Compulsory modules

Algebra: from sets to spaces
This module introduces you to the language of modern mathematics and the art of writing mathematical proofs. You will work with fundamental mathematical objects such as sets and functions, study the beautiful and elegant arguments of number theory, and explore algebraic and geometric perspectives on vectors in 2,3, or n-dimensional space. You will also learn how these concepts can be applied to develop strategies for solving a wide range of mathematical problems.

Problem Solving and Computer Programming
In the first part the module introduces the fundamental concepts underlying computer programming, together with techniques for applying these using Python. The module has a strong practical element. Examples will come from various areas of Computer Science and Data Science. You will gain skills of producing, compiling, and debugging simple programs in Python. These skills will be refined in later modules with applications in various areas of Computer Science.
In the second part this module teaches students modern programming practices in a different paradigm than they study in Introduction to Programming. Professional programming and modelling practices will be studied, and you will be introduced to the Java programming language, expanding your suite of practical skills. You will learn more about testing strategies of computer programs, and intermediate Java programming syntax.

Calculus: from Limits to Multivariable Methods
Many real-world problems are described by calculus; for instance, the oscillation of a pendulum and the population evolution of a fish species can all be described by ordinary differential equations. This module, being a prerequisite for several modules in the second and third years, will introduce you to the basic techniques for solving differential equations and familiarize you with multivariable calculus, including partial derivatives, double integrals, and their applications while you'll simultaneously dive into the study of the infinitely small and infinitely large, and explore the rigorous foundations of Calculus. You will develop the theory via lectures, and consolidate your knowledge via practical sessions.

Optional modules

Mathematical Methods
Mathematics provides a language to discuss concepts and ideas in a formal setting.  It is thus vital to develop the ability to reason logically and to recognise incorrect reasoning. This module will extend a range of mathematical skills and techniques and apply them in more difficult unstructured problems, using mathematics as an effective means of communication. The module will develop skills in reading and comprehending mathematical arguments and and improve confidence and speed in finding correct solutions. 

Introduction to Cybercrime: Systems, Society, and Security
This module will enable students to actively engage in the digital environment/e-society with an understanding of the risks that they will encounter and the measures that may be taken to counteract them, as well as help students to acquire a firm understanding of the technologies that underpin today's digital information society.

Fundamentals of Computer Systems
You will learn fundamental concepts of computer hardware and software and achieve a foundation for other computer science modules. You will obtain an overview of computer systems, bridging theoretical concepts with practical applications and gain an understanding of the capabilities and limitations of modern IT. You will see logic design for core hardware components, the architecture of operating systems, essential features of programming languages, a selection of computing applications, hardware design, operating systems, and computational principles like parallelism and caching.

Compulsory modules

Web Technologies and Databases
This module provides a comprehensive introduction to web technologies and databases, equipping students with the practical and analytical skills to design, develop, secure, and deploy modern web applications with robust data-driven backends. Upon completion, students will be able to apply industry-standard tools and best practices in contemporary web and database development.

Linear Differential Equations
Differential equations are used as mathematical models describing various processes in the real world. This helps us investigate problems related to population dynamics, heat dissipation in objects, vibrations of engineering structures and wave propagation, among many others. Some situations require more than one differential equation to be solved at once, e.g., modelling dynamics of two populations (e.g., foxes and rabbits). Within this module we will study a variety of methods for solving differential equations.

Human-Centred Software Engineering 
This module integrates principles and practices from software engineering and human-computer interaction (HCI) to provide a comprehensive exploration of the processes involved in designing, developing, and evaluating interactive software systems. Students will work both individually and in teams to apply agile software development methodologies alongside user-centred design techniques, ensuring that technical functionality and usability requirements are addressed throughout the development lifecycle.
The module introduces key concepts in requirements analysis, system design, implementation, and evaluation, with a particular emphasis on user needs, accessibility, and ethical considerations. Through case studies, practical exercises, and team-based projects, students will gain experience in:

• applying agile practices to collaborative software development,
• creating and evaluating prototypes and user interfaces,
• applying usability principles, guidelines, and evaluation methods,
• producing professional technical and design documentation, and
• reflecting critically on the integration of software engineering and HCI practices.

By combining technical and human-centred approaches, the module prepares students with the skills and knowledge required to deliver effective, usable, and sustainable software solutions in professional contexts.

Complex Variable I and Vector Calculus 
This module contains a first course on vector calculus and a first course in functions of a complex variable.  The topics covered include complex functions, differentiation and integration, Cauchy's Theorems, Taylor and Laurent Series, singularities, the Residue Theorem, differentiation of vectors, differential operators, line, volume and surface integrals, Green's Theorem, the Divergence Theorem and Stokes' Theorem. Complex variable leads to elegant results in pure mathematics and both complex variable and vector calculus provide a framework for solving physical and geometrical problems.

