Mathematics for Artificial Intelligence

Title: Mathematics for Artificial Intelligence
Author: JANE HAWKINS
ISBN: 1041161972 / 9781041161974
Format: Soft Cover
Pages: 238
Publisher: CHAPMAN & HALL
Year: 2026
Availability: In Stock

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Artificial intelligence (AI) and machine learning (ML) are rapidly growing fields, drawing great interest among students. Many students in a range of fields, including mathematics, computer science, statistics, data science, and more, see AI and ML as the keys to their futures.

Mathematics for Artificial Intelligence provides the basic mathematics needed to understand AI and ML. It serves both students of mathematics and those who want to fill any gaps in their mathematics experience. It is written as both a text for a course and as a focused look at mathematics needed for readers hoping to learn more.

The author has taught every topic in this book, often in different contexts, and the material and exercises are drawn from lecture notes. The material in the book represents a curated set of topics from the undergraduate math curriculum, some first-year seminar material, and some student project topics. Through carefully chosen examples and discussion in the text, the reader will learn how and where these tools are applied. AI and ML connections are raised along the way.

It presumes the reader has at least completed the traditional three-semester calculus course. Linear algebra is presented as needed and should not require a completed course. The book is also well-suited for self-paced learning. Each chapter can be read independently with the help of the index for cross-referencing. Exercises are included.

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Preface
Author
Introduction

1. Calculus of one variable

1.1 The exponential function and Euler’s identity
1.2 Gaussian functions and integrals
1.3 Fourier series and transforms
1.4 Sigmoid functions and their properties
1.5 The gamma function and Stirling’s formula
1.6 Exercises and solutions

2. Calculus of several variables

2.1 Differentiable maps f : ℝⁿ → ℝᵐ
2.2 The Hessian matrix and Newton’s method
2.3 Higher dimensional sigmoid functions and classifications
2.4 Backpropagation: chain rule and automatic differentiation
2.5 Exercises and solutions

3. Matrix Algebra

3.1 Systems of linear equations
3.2 Vector spaces
3.3 Bases and dimension
3.4 Inner products and norms
3.5 The determinant of a square matrix
3.6 Eigenvalues, eigenvectors, and eigenspaces
3.7 Special types of matrices and useful factorizations
3.8 Quaternions and rotation matrices
3.9 Convolutions of matrices
3.10 Exercises and solutions

4. Probability

4.1 Some basic probability
4.2 Random variables and distributions
4.3 The Borel-Cantelli lemma
4.4 Weak and strong laws of large numbers
4.5 Exercises and solutions

5. Graphs, shifts, and stochastic matrices

5.1 Graphs
5.2 Entropy and decision trees
5.3 Coding information with symbols
5.4 Markov shifts and subshifts of finite type
5.5 The Perron-Frobenius Theorem and applications
5.6 Exercises and solutions

6. Neural networks

6.1 Mathematical structure of a neural network
6.2 Backpropagation: training a neural network
6.3 Convolution layers
6.4 Exercises and solutions

Index