February Lectures

Week of February 4-8

Feb 4: Euler-Maclaurin formula; properties of Bernoulli numbers. Examples.
Feb 7: Comments about assignment 1. Examples of the use of the Euler-Maclaurin formula: Harmonic numbers.

Week of February 11-15

Feb 11: Examples of the use of the Euler-Maclaurin formula: Harmonic numbers (cont); Stirling's approximation; Catalan numbers. The Symbolic Method: basic definitions and constructions.
Feb 14: Comments about final project and assignment 1. The admissibility theorem for unlabelled constructions and ordinary generating functions. Examples: cartesian product, disjoint sums.

Week of February 18-22

Winter break. No lectures this week.

Week of February 25 - March 1 (tentative)

Feb 25: More examples of constructions: sequence, set and multiset. [A1 in; A2 out]
Feb 28: Examples of the use of the symbolic method: patterns; internal number of nodes in a binary tree.
Mar 1: Extra lecture (substitute January 3 lecture) Binary trees: internal, external, and total number of nodes; general trees and forests; polynomials over finite fields.

To March lectures.
To January lectures.