Mathematics of Machine Learning

Build a solid foundation in the core math behind machine learning algorithms with this comprehensive guide to linear algebra, calculus, and probability, explained through practical Python examples

Purchase of the print or Kindle book includes a free PDF eBook

Key Features

• Master linear algebra, calculus, and probability theory for ML
• Bridge the gap between theory and real-world applications
• Learn Python implementations of core mathematical concepts

Book Description

Mathematics of Machine Learning provides a rigorous yet accessible introduction to the mathematical underpinnings of machine learning, designed for engineers, developers, and data scientists ready to elevate their technical expertise. With this book, you’ll explore the core disciplines of linear algebra, calculus, and probability theory essential for mastering advanced machine learning concepts.

PhD mathematician turned ML engineer Tivadar Danka—known for his intuitive teaching style that has attracted 100k+ followers—guides you through complex concepts with clarity, providing the structured guidance you need to deepen your theoretical knowledge and enhance your ability to solve complex machine learning problems. Balancing theory with application, this book offers clear explanations of mathematical constructs and their direct relevance to machine learning tasks. Through practical Python examples, you’ll learn to implement and use these ideas in real-world scenarios, such as training machine learning models with gradient descent or working with vectors, matrices, and tensors.

By the end of this book, you’ll have gained the confidence to engage with advanced machine learning literature and tailor algorithms to meet specific project requirements.

What you will learn

• Understand core concepts of linear algebra, including matrices, eigenvalues, and decompositions
• Grasp fundamental principles of calculus, including differentiation and integration
• Explore advanced topics in multivariable calculus for optimization in high dimensions
• Master essential probability concepts like distributions, Bayes' theorem, and entropy
• Bring mathematical ideas to life through Python-based implementations

Who this book is for

This book is for aspiring machine learning engineers, data scientists, software developers, and researchers who want to gain a deeper understanding of the mathematics that drives machine learning. A foundational understanding of algebra and Python, and basic familiarity with machine learning tools are recommended.

Table of Contents

1. Vectors and vector spaces
2. The geometric structure of vector spaces
3. Linear algebra in practice spaces: measuring distances
4. Linear transformations
5. Matrices and equations
6. Eigenvalues and eigenvectors
7. Matrix factorizations
8. Matrices and graphs
9. Functions
10. Numbers, sequences, and series
11. Topology, limits, and continuity
12. Differentiation
13. Optimization
14. Integration
15. Multivariable functions
16. Derivatives and gradients
17. Optimization in multiple variables
18. What is probability?
19. Random variables and distributions
20. The expected value
21. The maximum likelihood estimation
22. It's just logic
23. The structure of mathematics
24. Basics of set theory
25. Complex numbers

Tivadar Danka is a mathematician by training, a machine learning engineer by profession, and an educator by passion. After finishing his PhD in 2016 (about the arcane subject of orthogonal polynomials), he switched career paths and has been working in machine learning ever since. His work includes applying deep learning to cell microscopy images to identify and phenotype cells, creating one of the most popular open source Python packages for active learning, building a full machine learning library from scratch, and collecting about a total of 100k followers on social media, all by posting high-quality educational content.