MSc Mathematics

MTHM021: Advanced Mathematics Project

In this module, you will gain experience of independent work by conducting in-depth research into an open-ended problem agreed with your Project Supervisor. A Good Research Practice portfolio (20%) recognises your professionalism and research performance, and your participation in the wider research, academic, or professional environment associated with your project. Partway through the project, you will present your work to date to a group of academics and fellow students in order to obtain feedback on your progress and to help guide the remainder of your study. This forms 10% of the assessment. At the end of the project, you will write a coherent and comprehensible account of your work in the form of a dissertation that forms 70% of the assessment. Computational work using appropriate software may form part of the Advanced Mathematics Project.

This module provides the opportunity for you to produce a well-researched project in mathematics, either complementing or extending material in the taught part of the programme. By taking this module, you will develop research skills, including literature review, problem formulation, analysis, and communication of mathematical results.

You will receive guidance on the responsible use of AI-assisted tools to support aspects of your research, report writing and presentation preparation, in line with University policy.

View an example full module specification

MTHM036: Research in Mathematical Sciences

This is a unique module that runs in several research themes and provides you with a taste for and experience in research in mathematical sciences. The themes are broadly aligned with Fourth Year options and would cover subjects from pure maths, applied maths and statistics, although the number and range of topics may change from year to year. Each theme consists of lectures, student-led discussion, reading, and practical sessions, getting deeper experience in research approaches and skills. Students will learn to write a short essay, make an oral presentation and write a longer scientific report.

Set in at least three distinct research themes, this module will introduce you to scientific thinking and abstraction and give you knowledge/experience in core research skills: reading (and understanding), writing and presenting for the mathematical sciences.

View an example full module specification

ECMM409: Nature-Inspired Computation

Traditional computation finds it either difficult or impossible to perform a wide range of tasks including product design, decision making, logistics and scheduling, pattern recognition and problem solving. However, nature is proven to be highly adept at solving problems making it possible to take inspiration from these methods and to create computing techniques based on natural systems. This module will provide you with the knowledge to create and apply techniques based on evolution, the intelligence of swarms of insects and flocks of animals, and the way the human brain is thought to process information. This module is appropriate for you if you have an interest in optimisation and data analysis, and have some programming and mathematical experience.

Non-requisites (cannot be taken with): ECM3412 Nature-Inspired Computation

This module aims to provide you with the necessary expertise to create, experiment with and analyse modern nature-inspired algorithms and techniques as applied to problems in industry and industrially-motivated research fields such as operations research.

The module also aims to provide you with knowledge of the limitations and advantages of each algorithm and the expertise to determine which algorithm to select for a given problem.

MEng AHEP3 ILOs covered on this module:

SM1m-SM6m, EA1m-EA6m, D1m, D3m-D8m, ET3m, EP1m, EP3m, EP4m, EP8m-EP11m, G1m-G4m

View an example full module specification

ECMM422: Machine Learning

Machine learning has emerged mainly from computer science and artificial intelligence, and draws on methods from a variety of related subjects including statistics, applied mathematics and more specialized fields, such as pattern recognition and neural computation. Applications are, for example, image and speech analysis, medical imaging, bioinformatics and exploratory data analysis in natural science and engineering. This module will provide you with a thorough grounding in the theory and application of machine learning, pattern recognition, classification, categorisation, and concept acquisition. Hence, it is particularly suitable for Computer Science, Mathematics and Engineering students and any students with some experience in probability and programming.

In this data-driven era, modern technologies are generating massive and high-dimensional datasets. This module aims to give you an understanding of computational methods used in modern data analysis.

View an example full module specification

ECMM423: Evolutionary Computation and Optimisation

Evolutionary computation is the study of computational systems that use ideas and derive their inspiration from natural evolution. Its techniques can be applied to optimisation, learning and design. Building on the foundations of evolutionary algorithms, this module develops an understanding of research trends in evolutionary computation and in particular advanced algorithm formulations to address more complex optimisation problems. Example topics covered in this module include algorithms designed to address many-objective, noisy and dynamic optimisation problems, and advanced methods including hyper-heuristics, human-in-the-loop and surrogate assisted optimisers. This is a research-led module appropriate for students with an interest and a background in bio-inspired problem-solving techniques and optimisation who have adequate programming and mathematical experience.

