January Lectures

Week of January 2-6

Jan 5 : No class; lecture to be taught later in the term.

Week of January 9-13

Jan 10: Introduction to the course. Basic ideas. Generating functions and their applications.
Jan 12: Examples of generating functions: derangements, binary sequences. Solving recurrence relations.

Week of January 16-20

Jan 17: Direct approach to generating functions. Bivariate generating functions. Computing averages.
Jan 19: Computing averages (cont). Set partitions.

Week of January 23-27

Jan 24 (this class substitute the class of Thursday January 5): Set partitions (cont). EGF for set partitions.
Jan 24 Introduction to formal power series. Rules for ordinary generating functions.
Jan 26: Rules for ordinary generating functions (cont).

Week of January 30 - February 3

Jan 31: Rules for exponential generating functions. Formal power series and inverses; analytic view.
Feb 2 : Multi-section formulas. Rooted plane trees and Catalan numbers. [A1 handed out.]

To February lectures.