Machine Learning
The complete theoretical and computational machinery of modern ML. Every algorithm is fitted to concrete student datasets, with complete derivations from gradient calculus to backpropagation and MDP reinforcement loops.
Linear equation systems, convex vs non-convex loss functions, gradient descent variants, entropy, information gain, and the bias-variance trade-off.
Six supervised algorithms fitted step-by-step to the same eight students: multiple regression, ridge, lasso, logistic regression, k-NN, hard/soft margin SVMs, and decision trees.
Confusion matrices, precision-recall trade-offs, ROC-AUC geometry, cost-based thresholds, regression metrics, and the mathematical impossibility theorem of fairness.
K-Means, Agglomerative Hierarchical, DBSCAN density reachability, Gaussian Mixture Models with EM, elbow and silhouette analysis, and full PCA variance derivation.
The biological and artificial neuron, the XOR proof of single-layer limitations, forward propagation matrix equations, and the complete chain-rule backpropagation algorithm.
Vanishing and exploding gradients, modern activation functions (ReLU, Leaky ReLU, GELU), weight initialisation heuristics (He, Xavier), optimizers (Momentum, RMSProp, Adam), and regularizers.
Markov Decision Processes (MDPs), the Bellman expectation and optimality equations, policy iteration, value iteration, Q-Learning update rule, and Deep Q-Networks (DQN).