Not proofs — pictures that stick. Matrices are motion, derivatives are slopes, probability is a shrinking world, training is walking downhill. Every idea here gets used within two phases: eigenvectors become PCA, the chain rule becomes backprop, Bayes becomes a classifier. Covers.
One notebook, four artifacts, all by hand then verified with NumPy: (1) eigen-decompose a covariance matrix and PCA a real 2-feature dataset; (2) implement gradient descent on a paraboloid and plot the path for three learning rates; (3) run the Bayes base-rate computation for a 1-in-1000 disease with a 99% test; (4) simulate the law of large numbers for a biased coin. Each one becomes an algorithm you'll use in Phase 3 — this is the proof you own the math, not just recognized it.
Full guide: phase-2-math.md ↗ · then start BYO-2 (regression + GD).