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Department of Mathematics

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Research for your business

Gain a competitive advantage through specialist collaboration with researchers in the Department of Mathematics.

Global collaboration

In the past we’ve collaborated with multinational companies including Dyson, Mondelez International and Rapiscan Systems. Read their case studies below.

We have a strong record of working with industry and other external partners. From helping you find skilled maths graduates to arranging specialist research projects for your organisation, we can help your business.

Additionally, our statistics researchers run a dedicated Statistical Advisory Unit, providing help and support on research activities where expertise in statistical modelling or data analysis is required.

Please get in touch with any enquiries about how your business could work with us.

Past collaborations


The collaboration with Manchester has brought together mathematical and engineering expertise resulting in effective software tools to help engineers identify modelling problems in today's increasingly complex structural models.

Stephen Hendry / Associate, Oasys Ltd

In a collaborative PhD project with Arup, condition estimation techniques developed in the Numerical Analysis group, have been incorporated into Oasys GSA - the structural analysis software developed by Arup and used by engineers around the world. The new functionality enables engineers to detect sources of ill conditioning in their models and rectify them.

Arup are now funding a further PhD student in order to develop algorithms and software for the numerical solution of quadratic eigenvalue problems, which arise in the analysis of structures with damping such as buildings and bridges. The aim is to provide new and improved techniques that can be used by engineers for performing dynamic analysis of structures, taking into account the effects of damping.


Collaboration between Dyson and the Department of Mathematics at Manchester began with a six month shorter Knowledge Transfer Partnership (sKTP) project entitled 'modelling the acoustic absorption properties of materials'.

The contribution to the company has been fantastic. There has been a genuine impact on our product development. We were lucky to find a brilliant candidate and the support from the University supervisors has been invaluable.

Hugh Hopper / Aeroacoustics Research, Dyson Technology Ltd

All Dyson products move air as part of their primary function. Getting air to move and then controlling it can be a noisy business. Dyson sought academic input from applied mathematicians to aid the investigation of solutions which allow maximum acoustic benefit within strict design constraints.

Research and development at Dyson is often mainly experimental, thus the sKTP introduced a greater level of mathematical analysis. The company now has a great enthusiasm for applying similar approaches in a wide variety of situations, and are continuing to work with the Department.

As a result of this project, a new silencing strategy and a novel design methodology have been introduced to Dyson.

Federal Mogul

The University of Manchester was the first to develop a new method of nonlinear statistical analysis which can be used to design efficient product development experiments.

Global vehicle parts supplier, Federal-Mogul Friction Products, used this approach to reduce product testing by up to 88%, cut manufacturing time by 30%, and reduce variation in its braking products.

New brake pads developed using this research are supplied with a variety of mainstream and premium brand cars for sale across the world.


In 2010 we completed a KTA feasibility study into the revenue management of internet pre-booking systems.

We were also awarded a KTP grant to embed the capability to build revenue management systems inside Inventive existing technologies. Working specifically in the area of airport car park pre-booking, we hope to develop a commercial product over the coming years.

Mondel─ôz International

Mondel─ôz sponsor a PhD research project that aims to analyse the effect of vibration on the redistribution of chocolate in various manufacturing processes.

Molten chocolate is a non-Newtonian fluid, a fluid whose viscosity decreases with increasing shear rate. Subjecting chocolate to vibration while it settles into moulds (or while it spreads on surfaces, as in the manufacture of the famous Cadbury's Buttons) facilitates the flow of the chocolate. The PhD project employs a combination of theoretical, numerical and experimental work to characterise the constitutive properties of chocolate and to analyse how vibration affects its flow.

Numerical Algorithms Group (NAG) Ltd

The Numerical Algorithms Group (NAG) Ltd. has been a world leader in the development and distribution of numerical software for more than 40 years and collaborations with The University of Manchester go back to the company's inception.

The KTP project has provided the company with a world-leading capability in matrix functions [...] The outcomes from the project have exceeded all expectation.

Craig Lucas / Senior Technical Consultant, NAG

Over the years NAG have sponsored MSc and PhD students and NAG staff have held visiting positions in the Department.

Between 2010 and 2013, two Knowledge Transfer Partnerships (both partly government funded) funded full-time KTP Associates to translate algorithms developed in the Numerical Analysis Group at the Department of Mathematics into codes in the NAG Library.

Major current areas of collaboration are in functions of matrices and algorithms related to correlation matrices, the latter being of particular interest in the finance sector.

Rapiscan Systems

Using our imaging techniques, coupled with algorithms developed by the University’s mathematicians, Rapiscan was able to deliver the first baggage scanner (RTT80) capable of imaging luggage in 3D and in real-time. Whereas scanning often takes tens of minutes, reconstructing the data to form an image can take many hours and images require expert human judgement. Software has been developed capable of collecting data in 0.1 of a second, reconstructing it to form a 3D image and interpreting the image in terms of likely threats. It is now possible to scan and assesses at a rate of 1000s of bags per hour, providing Rapiscan with a competitive advantage.

Rapiscan already has several orders for its RTT80 systems. The University and Rapiscan won The Engineer Innovation and Technology Award 2010 for this work, and the project contributed to the University winning the Queen’s Anniversary Prize for Higher and Further Education in November 2013, for its work in imaging techniques to support advanced materials and manufacturing.