Some of these are (annnotated) slides from Colloquium Lectures, and some are just topics I've been playing with.
Divergent Series
Continued Fractions, Continued
Counting with Groups
Probing for Primes
Slide Rules
A Tale of Two Sequences
Leonhard Euler, on His 300th Birthday
Proofs from the Other Book
Learning how to draw graphs in LATEX
Burnside's Lemma and Applications
Gravity and Calculus
Some Lemmas for the Fundamental Theorem of Algebra