Section 1

Mathematical Foundations

Section 1 builds the arithmetic of arrays on GPT-2 small, Llama 3.1 8B and scikit-learn's real datasets: the floating-point numbers a model stores, the shapes and similarity measures of its vectors and matrices, what a matrix product costs on a GPU, and what eigenvalues predict about repeated multiplication. Each chapter ends with a decision priced in bytes, FLOPs or recall, from the number format for Llama 3.1 8B on a 24 GB GPU to the solver for a PCA fit.