Mathematics

Extend single-variable calculus into 3D with multivariable functions, vectors, and surface integrals.

Learn to construct rigorous mathematical arguments using direct, contradiction, and induction techniques.

Work with matrices, vectors, and systems of equations used in graphics, AI, and engineering.

Solve equations describing how systems change over time, from circuits to population growth.

Study groups, rings, and fields — abstract structures that reveal deep patterns across mathematics.

Rigorously prove theorems about limits, continuity, and convergence that underpin all of calculus.

Prove the mathematical laws governing randomness, from coin flips to continuous distributions.

Investigate properties of integers — primes, divisibility, and encryption algorithms that secure the internet.

Extend calculus to complex numbers and discover elegant results about functions and integrals.

Explore properties of shapes that remain unchanged when stretched or bent, like connectedness and holes.

Study curves and surfaces using calculus — curvature, geodesics, and manifold theory.

Approximate solutions to math problems using algorithms — interpolation, integration, and root-finding.