United States of America Mathematical Olympiad

The United States of America Mathematical Olympiad (USAMO), along with the USAJMO, are the third exams in the series of exams used to challenge bright students on the path toward choosing the team that represents the United States at the International Mathematics Olympiad (IMO).

The top 12 students of the USAMO are invited to an awards ceremony in Washington, D.C. About 60 top scorers of the USAMO and USAJMO are invited to participate in the Math Olympiad Summer Program (MOP), a challenging 3 to 4 week math program for the brightest students in the country.

The USAMO is administered by the Mathematical Association of America (MAA). Art of Problem Solving (AoPS) is a proud sponsor of the MAA.

USAMO
Region: USA
Type: Proof
Difficulty: 7-9
Difficulty Breakdown:

Problem 1/4: 7
Problem 2/5: 8
Problem 3/6: 9

Format

The USAMO is a proof-based examination taken by approximately 250 of the highest scoring students in the AMC 12 and AIME exams. The competition takes place over 2 consecutive days. Each day, 3 problems are given to the students to work for 4.5 hours. Responses are assessed based on correctness, completeness, and clarity and are subsequently awarded between 0 and 7 points, making the maximum score 42. Since most students receive limited exposure to proofs in high school, scores in the single digits are common. The jump in difficulty and rigor from AIME to the USAMO is quite large, and many first-time USAMO participants receive lower scores than they expect.

Curriculum

The USAMO is best approached by students with a solid command of topics in algebra, geometry, number theory, and combinatorics and a host of rigorous methods such as induction and proof by contradiction. Students who do well on the USAMO have considerable experience in both solving highly challenging problems and writing proofs. Following the general format of high school competitions, the USAMO does not require calculus or related topics, though proofs using higher mathematics are accepted.

History

In the 1960s, Nura D. Turner was working to institute a USAMO and to have an American team for the IMO, but had little support. After she published the article "Why can't we have a USA Mathematical Olympiad?" in the American Mathematical Monthly 78 (1971), the MAA's National Contest Committee revived an Olympiad Subcommittee, which voted to start a USAMO at its first meeting in 1971. The MAA later endorsed this proposal, and the first USAMO was administered on May 9, 1972. The United States sent its first team to the IMO in 1974, where it received second place.

The first USAMO had five questions, which contestants had three hours to solve. Total scores were out of 100 points. Later, the time limit was extended to three and a half hours. In 1996, the format changed: there were now six questions, administered in two three-question, three-hour sessions with a one-hour break in between. The scoring was also changed, so that each question was worth seven points, for a maximum total score of 42. In 2002, the time for each of the problem sets was extended to four and a half hours, and the two parts of the olympiad were administered on separate days (the present format). In 2002, all participants were also invited to the MIT campus in Cambridge, Massachusetts, to take the olympiad, but this event has not been repeated.

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See also