Notes/Teaching
This page is for lecture notes and personal notes that I have written over the years. Many of those notes are for self-use, so be careful when using. Please contact me if you spot any mistake or if you have any suggestion.
I also list courses I was a TA for at USC, but material for them can only be found on the USC intranet.
Mathematics for economics and econometrics
Below is a list of 20 important mathematical theorems for economics with standalone proofs. The notes will be uploaded as they become available.
- 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
- 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 courses at USC
- ECON609 - Econometric Methods (PhD) - Spring 2024
- ECON611 - Probability and Statistics for Economists (PhD) - Fall 2023, Fall 2024
- ECON513 - Practice of Econometrics (Master) - Fall 2023, Fall 2024, Spring 2025