See current course offerings here.
GeodeMath courses are regularly offered at three levels (3, 4, 5). Courses at other levels or on specific topics may be offered according to demand (including more advanced content such as calculus or college content).
At each level, there are four courses named N, S, E, W, which may be taken in any order. Each course begins with a class related to proofs, then covers 25% algebra, 25% combinatorics, 25% geometry, 25% number theory. Taking all four classes at one level exposes the student to all GeodeMath curriculum in algebra, combinatorics, geometry, and number theory.
Level 3
Level 3 courses are designed for students who love math and are looking for a deeper understanding of high school level mathematics.
Level 4
Level 4 courses represent the pinnacle of a general education in non-calculus-based math for future leaders in mathematics and adjacent fields.
Level 5
Level 5 courses are very difficult. Students will be well-prepared to take math olympiads, pursue research projects, or study math at the most challenging universities.
Level 3 Prerequisites:
- fluency in arithmetic and algebra
- some problem solving experience
- basic familiarity with logic, proofs
Level 4 Prerequisites:
- high school geometry & algebra 2
- strong problem solving experience
(such as AIME problems 1-6) - knowledge of proof techniques (such as induction, contradiction)
Level 5 Prerequisites:
- precalculus
- strong problem solving experience
(such as AIME problems 6-12) - ability to write good proofs
Level 3 Goals:
- move beyond learning about math to actively doing math
- explain reasoning in paragraph form as proofs
- solve never-before-seen problems after initial failed attempts or extended exploration
- understand and apply the major ideas in classical algebra, combinatorics, geometry, number theory beyond high school level
For students who participate in AMC and AIME competitions, Level 3 is appropriate for those who are seeking to qualify for AIME. However, GeodeMath courses are not “competition prep” and may include additional content including proof and exploration.
Level 4 Goals:
- train problem solving and original, critical thinking
- produce clear, well-written proofs
- solve never-before-seen problems after initial failed attempts or hours of exploration
- understand and apply the major ideas in classical algebra, combinatorics, geometry, and number theory at the level of a college math major
For students who participate in AMC and AIME competitions, Level 4 is appropriate for those who are seeking to improve AIME performance. However, GeodeMath courses are not “competition prep” and may include additional content including proof and exploration.
Level 5 Goals:
- solve very challenging and original problems that most mathematicians find difficult
- write proofs fluently
- solve never-before seen problems, even after days of exploration
- understand and apply the major ideas in classical algebra, combinatorics, geometry, and number theory at the level of a mathematician
For students who participate in AMC and AIME competitions, Level 5 is appropriate for those who are seeking to qualify for USA(J)MO. However, GeodeMath courses are not “competition prep” and may include additional content.
The following is a rough idea of what content is covered each semester. Content varies from Level 3 to Level 5, and topics not listed may be covered as well.
W courses (Fall 2025)
- theory of sets and functions
- algebraic equations and inequalities
- theoretical foundations of number theory
- invariants and coloring
- angles, lengths, geometric formulas
N courses (Spring 2026)
- induction and recursion
- sequences and series in algebra and combinatorics
- numbers and ways of representing them
- factoring and divisibility
- triangle geometry
S courses
- non-constructive proof
- polynomials
- Diophantine equations
- graph theory
- circle geometry
E courses
- mathematical writing
- complex numbers and trigonometry
- modular arithmetic
- counting and probability
- analytic geometry
Less regular course offerings
Level 1 courses are prealgebra level enrichment based on curiosity and exploration.
Level 2 courses are enrichment at the level of algebra 1 and geometry, including first exposure to proofs and advanced problem solving.
Level 6 courses are for those who have completed Level 5.
Courses on specific topics – examples have included
- introduction to proof
- complex numbers and trigonometry
- AIME problem solving
Advanced math – topics may include
- calculus enrichment
- real or complex analysis
- axiomatic set theory
- group or ring theory
- algebraic or analytic number theory
- non-Euclidean geometry
- differential geometry and differential forms
- algebraic geometry
- algebraic topology
- etc.
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