatherhead.cwru.edu/solow).

Title:

How to read and do proofs : an introduction to mathematical thought processes / Daniel Solow (Department of Operations, Weatherhead School of Management, Case Western Reserve University, Cleveland, OH 44106, e-mail daniel.solow@case.edu, web http://weatherhead.cwru.edu/solow).

Personal Author:

Edition:

Sixth edition.

Publication:

Hoboken, New Jersey : John Wiley & Sons, Inc., [2014]

Publication Date:

2014

ISBN:

9781118164020

Bibliography Note:

Includes bibliographical references (pages 314-315) and index.

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 -- Nots of nots lead to knots -- The contradiction method -- The contrapositive method -- The uniqueness methods -- Induction -- The either/or methods -- The max/min methods -- Generalization -- Creating mathematical definintions -- Axiomatic systems -- Appendix A. Examples of proofs from discrete mathematics -- Appendix B. Examples of proofs from linear algebra -- Appendix C. Examples of proofs from modern algebra -- Appendix D. Examples of proofs from real analysis.

Abstract:

This book provides a systematic approach that will help you master the basic techniques that are used in all proofs, regardless of the mathematical subject matter in which the proof arises. Once you know these techniques, you'll be better equipped to read, understand, and actually do proofs. You'll also learn when each technique is likely to be successful, based on keywords that appear in the theorem. -- Publisher description

Content Type:

text

Carrier Type:

volume

Language:

English