This fall, I am teaching Brown's Multivariable Calculus with Theory, Math 0350. The information for this course can be found on the course's Canvas website. The goal of this course is twofold:
To cover the main results of a standard multivariable calculus course, which here means differentiation and integration in several variables, the major integral theorems (Green's, Stokes's, Gauss's), and optimization (including Lagrange multipliers)
To provide an introduction to theoretical mathematics, by introducing students to proof-based work, and asking them to read and write proofs in class, in homeworks, and in collaborative exercises in recitations.
At the end of this semester, I may link some of the course materials from this page, for future reference.
Previous Teaching at Brown
Last semester (Spring 2025), I was one of two instructors for Brown's Introduction to Analysis, Math 1010. I was also one of the instructors for Linear Algebra, Math 0520, coordinated by Jordan Kostiuk.
Last fall (2024), I also taught Brown's Multivariable Calculus with Theory, Math 0350. See above.
Previously at Brown, I have taught Single Variable Calculus (Part I), Math 0090 and Multivariable Calculus for Physics and Engineering, Math 0200.
In the Fall of 2022, I taught JHU's Single Variable Calculus with Theory course, Math 113. Similarly to the course I am teaching in Fall 2025, this course aimed both to cover the material of single-variable calculus (including integration techniques and series) and to introduce students to proofs and proof-writing.
As I continue to work on this website, I may link my course materials from this page.
In the summers of 2018--2024, I taught at Canada/USA Mathcamp. The courses are (usually) weeklong, and are targeted towards high-school students (albeit students who are very adept at mathematics & interested in the theoretical aspects of the subject).
The courses I've taught at Mathcamp can be grouped, broadly, into 3 categories. Within these categories, I give very brief notes on the content covered; I plan to link notes in the future:
Introductory real analysis
Convolutions, Fourier analysis, and the Borwein integrals
Volterra's Function & Lebesgue's theorem on Riemann integrability
The calculus of variations
Cantor's work on trigonometric series
Baire's category theorem
Chaotic dynamics, fractal curves
Cantor's Leaky Tent
Characterizations of the rational numbers and the Cantor set
Metrizability, Embeddings, Hedgehogs
Tychonoff's theorem
Buffon's Needle/Buffon's Noodle (probability theory)
Continued Fractions
Erdős's Distinct Distances Problem
The Sylow theorems
Liouville's theorem (differential algebra)
Voting theory
Game theory