Teaching
Math 325: Combinatorics
Lecture Notes
Draft of Lecture NotesCourse 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