How To Write Proofs
# How To Write Proofs

## Part I: The Mechanics of Proofs

- Introduction
- Direct Proof
- Proof by Contradiction
- Proof by Contrapositive
- If, and Only If
- Proof by Mathematical Induction

## Part II: Proof Strategies

- Unwinding Definitions (Getting Started)
- Constructive Versus Existential Proofs
- Counter Examples
- Proof by Exhaustion (Case by Case)
- What Does "Well Defined" Mean?
- The Pigeon Hole Principle