Mathematics for AI and Machine Learning

Understand why machine learning works, not just how to call the library.

Mathematics for AI and Machine Learning builds the theory behind modern AI from first principles and carries it all the way to large language models. Each chapter pairs clear definitions, theorems and worked derivations with short, runnable Python code, checked against NumPy, SciPy, scikit-learn and PyTorch, so you can see the mathematics produce the same numbers as the tools you already use.

What's inside

Part I – Foundations: linear algebra for learning systems, calculus and loss-surface geometry, probability, and statistical estimation.
Part II – The Core Machinery of Learning: convex optimization and duality, numerical and stochastic optimization, matrix decompositions, and statistical learning theory.
Part III – Probabilistic Foundations: information theory, Bayesian inference and graphical models, Markov chains and sampling (MCMC).
Part IV – Modern Deep Learning: automatic differentiation, approximation theory, optimization for deep nets, kernel methods and Gaussian processes, dimensionality reduction and manifold learning.
Part V – Modern Architectures and LLMs: attention and transformers, VAEs, GANs and diffusion, reinforcement learning, graph neural networks, LLM pretraining and scaling laws, RLHF and Direct Preference Optimization, and optimization and inference at scale.
Four appendices: a Python/NumPy/PyTorch primer, a notation glossary, extended proofs, and datasets, licenses and exercise hints, plus a bibliography and index.

Who it is for

Software engineers, data scientists, graduate and advanced undergraduate students, and researchers who want a rigorous but readable bridge from a first course in calculus and linear algebra to the mathematics used in today's models. Comfort with basic Python is assumed; no prior measure theory or advanced probability is required.

Features

23 chapters of derivations, theorems and proofs
Executable, verified code for every chapter
Exercises and hints
Reflowable EPUB with MathML equations and a full navigable table of contents

Material portions of this book were generated using generative AI tools, then reviewed, edited, designed, and curated by Choral Software.

Companion source code: Download the worked examples from https://pub-e945d7c8d1d640c7be2864f060e0f048.r2.dev/mathematics-for-ai-and-machine-learning-companion-v1.zip