Week 3

Chapters (Discrete Mathematics and Its Applications):

• 1.7 Introduction to Proofs
  • 1.7.1 Introduction
  • 1.7.2 Some Terminology
  • 1.7.3 Understanding How Theorems Are Stated
  • 1.7.4 Methods of Proving Theorems
  • 1.7.5 Direct Proofs
  • 1.7.6 Proof by Contraposition
  • 1.7.7 Proofs by Contradiction
  • 1.7.8 Mistakes in Proofs
• 5.1 Mathematical Induction

Videos:

• TrevTutor
  • Proofs
    • Direct Proof
    • Proof by Cases
    • Proof by Contrapositive
    • Proof by Contradiction
    • Mathematical Induction

• Neso Academy
  • Nested Quantifiers
    • Introduction to Nested Quantifiers
    • Negating the Nested Quantifiers
  • Rules of Inference for Quantified Statements
    • Part 1
    • Part 2
  • Universal Modus Ponens Rule
  • Universal Modus Tollens Rule
  • Proof by Contradiction
  • Proof by Contrapositive

Exercises:

• TrevTutor
  • Direct Proofs
  • Direct Proofs 2
  • Proof by Case
  • Proof by Case 2
  • Proof by Case 3
  • Proof by Contradiction
  • Mathematical Induction
  • Mathematical Induction 2
  • Mathematical Induction 3
  • Mathematical Induction 4

• Neso Academy
  • Nested Quantifiers (Solved Example 1)
  • Nested Quantifiers (Solved Example 2)
  • Nested Quantifiers (Solved Example 3)
  • Nested Quantifiers (Translating English Statements) - Example 1
  • Nested Quantifiers (Translating English Statements) - Example 2
  • Nested Quantifiers (Translating English Statements) - Example 3
  • Nested Quantifiers (Translating English Statements) - Example 4
  • Nested Quantifiers (Translating English Statements) - Example 5
  • Negating the Nested Quantifiers (Example 2)
  • Negating the Nested Quantifiers (Example 3)