Mathematics BSc (Hons) with foundation year

This module introduces you to fundamental algebraic concepts (sets, functions, basic group theory, linear systems, introductory eigenvalue/eigenvector theory and vector spaces). It should help you develop your computational skills in solving and interpreting linear equations. It aims to provide you with the essential building blocks in algebraic thinking, forming a foundation for more advanced topics in subsequent years.

Compulsory

This module introduces you to key statistics and data science techniques. In this module you will consider data summaries, exploratory data analysis, data visualisation, probability concepts, estimation and hypothesis testing. Explore the predictive analytics methods of regression and correlation and gain hands-on experience using modern software tools to analyse real datasets.

This module includes content on probability and statistics, data wrangling and data visualisation and the practical applications of software tools such as R, Python, MATLAB and Excel.

Compulsory

This module introduces you to single-variable calculus, covering limits, continuity, derivatives and integrals which should create a solid base for later study. Learn about ordinary differential equations, sequences and series. This module includes topics such as foundations of calculus and sequences, differential calculus, integral calculus, complex numbers, an introduction to ordinary differential equations and power series. It also focuses on real-world uses such as optimisation and rates of change, while building your problem-solving skills to prepare you for year two.

Compulsory

This module aims to provide you with a foundational understanding of how mathematics can be applied to real-world problems. The primary goal is to equip you with the ability to translate practical scenarios into mathematical frameworks, fostering critical thinking and problem-solving skills. It will also introduce you to fundamental programming skills, specifically tailored for mathematical and data science applications. Learn to implement simple numerical methods and data analysis techniques using a suitable programming language, enabling you to simulate and analyse simple mathematical models. This module introduces you to modelling and programming fundamentals, as well as optimisation and modelling with differential equations. It includes content on linear and non-linear models and data visualisation, curve fitting, model validation and error analysis.

Compulsory

Learn the fundamental concepts, models and applications of multiple regression, analysis of variance (ANOVA) and machine learning. These techniques will be explored and applied to a variety of real datasets. Hypothesis testing and estimation will be extended within a statistical data modelling framework.

The methods taught in this module are extensively used in industry, commerce, government, research and development. Module content will address wider social, ethical and professional issues of applying, evaluating and interpreting statistical and machine learning models. Develop key practical skills with appropriate software tools.

Compulsory

Extend your understanding of single-variable calculus into multivariable domains, exploring partial differentiation and multiple integrals. You will be introduced to vector calculus concepts (for example, gradient, divergence, curl) and apply these to geometric/physical problems. Develop knowledge of complex analysis, focusing on analytic functions, contour integrals and basic residue theory. These advanced calculus methods will be linked to real-world or theoretical scenarios to reinforce your computational and problem-solving skills.

Compulsory

Examine broader solution techniques (transform methods, series methods) for both linear and selected nonlinear equations. You will be introduced to Fourier-type expansions and Sturm–Liouville theory for solving boundary-value problems in ordinary differential equations.

Study systems of ordinary differential equations (ODEs), both linear and nonlinear, with a focus on stability and qualitative behaviour. This includes working with simple classifications and elementary solution strategies for partial differential equations (PDEs: wave, heat, Laplace). To reinforce modelling skills, real-world applications and computational approaches will be discussed.

Compulsory

Delve deeper into abstract algebra and build on your linear algebra knowledge with advanced topics like the Jordan normal form. Learn key results like Lagrange’s theorem and Sylow’s theorem, plus important ideas such as quotient groups, isomorphism theorems, direct products and group actions.

Explore rings, including encounter ideals, quotient rings and homomorphisms. Finally, by considering the ring of polynomials over a field, you will see how to construct finite fields.

Topics include advanced group theory, rings and polynomials, constructing finite fields and advanced linear algebra.

Compulsory

This module² provides you with an opportunity to reflect upon and gain experience for an approved placement undertaken during your programme. A placement should usually be at least 26 weeks or equivalent; however, each placement will be considered on its own merits, having regard to the ability to achieve the learning outcomes. 

Optional

This module² provides you with an opportunity to reflect upon and gain experience for an approved international study/work placement undertaken during your programme. A work/study placement should usually be at least 26 weeks or equivalent; however, each placement will be considered on its own merits, having regard to the ability to achieve the learning outcomes. 

Optional

Get an understanding of optimisation techniques and how they are used in artificial intelligence (AI) and machine learning (ML). Explore the maths behind solving different types of optimisation problems, both with and without constraints and with discrete or continuous variables. This module will explore a variety of optimisation techniques in AI and ML, including gradient descent, batch gradient descent, stochastic gradient descent, Mini-batch gradient descent and Adam. You will investigate advanced topics in optimisation, including second-order, convex, non-convex and constrained, and unconstrained optimisation techniques. You will also get hands-on experience using optimisation methods to train machine learning models and neural networks. These problems outlined in this module are found in areas such as operations research, finance and the sciences, so the skills you develop could be useful in a variety of careers.

Compulsory

This module introduces you to advanced topics in statistics and data science. Using relevant software, learn how to critically examine data and choose and apply appropriate analyses using a range of methods. The material will be set within a range of different contexts taken from industry, medicine, agriculture and engineering. This module will be particularly useful if you are interested in postgraduate study in statistics, or a career in statistics or data science.

Compulsory

The individual project module provides you with an opportunity to apply and integrate knowledge and skills acquired throughout your degree programme in a substantial individual piece of work. The module aims to develop your ability to solve real-world problems, engage in independent research, enhance your professional skills and demonstrate technical proficiency in your chosen subject area. This module should help you develop your project planning and time management skills. It will also test your ability to collect, analyse and validate data as well as your research methodology and literature review technique.

Compulsory

Cryptography and Information Theory – 30 credits

This module integrates higher-level algebraic and number-theoretic concepts (modular arithmetic, finite fields) into the study of cryptography and basic information theory. Learn how abstract algebra underpins classical and modern cryptographic protocols, as well as the fundamentals of encoding/decoding information.

Financial Maths – 20 credits
Get introduced to the core ideas of modern finance like no-arbitrage and risk-neutral valuation and explore the math behind them. Learn key models for fixed-income products, derivatives and portfolios using tools like stochastic processes and partial differential equations. Study key concepts, including the fundamental theorem of asset pricing, Markowitz portfolio theory and the capital asset pricing model (CAPM). Gain both theoretical knowledge and computational skills to tackle real-world financial problems and advanced mathematical finance techniques. Topics include no-arbitrage principles, fixed-income instruments, portfolio optimisation, equities and options, stochastic processes and exotic derivatives with hedging strategies.

Availability of optional modules may vary depending on student demand.

Optional