The Math That Powers AI: Foundations of Linear Algebra, Probability, and Calculus

Every AI breakthrough starts with the same foundation: mathematics. When GPT predicts the next word, it's doing linear algebra. When a recommendation system learns your preferences, it's computing matrix factorizations. When a neural network trains, it's following gradients through high-dimensional space. This book teaches you the math that makes it all work. What You'll Learn:Linear Algebra — Vectors, matrices, and transformations. Understand why "king − man + woman = queen" works mathematically, and how attention mechanisms compute similarity through dot products. Probability & Statistics — From Bayes' theorem to maximum likelihood estimation. Learn the probabilistic thinking that underlies every machine learning model.Calculus — Gradients, chain rule, and optimization. See derivatives not as abstract formulas but as the engine driving neural network training. Information Theory — Entropy, cross-entropy, and KL divergence. Discover why cross-entropy is the right loss function and what "bits" really mean for model performance. - Numerical Methods — Floating-point arithmetic, numerical stability, and debugging NaN errors. Write code that survives contact with real hardware. Who This Book Is For: Software engineers transitioning to ML, data scientists wanting deeper foundations, and students preparing for AI research. You should be comfortable with basic programming; calculus and linear algebra exposurehelps but isn't required. What Makes This Book Different: Every concept connects to real ML applications. No theorem without intuition. No formula without code. By the final capstone project, you'll implement PCA from scratch, understanding every line. Eight chapters. One capstone. The mathematical foundation for everything that comes next. Read more