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

Synopsis

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