Interactive Stochastic Differential Equations

Random walks and Brownian motion, stochastic processes and the Markov property, Itô calculus and SDEs, and finally the Fokker–Planck equation and the probability flow ODE that underpins diffusion models.

Interactive Differential Equations

ODEs and their numerical solvers — direction fields, initial value problems, phase portraits, Euler and Runge–Kutta, and numerical stability — then PDEs: the transport, continuity and diffusion equations.

Interactive Calculus

Functions, limits, derivatives and the chain rule, Taylor expansion and integrals, then partial derivatives, the gradient, Jacobian, Hessian, vector fields, divergence and the Laplacian.

Interactive Information Theory

Self-information, entropy and coding length, cross-entropy and KL divergence, mutual information, and the losses built on them — cross-entropy, perplexity, the ELBO, and InfoNCE.

Interactive Probability

Random variables, joint and conditional distributions, expectation, the distributions machine learning actually uses, and the road from likelihood to NLL, Bayes' rule, and MAP.

Interactive Linear Algebra

Vectors, inner products, eigenvalues, the four fundamental subspaces, change of basis, and PyTorch einsum/permute/view/reshape.