Difference between revisions of "United States of America Mathematical Olympiad"
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| − | The '''United States of America | + | 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 USAMO | + | 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. | ||
| − | == | + | {{Contest Info|name=USAMO|region=USA|type=Proof|difficulty=7-9|breakdown=<u>Problem 1/4</u>: 7<br><u>Problem 2/5</u>: 8<br><u>Problem 3/6</u>: 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 | + | 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. | ||
== Resources == | == Resources == | ||
=== Links === | === Links === | ||
| − | * [ | + | * The MAA's [https://maa.org/student-programs/amc/ official webpage] for the AMC and its [https://maa.org/maa-invitational-competitions/ Invitational Competitions] page |
| − | * The [[ | + | * The AoPS Wiki's [[USAMO Problems and Solutions]] page |
| − | + | * The AoPS Contest's [https://artofproblemsolving.com/community/c3409_usamo USAMO], [https://artofproblemsolving.com/community/c58_national_olympiads National Olympiads], and [https://artofproblemsolving.com/community/c59_team_selection_tests Team Selection Tests] folders | |
| − | * The [ | + | * The [[USAMO historical results]] page |
| − | * [ | + | * The AoPS [https://artofproblemsolving.com/community/c5_contests_amp_programs Contests & Programs Forum] for contest related discussions |
| + | * AoPS [[Mock USAMO | User created mock USAMOs]], an abundance of mocks designed to mimic real USAMO tests, compiled [https://artofproblemsolving.com/community/c2439873_usamo_mocks here] in AoPS Contests | ||
| + | * Evan Chen's [https://blog.evanchen.cc/2019/01/31/math-contest-platitudes-v3/ Math Contest Platitudes] blog, a guide to contest preparation, and [https://web.evanchen.cc website] | ||
| − | === | + | === Books & Classes === |
| − | * [http://www.artofproblemsolving.com/ | + | * [http://www.artofproblemsolving.com/Store/viewitem.php?item=ps:aops2 The Art of Problem Solving Volume 2] by [[Richard Rusczyk]] and [[Sandor Lehoczky]] |
| − | + | * [https://web.evanchen.cc/geombook.html Euclidean Geometry in Mathematical Olympiads] and [https://web.evanchen.cc/excerpts.html The OTIS Excerpts] by Evan Chen | |
| + | * ''USA Mathematical Olympiads 1972-1986'' by Murray Klamkin (Editor) (ISBN 978-0883856345) | ||
| + | * ''Countdown: The Race for Beautiful Solutions at the International Mathematical Olympiad'' by Steve Olson (ISBN 0-618-56212-5) | ||
| + | * The AoPS [http://www.artofproblemsolving.com/Classes/AoPS_C_About.php Online School], including the [[Worldwide Online Olympiad Training]] (WOOT) program designed to help students train for the USAMO, other national [[Mathematics Olympiads]], and the IMO. | ||
| + | * The AoPS [https://artofproblemsolving.com/school/mathjams Math Jams], some of which are devoted to discussing problems of the USAMO | ||
| + | == See also == | ||
| + | * [[American Mathematics Competitions]] | ||
| + | * [[USAMO Problems and Solutions]] | ||
| + | * [[USAMO historical results]] | ||
| + | * [[Resources for mathematics competitions]] | ||
| + | * [[How should I prepare?]] | ||
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| − | + | [[Category:Mathematics competitions]] | |
| − | + | [[Category:Hard Olympiad mathematics competitions]] | |
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Latest revision as of 03:57, 3 February 2025
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 |
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.
Resources
Links
- The MAA's official webpage for the AMC and its Invitational Competitions page
- The AoPS Wiki's USAMO Problems and Solutions page
- The AoPS Contest's USAMO, National Olympiads, and Team Selection Tests folders
- The USAMO historical results page
- The AoPS Contests & Programs Forum for contest related discussions
- AoPS User created mock USAMOs, an abundance of mocks designed to mimic real USAMO tests, compiled here in AoPS Contests
- Evan Chen's Math Contest Platitudes blog, a guide to contest preparation, and website
Books & Classes
- The Art of Problem Solving Volume 2 by Richard Rusczyk and Sandor Lehoczky
- Euclidean Geometry in Mathematical Olympiads and The OTIS Excerpts by Evan Chen
- USA Mathematical Olympiads 1972-1986 by Murray Klamkin (Editor) (ISBN 978-0883856345)
- Countdown: The Race for Beautiful Solutions at the International Mathematical Olympiad by Steve Olson (ISBN 0-618-56212-5)
- The AoPS Online School, including the Worldwide Online Olympiad Training (WOOT) program designed to help students train for the USAMO, other national Mathematics Olympiads, and the IMO.
- The AoPS Math Jams, some of which are devoted to discussing problems of the USAMO
