Course Notes and Other Material

The following are personal notes, problem sets, and background materials from selected graduate courses. They are intended primarily as study resources; any errors are my own.

1. Selected Course Notes

•  MATH 718--Randomized Linear Algebra and Applications

    Lecture notes taught by Prof. Li

• MATH 719--Partial Differential Equations I

     Homeworks     Problem set 1     Problem set 2      

•  MATH 720--Partial Differential Equations II

    Homeworks     Midterm     Final Exam

• MATH 725--A Second Course in Real Analysis

     Lecture notes taught by Prof. Seeger 

•  MATH 733--Theory of Probability I

     Lecture notes taught by Prof. Seppäläinen

•  MATH 734--Theory of Probability II

     Lecture notes taught by Prof. Seppäläinen

•  MATH 821--Selected Topics in Functional Analysis

     Lecture notes taught by Prof. Tran      Problem set 1     Problem set 2

2. Summer Schools

• Minicourse: Stochastic Modeling of Microswimmers, taught by Prof. Thiffeault, May 11-13, 2026

• Differential Geometry in Continuum Mechanic, taught by Prof. Thiffeault, May 2025

• Stochastic Modeling of Particles, taught by Prof. Thiffeault

• Calculus and convergence in metric measure spaces, taught by Prof. Ambrosio

• Isoperimetric properties of smooth and non-smooth spaces with lower curvature bounds, taught by Prof. Antonelli

• Compact Manifolds with Positive Ricci Curvature and Unbounded Nilpotent Fundamental Groups, taught by Prof. Naber

3. Qualifying Exams

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