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Math Olympiad teaching notes Math Olympiad teaching notes Last updated 10 June 2014. Note to high-school students In 2010, I and my Associate Department Head John Mackey, with the direct support of Carnegie Mellon President Jared Cohon and two significant alumni donors, launched a new “ultra-honors” talent incubator program for extremely motivated and advanced students. The curriculum is individually customized to suit each scholar's background and aspiration, and all students are personally mentored by myself and John. 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.
NOTE: Other FOLLOW-UP problems related to some of the above can be found in our three contest problem books and in “Creative Problem Solving in School Mathematics.” Visit www.moems.org for details and to order. METHOD 2 Strategy: Use spatial reasoning. The area of the original rectangle is 8 212 = 96 cm.
2014 United States Math Olympiad Program Starting this season, I will be the Leader for the United States delegation to the International Mathematical Olympiad, which will be held in 2014 in South Africa. The class schedule has been posted.
2013 United States Math Olympiad Program I was the Deputy Team Leader for the United States at the, in Santa Marta, Colombia. At the Math Olympiad Summer Program, I led an 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. Our research produced a, which we have submitted for publication. Lecture notes for the courses are below: Topic Level Red Blue Blue/Red Red/Blue Red/Blue Black/Blue 2012 United States Math Olympiad Program I was the Deputy Team Leader for the United States at the, in Mar del Plata, Argentina. At the Math Olympiad Summer Program, I led an 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.
Our research produced a, which we have submitted for publication. Lecture notes for the courses are below: Topic Level Red Red Blue Black A strong combinatorics background came in handy on problem 3 of the IMO, which was the most challenging problem on Day 1 (and ). Team USA over all other countries on this problem, but lost the lead through the on Day 2. 2011 United States Math Olympiad Program I was the Deputy Team Leader for the United States at the, 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 ) to connect Olympiad mathematics with research mathematics. Lecture notes are below: Topic Level Red, Green, Blue Black Red, Green, Blue, Black Black 2010 United States Math Olympiad Program I was the Deputy Team Leader for the United States at the, in Astana, Kazakhstan, and the Team Leader at the 2010 in Bucharest.
I returned to the Math Olympiad Summer Program for a week, teaching several courses in Combinatorics. Lecture notes are below. Topic Level Red Red, Green, Blue Blue Red, Green, Blue Blue 2009 United States Math Olympiad Summer Program 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 Blue, Black Red, Blue Red, Blue Black Red, Blue Blue, Black 2008 United States Math Olympiad Summer Program 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.
The two highlighted lectures introduce concepts and methods that I learned through my Ph.D. Research with, and illustrate how these beautiful techniques from research mathematics are also useful in the context of Olympiad problem solving.
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Topic Level Red Red, Blue Black Red, Blue Black Useful references for some of the above topics:. The Probabilistic Method, by Noga Alon and Joel Spencer. The is already available for pre-order, but the may be present in your university library. This is well-written text which is very readable, but has quite challenging exercises.
Algebraic Methods in Combinatorics, lecture notes by, written for his graduate course at the University of Cambridge. These are available on the author's website, and a. Graph Theory, by Reinhard Diestel. There is a free electronic edition available on. 2004 United States Math Olympiad Summer Program 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. Polynomials (Blue group):.
Inequalities (Blue group):. Functional Equations (Blue group):. Graph Theory (Blue group):. Polynomials (Red group): (I prepared fewer handouts compared to 2003 because I mostly lectured from the book, by Titu Andreescu and Zuming Feng.) 2003 United States Math Olympiad Summer Program This was the first year that I did a significant amount of teaching; I was a Junior Instructor. My notes are below. Induction:. Inequalities:.
Telescoping Sums/Products:. Triangles:. Cyclic Quadrilaterals:. Collinearity and Concurrence:. Sequences:.
Brutal Force:. Number Theory: 2002 United States Math Olympiad Summer Program Akamai made a very substantial gift to the national Math Olympiad program in 2002, enabling the centralized USAMO, and a vastly enlarged MOP (up to about 180 students, compared to around 30 the previous year).
Many IMO alumni returned as first-time staff members that year. I came as a grader, but I volunteered several lectures because teaching was exhilarating. Geometry Revisited:. Geometry (Yellow group):.
Brutal Force. Concurrence: 2001 International Mathematical Olympiad (Washington, D.C., United States of America) Former members of the USA IMO team were invited back to assist at IMO 2001, which was hosted in Washington, D.C. Older alumni served as coordinators. Several of us were still in college at the time, and came back as tour guides. I was the guide for.
1999 United States Math Olympiad Summer Program I was wrong in 1998, and returned to MOP again. Since the USA Team Leader, Titu Andreescu, had close connections with the Romanian Math Olympiad movement, we also spent a week training with the Romanian team in before the IMO, which was in Bucharest, Romania that year. 1998 United States Math Olympiad Summer Program I returned as a veteran this year. Back then, students sometimes contributed lectures for fun, and I gave the last lecture on the last day, on an unusual technique that I had come up with to solve geometry problems (my favorite subject at the time).
The handout is unedited, hence the high-schoolish humor. Brutal force: (To put the first sentence on the handout in context: in the previous millenium, the “three-year rule” stated that if a student had already been to MOP twice, then he or she would only be invited to MOP again if he or she made the IMO team. I thought it would be a long shot to make the IMO team, and so I expected that this would be my first, last, and only lecture at the program.) 1997 United States Math Olympiad Summer Program This was my introduction to the MOP world. You are visitor number since 20 February 2006.