Writing
Mathematical writing
Here is some mathematical writing I've done over the years. Many of these are work-in-progress lecture notes.
Real Analysis, a nearly complete set of lecture notes on real analysis at the introductory level, based on a Math 131A course I taught at UCLA.
Morse Theory in Smooth, Contact, and Symplectic Topology, an incomplete set of lecture notes based on a Math 7400 course I taught at the University of Iowa.
Linear Algebra and Beyond, a work-in-progress manuscript based on lecture notes from a Math 115A course I taught at UCLA. This covers introductory proof-based linear algebra and some additional topics beyond the standard curriculum, like symplectic linear algebra.
Advanced Multivariable Differential Calculus, a work-in-progress manuscript that gives a rigorous introduction to multivariable calculus, based on a Math 32AH course I taught at UCLA.
Topics in Integration and Infinite Series, a work-in-progress manuscript on topics in calculus beyond the traditional curriculum.
A Guide to the Limit Comparison Test, an appropriately named comprehensive guide to using the limit comparison test, beyond what I've seen in traditional calculus textbooks.
The Basel Problem, a work-in-progress article on some nice calculus-based solutions of one of the most famous Slides problems in math.
Lectures in Harmonic Analysis , a work-in-progress manuscript based on two courses taught by by Monica Visan at UCLA.
Fredholm operators and the family index, a senior undergraduate project written at Northwestern.
An Introduction to Index Theory, a more accessible version of the above project.
Slides for Panorama of Topology, University of Iowa 2024: Panorama.key , Panorama.ppt , Panorama.pdf