Mathematics MMath (Hons)

First you’ll be introduced to the world of rigorous mathematics, which is ruled by the laws of mathematical logic and is based on the concept of mathematical proof. Set theory will then be introduced and through looking at real-world examples, you’ll learn about the other important algebraic structures, such as vector spaces and groups.

The module aims to consolidate and extend previous knowledge of calculus, with emphasis on the underlying intuition of the techniques. Methods taught will include professional mathematical writing, definitions of limits and functions, differentiation and integration, from the fundamental principles, to integrating and differentiating complicated functions. This is then extended to multi-dimensional coordinate systems.

Finally, we will study ordinary differential equations, which describe changes in real-world systems. These will be solved by applying the techniques from the first part of the module. Overall, this module will underpin material that you will encounter in many subsequent modules, both in the same and other fields.

This module provides a foundation  to data analysis and statistics, designed for students with no prior background in the subject. Using user-friendly statistical software, it offers a practical approach to exploring key concepts. Assessments are structured around work like experience, incorporating big data applications and global sustainability targets.

Beyond technical skills, the module fosters employability by developing teamwork, oral presentation abilities, and effective communication with non-specialist audiences. Beginning with data visualisation and fundamental statistical principles, it progresses to more advanced topics such as expectation and conditional probability, ensuring a solid foundation in statistical reasoning needed for the advance topics in higher years.

Studying Linear Algebra gives you a great base knowledge you’ll use in many modules during your course. Concepts include complex numbers, vectors and matrices. Using mathematical software packages you’ll focus on computational and numerical methods that can be used to find approximate solutions to problems that cannot be solved analytically.

Develop a range of skills appropriate to conducting open-ended mathematical investigations. Learn about the importance of rigour and techniques of proof in mathematical contexts.

You’ll start by learning how to program using Python before investigating several problems in discrete mathematics. Working in groups, you’ll discover potential solutions, which will be formalised into algorithms that can be implemented in Python.

This module will build your conceptual and technical background, and, in particular, work on vector spaces will be extended and generalised to linear transformations. You will be introduced to coding theory by applying linear algebra to linear codes.

This module develops your understanding of differential equations and how they can be used to model real-world systems. You'll explore advanced analytical and numerical solution techniques while gaining practical experience with tools such as MATLAB and LaTeX.  Strengthen your computational, problem-solving and teamwork skills needed for higher-level mathematics and a range of technical careers.

Refine your statistical inference and modelling knowledge and develop essential computational and IT skills.

Broaden your knowledge, understanding and skills in advanced higher calculus to topics including Fourier series, partial differential equations and complex analysis.

In this module you’ll work in small teams to develop a plan for a new business or enterprise, using your mathematical skills to showcase the viability of your venture. This module is run in conjunction with local businesses.

Learn how to select and apply appropriate techniques and use computer programming and specialist mathematical software to help solve problems. You’ll look at the need to develop more and more sophisticated ways of protecting information through cryptography. Analyse the hardness and limitations of mathematical algorithms using computational complexity theory.

Develop your knowledge of numerical methods with an emphasis on numerical optimisation techniques, advanced methods for the numerical solution of ordinary differential equations, and the analysis of dynamical systems. The real-world applications of these techniques are many and varied and include fascinating problems in the physical and life sciences.

Extend your understanding of probabilistic modelling to include stochastic processes and learn advanced techniques for investigating the behaviour of stochastic processes.

You will continue your previous studies in linear algebra and differential and difference equations.

In this module  you will undertake a small mathematics project with dedicated support and supervision to prepare you for the larger final-year project. The project will hone your skills, knowledge, and problem-solving abilities and you’ll explore your career options after graduation.

Apply your knowledge of advanced calculus and differential equations to solve differential and integral equations.

The optimisation is the art of optimal decision-making under constraints. This module introduces you to optimisation, focussing on the theoretical foundations of the subject, the practical modelling aspects, and the algorithm analysis and design.

This module will show you how to get the most of real-life data. In the experimental design half, you’ll learn the methodology and techniques to design, conduct and analyse an experiment before applying statistical analysis to your results to ensure you get the best data possible. The machine learning half will show you how to get the most out of any dataset you may come across in your future career.

Partial differential equations are an important topic in both pure and applied mathematics. This topic builds on earlier content to consider linear partial equations in non-trivial domains and to introduce methods of analysing nonlinear first order partial differential equations. Attention will be given to the derivation of such equations, as well as the numerical techniques that can be applied to these equations.

The medical side will focus on clinical trial design (how to test novel drugs, when to use placebos etc.) and survival analysis (how we display fatality rates and compare survival chances). The financial side will look at Time Series modelling; the dark arts of using statistical models to predict envelopes for future stock performance! This model gets you to practically apply analytical skills in two of the big growth fields for Maths employment.

This module introduces some research-informed topics in discrete mathematics by extending and building on ideas introduced in earlier years. It provides a blend of mathematical concepts and techniques that are widely applicable in areas such as data science, operational research, chemistry, engineering, computer science, information technology, statistics, sociology and genetics.

You will demonstrate your skills and knowledge by producing a substantial, individual piece of work in mathematics or statistics selected from a list of approved titles and reflecting the modules you have taken in earlier years.

Introduces you to quantum information theory and how quantum computing can deliver unprecedented computational power. A new generation of quantum computers will be able to solve currently intractable problems, which, for example, will unlock new opportunities for banks in risk assessment and trading, allowing much faster computations over existing conventional computers.

Examine the use of differential equations and their application to biological systems. You will study network models for a range of biological processes, including models of drug delivery, tumour growth and multicellular systems.

This module offers a rigorous introduction to applied mathematics, demonstrating its relevance in physics and engineering. A central theme throughout the six topics covered is Green's functions, named after Nottingham's notable mathematician George Green. You'll learn how to construct these functions from fundamental principles, through eigenfunction expansions, and using integral transforms.