Teaching

I display the following information line-by-line:

• Course Title (Course Code)
• Institution
• Role; Semesters ~ e.g. S24 = Spring Semester, 2024.
• Concepts covered.
• Instructor(s).

Cryptography

Euler Circle

Teaching Assistant; Summer 24.

Instructor: Simon Rubinstein-Salzedo

Substitution Ciphers, Vignere Ciphers, Hill Cipheres, Number Theory, Diffie-Hellman, RSA, Elliptic Curve Cryptography, Cryptographic Voting, Secret-Sharing, Zero-Knowledge Proofs, Common Attacks

I served on the teaching staff for a cryptography course taught by Euler Circle, a mathematics institute dedicated to teaching college-level math to high schoolers. It followed a textbook by Dr. Rubinstein-Salzedo aimed at covering a wide bredth of subjects relevant to modern cryptographic research, with a particular focus given to the most mathematically interesting material, including prime factorization and number theory, elliptic curves, and cryptographic voting.

Linear Algebra (MATH 120)

Harvard University

Course Assistant; S24.

Instructor: Janet Chen

Vector Spaces / Subspaces, Linear Independence, Linear Maps, Fundamental Theorem of Linear Maps, Quotent Spaces, Dual Spaces, (Generalized) Eigenvectors / Eigenvalues, Diagonalization, Riesz Representation Theorem, Adjoints, Nilotent Maps, Jordan Forms, Spectral Theorem.

MATH 120 is intended as a second course in linear algebra, emphasizing proofwriting, extending many results to the complex numbers, and integrating linear algebraic structures into a broader algebraic vocabulary fit for more advanced study. The course followed Axler’s classic textbook Linear Algebra Done Right.

Introduction to Reinforcement Learning (CS/STAT 184)

Harvard University

Teaching Fellow; F23.

Co-Instructors: Sham Kakade, Lucas Janson.

Markov Decision Processes (MDPs), Value / Policy Iteration, Linear Quadratic Control (LQR), Bandits, Supervised Learning, Policy Gradient Methods, Trust Region Methods, Proximal Policy Optimization, Importance Sampling, Behavior Cloning, DAgger, Monte Carlo Tree Search.

After taking the first iteration of this course at Harvard in 2022, I entered the course staff for its second offering. The course, jointly listed with the statistics and computer science departments, provided a comprehensive introduction to reinforcement learning, focusing in particular on using techniques from statistics and optimization to derive bounds on complexity and performance guarantees for each algorithm. The course did not follow any particular textbook, but frequently referenced Professor Kakade’s Reinforcement Learning: Theory and Algorithms, as well as Sutton and Barto’s classic Reinforcement Learning: An Introduction.

Vector Calculus and Linear Algebra II (MATH 22B)

Harvard University

Course Assistant; S22, S23.

Instructors: Dusty Grundmeier (S22), Oliver Knill (S23).

Inner Products / Metric Spaces, Paths / Directional Derivatives, Total Derivatives, Lagrange Multipliers, Vector Fields, Double and Triple Integrals, Change of Variables, Path / Line / Surface Integrals, Stokes' Theorem, Differential Forms.

Math 22B is the second half of a year-long advanced introduction to proofwriting and mathematical thinking, focusing in particular on vector calculus. Having a strong proowriting background from 22A, students spend the bulk of the time proving important results from multivariable calculus, including differentiation and integration for functions of more than one variable. Unlike traditional multivariable calculus courses, this introduction is able to move at a much faster pace using the language of linear algebra, following Marsden’s Vector Calculus. The course likewise concludes with an expository final paper on a subject of the student’s choosing—see mine here!

Vector Calculus and Linear Algebra I (MATH 22A)

Harvard University

Course Assistant; F21, F22.

Instructor: Dusty Grundmeier.

Set Theory, Functions, Proofwriting, Induction. Vector and Matrix Algebra, Vector Spaces, Linear Transformations, Bases/Coordinates, Eigenvectors/Eigenvalues, Diagonalization, Spectral Theorem.

Math 22A is the first half of a year-long advanced introduction to proofwriting and mathematical thinking, focusing in particular on set theory and linear algebra. In the first semester, students are exposed to proofwriting through the classic Hammack Book of Proof, and they use these tools to begin to prove many of the major results from linear algebra, loosely following the textbook Linear Algebra and Its Applications by David Lay. The course concludes with an expository final paper on a subject of the student’s choosing—see mine here!