Part I: Mathematical and Computational Foundations
"Mathematics is the language in which God has written the universe." — Galileo Galilei
Every powerful AI system rests on a foundation of mathematics and computation. Before you can understand why a transformer attends to certain tokens, why gradient descent converges, or why a probability distribution captures uncertainty, you need to be fluent in the languages that describe these phenomena.
Part I builds that fluency. We begin with a panoramic view of AI engineering — its history, its subfields, and the modern technology stack you will master throughout this book. Then we dive into three pillars of mathematical understanding: linear algebra, which gives us the language of data representation and transformation; calculus and optimization, which power the learning algorithms that make neural networks work; and probability and information theory, which provide the framework for reasoning under uncertainty.
We close Part I with a practical chapter on Python for AI engineering, ensuring your computational toolkit matches your mathematical one. By the end of these five chapters, you will have the vocabulary, notation, and programming skills to tackle any AI concept in this book.
Chapters in This Part
| Chapter | Title | Key Question |
|---|---|---|
| 1 | The Landscape of AI Engineering | What is AI engineering, and where does it fit in the broader AI landscape? |
| 2 | Linear Algebra for AI | How do we represent and transform data mathematically? |
| 3 | Calculus, Optimization, and Automatic Differentiation | How do machines learn from data through optimization? |
| 4 | Probability, Statistics, and Information Theory | How do we reason about uncertainty and measure information? |
| 5 | Python for AI Engineering | What tools and practices make a Python programmer effective in AI? |
What You Will Be Able to Do After Part I
- Describe the major subfields of AI and how they connect
- Perform matrix operations and decompositions relevant to ML
- Compute gradients and understand how optimizers use them
- Apply probability theory to model real-world uncertainty
- Write efficient, well-structured Python code using NumPy, pandas, and matplotlib
Prerequisites
- Basic Python programming (functions, classes, modules)
- High school mathematics (algebra, basic functions)
- Curiosity about how AI systems work under the hood