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Level 4 · Master In Progress

Goal: the mathematical foundations behind advanced and research-level ML — convex optimization guarantees, constrained optimization via Lagrange multipliers, information theory, logistic regression derived fully from scratch, kernel methods, a deep dive into SVD, Bayesian inference, the numerical optimization methods that power modern training (beyond plain SGD), the math behind transformer attention, and a capstone that implements linear regression from scratch in NumPy using everything from Levels 1–4.

Modules

  1. Convexity & Optimization
  2. Lagrange Multipliers & Constrained Optimization
  3. Information Theory Basics
  4. Logistic Regression Gradient from Scratch
  5. Kernel Methods & the Kernel Trick
  6. Singular Value Decomposition Deep Dive
  7. Bayesian Inference Foundations
  8. Numerical Optimization Methods
  9. Math Behind Transformer Attention
  10. Capstone — Linear Regression from Scratch in NumPy

By the end of this level you'll be able to prove why convex problems have no bad local minima, solve constrained optimization problems by hand, quantify information with entropy and KL divergence, derive logistic regression's gradient and Hessian from first principles, explain the kernel trick geometrically, decompose any matrix with SVD and interpret each factor, reason about ML as Bayesian updating, compare Newton's method to gradient descent, and derive the scaled dot-product attention formula that underlies transformers — all backed by NumPy-verified derivations.