Mathematical Sciences

Our Mathematics research covers many topics, from the abstract to the practical. We're exploring the immense mathematical complexity all around us, and using our knowledge and expertise to develop practical solutions to pressing issues in science and industry.

Within our industrial mathematics research, we're using mathematical modelling and analysis to improve the efficiency of renewable batteries and solar cells, and shaping the development of the next generation of technology.

In logistics, operational research, and analytics we are transforming our knowledge and expertise into action, by helping to develop new and better transportation and maritime systems. We're showing how better analytics for healthcare, risk and security can have a positive impact on the lives and wellbeing of people around the world, and we're finding new ways to create more sustainable and efficient renewable energy.

Among our applied mathematics, nonlinear and complex systems research, we're using mathematical models to study infectious diseases, plant-soil-atmosphere interactions, and cancer cell dynamics. We are taking inspiration from statistical physics to understand the spread of languages and dialects. We're also looking at the periodic orbits and stability of Solar Sails – a novel type of spacecraft which uses sunlight for its propulsion, and is therefore capable of completing orbits and missions which conventional spacecraft cannot.

Research Excellence (REF 2021)

We're ranked top among modern universities for research in Mathematical Sciences, with a vital and sustainable research environment. Read more about Mathematical Sciences in REF 2021.

REF case study – Improving lithium-ion batteries for electric vehicles through mathematical modelling

Our researchers created mathematical models that provide new methods to improve the lifetime, performance, safety and reliability of batteries — making electric vehicles safer, cheaper, more efficient and able to last longer between charges. This is crucial to the future uptake of electric vehicles and contributes to global goals to reduce emissions, waste and environmental impact. Results include the globally-used software tool Dandeliion for modelling prototypes of new batteries. The work significantly reduces the time and cost for companies developing electric vehicles. We work directly with the automotive industry (including General Motors), industrial partners (including Dassault Systèmes) and the universities of Southampton and Oxford in the UK and McMaster University in Canada. We also contribute to the Faraday Institution that works to power Britain’s battery revolution.

REF case study – Intelligent Gatelines (ticket barriers): improving throughput, safety, customer experience, and staff effectiveness, at mainline and metro stations

Our researchers worked to create automated railway station ticket barriers (gatelines) that can optimise the passenger flow through underground and mainline stations. The result is an increased throughput of people, a reduction in delays, and automatic crowd management that reduces congestion and improves safety. We used operational research techniques to design an “Adaptive Intelligent Controller” that sits at the heart of the system, analysing the crowd flow to predict in advance the best way to open and close gates in both directions. The project was funded by the Rail Safety and Standards Board, with industrial partners including Cubic Transportation Systems Ltd, Transport for London, Arriva UK Ltd and the Connected Places Catapult.

Interested in a PhD in Mathematics?

Explore our Mathematics postgraduate research degrees – including PhDs and MPhils.

Explore our areas of expertise

Applied Mathematics, Nonlinear and Complex Systems

We're studying how complexity and order arise from the simple underlying rules of physics. Explore our applied mathematics nonlinear and complex systems research.

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Industrial Mathematics

We're delivering insight into roles of different physical mechanisms within a process to develop practical solutions and guidance in science and industry. Explore our industrial mathematics research.

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Operational Research and Logistics

We're researching how we can apply quantitative methodologies to improve decision-making across a range of diverse fields of application.

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Research groups

Nonlinear and Complex Systems Research Group

Our Nonlinear and Complex systems researchers are engaged in the study of how such complexity and order arises from simple rules. The subject is vast, spanning many topics from the highly abstract to the intensely practical.

Logistics, Operational Research and Analytics Group

Our Logistics, Operational Research and Analytics Research Group members conduct and supervise research in a wide range of fields.

Intelligent Transport Cluster

The cross-faculty Intelligent Transport Cluster unites innovators and users with academics across the University, to promote long-term competitiveness in Land, Air and Marine transport systems.