The Catalog
Hours indicate scheduled teaching time per semester. Each course also assumes roughly two hours of independent problem solving per scheduled hour.
| Course | Level | Hours | Description |
|---|---|---|---|
| Calculus I | beginner | 45 | Limits, continuity, derivatives, and the fundamental theorem of calculus. |
| Calculus II | intermediate | 45 | Techniques of integration, improper integrals, sequences, series, and convergence tests. |
| Calculus III | advanced | 45 | Multivariable functions, partial derivatives, multiple integrals, gradients, and vector fields. |
| Linear Algebra | beginner | 40 | Vector spaces, linear maps, matrices, determinants, and eigenvalue decompositions. |
| Abstract Algebra | advanced | 45 | Groups, rings, and fields, with classification results and Galois theory previewed. |
| Real Analysis | advanced | 50 | Rigorous epsilon-delta proofs, sequences, compactness, continuity, and the derivative as a limit. |
| Complex Analysis | advanced | 45 | Holomorphic functions, Cauchy's theorem, power series, and residue calculus for contour integrals. |
| Differential Equations | intermediate | 40 | First-order ODEs, linear systems, Laplace transforms, and qualitative phase-plane analysis. |
| Probability and Statistics | intermediate | 42 | Random variables, expectation, convergence theorems, estimation, and hypothesis testing. |
| Discrete Mathematics | beginner | 38 | Logic, induction, combinatorics, graph theory, and an introduction to generating functions. |
| Numerical Methods | intermediate | 40 | Root finding, interpolation, numerical integration, and iterative solvers for linear systems. |
| Topology | advanced | 45 | Topological spaces, open and closed sets, connectedness, compactness, and quotient spaces. |
| Number Theory | intermediate | 36 | Divisibility, congruences, quadratic reciprocity, and the prime number theorem. |
Prerequisites. Beginner courses assume high school algebra and geometry. Intermediate courses require Calculus I and Linear Algebra or their equivalents, which we verify with a placement quiz. Advanced courses require the relevant intermediate sequence and a passing score on a proof-writing assessment.
All materials are free. Lecture notes, worked problem sets, solutions, and past papers are published openly and never bundled into fees. Tuition pays for live teaching, marking, and feedback; the right to learn is never gated.
How Courses Run
Live
Taught Seminars
Groups of at most twenty meet weekly for an interactive session where definitions are tested, proofs are constructed on the board, and every student is expected to participate.
Assessed
Problem Sets
Each course sets weekly written work that is marked by hand with line-level comments. Solutions are released a week later, always before the next set is due.