Lecture 19-A: The Heine-Borel theorem

Lecture 23-B: The infinite Ramsey theorem

Lecture 22-B: Stars and bars

Counting the number of surjective functions between two finite sets

Lecture 22-C: Ramsey's theorem

Lecture 21: The inclusion-exclusion principle

Lecture 20: Permutations and combinations

Lecture 19-B: Nested set implies Bolzano-Weierstrass (lion hunt)

Lecture 19-C: Sequential compactness

Lecture 19-A: The Heine-Borel theorem

Lecture 18: Compactness

Lecture 17-B: Proof that Cauchy-reals are order-complete

Lecture 17-A: The closure operator

Lecture 16: R^n as a metric and topological space

Lecture 15-B: Regularity of Aleph_1

Lecture 15-A: The smallest infinity

Lecture 14: Aleph naught

Lecture 13: Finitary cardinal arithmetic

Lecture 12: Ordering the reals

Lecture 11: Construction of the reals

Lecture 10: Fermat's little theorem

Lecture 9-A: Applications of modular arithmetic

Lecture 9-B: Systems of linear congruences

Lecture 8: The ring of congruence classes

Lecture 7: Shortcut to the fundamental theorem of arithmetic