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 TAed for at USC, but material can only be found on Blackboard.

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.

1. Kakutani–Glicksberg–Ky Fan fixed point theorem
2. Von Neumann–Sion minimax theorem
3. Tarski’s fixed point theorem
4. Banach’s fixed point theorem
5. Hahn–Banach extension theorem
6. Farkas’ lemma
7. Karush–Kuhn–Tucker conditions
8. Pontryagin’s maximum principle
9. Hamilton–Jacobi–Bellman equation
10. Berge’s maximum theorem
11. Envelope theorem
12. Milgrom–Shannon monotonicity theorem
13. Riesz–Markov–Kakutani representation theorem
14. Radon–Nikodym theorem
15. Disintegration theorem
16. Prokhorov’s theorem
17. Lévy’s continuity theorem
18. Glivenko–Cantelli theorem
19. Donsker’s theorem
20. 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

• ECON611 - Probability and Statistics for Economists (PhD) - Fall 2023
• ECON513 - Practicte of Econometrics (Master) - Fall 2023