Last updated 21 June 2009.
In particular, if you were in my classes at the Math Olympiad Summer Program, please let me know if you apply to Carnegie Mellon. I will try my best to help you.
I returned as an Instructor for the week of June 14, to teach several courses in Combinatorics. Lecture notes are below. The three highlighted lectures include topics that I encountered during graduate school, which also illustrate techniques relevant to Olympiad problem solving.
| Topic | Level |
| Probabilistic methods in combinatorics | Blue, Black |
| Graph theory: introduction | Red, Blue |
| Graph theory II | Red, Blue |
| Algebraic methods in combinatorics | Black |
| Extremal graph theory | Red, Blue |
| Combinatorial gems | Blue, Black |
I returned as an Instructor for the week of June 23. Unfortunately, I did not have time time to stay for the entire program because I was concentrating on my Ph.D. research.
The two highlighted lectures introduce concepts and methods that I learned through my Ph.D. research with Benny Sudakov, and illustrate how these beautiful techniques from research mathematics are also useful in the context of Olympiad problem solving.
| Topic | Level |
| Collinearity and concurrence | Red |
| Graph theory | Red, Blue |
| Probabilistic methods in combinatorics | Black |
| Convexity (inequalities) | Red, Blue |
| Algebraic methods in combinatorics | Black |
Useful references for some of the above topics:
I was the Deputy Team Leader for the United States at the 2004 International Mathematical Olympiad (Athens, Greece), and an Instructor at the Summer Program.
(I prepared fewer handouts compared to 2003 because I mostly lectured from the book A Path to Combinatorics for Undergraduates: Counting Strategies, by Titu Andreescu and Zuming Feng.)
This was the first year that I did a significant amount of teaching; I was a Junior Instructor. My notes are below.
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