Discrete Math Part II: Relational Thinking

Course Description
Topics include Graphs: Edges and Vertices, Terminology, Modeling Relationships with Graphs; Sets: Membership and Containment, New Sets from Old, Identities; Functions: One-to-One and Onto Functions, New Functions from Old; Relations and Equivalences: Graphs of Relations, Relations vs. Functions, Equivalence Relations, Modular Arithmetic; Partial Orderings: Hasse Diagrams, Topological Sorting, Isomorphisms, Boolean Algebras; Graph Theory: Formal Definitions of Graphs, Isomorphisms of Graphs, Degree Counting, Euler Paths and Circuits, Hamilton Paths and Circuits, Trees.

Prerequisites
The class is taught with the assumption that the student has a strong understanding of Algebra and Discrete Logic.

Calculator
Although this is a Mathematics course, a calculator will be of little to no use for the topics and problems we will discuss.

Purpose
Discrete Mathematics is designed for prospective math/computer science majors as well as for students whose primary interest is engineering or the physical and social sciences.

Discrete Mathematics Part II
Course Schedule
Class meets twice weekly

Week 1: Graphs and Sets
Lesson 1: Graphs: Edges and Vertices/Terminology/Modeling Relationships with Graphs
Lesson 2: Sets: Membership and Containment/New Sets from Old/Identities

Week 2: Functions, Relations, and Equivalences
Lesson 1: Functions: Definitions and Examples/On-to-One and Onto Functions/New Functions from Old
Lesson 2: Relations and Equivalences: Definitions and Examples/Graphs of Relations/Relations vs. Functions/Equivalence Relations/Modular Arithmetic

Week 3: Partial Orderings/Graph Theory
Lesson 1: Partial Orderings: Definition and Examples/Hasse Diagrams/Topological Sorting/Isomorphisms
Lesson 2: Partial Orderings: Boolean Algebras/Graph Theory: Formal Definitions of Graphs/Isomorphisms of Graphs

Week 4: Graph Theory
Lesson 1: Graph Theory: Degree Counting/Euler Paths and Circuits/Hamilton Paths and Circuits/Trees
Lesson 2: Exam