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International Mathematical Olympiad Info Page


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Each year since 1974, a small team of exceptionally talented high school students has represented the United States at the International Mathematical Olympiad (IMO), a rigorous two day competition including problems that would challenge most professional mathematicians. In addition to comprehensive mathematical knowledge, success on the IMO requires truly exceptional mathematical creativity and inventiveness. As an example, here is a problem from the 1998 IMO:

Let I be the incenter of triangle ABC. Let the incircle of ABC touch
the sides BC, CA, and AB at K, L and M, respectively. The line through
B parallel to MK meets the lines LM and LK at R and S, respectively.
Prove that angle RIS is acute.

The team selection process commences with a sequence of three examinations designed and administered by the Committee on the American Mathematics Competitions (CAMC), sponsored by the Mathematical Association of America (MAA) and eight other national organizations of mathematicians and educators. The first step is the American Mathematics Contest, which is taken by approximately 350,000 students each year. Those scoring very high, about 17,000 students, proceed to take the American Invitational Mathematics Examination. From this latter group, about 160 take the USA Mathematical Olympiad (USAMO). Like the IMO, the USAMO is an essay proof examination requiring deep insight and ingenuity as well as broad technical expertise.

The Army Research Office has traditionally provided funds for travel to the IMO of the team and Leaders.

The eight top scoring USAMO contestants are invited to a two day Olympiad Awards Ceremony sponsored by the MAA, the Microsoft Corporation and the Matilda Wilson Foundation. This festive ceremony is held in Washington, DC, and includes scientific lectures at the National Academy of Sciences and the National Science Foundation, the presentation of Olympiad Medals, and a formal dinner in the Diplomatic Reception Rooms of the Department of State. The activities associated with the Awards Ceremony provide an opportunity for our top high school mathematics scholars to meet some of the nation's best scientists and mathematicians.

Following the Awards Ceremony, the 8 USAMO winners and 16 other finalists participate in an intensive month long Mathematical Olympiad Summer Program (MOSP). The top six students on the USAMO form the team that represents the United States in the IMO. All participants receive in-depth enrichment and they are given specialized coaching in important mathematical topics to stimulate their continuing interest in mathematics and help prepare them for future study of mathematics.

Following the 4 week Mathematical Olympiad Summer Program (MOSP), the U.S. Team and the adult leaders travel to the site of the International Mathematical Olympiad (IMO). There, the most talented high school students from over 70 nations compete in an extremely challenging two day examination. The examination is constructed by the leaders of the participating teams from a pool of problems submitted earlier by the invited nations. Both the construction of the examination and the subsequent grading of the papers are conducted in elaborate and highly democratic proceedings designed to preserve security and objectivity.

During the period of the IMO, the students are entertained by the host nation. In addition to visiting local points of interest in the host city, there is ample opportunity for informal interaction among the team members and leaders and their counterparts from the other participating countries. The officers of the Mathematical Association of America (MAA) and the Committee on the American Mathematics Competitions (CAMC) endorse the following objectives of participation by the United States in the IMO:

  1. To provide opportunities for meetings and contacts among present and future mathematicians and scientists of different countries.
  2. To enrich the education and training for research in the mathematical sciences of 30 of our nation's most talented students by means of an intensive four week seminar in mathematics and problem solving beyond the standard syllabus.
  3. To stimulate and encourage mathematical excellence among the students and teachers of America's high schools through the example set by these talented students and the favorable publicity the United States Team receives as a consequence of its participation in the IMO.
  4. To use this friendly competition as a forum for the exchange of mathematical and educational ideas that might prove helpful in setting priorities for secondary school mathematics in the United States.
  5. To foster unity of interest among all nations. Mathematics, because of its universal nature, is ideally suited for this role.

Titu Andreescu, Director
American Mathematics Competitions
University of Nebraska-Lincoln
Lincoln, NE 68588-0658 U.S.A.
Tel: 402-472-6566, Fax: 402-472-6087