Math Foundation for AI

Before studying the math section in depth, this overview is strongly recommended.

What This Section Covers

• Linear Algebra
• Calculus
• Probability and Statistics
• Information Theory

Recommended Resources

• Math Resources

Core Idea

This section is model-driven rather than textbook-driven. Instead of listing isolated math topics, we ask two practical questions:

1. What math tools are required by each part of an AI model?
2. Where exactly does each math concept appear in model design, training, and analysis?

A Generic AI Model System

We use a unified training pipeline:

Data
-> Representation
-> Parameterized Function
-> Prediction Distribution
-> Loss
-> Gradient
-> Optimization
-> Trained Model

Mathematical tools map to pipeline stages:

• Linear algebra and tensors for representation and transformations
• Calculus and matrix calculus for gradients and backpropagation
• Probability for uncertainty modeling
• Information theory and statistics for objectives and evaluation
• Optimization and numerical methods for stable training

Suggested Reading Path

1. Linear Algebra
2. Calculus
3. Probability & Statistics
4. Information Theory