Teaching

This page contains information about the courses I am currently teaching, and also some resources (practice problems, notes, videos) from previous courses I have taught.

Current teaching (Spring 2023)

This semester, I am teaching Math 1860: Calculus II. For a course website, we are using ICON / Canvas.

Math 7400: Current Geometry and Topology I

In Fall 2022, I was the instructor for Math 7400, which covered Morse theory, techniques in low-dimensional topology, and contact and symplectic topology.

• Work-in-progress lecture notes: (pdf link)

Math 131A: Real Analysis

In Spring 2022, I was an instructor for Math 131A, which is an introduction to real analysis.

• Work-in-progress lecture notes: (pdf link)

Math 115A: Linear Algebra

In Spring 2021, I was an instructor for Math 115A, which is an introduction to proof-based linear algebra.

• Work-in-progress lecture notes: (pdf link)

Math 32AH: Calculus of Several Variables (Honors)

In Fall 2020, I was the instructor for Math 32AH, which is a rigorous introduction to multivariable calculus.

• Work-in-progress lecture notes: (pdf link)

Math 32B: Calculus of Several Variables (Integral)

In Spring 2020 I was a teaching assistant for a 32B course and made many instructional videos throughout the quarter. Here is a link to the full playlist of videos. The quality starts out poor, but then over the course of the quarter I become a better video producer. Here is a selection of videos.

• Stokes' theorem.

• Vector surface integrals.

• Spherical coordinates in integrals.

• The spherical coordinate dance, the most important and educational video I have ever made.

Here is a list of expository notes I have written on multivariable calculus. Most of these were written a long time ago (when I was an undergrad), so take the content with a grain of salt. Some of these links may be dead, sorry --- I'll get around to updating everything eventually. If there is a particular dead document that strikes your interest, feel free to reach out to me.

• The meaning of line integrals and surface integrals.

• The meaning of Green's theorem.

• The theorems of vector calculus, a set of notes explaining all of the main theorems (Green's, Stokes', divergence, and so on).

• A fun graphic summarizing all of the integrals and fundamental theorems in multivariable calculus.

Math 32A: Calculus of Several Variables (Differential)

Here is a list of resources containing practice problems that I have written and curated for 32A. Some of these links may be dead, sorry --- I'll get around to updating everything eventually. If there is a particular dead document that strikes your interest, feel free to reach out to me.

• A practice midterm 1. Solutions can be found here.

• A practice midterm 2. Solutions can be found here.

• Plane practice problems. Practice problems for finding equations of planes, solutions included. This collection includes just about every standard type of question, as well as some fun and challenging extra problems.

Here is a list of other notes relevant for 32A.

• A short note on the gradient vector. This describes how you can use the gradient vector to find tangent planes and tangent lines and makes explicit the notion of using different perspectives to tackle the same kind of problem.

Here are some helpful YouTube videos I have produced for 32A topics.

• Multivariable limit examples.

• Computing a tangent plane in two different ways.

• Multivariable implicit differentiation.

• 32A final exam review session, a filmed review session where I cover a range of topics from 32A.

Math 31B: Integration and Infinite Series

Here is a list of resources containing practice problems that I have written and curated for 31B over the years. Some of these links may be dead, sorry --- I'll get around to updating everything eventually. If there is a particular dead document that strikes your interest, feel free to reach out to me.

• • Infinite series practice problems

  • Extra challenging integral problems

  • Extra challenging sequence and series problems

  • Extra challenging power series and Taylor series problems

Here is a list of other notes and guides relevant for 31B.

• • An infinite series convergence flowchart

  • A comprehensive guide to the limit comparison test, the best series convergence test

  • A collection of well-written model solutions for most types of problems in 31B

  • Notes on computing Taylor polynomials

  • Notes on the intuition behind series convergence

  • Topics in Integration and Infinite Series, a long-forgotten work-in-progress about extra topics in single variable calculus that aren't taught in 31B

Here are some helpful YouTube videos I have produced for 31B topics.

• • A guide to partial fractions, a video where I go over all types of partial fractions problems with solved examples

  • An introduction to sequences

  • A trig substitution integral example, the first YouTube video I ever made

  • Examples of improper integrals

  • 31B final exam review session, a filmed review session I held that covers a range of topics from 31B