Teaching & Mentoring

Teaching Experience

Instructor of Record

University of Arizona

Recipient of 2022 University of Arizona Mathematics Departmental Teaching and Service Award 

Notes and Assignments from a two semester Real Analysis course (Math 425A/B). Modules 1-6 largely follow Introduction to Real Analysis by William Trench (https://digitalcommons.trinity.edu/mono/7), though many of the proofs and examples are my own and Module 4 is significantly rearranged. Modules 7 & 8 do not follow a specific text.  

Teaching Assistant

University of California, Los Angeles

Recipient of 2018 UCLA Mathematics Departmental Teaching Award 

Colorado School of Mines

Mentoring

Some of my most satisfying academic experiences have been mentoring undergraduate research as part of several different summer REU programs. In all, I have been mentor or co-mentor for more than two dozen students split across 7 programs (and ~10 projects depending on how you count the subdivisions). The main thrust of each project is described below.

Interpretable Semi-Real-Time Algorithms for Path Planning in the Hamilton-Jacobi Formulation - Summer 2023 - 1 student

Studied minimal time optimal path planning in a feedback control formulation using numerical methods for Hamilton-Jacobi equations which scale well to high dimensions, with specific emphasis on real-time concerns such as obstacle discovery. 

Efficient and Scalable Algorithms for Path Planning in the Hamilton-Jacobi Formulation - Summer 2022 - 1 student

Studied minimal time optimal path planning for Dubins' cars using algorithms for high-dimensional Hamilton-Jacobi equations. Developed algorithms based on Hopf-Lax type formulas that are much nearer to being applicable in real-time scenarios. 

Optimal Path Planning for Simple Self-Driving Cars - Summer 2021 - 1 student

Studied minimal time optimal path planning for Dubins' cars using dynamic programming and optimal control theory. Improved current formulations by allowing for moving obstacles. Developed an upwind finite difference scheme to solve the Hamilton-Jacobi-Bellman equation for the value function and resolve optimal trajectories.

Epidemic Modeling in the Time of COVID-19 -  Summer 2020 - 10 students

Explored three different types of mathematical models for epidemiology (compartmental modeling, point-process modeling such as the Hawkes model and generalizations, and network scientific modeling) with special focus on the interaction between certain social behavior and disease spread. [Co-mentored with Mike Lindstrom and Chuntian Wang]

Modeling Illegal Deforestation in the Brazilian Rainforest - Summer 2019 - 5 students

Developed two models for deforestation in the Brazilian rainforest, following the lead of social scientists who identify two primary types of illegal deforestation: (1) a control-theoretic model for timber extraction (building on the work from Summer 2017), and (2) a point-process type model for agricultural land clearance. 

Spatio-Temporal Analysis of Los Angeles Twitter Data - Summer 2018 - 7 students

Applied machine learning algorithms to classify time-stamped and geolocated tweets from Los Angeles so as to understand trends in both time and space. Used two methods for topic modeling (latent Dirichlet allocation and non-negative matrix factorization), and focused on improving/specifying methods for our application, as well as analyzing our particular data set. [Co-mentored with David Arnold and Mike Lindstrom] 

Mathematical Modeling of Environmental Crime - Summer 2017 - 4 students

Developed a game-theoretic level-set based model for environmental crime. Built off previous work by ecologists and computer scientists, but removed a number of overly restrictive assumptions regarding the shape of the domain, and included a number of realistic features such as terrain information. [Co-mentored with David Arnold]

Miscellaneous Resources (which may be vaguely instructive)

Math Subject GRE Prep

As part of the mentoring for the Summer REU program at UCLA, I taught a short preparatory course for the math subject GRE. We met twice per week for 6 weeks. The first meeting each week was more lecture style wherein I would introduce a topic and recall all important facts about it in rapid-fire fashion, and the second meeting was problem-solving using all the information covered in the first meeting. 

All resources I created for this course are here: Math GRE Prep. Resources. Feel free to share/link/post these resources at will, but please give proper credit. 

My best advice to anyone studying for the math subject GRE: relearn everything from calculus before you even start on the other topics. Calculus makes up more than 50% of the exam, and they find clever/tricky ways to ask calculus questions that are much more difficult than what you likely saw in your calculus sequence. This is why I decided to give  each of Calc. I,II and III their own week in my materials, whereas the others share time.  

The topics are as follows:


UCLA Basic Exam Solutions

While studying for the UCLA Basic Exam (the first qualifying exam to be passed as a UCLA graduate student), I typed up answers to past exam questions. This includes most answers up to and including my exam which was Fall 2015. (Caveat emptor! These solutions are sure to have some errors; trust them at your own risk.)