A Logical Introduction to Proof

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Springer Science & Business Media, Sep 19, 2012 - Mathematics - 356 pages
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The book is intended for students who want to learn how to prove theorems and be better prepared for the rigors required in more advance mathematics. One of the key components in this textbook is the development of a methodology to lay bare the structure underpinning the construction of a proof, much as diagramming a sentence lays bare its grammatical structure. Diagramming a proof is a way of presenting the relationships between the various parts of a proof. A proof diagram provides a tool for showing students how to write correct mathematical proofs.
 

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Contents

Chapter 1 Propositional Logic
1
Chapter 2 Predicate Logic
29
Chapter 3 Proof Strategies and Diagrams
61
Chapter 4 Mathematical Induction
99
Chapter 5 Set Theory
143
Chapter 6 Functions
169
Chapter 7 Relations
209
Chapter 8 Core Concepts in Abstract Algebra
239
Chapter 9 Core Concepts in Real Analysis
293
Appendix Summary of Strategies
341
References
347
Index of Special Symbols
349
Index
351
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