Notes/Teaching
This page collects some mathematical notes that I wrote during my PhD. Please be careful when using them as they likely contain mistakes and typos. If you spot any errors or if you have any suggestions, please contact me.
Mathematics for economics and econometrics
This is a collection of 20 mathematical theorems - and their standalone proofs - chosen for their prevalence in economic and econometric theory. Only 12 theorems and proofs are available now. I plan to complete the project and reorganize the notes to briefly explain the purpose of each theorem, provide historical context, and include some applications in economics, statistics, and operations research.
- Kakutani–Glicksberg–Ky Fan fixed point theorem
- Von Neumann–Sion minimax theorem
- Tarski’s fixed point theorem
- Banach’s fixed point theorem
- Hahn–Banach extension theorem
- Farkas’ lemma
- Karush–Kuhn–Tucker conditions
- Pontryagin’s maximum principle
- Hamilton–Jacobi–Bellman equation
- Berge’s maximum theorem
- Envelope theorem
- Milgrom–Shannon monotonicity theorem
- Riesz–Markov–Kakutani representation theorem
- Radon–Nikodym theorem
- Disintegration theorem
- Prokhorov’s theorem
- Lévy’s continuity theorem
- Glivenko–Cantelli theorem
- Donsker’s theorem
- Hájek–Le Cam convolution theorem
Miscellaneous topics in probability and statistics
This is a collection of notes I wrote to (re-)familiarize myself with some topics in probability and statistics while working on related problems. Please be careful when using the notes as they are not organized carefully and likely contain mistakes and typos.
- Concentration inequalities
- Maximal inequalities
- Superefficient estimation and Le Cam’s rescue
- Gaussian sequence models
- Minimax upper and lower bounds
- Le Cam’s comparison of experiments
- Semiparametric estimation: efficiency bounds
- Continuous-time Markov processes, martingale problem, and diffusion approximation
TA classes at USC
This is the list of classes I was a TA for at USC during my PhD. I was also in charge of organizing review sessions on mathematics, Stata, and Python.
- ECON611 - Probability and Statistics for Economists (PhD) - Fall 2023, Fall 2024, Fall 2025
- ECON513 - Practice of Econometrics (Master) - Fall 2023, Fall 2024, Spring 2025, Fall 2025
- ECON609 - Econometric Methods (PhD) - Spring 2024, Spring 2026
- ECON480 - Economics of Industrial Organization (B.Sc.) - Spring 2026