Mathematics for Artificial Intelligence

The Mathematical Foundations of AI and Machine Learning 🧮

Artificial intelligence and machine learning are often introduced through code, frameworks, and models. But underneath those layers sits a core set of mathematical ideas that make learning, optimization, and prediction possible. Mathematics for Artificial Intelligence by Jane Hawkins brings those ideas together in one focused textbook, designed for students and self-learners who want to understand the mathematical machinery behind modern AI.

Published by CRC Press in the Textbooks in Mathematics series, the book draws on the author’s lecture notes and classroom experience. It assumes a background through the traditional three-semester calculus sequence, while introducing linear algebra as needed. That balance makes it suitable for mathematics students as well as readers from computer science, statistics, and data science who want to strengthen their mathematical foundations.

What the Book Covers 📘

The material is organized into six main chapters, each exploring a different mathematical area and connecting it to AI and ML applications:

• Calculus of one variable: exponential functions, Euler’s identity, Gaussian integrals, Fourier series and transforms, sigmoid functions, the gamma function, and Stirling’s formula.
• Calculus of several variables: differentiable maps, partial and directional derivatives, Jacobian and Hessian matrices, gradient descent, Newton’s method, higher-dimensional sigmoid functions, backpropagation, chain rule, and automatic differentiation.
• Matrix algebra: systems of linear equations, vector spaces, bases and dimension, inner products and norms, cosine similarity, determinants, eigenvalues and eigenvectors, matrix factorizations (LU, Cholesky, SVD), quaternions, rotation matrices, least squares, and convolutions.
• Probability: probability spaces, random variables and distributions, independent random variables, Borel–Cantelli lemma, and the weak and strong laws of large numbers.
• Graphs, shifts, and stochastic matrices: entropy, decision trees, symbolic dynamics, Markov shifts and subshifts of finite type, Perron–Frobenius theorem, and PageRank methods.
• Neural networks: mathematical structure of neural networks, width and depth, weights and biases, backpropagation for training, and convolution layers.

How the Material Is Organized 🧭

Each chapter can be read independently, and an index helps readers cross-reference topics. Exercises and solutions are included throughout, making the book useful for coursework, independent study, or review. The author raises AI and ML connections along the way, so abstract concepts are consistently tied back to practical applications.

Who Will Find This Useful

This book is intended for readers who have completed a standard three-semester calculus sequence. Linear algebra is presented as needed, so a previous linear algebra course is not required. It will appeal to undergraduate and graduate students in mathematics, computer science, statistics, and data science, as well as professionals and self-learners who want a rigorous but accessible mathematical grounding for AI and machine learning.

Why the Mathematics Matters

AI systems are built on ideas like gradients, matrix decompositions, probability distributions, and optimization. Understanding those ideas helps practitioners reason about why models behave as they do, how they learn from data, and where their limitations lie. Mathematics for Artificial Intelligence offers a structured path through that foundational material, with an emphasis on clarity, examples, and the connections that make the mathematics relevant to modern AI.