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Level 2 · Intermediate In Progress

Goal: turn the single-variable calculus and vector/matrix basics from Level 1 into the actual machinery of training a model — full gradient descent, multivariable chain rule, Jacobians/Hessians, the linear-algebra structure behind PCA and least squares, and the probability foundations (distributions, expectation, variance, Bayes' theorem) that show up in every ML algorithm from naive Bayes to loss functions themselves.

Modules

  1. Gradient Descent Step-by-Step
  2. Chain Rule Deep Dive
  3. Jacobians & Hessians
  4. Eigenvalues & Eigenvectors Intuition
  5. Matrix Decompositions Overview
  6. Probability Basics
  7. Expectation & Variance
  8. Bayes' Theorem
  9. Distributions Used in ML
  10. Capstone — Probability & Optimization Mini-Project

By the end of this level you'll be able to run gradient descent by hand for several steps, differentiate composite multivariable functions, read eigen-decompositions and know why they matter for PCA, and reason about uncertainty with distributions, expectation, variance, and Bayes' theorem — with every hand-derived result checked in NumPy/SciPy.