January Lectures

Week of January 4-8

Jan 5: Introduction to the course. Basic ideas. Generating functions and their applications.
Jan 7: Examples of generating functions: derangements, binary sequences. Solving recurrence relations.

Week of January 11-15

Jan 12: Derangements (cont). Direct approach to generating functions.
Jan 14: Bivariate generating functions. Computing averages.

Week of January 18-22

Jan 19: Set partitions.
Jan 21: EGF for set partitions. Introduction to formal power series. [A1 handed out.]

Week of January 25-29

Jan 26: Rules for ordinary generating functions.
Jan 28: Rules for exponential generating functions. Formal power series and inverses; analytic view.
Jan 28 (this class substitute the class of Tuesday February 23):
Multi-section formulas. Rooted plane trees and Catalan numbers.

To February lectures.