Foundations of Machine Learning and AI Geometry, Probability and Optimization

This book builds a single, coherent pathway from linear algebra to probability and statistical learning—the twin pillars behind modern Data Science, AI, and ML. With equal emphasis on geometry (matrices, spectra, projections) and uncertainty (randomness, estimation, generalization) , it equips readers to derive algorithms from first principles and implement them robustly at scale. Throughout, geometric pictures (projections, angles, spectra) and probabilistic arguments (risk, concentration, generalization) are developed side-by-side. Each concept is motivated by a real ML use case—denoising with PCA, ill-conditioning in regression, choosing regularization via validation curves, or accelerating large least-squares with sketching.