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.
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.
Winter break. No lectures this week.
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.