MAGIC117: Mathematical Foundations of AI

Course details

A core MAGIC course

Semester

Spring 2026
Monday, January 26th to Friday, April 3rd

Hours

Live lecture hours
20
Recorded lecture hours
0
Total advised study hours
80

Timetable

Tuesdays
15:05 - 15:55 (UK)
Wednesdays
15:05 - 15:55 (UK)

Announcements

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Course forum

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Description

This module provides a rigorous introduction to the mathematical foundations of modern AI systems. The module will cover timeless mathematical foundations from approximation theory to concentration inequalities, as well as state-of-the art methods.a

Prerequisites

Modern AI theory draws upon a wide range of mathematical subjects. For this course it will be useful to have solid foundations in analysis, linear algebra, probability theory and a workin knowledge of functional analysis.

Syllabus

  • Introduction to AI:
    •  Deep Neural Networks (DNNs), Transformers & Large Language Models (LLMs), Diffusion Models, Neural Operators and Deep Reinforcement Learning 
  • Statistical Learning Theory Foundations: Concentration inequalities, Rademacher Complexities, Metric Entropy, and Basics of Approximation Theory
  • Stochastic Gradient Descent (Convergence behaviour, rates of convergence, generalisation behaviour)
  • Minimax Optimality of DNNs for Hierarchical Models
  • Wide Limits of DNNs with links to Gaussian and Deep Gaussian Processes
  • Double Descent and Benign Overfitting
  • (Some) Theory for Transformers & LLMs
  • Analysis of Diffusion Models
  • Neural Operators for Solving Partial Differential Equations
  • Deep Reinforcement Learning and the Alignment Problem

Lecturer

  • SG

    Steffen Grunewalder

    University
    University of York

Bibliography

No bibliography has been specified for this course.

Assessment

The assessment for this course will be released on Monday 27th April 2026 at 00:00 and is due in before Friday 8th May 2026 at 11:00.

Assessment for all MAGIC courses is via take-home exam which will be made available at the release date (the start of the exam period).

You will need to upload a PDF file with your own attempted solutions by the due date (the end of the exam period).

If you have kept up-to-date with the course, the expectation is it should take at most 3 hours’ work to attain the pass mark, which is 50%.

Please note that you are not registered for assessment on this course.

Files

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Lectures

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