Math

• Calculus Derivatives, integrals and Taylor expansions in one and several variables. 3 lessons open · 11 plannedOpen now: What a derivative measures when you zoom in, Why the chain rule multiplies, What the fundamental theorem of calculus connects
• Linear algebra Matrices as maps: rank, projections, eigenvectors and matrix factorizations. 3 lessons open · 15 plannedOpen now: A matrix moves the plane, Matrix multiplication is composition, What the determinant measures
• Proof, logic and sets Quantifiers, proof techniques, functions, and how to compare the sizes of infinite sets. 1 lesson open · 9 plannedOpen now: Cantor's diagonal argument

Analysis

• Real analysis Limits, convergence, continuity and integration, stated precisely. 1 lesson open · 13 plannedOpen now: The ε–δ definition of a limit
• Complex analysis Complex numbers as rotations, holomorphic maps, contour integrals, residues and the Fourier transform. 7 planned

Algebra and number theory

• Number theory Divisibility, modular arithmetic, primes and the number theory behind RSA encryption. 7 planned
• Abstract algebra Groups as symmetries, cosets and Lagrange's theorem, quotient groups, permutations and finite fields. 6 planned

Geometry and topology

• Geometry Transformations of the plane, curvature of curves and surfaces, geodesics and non-Euclidean geometry. 9 planned
• Topology Open sets and continuity without distances, connectedness, and invariants such as the Euler characteristic. 5 planned

Applied mathematics

• Differential equations ODEs and PDEs, from exponential growth to the heat equation. 18 planned
• Optimization Convexity, Lagrange multipliers, duality and dynamic programming. 16 planned
• Numerical methods Root finding, finite differences, quadrature and Monte Carlo, and how their errors behave. 16 planned

Probability

• Probability Distributions, expectation, conditional expectation and the limit theorems. 3 lessons open · 28 plannedOpen now: Monty Hall and conditional probability, PMF, PDF and CDF, Expectation and variance
• Stochastic processes Random walks, Markov chains, Brownian motion, quadratic variation and martingales. 3 lessons open · 20 plannedOpen now: From random walk to Brownian motion, Martingales, Quadratic variation and (dW)² = dt

Statistics

• Statistical inference Estimators, confidence intervals, hypothesis tests and p-values. 17 planned
• Regression Least squares, regression diagnostics, regularization, logistic regression and generalized linear models. 14 planned
• Time series Autocorrelation, ARMA models, unit roots, GARCH and the Kalman filter. 12 planned
• Bayesian statistics Priors, posteriors, credible intervals and hierarchical models. 8 planned
• Computational statistics The bootstrap, cross-validation, PCA and Markov chain Monte Carlo. 13 planned