Math Coursework Listing
Spring 2024
Math Coursework I am currently enrolled in:
- 18.156: Differential Analysis II, taught by Prof. Larry Guth
- 18.099: Independent study on restriction theory, with by Prof. Larry Guth
Fall 2023
- 18.225: Graph Theory and Additive Combinatorics, taught by Prof. Yufei Zhao
- 18.675: Theory of Probability, taught by Prof. Konstantinos Kavvadias
- 18.905: Algebraic Topology I, taught by Prof. Paul Seidel
Spring 2023
- 18.156: Differential Analysis II, taught by Prof. David Jerison
- Typing lecture notes for some lectures (to be uploaded here)
- Learning about Hardy spaces and BMO on my own using Elias Stein's "Harmonic Analysis".
- 18.158: Fourier Analysis to Analytic Number Theory, taught by Prof. Larry Guth
- 18.821: Project Lab in Mathematics, taught by Prof. Lisa Piccirillo
- Project 1: Exploring the relation between random walks and harmonic functions, solving the Discrete Dirichlet Problem using probabilty.
- Project 2: Exploring Young Tableau with linear algebraic conditions, with relations to combinatorics.
- 18.966: Geometry of Manifolds II, taught by Prof. Tobias Colding
Fall 2022
- 18.112: Complex Analysis, taught by Prof. Roman Bezrukavnikov
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Using this time to explore deRham theory on real and complex manifolds so I can better understand the algebraic topology/homology theory behind certain theorems in complex analysis. Reading Bott and Tu's book on this matter.
- 18.965: Geometry of Manifolds I, taught by Prof. Bill Minicozzi
- 18.994: Seminar in Geometry, taught by Prof. Qin Deng
- On minimal surfaces, using the textbook developed by Bill Minicozzi and Tobias Colding.
- Presented on Section 3.3 of do Carmo's text with Victor Luo, discussing the minimizing properties of Geodesics.
- Presented on the first variation formula for minimal surfaces, defining minimal surfaces as being a critical point of the volume functional, and showing that this implies the mean curvature must be zero everywhere on the minimal surface (in fact this is an equivalent relationship).
- Presented on Section 4.3-4.5.1 with Carlos on 1) Solving the Plateau problem and 2) harmonic maps.
- Final project: Studying the relationship and the proofs of Sobolev inequalities and the Isoperimetric inequality on minimal surfaces. If time permits, trying to develop a proof of my own using techniques developed in my 2021 Summer UROP (see below). In particular, studying the equivalence of these inequalities.
Spring 2022
- 18.157: Microlocal Analysis, taught by Prof. Richard Melrose
- 18.099: Independent Study with Prof. Richard Melrose
- To ask clarifying questions about Microlocal Analysis over the course of the semester.
- 18.118: Introduction to Chaotic Dynamics, taught by Prof. Semyon Dyatlov
- 18.952: Introduction to Differential Forms, taught by Prof. Victor Guillemin
Fall 2021
- 18.155: Differential Analysis, taught by Prof. Semyon Dyatlov
- 18.101: Analysis and Manifolds, taught by Prof. Richard Melrose
- 18.705: Commutative Algebra, taught by Prof. Wei Zhang
Spring 2021
- 18.702: Algebra II, taught by Prof. Michael Artin
- 18.102: Introduction to Functional Analysis, taught by Prof. Casey Rodriguez
- 18.901: Introduction to Topology, taught by Prof. George Lusztig
IAP 2021
- 18.03: Differential Equations (ASE)
Fall 2020
- 18.701: Algebra I, taught by Prof. Bjorn Poonen
- 18.100B: Real Analysis, taught by Prof. Tobias Colding
- 18.A06: What is a Number, taught by Prof. Haynes Miller
- A first year seminar on the construction of numbers, with numerous philosophical conversations on what objects should or shouldn't be considered numbers.
- Discussing Peano Axioms, Dedekind cuts, constructions of the real numbers, construction of the complex numbers, quarternions, surreal numbers, p-adic numbers, etc.
At Fresno City College
- Math 5A: Mathematical Analysis I (Differential Calculus)
- Math 5B: Mathematical Analysis II (Integral Calculus), taught by Travis McDonald
- Math 6: Mathematical Analysis III (Multivariable Calculus), taught by Matt Woods
- Math 7: Differential Equations, taught by Travis McDonald
- Math 26: Linear Algebra, taught by Matt Woods
Last updated: May 29, 2023