A1Linear algebra

Linear algebra is the language of data once you stack it into vectors and matrices. Almost everything downstream, from a least-squares fit to a transformer's attention block, is some arrangement of linear maps acting on high-dimensional points, so this discipline is where you learn to see those operations clearly instead of as opaque tensor shapes.

You will build from vector spaces, bases, and the four fundamental subspaces up through eigenvalues, the spectral theorem, and the singular value decomposition, then put them to work: low-rank approximation and PCA, the LU/QR/Cholesky factorizations that solve linear systems without inverting anything, least squares and the pseudo-inverse, and the matrix calculus and einsum notation that make backpropagation just the chain rule on arrays. By the end you can decompose a matrix, reason about why a system is solvable, and differentiate vector-valued expressions by hand.

This is the most reused pillar in the tree. PCA, recommender factorizations, the geometry of embeddings, and the entire training loop of deep networks all rest on what you build here, so fluency now pays off in every later subject.