Mathematics for AI

The math behind AI, taught from scratch to advanced: foundations, linear algebra, calculus, and probability/statistics, with every formula shown step by step.

What this course covers

1. Why Math for AI?
2. Numbers, Variables and Notation
3. Functions and Graphs
4. Exponents and Logarithms
5. The Coordinate Plane
6. Vectors: a List of Numbers
7. Adding and Scaling Vectors
8. The Dot Product
9. Vector Length and Distance
10. Matrices: a Grid of Numbers
11. Matrix times Vector
12. Matrix Multiplication
13. Transpose, Identity and Special Matrices
14. Eigenvectors and PCA (intuitively)
15. Rate of Change and Slope
16. The Derivative
17. Basic Derivative Rules
18. Partial Derivatives (Multivariable)
19. Gradients: Slope in Many Directions
20. The Chain Rule
21. Optimization and Gradient Descent
22. Gradient Descent Variants: Momentum, RMSprop, and Adam
23. Probability Basics
24. Mean, Variance and Standard Deviation
25. Distributions and the Normal Curve
26. Conditional Probability and Bayes Theorem
27. Correlation and Covariance
28. Entropy and Cross-Entropy
29. KL Divergence: Measuring the Gap Between Distributions
30. Likelihood and Sampling (for Evaluation)
31. Expectation and Variance
32. Covariance and the Covariance Matrix
33. Eigen-Decomposition and PCA
34. Singular Value Decomposition (SVD)
35. The Multivariable Chain Rule and Backpropagation
36. Maximum Likelihood and the Softmax Gradient
37. Convexity: Why Gradient Descent Works
38. The Math Behind Training a Model

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