Course Meeting Times
Lectures: 3 sessions / week, 1 hour / session
Algebra I (18.701) or Modern Algebra (18.703)
This is an introductory course in algebraic combinatorics. No prior knowledge of combinatorics is expected, but I will assume a familiarity with linear algebra and finite groups. We will cover a number of topics chosen to show the beauty and power of techniques in algebraic combinatorics. Rigorous mathematical proofs are expected.
- Rational generating functions and Recurrence relations
- Walks in graphs and the Radon transform
- Adjacency and Laplacian matrices of graphs
- Introduction to Posets and Sperner's theorem
- Partitions and Euler's Pentagonal theorem
- Young diagrams and q-binomial coefficients
- Young Tableaux and introduction to Schur functions
- Robinson-Schensted-Knuth algorithm and applications
- Polya theory and group actions on boolean algebras
- Matrix Tree theorem, Spanning trees, and Eulerian digraphs
"Topics in Algebraic Combinatorics." by Richard Stanley
Notes available online (PDF).
Homework: Homework will be assigned and collected in class, typically every week. Your lowest homework score will be dropped.
Exams: There will be two in-class quizzes during the semester.
Research Project: You will be expected to write a 5-10 page expository paper on a topic in algebraic combinatorics related to the course material.
Participation: Participation in class is encouraged. Please feel free to stop me and ask questions. Otherwise, I might stop and ask you questions.