March Lectures

Week of March 1-5

Mar 2: Sieve method (inclusion-exclusion). Comments about midterm and assignment 2.
Mar 4: Midterm test.

Week of March 8-12

Mar 9: Snake oil method.
Mar 11: Cycle index.

Week of March 15-19

Mar 16: Cycle index (cont). Transform-matrix method and walks in digraphs. [A2 handed in; A3 handed out.]
Mar 18: Walks in digraphs (cont). Analytic functions. Cauchy formula. Radius of convergence.

Week of March 22-26

Mar 23: Meromorphic functions and singularity analysis. Examples: ordered set partitions, Bernoulii numbers. Algebraic singularities.
Mar 25: Darboux method. Example: 2-regular graphs.

Week of March 29 - April 2

Mar 30: Lagrange inversion formula. Example: rooted labelled trees. Comments about assignment 3.
Apr 1: Example of Lagrange inversion formula: inversion of recurrences. Example of computation of moments and asymptotic analysis: finite fields. Comments about the exam. [A3 handed in.]

To February lectures.