CHAPTER
Mathematical Foundations
The first chapter establishes the language the rest of the curriculum depends on: how we represent quantities, define collections, reason precisely, describe functions, compress repeated structure with notation, and justify claims with proofs.
Every later chapter uses these tools directly. Linear algebra relies on functions and set language, calculus formalizes continuity and change, probability depends on set structure, and modern ML papers assume comfort with concise symbolic notation and proof patterns.
How To Use This Chapter
Each section follows the same learning flow:
| File | Role |
|---|---|
| notes.md | Long-form explanation and reference |
theory.ipynb |
Interactive derivations and computational intuition |
exercises.ipynb |
Practice with scaffolded problems and worked solutions |
Recommended order:
| Section | Focus |
|---|---|
| 01 Number Systems | Representation, precision, and numeric formats for AI |
| 02 Sets and Logic | Membership, structure, predicates, and formal reasoning |
| 03 Functions and Mappings | Domain/codomain thinking, composition, and function properties |
| 04 Summation and Product Notation | Compact symbolic language for repeated operations |
| 05 Einstein Summation and Index Notation | Tensor-aware notation used across modern ML systems |
| 06 Proof Techniques | Direct proof, contradiction, induction, and proof patterns used in theory |
Why This Chapter Matters
- It gives you the notation needed to read later sections without friction.
- It turns symbolic ML formulas into understandable objects instead of memorized syntax.
- It builds the proof literacy needed for optimization, generalization, and convergence arguments.
Next Step
Continue to Number Systems, then work forward in order.