How To Write Proofs

How To Write Proofs

Part I: The Mechanics of Proofs

  1. Introduction
  2. Direct Proof
  3. Proof by Contradiction
  4. Proof by Contrapositive
  5. If, and Only If
  6. Proof by Mathematical Induction

Part II: Proof Strategies

  1. Unwinding Definitions (Getting Started)
  2. Constructive Versus Existential Proofs
  3. Counter Examples
  4. Proof by Exhaustion (Case by Case)
  5. What Does "Well Defined" Mean?
  6. The Pigeon Hole Principle