Lectures

This page contains all the video lectures for the rest of our class, along with pdf documents of the slides I'm using.

Chapter 7 slides: Link

Lecture 1 (3/23): Conditional probability and independence (7.2)

Errors: In the weighted dice example in a few places I accidentally had r(6) = 0.6 instead of 0.5. So for example p(6,6) = 0.25, not 0.36. The definition of mutual independence should also be modified so the equation holds for any sub-collection of E_1,..., E_n; see Definition 5 on pg. 458 of the text.

Lecture 2 (3/25): Binomial distribution and Bayes' theorem (7.2 and 7.3)

Chapter 8 slides: Link

Lecture 3 (3/27): Recurrence relations (8.1 and 8.2)

Note: At two points the video recording dropped out because Zoom lost connection, apologies in advance!

Lecture 4 (4/1): Generalized Inclusion-Exclusion (8.5 and 8.6)

Chapter 9 Slides: Link

Lecture 5 (4/3): Introduction to relations (9.1, 9.3)

Note: There's a typo in the definition of 'a divides b' which I realized while recording (the fraction should be reversed); apologies for any confusion!

Correction: The transitive example should also contain (2,4) since (2,3) and (3,4) are in the relation.

Lecture 6 (4/6): Equivalence relations (9.5)

Lecture 7: Introduction to graph theory (10.1, 10.2)

Lecture 8: Bipartite graphs, subgraphs (10.2)

Notes pdf for Lectures 7 and 8: Link

Lecture 9: Graph isomorphisms (10.3)

Lecture 10: Paths and Connectivity (10.4)

Error: Near the end of the lecture there's an example discussing how you can use circuits of a given length to determine whether or not two graphs are isomorphic. In the example both graphs have a circuit of length 4. But H has a circuit of length 3 and G doesn't. Sorry!