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The Nuts and Bolts of Proofs: An Introduction to Mathematical Proofs provides basic logic of mathematical proofs and shows how mathematical proofs work. It offers techniques for bo… Read more
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Chapter 1. Getting Started
Introduction and Basic Terminology
General Suggestions
Chapter 2. Basic Techniques to Prove If/Then Statements
What Does “If/Then” Mean?
The Negation of a Statement: AND/OR
Proof by Contrapositive
Proof by Contradiction
Chapter 3. Special Kinds of Theorems
“If and Only If” or “Equivalence Theorems”
Use of Counter Examples
Mathematical Induction
Existence Theorems
Uniqueness Theorems
Composite Statements
Equality of Numbers
Chapter 4. Some Mathematical Topics on Which to Practice Proof Techniques
Basic Set Theory and Indexed Families
About Functions
Relations
The Basics of Groups
Limits
Sizes of Infinity
Chapter 5. Review Exercises
Exercises without Solutions
Collection of “Proofs”
Solutions for the Exercises at the End of the Sections and the Review Exercises
Solutions for the Exercises at the End of the Sections
Solutions for the Review Exercises
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