Optional modules

Computational Mathematics with Python
Scientific computing is one of the cornerstones of modern applied mathematics. By arming students with a high-level general purpose programming language “Python”, they will be well equipped to explore a plethora of mathematical problems otherwise inaccessible to them. Moreover, students will possess a valuable, transferable skill, necessary in a large number of industries, for example, data science, engineering, meteorology and finance. This module also will embed the use of technology to aid undergraduate mathematical studies.

Cloud and Distributed Computing 
This module introduces cloud technologies and distributed computing, focusing on both principles and practical applications. You will explore big data technologies like Hadoop and NoSQL databases and gain hands-on experience with cloud platforms such as Amazon Web Services. You will also develop skills in digital communication principles, as well as cloud and network security and compliance.

Flexible Work Placement (Level 5)
In a competitive job market, practical skills and understanding workplace dynamics are crucial.  This module allows you to gain hands-on experience, enhancing your employability, and the opportunity to gain valuable professional insights via a 75-hour placement. You will be supported by various activities to secure a role and can source your own placement or apply to university-sourced roles. This module offers flexibility on when and how you complete your placement, enabling you to balance your placement around existing demands.

Artificial Intelligence and Machine Learning
This module will provide students with an introduction to artificial intelligence. Topics will including neural networks, deep learning, evolutionary algorithms and neuroevolution. The focus will initially be on understanding the underlying principles, structures, algorithms and capabilities of AI systems, and then on writing programs that use appropriate machine learning software libraries to pre-process data and apply AI to tasks such as text analysis, data analytics and visualisation, computer vision, image processing and pattern recognition.

Abstract Algebra
Abstraction is a powerful idea in Mathematics: by focusing on the underlying properties of Mathematical systems we can identify connections and similarities that are not visible on the surface. In this module you will explore these techniques and styles of thinking. The central concept is that of a group. You will study some of the fundamental abstract results concerning groups, and discuss applications in combinatorics, geometry, and number theory. You will encounter new topics via guided investigations, develop the theory via lectures, and consolidate your knowledge via practice sessions.

Professional Mathematics and Data Analysis
This module gives the opportunity to further develop skills of mathematical problem solving and application of mathematical results to real-world scenarios, especially those involving the analysis and interpretation of large data sets. This aims to develop skills that are needed when undertaking employment or research, such as working in depth on a problem over an extended period, writing reports, communicating mathematical and data-informed results to different audiences, working in collaboration with others, and basic data analysis using Pandas. This module will provide employability skills experiences and develop students’ ability to articulate their skills, which will be useful to draw on when applying for jobs.

Compulsory modules

Software Engineering Practice
This module provides a deeper understanding of object-oriented programming and the concept of concurrent programming, using Java as a working language. You will learn more advanced design patterns which can be applied in a range of real-world application areas. You will gain a comprehensive foundation in software development management and its associated processes. This will cover the skills needed to manage software products and their quality and explore Test-Driven development. You will be able to apply software testing and planning to real-world scenarios and systems and gain familiarity with industry-relevant skills.

Partial Differential Equations
This module provides an introduction to analytical methods for solving partial differential equations (PDEs). Throughout the module focuses on PDEs in two independent variables, although generalisation to three, or more, independent variables is briefly discussed. The module begins by introducing the method of characteristics for solving first order linear and quasi-linear PDEs. This is followed by the classification of linear second order PDEs into hyperbolic, parabolic or elliptic type, with a detailed treatment of the reduction to canonical form in each case. Thereafter, the module introduces the separation of variables technique and transform methods to solve the wave, diffusion, Laplace and Poisson equations. These PDEs are frequently encountered in many branches of applied mathematics, including fluid dynamics, mathematical biology, financial mathematics and electromagnetism. Finally the module introduces the technique of eigenfunction expansions for solving inhomogeneous PDEs, and the technique of Green's functions.

Computer Science and Mathematics Project
You will undertake an individual project across two semesters, involving Computer Science and Mathematics. The module enables you to apply theoretical knowledge and problem-solving skills to a technical, software, programming, research or business problem within the discipline, potentially with industrial input. You will be allocated an academic supervisor, providing guidance alongside taught lectures. You will develop essential transferrable skills including self-directed learning, critical thinking, reflective practice, communication, adaptability, and time management.

