Mathematics for Deep Learning

This appendix gathers the mathematical results the main text relies on, developed far enough to be useful and no further. It is organized as six chapters, each intuition-first and paired with runnable examples. Linear algebra covers vectors, matrices, norms, and the decompositions behind every layer. Calculus develops derivatives, the chain rule, and the multivariable and matrix calculus that backpropagation automates. Optimization treats convexity, gradient methods, and the convergence and conditioning results the training loop depends on.

The remaining chapters supply the probabilistic and dynamical foundations: probability and statistical learning (distributions, estimation, and generalization), information theory (entropy, cross-entropy, and the KL divergence that most losses descend from), and dynamics (differential equations and the continuous-time view that connects to modern normalizing-flow and diffusion models). Read it start to finish, or dip in when a main-text chapter cites a result.