United States of America Mathematical Olympiad
The United States of America Mathematical Olympiad (USAMO) is the third test in a 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 is administered by the American Mathematics Competitions (AMC). Art of Problem Solving (AoPS) is a proud sponsor of the AMC and of the recent expansion of USAMO participants from around 250 to around 400.
Contents
USAMO Curriculum
The USAMO is best approached by students with a solid command of topics in algebra, geometry, number theory, combinatorics, probability, and a host of rigorous methods such as induction and proof by contradiction. Students who do well on the USAMO have considerable experience both solving highly challenging problems and writing proofs.
Format
The USAMO is an invitation-only proof-type examination administered to approximately 500 of the best and brightest students from the U.S. and Canada. Qualification is based on AMC 10, AMC 12, and AIME scores. No calculators are allowed on this two day, 9 hour exam (two 4.5 hour sessions). All six questions can be solved using precalculus methods, but an extensive understanding of the material and creative thinking is essential to performing well.
Scoring
Each response is assessed for correctness, completeness, and clarity and is subsequently awarded between 0 and 7 points, with a total maximum score of 42 points. Since most students receive very limited exposure to proofs in high school, scores in the single digits are common. The jump in difficulty and rigor from AIME to USAMO is quite large, and many first-time USAMO participants receive lower scores than they expect.
The top 12 students are invited to an awards ceremony in Washington, D.C., and six of them are later selected to form the United States IMO team. These students and a number of other top scorers from the USAMO 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.
Resources
Links
- USAMO Problems and Solutions
- AMC homepage and their USAMO page
- The AoPS USAMO guide.
- AoPS hosts a Pre-Olympiad Forum for students learning how to solve Olympiad problems as well as a host of Olympiad level forums.
- The AoPS Contest Archive includes problems and solutions from past USAMO exams.
- USAMO problems at kalva.
- Mock USAMOs (practice exams)
Recommended reading
- Problem and solution book for USAMOs 1972-1986.
- The Art of Problem Solving Volume II by Sandor Lehoczky and Richard Rusczyk. Information.
- USA and International Math Olympiads 2005.
USAMO Preparation Classes
- AoPS hosts an online school which including the Worldwide Online Olympiad Training (WOOT) program designed to help students competing in the USAMO, national Mathematics Olympiads, and the IMO.
- AoPS holds many free Math Jams, some of which are devoted to discussing problems on the USAMO. Math Jam Schedule
