AI & Machine Learning Theory

Derive the Linear Algebra Behind Machine Learning

Required mathematical foundation. You cannot understand gradient descent without understanding the Jacobian. You cannot understand PCA without eigendecomposition. You cannot understand attention without matrix multiplication. This is the mathematical prerequisite for everything that follows — all derivations must be hand-worked, not NumPy.

Apply Statistical Learning Theory to Your Own Dataset

Required. Statistical learning theory builds on linear algebra — you cannot rigorously analyse bias-variance trade-off without matrix calculus, and you cannot design valid cross-validation without understanding sampling theory. Must use your own collected dataset (not Kaggle) to prove the analysis is grounded in real data.

Implement Machine Learning Algorithms From Scratch (NumPy Only)

Required. Implementing ML algorithms from scratch (NumPy only, no frameworks) after studying the theory is the UG/PG distinction from the existing skills-become-ai-engineer practitioner path. It is possible to use PyTorch without understanding gradient descent. It is not possible to implement gradient descent in NumPy without understanding it.

Implement a Transformer Component From a Published Paper Specification

Elective — postgraduate-tier depth. Implement a core transformer component (attention, positional encoding, or tokeniser) from the published paper specification. Code must link every line to the specific equation in the paper. Reviewed by an ML researcher or senior ML engineer who will ask what changes when you modify a specific architectural choice.

Master Statistics for Data Analysis

Elective complement. Applied statistical reasoning on real data — already has Tier 1 richMilestones. A strong theoretical ML background combined with applied statistics is the full picture. Students who completed the Data Science Credential path have already satisfied this step.

The best visual introduction to linear algebra — eigenvalues, matrix transformations, and dot products explained geometrically before algebraically. Watch before attempting the proof exercises to build the right mental model.

Free textbook covering linear algebra, calculus, probability, and optimisation specifically for ML. Bridges the gap between pure mathematics and ML applications — the standard reference for the linear algebra and statistical learning theory steps.

Free video series implementing neural networks from scratch in Python/NumPy. The most influential from-scratch ML implementation series available — directly relevant to the cs-implement-ml-algorithms step. Karpathy's micrograd and makemore implementations are excellent reference implementations.

The standard graduate ML textbook. Mathematically rigorous treatment of probabilistic graphical models, Bayesian methods, and kernel methods. The reference for the statistical learning theory step — Bishop's treatment of bias-variance decomposition is particularly rigorous.