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Projects

Calculus Resources

While at the University of Texas at San Antonio, I served as a teaching assistant for MAT 1224 (now MAT 1223), Calculus II. I created a series of videos to help students understand the material. The videos can be found here. All material is based on the OpenStax Calculus, Volume 2 text.

Also included here is a flowchart on how to think about the convergence of series.

A study guide for the third exam in the course is also available, along with its solutions.

Photoacoustic Sensing
As part of an internship project in the fall of 2023, I worked with Drs. Randolph Glickman and Saher Maswadi to examine the use of photoacoustic sensing in the detection of defects in a known material. The project combined elements of signal processing, laser physics, and materials science. The project report can be read here.
Vector Calculus, Linear Algebra, and Differential Forms
Project paper written for an independent study course on vector calculus at Texas A&M University - San Antonio. The aim was to examine the applications of differential forms in electromagnetism - in particular, the condensation of Maxwell's equations from 4 to 2. Read the paper here.
Bounds on the Traveling Salesman Problem
Project paper on the Traveling Salesman Problem, written for a course in graph theory at Texas A&M University. Read the paper here.
Gaussian Integers
Project paper on Gaussian integers, written for an undergraduate course in abstract algebra at Texas A&M University - San Antonio. Read the paper here.
Stochastic Calculus
As part of an independent study course at Texas A&M, I began reading on the foundations of stochastic calculus. I then presented an introductory talk on the topic at a talk for the graduate student organization in the math department. See the presentation here.
Euler-Maruyama Method
As part of a project for a course in an introduction to applied mathematics, I presented on the Euler-Maruyama method, a numerical method to solve stochastic differential equations. The project paper can be read here, and a video presentation based on this paper can be watched here. The slides can be viewed as well.
A Mathematician's Guide to Machine Learning
An introductory talk about machine learning, focusing on the mathematical framework. A short version of the talk was given at a DevSA event, whose slides are here.
For RowdyHacks X, a slightly expanded version of the talk is available at here, with a code notebook available on Kaggle, and the actual Jupyter notebook is available for download here.
Traffic Flow
A project for the UTSA course MAT 5673, Partial Differential Equations I. The project was to model traffic flow using the one-dimensional transport equation. The presentation, whose slides are here, culminated in the creation of a solver using the Godunov method to solve nonlinear transport equations. Joint work with C. Ayo, E. Jones, and B. Morgan.