EECS2060 Discrete Mathematics

Content

Lecture 1 Logic: Propositional Logic

Proposition | Propositional Logic | Applications | Propositional Equivalences

Lecture 2 Logic: Predicate Calculus

Predicates | Quantifiers | Binding | Applications | Logical Equivalences

Lecture 3 Logic: Rules of Inference

Mathematical Argument | Rules of Inference

Lecture 4 Proofs: Methods and Strategies

What is a Proof? | Methods of Proving | Common Mistakes in Proofs | Strategies : How to Find a Proof?

Lecture 5 Proofs: Mathematical Induction

What is a Mathematical Induction? | Strong Induction | Common Mistakes

Lecture 6 Proofs: Pigeonhole Principle

What is a Pigeonhole Principle? | The Generalized Version

Lecture 7 Counting: Basics

Rule of Sum | Rule of Product | Principle of Inclusion-Exclusion | Tree Diagrams

Lecture 8 Counting: Permutations and Combinations

Definitions | Permutation | Combination | Interesting Identities

Lecture 9 Sets, Functions, and Relations: Part I

What is a Set? | Set Operations | Identities | Cardinality of a Set

Lecture 10 Sets, Functions, and Relations: Part II

What is a Function? | Types of Functions | Floor and Ceiling Functions | An Interesting Result

Lecture 11 Sets, Functions, and Relations: Part III

What is a Relation? | Types of Binary Relations | Representing Binary Relations | Closures

Lecture 12 Sets, Functions, and Relations: Part IV

Equivalence Relations | Partial Orderings

Lecture 13 Graphs: Introduction

What is a Graph? | Terminology | Some Special Simple Graphs | Subgraphs and Complements | Graph Isomorphism

Lecture 14 Graphs: Euler and Hamilton Paths

What is a Path? | Euler Paths and Circuits | Hamilton Paths and Circuits

Lecture 15 Graphs: Planar Graphs

What is a Planar Graph? | Euler Planar Formula | Kuratowski's Theorem