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

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Format: Hardcover
Pub. Date: 2013-10-22
Publisher(s): Wiley
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Summary

This straightforward guide describes the main methods used to prove mathematical theorems. Shows how and when to use each technique such as the contrapositive, induction and proof by contradiction. Each method is illustrated by step-by-step examples. The Second Edition features new chapters on nested quantifiers and proof by cases, and the number of exercises has been doubled with answers to odd-numbered exercises provided. This text will be useful as a supplement in mathematics and logic courses. Prerequisite is high-school algebra.

Table of 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: Induction
Quantifiers IV: Specialization
Quantifiers V: Nested Quantifiers
The Contradiction Method
The Contrapositive Method
Nots of Nots Lead to Knots
Special Proof Techniques
Summary
Appendices
Solutions to Exercises
Glossary of Mathematical Symbols
Index
Table of Contents provided by Publisher. All Rights Reserved.

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