March Lectures

Week of March 4-8

Mar 4: Polynomials over finite fields (cont). Comments about Assignment 2.
Mar 7: Introduction to multivariate generating functions. Parameters. Their usage in computing expected values, variances and other moments. Example of binomial distribution. [Deadline minor project.]

Week of March 11-15

Mar 11: Comments about Assignment 2. Labelled constructions and exponential generating functions. The admissibility theorem for labelled constructions. Permutations: basic countings, involutions.
Mar 14: Expectation and variance of the number of cyles in a random permutation. Generalization to the number of components in admissible constructions.
Mar 15: Extra lecture (substitute April 1 lecture): Comments about assignment 2. Complex asymptotics: the connection between generating functions and complex asymptotics.

Week of March 18-22

Mar 18: Complex asymptotics: analytic functions, singularities, radius of convergence, dominant singularity, etc. The exponential growth formula and examples. Meromorphic functions and residues: Cauchy's residue theorem, and Cauchy's coefficient formula. [A2 in; A3 out]
Mar 21: Asymptotics of rational functions and examples. Asymptotics of meromorphic functions and examples.

Week of March 25-29

Mar 25: Comments about assignment 3. Singularity analysis: brief comments on the Gamma function, Hankel contours, and transfer lemmas; examples of its usage.
Mar 28: Polynomials over finite fields.

Week of April 1-5

Apr 1: No lecture this day (class given on March 15).

Week of April 10-16

Apr 10: [A3 in]
Apr 12: deadline major project.
Apr 16: oral presentations.

To February lectures.