EDW 524: Workshop in Discrete Mathematics

Topics in Discrete Math are integrated throughout the math curricula at the middle and high school levels. Join this workshop and we'll explore selected topics in graph theory,  combinatorics,  recursion relations, and cryptography. This workshop will help prepare you to teach these topics with depth and enthusiasm.

Chapter 1: Sets, Functions, and Proof Technique

Chapter 2: Logic

Chapter 3: Graph Theory

• Elementary Concepts of Graph Theory

• Connection Problems: Trees

• The Reliable Network Problem: Connectivity

• The Konigsberg Bridge Problem: Eulerian Graphs

• The Salesman's Problem: Hamiltonian Graphs

• The Problem of the Eccentric Hosts: Ramsey Numbers

• The Dancing Problem: Matching

• The Scheduling Problem: Vertex Coloring

• The Scheduling Class Times Problem: Edge Coloring

Chapter 4: Counting

• The basics of Counting

• The Pigeonhole Principle

• Permutations and Combinations

• Binomial Coefficients

• Generalized Permutations and Combinations

Chapter 5: Discrete Probability

• An Introduction to Discrete Probability

• Probability Theory

• Random Variables

• Expected Values and Variance

Chapter 6: Recurrence Relations

• Recurrence Relations

• Solving Linear Recurrence Relations

• Inclusion-Exclusion

• Applications of Inclusion-Exclusion

Chapter 7: Classical Cryptography

• Shift Cipher

• Affine Cipher

• Vigenere Cipher

• Playfair Cipher

• Hill Cipher