Module manager: Dr Zeeshan Babar
Email: M.Z.Babar@leeds.ac.uk
Taught: 1 Jan to 28 Feb, 1 Jan to 28 Feb (adv year), 1 Jul to 31 Aug View Timetable
Year running 2025/26
N/A
This module is not approved as an Elective
This module develops the core mathematical foundations underpinning artificial intelligence (AI) and machine learning. It introduces key concepts from linear algebra, vector calculus, probability, and analytical geometry that support the quantitative reasoning essential to AI. Emphasis is placed on building intuition for how mathematical structures explain and enable the principles by which algorithms learn from data, providing a coherent framework for understanding the behaviour and design of modern learning systems.
This module aims to equip students with the mathematical understanding and intuition necessary to interpret, analyse, and design the methods that underpin modern AI. Building on key areas of linear algebra, vector calculus, probability, and analytical geometry, the module connects these concepts to the four foundational pillars of machine learning: classification, regression, density estimation, and dimensionality reduction. The module highlights how these mathematical principles give rise to practical modelling techniques that capture the process of learning from data and underpin approaches across the full spectrum of modern machine learning, from classical statistical models to artificial neural networks and generative AI. Learning activities combine explanatory notes, visual and geometric illustrations, worked examples, and guided problem-solving exercises to progressively develop both conceptual insight and analytical fluency.
On successful completion of the module students will have demonstrated the following learning outcomes relevant to the subject:
1. Apply mathematical reasoning to analyse and solve quantitative problems central to data science and machine learning.
2. Explain key mathematical concepts from linear algebra, vector calculus, probability, and analytical geometry and demonstrate how they underpin modern AI.
3. Demonstrate how key mathematical concepts give rise to practical techniques that enable algorithms to learn from data.
4. Illustrate how fundamental mathematical principles manifest in practical modelling approaches.
5. Formulate problems in mathematical terms and solve them to demonstrate understanding of how quantitative reasoning supports AI.
On successful completion of the module students will have demonstrated the following skills learning outcomes:
1. Apply logical and analytical reasoning to formulate, evaluate, and solve complex quantitative problems systematically.
2. Use abstract thinking and modelling skills to represent real-world problems in a structured and generalisable way.
3. Communicate mathematical reasoning and conclusions clearly and effectively, using appropriate notation, visualisation, and narrative explanation for diverse audiences.
4. Demonstrate persistence and adaptability in tackling unfamiliar or challenging problems through iterative exploration and self-directed learning.
5. Exercise critical evaluation to assess assumptions and validate alternative mathematical approaches.
Indicative content for this module includes:
1. Linear algebra as a systematic way of representing data and relationships using vectors, matrices, and operations that reveal structure and dependencies.
2. Vector calculus as a framework for describing change, sensitivity, and optimisation in learning systems through gradients and differential relationships.
3. Analytical geometry as a means of interpreting mathematical relationships geometrically, linking algebraic formulations to spatial intuition through lines, planes, and projections.
4. Probability and distributions as a foundation for reasoning about uncertainty, variability, and inference in data-driven contexts.
5. Mathematical formulation of core problems of machine learning: classification, regression, density estimation, and dimensionality reduction as expressions of these foundational principles.
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Discussion forum | 6 | 1 | 6 |
| WEBINAR | 6 | 1 | 6 |
| Independent online learning hours | 42 | ||
| Private study hours | 96 | ||
| Total Contact hours | 12 | ||
| Total hours (100hr per 10 credits) | 150 | ||
1. Webinar-Based Discussion and Q&A.
2. Weekly Practical Exercises.
| Assessment type | Notes | % of formal assessment |
|---|---|---|
| Assignment | 3 multi-part problem sets with the number and scope depending on the difficulty of the questions. | 70 |
| Coursework | Technical Report | 30 |
| Total percentage (Assessment Coursework) | 100 | |
This module will be reassessed through a 100% individual assessment containing a problem set and a brief written component that requires students to articulate and interpret their mathematical reasoning clearly.
Check the module area in Minerva for your reading list
Last updated: 18/02/2026
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