Overview

Machine learning is often introduced as a collection of algorithms and software tools. This course takes a different approach. It studies the mathematical structures that make learning from data possible: probability, optimisation, linear algebra, approximation and statistical decision-making.

The course develops these foundations through recurring questions about finite samples, generalisation, model flexibility, assumptions and prediction. Mathematical derivation is paired with computational evidence so that formal results can be connected to observed model behaviour.

The emphasis is on reasoning rather than software proficiency. Learners are expected to understand why established methods work, when they fail and what their limitations imply for applied research.

Learning objectives

By the end of the course, learners should be able to:

• formulate supervised-learning problems using probabilistic and decision-theoretic language;
• explain the relationship between empirical loss, expected risk and generalisation;
• derive and interpret ordinary least squares, regularised regression and selected classification methods;
• analyse the role of convexity, gradients and numerical optimisation in model estimation;
• distinguish model complexity from computational complexity;
• use simulation and numerical experiments to test claims about learning systems.

Intended participants and prerequisites

Course structure

The course is organised into six units. Each unit combines concise explanation, worked examples and short analytical exercises.

Unit	Subject	Principal questions
1	Learning as statistical decision-making	How are data, models, loss functions and decisions connected?
2	Linear prediction and projection	Why is least squares a projection problem?
3	Generalisation and model complexity	Why does performance on observed data differ from performance on new data?
4	Regularisation and constrained estimation	How do penalties encode structure?
5	Classification and probabilistic boundaries	How do likelihood and geometry lead to different decision rules?
6	Optimisation, computation and model failure	When does a numerical solution correspond to a meaningful learning solution?

Teaching and assessment

Teaching is delivered through concise lectures, technical notes, worked examples and guided exercises. AI-supported interaction may be used to explain concepts, generate additional practice and challenge a learner's reasoning, but assessment remains based on the learner's demonstrated understanding.

Component	Purpose	Weight
Short exercises	Check understanding of the principal concepts	40%
Applied investigation	Use the course framework on a new problem or dataset	30%
Final assessment	Integrated reasoning across the course	30%

A certificate of completion is issued only when the required assessments have been completed at the stated standard. Participation alone does not constitute completion.

Faculty

Materials and technical requirements

Learning environment

Learners need a current web browser and access to the Gordon learning platform. Where a course uses code, spreadsheets, datasets or external readings, the relevant requirements are identified inside the unit.

Course materials

Required readings, datasets and practice materials are identified within each unit. Public courses are designed so that required core materials can be accessed without a separate tuition charge.