I. Foundations of Probability

1. Introductions to:

   1. Probability

   2. Distributions:

   3. Probability Spaces

   4. Independence and Conditional Probabilities:

   5. Random Variables:

   6. Bayes' Theorem:

II. Foundations of Entropy and Information

1. Introductions to:

   1. Entropy and Information: Introduction to Claude Shannon's Information Theory.

III. Frequentist and Bayesian Probability

1. Introductions to:

   1. Entropy and Information: Introduction to Claude Shannon's Information Theory.

IV. Linear Algebra

1. Introductions to:

   1. Kernel Trick: Introduction to the Kernel Trick.

V. Mathematical Methods to Machine Learning

1. Introductions to:

   1. Generative Adversarial Networks: Introduction to GANs.

VI. Sampling and Approximations

1. Introductions to:

   1. Monte Carlo: Introduction to Monte Carlo approximations.