Teaching

Math 325: Combinatorics

Lecture Notes

Course Outline:

• Weeks 1-2: Intro to Combinatorics
• Classic combinatorial problems
• Set theory, bijection, & double counting
• Essential principles (pigeonhole, multiplication, etc.)
• Permutations & combinations
• Weeks 3-5: Elements of Counting
• Counting practicum
• Applying principles
• Combinatorial models
• Weeks 6-9: Advanced Methods
• Generating functions
• Inclusion-Exclusion
• Recurrence relations
• Week 10: Spring Break
• Weeks 11-13: Probability, Graphs, and Ramsey Theory
• Probability basics & the probabilistic method
• Graph theory basics & Ramsey Theory
• Weeks 14-15: Special Topics & Student Presentations
• Spectral graph theory
• Social choice theory, Gerrymandering & redistricting
• Student presentations