March Lectures

Week of March 5-9

Mar 6: Sieve method (inclusion-exclusion).
Mar 8: Snake oil method. Cycle index. [A1 handed in and A2 handed out.]

Week of March 12-16

Mar 13: Cycle index (cont).
Mar 15: Cycle index examples. Transform-matrix method and walks in digraphs. Money changing problem.

Week of March 19-23

Mar 20: Analytic functions. Radius of convergence. Dominant singularities.
Mar 22: Cauchy formula. Meromorphic functions and singularity analysis. Examples.

Week of March 26-30

Mar 27: Review of meromorphic functions. Algebraic singularities. Darboux method.
Mar 27 (this class substitute the class of Thursday March 29):
Darboux method (cont). Example: 2-regular graphs. Example of computation of moments and asymptotic analysis: finite fields.
Mar 29: Midterm test #2.

Week of April 2-6

Apr 3: Example of computation of moments and asymptotic analysis: finite fields (cont). Lagrange inversion formula.
Apr 5: Examples of Lagrange inversion formula: rooted labelled trees and inversion of recurrences. Course evaluations and comments about the exam. [A2 handed in.]

To February lectures.