USAMO Syllabus
The USAMO does not have a formal syllabus like a school exam. It tests deep understanding of topics from the high school curriculum and beyond, focusing on proof-writing and problem-solving.
Success on the USAMO depends on ingenuity and the ability to construct rigorous proofs, not on memorizing a wide range of formulas. The problems are designed to be solvable with clever application of core mathematical principles. The exam covers four main areas of classical mathematics, with problems often blending concepts from multiple subjects. Mastery of these areas and their common proof techniques is the true 'syllabus' for the competition.
Core Subject Areas
- Algebra Includes polynomials, functional equations, inequalities, sequences, and series.
- Combinatorics Covers counting arguments, graph theory, the pigeonhole principle, and combinatorial games.
- Geometry Focuses on Euclidean geometry, transformations, trigonometry, and geometric inequalities.
- Number Theory Tests divisibility, modular arithmetic, Diophantine equations, and properties of integers.