Last updated 17 August 2012.
If you enjoyed the high-school Olympiad competitions, and are interested in the possibility of joining our program, please feel free to contact me for further discussion. For example, if you were in my classes at the Math Olympiad Summer Program, or if I met you at an international competition, please let me know if you send us an application for undergraduate admission. I will try my best to help you.
I was the Deputy Team Leader for the United States at the 2012 International Mathematical Olympiad, in Mar del Plata, Argentina. At the Math Olympiad Summer Program, I led an NSF-supported initiative to bridge the gap between Olympiad training and research mathematics, supervising fast-paced undergraduate research projects in combinatorics, in addition to teaching several courses to high-school students. Lecture notes for the courses are below:
| Topic | Level |
| Pigeonhole principle | Red |
| Introductory graph theory | Red |
| Graph theory and designs | Blue |
| Applications of probabilistic and algebraic methods in combinatorics | Black |
A strong combinatorics background came in handy on problem 3 of the IMO, which was the most challenging problem on Day 1 (and highlighted by Terry Tao on his blog). Team USA built up a substantial lead over all other countries on this problem, but lost the lead through the Euclidean geometry problem on Day 2.
I was the Deputy Team Leader for the United States at the 2011 International Mathematical Olympiad, in Amsterdam, Netherlands. I returned to the Math Olympiad Summer Program for two weeks. This time, in addition to teaching several courses in Combinatorics, I also directed a new initiative (sponsored by a new grant from the National Science Foundation) to connect Olympiad mathematics with research mathematics. Lecture notes are below:
| Topic | Level |
| Graph theory | Red, Green, Blue |
| Algebraic methods in combinatorics | Black |
| Combinatorics of sets | Red, Green, Blue, Black |
| Probabilistic methods in combinatorics | Black |
I was the Deputy Team Leader for the United States at the 2010 International Mathematical Olympiad, in Astana, Kazakhstan, and the Team Leader at the 2010 Romanian Masters in Mathematics in Bucharest. I returned to the Math Olympiad Summer Program for a week, teaching several courses in Combinatorics. Lecture notes are below.
| Topic | Level |
| Pigeonhole principle | Red |
| Trees | Red, Green, Blue |
| Extremal arguments | Blue |
| Matching and planarity | Red, Green, Blue |
| Probabilistic methods in combinatorics | Blue |
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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