Elementary number theory, Summer 2020 .
Online course given entirely through blackboard; the linked page is mainly a record to keep track of what I covered for posterity.
Honors Analysis 2, Spring 2020
This was an undergraduate course where measure theory on the real line was developed, following Carothers. At the end we also covered a bit of Sobolev spaces out of Evans' PDE book.
Introduction to Lie groups and Lie algebras, Spring 2020
This was a graduate course on Lie groups and Lie algebras. First to whet our appetite we discussed some really ancient but interesting work by Lie on solving ODE's with solvable symmetry groups by repeated quadarature (i.e. integration), a natural parallel in ODE theory to ``polynomials with solvable Galois group can be solved by radicals.'' This part we followed Hydon. Then we covered some smooth manifold theory culimating in Frobenius theorem, allowing us to give the correspondence between Lie groups and Lie algebras (roughly stated) following John Lee's book. The last part of the course we discussed the classification theorem of semisimple Lie algebras following Kirilov.
Introduction to Differential Geometry, Fall 2019
This was an undergraduate course on curves and surfaces following Do Carmo, ending with Gauss-Bonnet.