The aims of this module are to:

• Introduce advanced concepts and techniques in the field of evolutionary computation and their application to complex optimisation problems
• Provide students with experience of presenting complex topics to their peers and to participate in Q&A sessions similar to those experience in a conference setting

View an example full module specification

ECMM424: Computer Modelling and Simulation

This module is designed to equip you with foundational knowledge and useful skills in computer modelling and simulation. Numerous architectures, protocols and algorithms have been proposed for contemporary computer and communication systems. Analytical modelling and simulation play an increasingly important role in computer science and modern engineering, particularly in the design, performance prediction, evaluation, and optimisation of computer and communication systems. In this module, you will acquire useful knowledge of developing cost-effective analytical performance models and gain important skills in design and implementation of computer simulators. A range of case studies are examined, both in the lectures and workshops (laboratory exercises).

PRE-REQUISITE MODULES ECM1410, ECM2414

View an example full module specification

ECMM426: Computer Vision

How do we recognise objects and people? How can we catch a ball or navigate a busy room without collisions? These everyday tasks have challenged AI scientists for decades. Recent advances in computer vision have led to major improvements in applications such as face detection, body tracking, autonomous vehicles, and action recognition.

This module introduces the fundamentals of computer vision, covering both classical and state-of-the-art methods. You will gain a theoretical understanding of key algorithms, along with practical skills in image processing, feature extraction, object detection, segmentation, and deep learning for vision tasks. The course also explores 3D vision and modern topics such as video analysis and low-shot learning, providing a broad foundation for solving real-world vision problems.

View an example full module specification

ECMM443: Introduction to Data Science

In this module, you will learn about the broad and fast-moving field of data science. You will be introduced to the core competencies and application areas associated with data science, including data handling and visualisation, statistical modelling, network and text data analysis. You will also explore the ways in which data science is transforming business and society, and learn about ethical and governance aspects of data science. Practical exercises and individual study will consolidate your learning and provide the foundations for later study.

This module will cover the breadth of data science to equip students with the context and vocabulary to support more detailed study in future modules. Topics will evolve to reflect current issues in data science, providing students with the tools to formulate data science problems and construct pipelines to begin to solve them technically.

Lectures will be accompanied by data analysis exercises. A series of guided practical exercises will develop skills in programming (in Python), data handling and visualisation.

View an example full module specification

ECMM445: Learning from Data

Artificially intelligent machines and software must assimilate data from their environment and make decisions based upon it. Likewise, we live in a data-rich society and must be able to make sense of complex datasets. This module will introduce you to machine learning methods for learning from data. You will learn about the principal learning paradigms from a theoretical point of view and gain practical experience through a series of workshops. Throughout the module, there will be an emphasis on dealing with real data, and you will use, modify and write software to implement learning algorithms. It is often useful to be able to visualise data and you will gain experience of methods of reducing the dimension of large datasets to facilitate visualisation and understanding.

The module will also cover some recent neural network architectures and related learning algorithms.

This module aims to equip you with the fundamentals of machine learning and at the same time discuss technical aspects of some well-known machine learning models and related learning algorithms. It will provide a thorough grounding in the theory and application of machine learning and statistical techniques for classification, regression and unsupervised methods (clustering and dimension reduction). The module will cover kernel methods and neural networks (feed-forward architectures only).

View an example full module specification

ECMM447: Social Networks and Text Analysis

The rise of the Web has created huge datasets relating to the interaction of users and online content. Much of this content is relational and is best understood using a network perspective (for example, hyperlinked web pages; users linking to content; users linking to users on social platforms). Much of this content consists of unstructured text (for example, webpages, blogs, social media posts) that requires computational methods for analysis at scale. In this module you will learn the core principles of social network analysis and computational text analysis, enabling you to gain insight from the rich data available on the Web.

