Teaching

In the 2022-2023 academic year, I am on sabbatical at the University of Illinois and not teaching.

Here are some notes and related materials from past courses that some people might find helpful:

• Notes on Geometry and Mechanics: Introduces Hamiltonian and Lagrangian mechanics from the mathematical perspective, with emphasis on the relationship between symmetries and conserved quantities (Noether's Theorem). This version is from the last time I taught the course, in Fall 2019.
• Linear Algebra:
  • My YouTube channel has videos that I created for Linear Algebra in Fall 2020, as well as some videos for other courses that I am slowly working on uploading.
  • Notes on Matrix Factorizations: Introduces elementary matrices, explains how row operations can be interpreted in terms of matrix factorization, explains how to find and use an LU factorization.
  • Notes on Eigenvalues, Eigenvectors, and Diagonalization: Starting with the problem of solving linear systems of differential equations, these notes try to develop the concepts of diagonalization, eigenvalues, and eigenvectors in a natural way.