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Chapter 02 — Basis, Dimension, and Coordinate Systems
Chapter 03 — Linear Maps and Matrix Representations
Chapter 04 — Norms, Inner Products, and Geometry
Chapter 05 — Orthogonality, Least Squares, and Projections
Chapter 06 — Eigenvalues, Eigenvectors, and Spectral Geometry
Chapter 07 — Singular Value Decomposition & Low-Rank Approximation
Chapter 08 — Quadratic Forms, PSD Matrices & Convex Geometry
Chapter 09 — Gradients, Optimization Geometry & Descent Methods
Chapter 10 — Momentum, Nesterov, Adam & Adaptive Methods
Chapter 11 — Implicit Bias, Flat vs Sharp Minima, and Generalization
Chapter 12 — Robustness, Adversarial Examples, Stability
Chapter 13 — Distribution Shift & Continual Learning
Chapter 14 — Optimization Under Constraints & Alignment
Chapter 15 — Emergent Behavior & Scaling Laws
Chapter 16 — Governance, Responsible ML & System-Level Risks
Chapter 17 — Limits of Optimization & The Future of ML
Chapter 18 — Representation Learning as Optimization Geometry
Chapter 19 — Stochastic Gradient Dynamics, Noise Geometry & Basin Selection
Chapter 20 — Distributional Robustness, Min–Max Optimization & Uncertainty Geometry
Chapter 21 — Distribution Shift, Regret & Continual Learning
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