The aim of this module is to equip you with a range of knowledge and skills needed to make effective use of data from the Web. This module will cover various topics in social network analysis and text analysis, which together allow relational and unstructured text data to be analysed at scale. The module will be taught using the Python language and various open-source packages.

The module will be taught in weekly lectures and associated practical work, together with individual self-study and labs. Lectures will introduce the topics of social network analysis and text analysis, accompanied by practical exercises based on lecture material.

View an example full module specification

ECMM461: High-Performance Computing

The demand for ever-increasing computational power drives the development and exploitation of high-performance computing that underpins leading edge research in computationally intensive engineering technologies fields. This module is designed to equip you with a solid foundation and useful skills in high-performance and distributed computing. In this module, you will learn about current high-performance computer architectures and how the computer architecture influences the performance of algorithms and programs. You will also develop skills in parallel algorithm design and parallel programming, and will gain experience of using a high-performance computing system.

This module aims to provide you with a thorough grounding in parallel programming and the architectures used in high-performance computing. After presenting the fundamental ideas and basic concepts of high-performance computing, the module outlines the architectures, components and parallel programming of high-performance computers. The module will introduce you to recent developments and future trends in architecture and algorithms in high-performance computing.

View an example full module specification

ECMM462: Fundamentals of Security

Our modern life depends on the security of computerised systems ranging from social aspects (e.g. phishing) to technical and mathematical aspects (e.g. access control, encryption). In this module, you will learn the fundamental concepts required for starting a career in various areas related to security (e.g. cyber security, data security, information security, computer security). You will learn core security concepts (e.g. authenticity, confidentiality, anonymity, privacy) and core technologies (e.g. encryption, authentication, authorisation). Moreover, you will learn the basic attacks on security systems and approaches for reasoning about the correctness of security techniques.

The aim of this module to create awareness of the need for security and privacy in modern life, and to introduce the fundamental security and privacy mechanism used in modern computer systems. We will explore topics such as fundamentals of computer security, technology and principles of network security, cryptography, authentication and digital signatures, access control mechanisms, privacy, and anonymisation.

In more detail, the aims of the module are to give you an understanding of:

View an example full module specification

ECMM463: Building Secure and Trustworthy Systems

Building secure and trustworthy systems, i.e. systems that are hard to attack and protect the privacy of their users, are extremely hard to build. In this module, you will learn the foundations of building secure (software) systems ‘right from the beginning’. You will learn how to assess the threats of a system that need to be mitigated while building it, the risk assessment of vulnerabilities, as well as various approaches (e.g., defensive programming) and techniques for building secure systems. The module focuses on defensive security techniques that might be used by “blue teams.”

This module aims to give you a broad understanding of techniques for assessing the risks a modern IT system is exposed to. Driven by these risks, we will discuss several defensive security techniques for building security and trustworthy (software) systems. In more detail, the aims of the module are to enable you to assess the security of software architectures understand the principles of secure software architectures understand software vulnerabilities, their causes, and impact to develop secure software using defensive programming techniques to understand the principles of security testing and verification techniques.

View an example full module specification

ECMM464: Security Assessment and Validation

Even if systems have been developed with security in mind, their security needs to be assessed regularly, as, e.g., new attacks might be developed. Thus, assessing and validating the security of systems, e.g., penetration testing is an important part of cyber security. In this module you will learn the theory and practice of assessing the security of systems and applications both using manual techniques as well as automated approaches. The module focuses on offensive security that might be used by “red teams.”

This module aims to give you a broad understanding in analysing the weaknesses of a system, i.e., the areas an attacker would most likely attack a system. Driven by the discovered weaknesses, we will discuss several offensive security techniques, I.e., simulate how a threat actor (attacker) might gain access to a system or the data processed by a system. In more detail, the aims of the module are to enable you to assess the security weaknesses of a system develop a strategy how to attack a system understand the both the social and technical foundations for attacking systems or organisations understand the ethical responsibilities of an offensive security researcher.

View an example full module specification