CSE 16 — Discrete Mathematics

Resources

• Textbook

Chapter 1 — Sets

• 1.1 Introduction to Sets
• 1.2 The Cartesian Product
• 1.3 Subsets
• 1.4 Power Sets
• 1.5 Union, Intersection, Difference
• 1.6 Complement
• 1.8 Indexed Sets
• 1.9 Sets That Are Number Systems

Chapter 2 — Logic

• 2.1 Statements
• 2.2 And, Or, Not
• 2.3 Conditional Statements
• 2.4 Biconditional Statements
• 2.6 Logical Equivalence
• 2.7 Quantifiers
• 2.10 Negating Statements
• 2.11 Logical Inference

Chapter 3 — Counting

• 3.1 Lists
• 3.2 The Multiplication Principle
• 3.3 The Addition and Subtraction Principles
• 3.4 Factorials and Permutations
• 3.5 Counting Subsets
• 3.6 Pascal’s Triangle and the Binomial Theorem

Chapter 4 — Direct Proof

• 4.1 Theorems
• 4.2 Definitions
• 4.3 Direct Proof
• 4.4 Using Cases
• 4.5 Treating Similar Cases

Chapter 5 — Contrapositive Proof

• 5.1 Contrapositive Proof
• 5.2 Congruence of Integers
• 5.3 Mathematical Writing

Chapter 6 — Proof by Contradiction

• 6.1 Proving Statements with Contradiction
• 6.2 Proving Conditional Statements by Contradiction
• 6.3 Combining Techniques

Chapter 7 — Non-Conditional Statements

• 7.1 If-and-Only-If Proof
• 7.2 Equivalent Statements
• 7.3 Existence Proofs; Existence and Uniqueness Proofs
• 7.4 Constructive Versus Non-Constructive Proofs

Chapter 8 — Proofs Involving Sets

• 8.1 How to Prove a ∈ A
• 8.2 How to Prove A ⊆ B
• 8.3 How to Prove A = B

Chapter 9 — Disproof

• 9.1 Counter Examples
• 9.2 Disproving Existence Statements
• 9.3 Disproof by Contradiction

Chapters 10–12

• Chapter 10 Induction
• Chapter 11 Relations
• Chapter 12