Teaching

In the 2026-2027 academic year, I will be on sabbatical.

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 Spring 2025.
• Advanced Calculus Notes: Introduces differential forms on R^n, integration on (cubical) chains, and Stokes' Theorem, with an emphasis on the correspondence with concepts from multivariable calculus (when n=2 or 3). Special topics include the Gauss linking number and Maxwell's equations. If I had more time I would add more pictures.
• 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.