Past courses:


Calculus 2 for biological and social sciences, Fall 2021.
For its level this course covered a pretty wide range; besides some multivariable calculus, we covered a nice selection of topics from linear algebra, ODEs, and probability.

Real analysis 2, Spring 2020.
I ran this course out of blackboard. I continued with Strichartz, although at a faster pace. I covered chapters 7 - 12 and a bit of 13, or more accurately chapters 7-11, 13, and then chapter 12. I didn't cover every thing out of every chapter but we did cover a lot of the big stuff, including the ODE theorem, Dirichlet's and Fejers theorem, and the implicit function theorem.

Introduction to curvature flows, Fall 2020.
We covered up to Grayson's theorem (CSF flows closed curves to round points).

Real analysis 1, Fall 2020.
I ran this course out of blackboard and I didn't really get around to building a page for it here. We covered chapters 1-6 of Strichartz's book ''Way of analysis,'' which in short was the construction of the real numbers, continuous functions, differentiation, and integration (all over the real line).

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.