20 courses, 932 lessons
Each one a map of topics: start anywhere, see what a topic builds on, and review what you've learned before it fades.
Mathematics
Geometry Proof, transformations, similarity, trigonometry and circles, with figures you drag
AP Calculus Limits, derivatives, integrals, differential equations and series
Linear Algebra Vectors, matrices as maps of the plane, eigenvectors, least squares and the SVD
Multivariable Calculus Surfaces in 3D, partial derivatives, multiple integrals and the big theorems After AP Calculus, Linear Algebra
Differential Equations First and second order, the Laplace transform, phase portraits and nonlinear systems After AP Calculus, Linear Algebra
Probability and Statistics Random variables, distributions, limit theorems, inference and regression After AP Calculus, Discrete Mathematics
Discrete Mathematics Logic and proof, counting, number theory, recurrences and graphs
Further mathematics
Real Analysis The real numbers, sequences, continuity and the Riemann integral, proved After AP Calculus
Complex Analysis Analytic functions, conformal maps, contour integrals and residues After Multivariable Calculus, Linear Algebra
Abstract Algebra Groups, subgroups, permutations, quotients, rings and fields After Discrete Mathematics, Linear Algebra
Numerical Methods Floating point, root finding, interpolation, quadrature and ODE solvers After AP Calculus, Linear Algebra
PDEs and Fourier Analysis Fourier series and transforms, and the heat, wave and Laplace equations After Differential Equations, Multivariable Calculus
Physics
AP Physics 1 Motion, forces, energy, momentum, rotation, oscillations and fluids After Geometry
AP Physics 2 Thermodynamics, electricity, circuits, magnetism, optics and modern physics After AP Physics 1
AP Physics C: Mechanics Mechanics with calculus: dynamics, energy, momentum and rotation After AP Calculus, AP Physics 1
AP Physics C: Electricity and Magnetism Fields, Gauss's law, potential, circuits and induction, with calculus After AP Physics C: Mechanics, AP Calculus
Vibrations and Waves Oscillators, normal modes, the wave equation, interference and diffraction After AP Physics C: Mechanics, AP Physics C: Electricity and Magnetism, Multivariable Calculus, Linear Algebra
Relativity Spacetime diagrams, paradoxes, four-vectors and an introduction to gravity After AP Physics C: Mechanics, AP Physics C: Electricity and Magnetism, Multivariable Calculus, Linear Algebra, Vibrations and Waves
Quantum Physics The Schrödinger equation, wave packets, oscillators, scattering and hydrogen After AP Physics C: Mechanics, AP Physics C: Electricity and Magnetism, Multivariable Calculus, Linear Algebra, Vibrations and Waves, Relativity
Statistical Physics Entropy, ensembles, heat engines and quantum statistics After AP Physics C: Mechanics, AP Physics C: Electricity and Magnetism, Multivariable Calculus, Linear Algebra, Discrete Mathematics, Vibrations and Waves, Quantum Physics
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