All the math you need to truly understand modern machine learning and AI — told simply, built to be touched. Every idea opens as a story, every concept is something you can drag, spin, and break, and every unit ends with its full problem set solved step by step. Curiosity is the only prerequisite.
A matrix is a machine that moves space. Three windows on Ax = b, the three fates, and elimination — the algorithm that never lies.
The universe where vectors live: groups, subspaces, span, independence, basis, dimension — the architecture of ML math.
The board gets its ruler: norms, inner products, angles, orthogonality — and Gram–Schmidt, the cleanest grid a geometry can have.
A matrix's fingerprints: the volume dial, the directions it cannot turn, A = QΛQᵀ — and Cholesky, the covariance square root.
Prime factorization for transformations: the ladder from spectral to eigen to SVD — ending with a real photograph compressed live.
Which way is down? From a shrinking secant to the Jacobian matrices behind backpropagation — the language every learning machine speaks.
The chain rule, industrialized: watch blame flow backwards through a graph, train a neuron with your own hands, and see why a million derivatives cost one sweep.
Polynomial impostors: where Taylor's formula comes from, exactly how big the lie (the remainder) is — and the Hessian, the judge that tells a bowl from a dome from a saddle.
Walk downhill in thick fog: steps, step sizes, and why a little noise helps you scale.
Nonlinear optimization and the minutiae that make or break gradient methods.
Momentum, AdaGrad, RMSProp, Adam — and the cliffs and valleys that defeat naive descent.
Compress a thousand dimensions without losing the story: variance, projections, eigenvectors.
Principal components at work — linear algebra earning its keep on real data.
Lagrange multipliers, KKT conditions, duality, and the kernel trick — the math that draws the widest possible line.
From primal to dual to solution — and soft margins for a messy world.
Where every thread ties together — the last stop on the route from lines to learning machines.