Optional modules

Advanced Artificial Intelligence and Data Ethics
This module will expand on the range of artificial intelligence themes introduced earlier in the degree. It will allow students to explore in greater depth, selected research-led topics at the forefront of current thinking in the rapidly evolving field of AI. The module will also provide students with insights and understanding of fundamental issues relevant to data ethics, security and AI governance. Students will acquire practical data science and machine learning skills such as dataset analysis, anonymisation and fairness testing. Students who successfully complete this module can potentially pursue further research in industry or in education (e.g. as MSc or PhD students), or careers involving data protection and AI governance

Non-linear Differential Equations
This module introduces a number of methods for identifying and classifying various types of behaviour in various types of differential equation. While linear differential equations model some processes, the majority are described by nonlinear equations, and it is these that display the greatest diversity of behaviour. However, very few nonlinear differential equations have exact solutions. Nevertheless, a great deal of insight can be obtained from qualitative methods. This module focuses on geometric methods for constructing phase plane representations of dynamics and perturbation methods for obtaining approximate solutions. With these tools it is then possible to examine the changes in behaviour that can occur when a parameter is varied, and bifurcation theory is introduced to describe this. The relation between the evolution of differential equations and the evolution of maps is explained, and more exotic behaviour, like period doubling and chaos, are then studied in terms of the dynamics of maps.

Group Theory
This module builds on the Group Theory introduced in MAT-20025 to develop some of the mathematics underlying the classification of finite groups.  This culminates in a proof of Sylow's First Theorem which offers a partial converse to Lagrange's Theorem proved in MAT-20025.  The module also develops some applications of Group Theory, the natural setting for which is that of group actions. Several examples of applying group theoretic ideas to counting combinatorial configurations are presented.

Number Theory and Cryptography
Number Theory studies the properties of the natural numbers and the integers. It is one of the oldest and most beautiful areas of Pure Mathematics, and also one of the most active areas of modern research. Recently, ideas from Number Theory have been applied to problems in Cryptography, such as the design of ciphers and secret sharing schemes. This module will trace the development of the subject from ancient problems to these modern applications.

Advanced Web Development and Databases
This module provides an advanced understanding of database techniques and the contemporary issues involved in deploying modern database systems. It aims to equip students with the knowledge and skills needed to develop secure, distributed, multi‑tier web applications using current and emerging technologies. Designed with industry relevance in mind, the module focuses on practical competencies that prepare students for professional web development and database‑driven application design.

Flexible Work Placement (Level 6)
In a competitive job market, practical skills and understanding workplace dynamics are crucial.  This module allows you to gain hands-on experience, enhancing your employability, and the opportunity to gain valuable professional insights via a 75-hour placement. You will be supported by various activities to secure a role and can source your own placement or apply to university-sourced roles.  This module offers flexibility on when and how you complete your placement, enabling you to balance your placement around existing demands.

Professional Experience in Education 
This module gives students interested in pursuing teaching or training as a career the opportunity to gain experience in the world of teaching in schools, colleges and other educational settings. You will develop skills highly valued by employers such as communication, and interpersonal skills, whilst learning to address individual needs and developing engaging teaching materials. You will be supported via a range of activities to prepare for your placement and have the choice to source your own placement or apply to university sourced roles.

Cyber Security and Application
Cybersecurity sits at the heart of today’s interconnected world, where every organisation faces complex and evolving digital threats. This 30-credit module gives you the knowledge, practical skills, and professional insight needed to meet those challenges with confidence. Bringing together a solid foundation in cybersecurity principles with application-focused content, the module blends lectures, hands-on labs, and team-based projects to simulate real-world problem-solving. You will explore the legal, organisational, human, and technical aspects of security, gain experience with modern tools and techniques, and develop critical thinking, communication, and reflective skills valued by employers across the sector.

Waves
The module aims to give an account of the underlying mathematical theory that describes the behaviour of waves. The mathematical development of the subject is combined with a discussion of applications, for example musical instruments. The module material is illuminated by small demonstrations and by computer-generated animations of wave processes. The topics include: the wave equation, waves on stretched strings, waves on membranes, waves on beams, sound waves, and waves in liquids with a free surface.

Mathematical Modelling
The aim of the module is to demonstrate how real-world problems can be modelled mathematically. The mathematical modelling process will be introduced through a six-step problem-solving approach: identifying a suitable problem from the particular real-world scenario, making assumptions to simplify the problem, classifying variables influencing the problem, constructing a mathematical model to determine interrelationships among the variables, solving and interpreting the model and finally validating the model with real-world data.

Mathematical tools that will be used in the model construction and solution process include: linear and nonlinear ordinary differential equations and their solution methods, such as phase-plane analysis,  and partial differential equations and their solution techniques, such as separation of variables and method of characteristics. 
Computational tools will include programming using Python for the numerical solutions of ordinary and partial differential equations. The modelling ideas  will be developed through novel and innovative case studies of real-world scenarios and through individual/group projects.