Course Notes and Other Materials

The materials below include my personal course notes, solutions to selected problem sets, qualifying exam solutions, and background notes from minicourses and summer schools. They are intended primarily as study resources. These materials have not been formally reviewed, and any errors are my own.

1. Selected Course Notes

•  MATH 718--Randomized Linear Algebra and Applications

    Personal notes from a course taught by Professor Li

• MATH 719--Partial Differential Equations I

     Homework     Problem set 1     Problem set 2      

•  MATH 720--Partial Differential Equations II

    Homework     Midterm     Final Exam

• MATH 725--A Second Course in Real Analysis

     Personal notes from a course taught by Professor Seeger

•  MATH 733--Theory of Probability I

     Personal notes from a course taught by Professor Seppäläinen

•  MATH 734--Theory of Probability II

     Personal notes from a course taught by Professor Seppäläinen

•  MATH 821--Selected Topics in Functional Analysis

     Personal notes from a course taught by Professor Tran      Problem set 1     Problem set 2

2. Qualifying Exams Solutions

While preparing for my qualifying exams, I found it extremely helpful to type out my solutions to past problems. My hope is that these resources will serve as a useful guide for future students as they prepare for their exams. These solutions are based on past qualifying exams from UW-Madison, which are available on the math department’s website. If you spot any errors, I would appreciate it if you could let me know. Also, if you are not able to download this document yourself, please email me.

• Analysis

• Applied Math

3. Summer Schools

• Minicourse: Stochastic Modeling of Microswimmers

Minicourse taught by Professor Jean-Luc Thiffeault, May 11–13, 2026

• Differential Geometry in Continuum Mechanic

     Course taught by Professor Jean-Luc Thiffeault, May 1–3, 2025

• Stochastic Modeling of Particles

Course taught by Professor Jean-Luc Thiffeault, May 2024

• Calculus and convergence in metric measure spaces

Course taught by Professor Luigi Ambrosio 

• Compact Manifolds with Positive Ricci Curvature and Unbounded Nilpotent Fundamental Groups

Course taught by Professor Aaron Naber

• Isoperimetric properties of smooth and non-smooth spaces with lower curvature bounds

Course taught by Professor Antonelli