Course description
Permutations are fundamental objects in discrete mathematics, with deep connections to algebra, probability, and computer science. This graduate-level course explores the combinatorial structure of the symmetric group, covering both classical enumeration and modern structural theories. By integrating geometric, algebraic, and analytic techniques, students investigate how permutations can be decomposed, restricted, and quantified.
The course has two major themes: permutation statistics and q-analogues, and the theory of pattern avoidance.
Grading
- Assignments 40% — biweekly
- Mid-semester exam 30% — 120 minutes, written
- End-semester exam 30% — 180 minutes, written
An A requires at least 80% overall, though 80% does not automatically guarantee one.
Lectures
The lecture log is not up yet. It will be filled in week by week once the term starts.