Mathematics for Machine Learning

The mathematical floor of AI.

Duration: 15 weeks
Tier: Tier 1 · Foundations
Certificate: WIATech Certificate in Mathematics for Machine Learning

A fifteen-week intensive that builds the mathematical foundation AIE 300 rests on — linear algebra at substantive depth, calculus and optimisation, probability and statistics-for-machine-learning, and information theory. Machine learning is mathematics that runs on computers, and MTH 85 builds the vocabulary and intuition an engineer needs to open a modern machine learning paper, recognise the notation, and follow the argument. As the only surviving bridge course in the WIATech architecture, it exists to prepare students for one diploma: Artificial Intelligence and Machine Learning.

§ What you'll be able to do

Read and write mathematical notation fluently, in the form used by modern machine learning papers
Reason about vectors and matrices as both algebraic objects and geometric transformations
Compute gradients by hand for the functions used in real machine learning loss surfaces
Implement gradient descent from scratch and explain why and when it converges
Reason about probability distributions and conditional probability at the level machine learning uses
Apply statistical thinking to machine learning — bias-variance, sampling, cross-validation, leakage avoidance
Understand entropy and cross-entropy as the mathematical foundation of classification loss
Open a machine learning research paper, follow the argument, and implement core algorithms from their own library

§ What you'll cover

Mathematical Foundations & Function Literacy

Brings every student to a shared mathematical floor — set theory, notation, functions and graphs — before the substantive machine learning mathematics begins.

Linear Algebra Foundations

The first substantive machine learning mathematics: vectors, norms, the dot product, cosine similarity, matrices as transformations, and matrix multiplication as the forward pass.

Advanced Linear Algebra for Machine Learning

Structural concepts — vector spaces, eigenvalues, diagonalisation, SVD and PCA — that distinguish students who can read machine learning papers from those who can't.

Calculus Foundations

The mechanism by which networks learn: derivatives, the chain rule, partial derivatives and the gradient, and the derivatives of machine learning activation functions.

Optimisation for Machine Learning

Applied calculus — loss functions, convexity, gradient descent and its variants, learning rates, and momentum and Adam at literacy level.

Probability for Machine Learning

The framework for reasoning about uncertainty — conditional probability and Bayes' theorem, random variables, the named distributions, and the Gaussian at depth.

Statistics for Machine Learning

Statistical reasoning at the level machine learning uses — sampling, train/test/validation splits, the bias-variance trade-off, cross-validation, and data leakage.

Information Theory

The bounded but essential foundation for classification: information content, entropy, cross-entropy, KL divergence, mutual information and information gain.

Capstone

The Machine Learning Math Toolkit

A working Python library — the student's own miniature NumPy — implementing the mathematical foundation of machine learning from scratch, with an applied demonstration on a real Sierra Leone dataset, a mathematical writeup, a paper-reading exercise, and an oral defence.

§ Tools you'll use

Python 3.12+
VS Code
NumPy
Matplotlib
Jupyter Notebook
Git
Pen and paper
SymPy
SciPy

§ Where it leads

The only surviving bridge course in the WIATech architecture, preparing students specifically for AIE 300 — so the diploma can build on a mathematical foundation rather than construct it.

Required by

AIE 300