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The MAC-MIGS PhD Programme

A PhD with Integrated Study in Mathematical Modelling, Analysis and Computation

The PhD programme will provide a broad training that cuts across disciplinary boundaries to include mathematical analysis - pure, applied, numerical and stochastic - data-science and statistical techniques and the domain-specific advanced knowledge necessary for cutting-edge applications.

Students on this integrated degree will join the broader Maxwell Institute Graduate School in its Bayes Centre. They will benefit from dedicated academic training in subjects that include mathematical analysis, computational mathematics, multi-scale modelling, model reduction, Bayesian inference, uncertainty quantification, inverse problems and data assimilation, and machine learning; extensive experience of collaborative and interdisciplinary work through projects, modelling camps, industrial sandpits and internships;  outstanding early-career training, with a strong focus on entrepreneurship;  a dynamic and forward-looking community of mathematicians, scientists and engineers, sharing strong values of collaboration, respect, and social and scientific responsibility. 

The students trained on this programme will have expertise in a broad array of mathematical modelling techniques and of their application in multidisciplinary contexts as well as experience of industrial collaboration. Their skills will be highly valuable for all sectors of business and government as is reflected by our wide network of industry and agency partners covering manufacturing, energy, finance, healthcare, digital technologies, and environmental protection. Immediate benefits to these sectors will be realised through the projects carried out by the students in collaboration with these partners; long-term benefits will be achieved throughout the students' careers, as they take up leadership positions and influence the future of their sectors.

Industrial and agency partners who will provide internships, development programmes and research projects, and help maximise the impact of the students' work. Our collaborations with academic partners representing ten leading institutions in the US and Europe, will provide further opportunities for collaborations and research visits.

The students will integrate into a vibrant research environment, closely interacting with many academics drawn from the faculties of both Edinburgh and Heriot-Watt Universities.

Entry to the programme

Students are expected to have an undergraduate degree in mathematics or in an area of science or engineering.  Students with masters are also encouraged to apply.  If the first degree is not in mathematics, students are expected to have undertaken significant mathematical training during their studies. Because this is an integrated programme of study, second year entry would be exceptional and only considered in special circumstances.   This programme recruits worldwide, although as the programme is mostly funded by the UK government, most students must be UK-based.     MAC-MIGS is open to considering students who have funding from an external source (e.g. a government scholarship or arranged industry support).


First Year
All students are based in the Bayes Centre during their first year.  Students take around 180 credits of study, divided as follows:
• A 15 credit module on Computational Methods for Data-Driven Modelling
• A 15 credit module on Mathematical Modelling and Applied Analysis
• 60-70 units of additional approved coursework (typically at Master's level) from the Scottish Mathematical Sciences Training Centre, or the two universities, to be agreed with the Cohort Director
• A 15 credit Group Project
• A 15 credit Group Project on an industry or government-relevant theme
• A 60 credit Extended Invidual Project 

In addition, during the first year, students engage in a Modelling Camp, an Industrial Sandpit, training in and Presentation Skills.  Near the end of their first year, all students participate in the 3-day Residential Camp, held at The Burn, a large country house in the Scottish Highlands where they gain practice in presentation, hear science lectures and talks on responsible research and innovation, and learn about state of the art industrial challenges.

Years 2-4
In the second year, students are based in the same building as their supervisor, at one of the campuses of Edinburgh and Heriot-Watt Universities.  The work is focussed on the student's agreed research project, which is typically supervised by a team including staff from both Edinburgh and Heriot-Watt Universities.   Students are expected to take around 20 credits of academic coursework in each year.  They are also required to participate in MAC-MIGS Skills and Citizenship courses which provide training in responsible research and innovation, equality, diversity and inclusion, project and time management, and other important topics. They also obtain specific instruction in Entrepreneurship.

Students return frequently to the Bayes Centre throughout their studies, for cohort activites, for seminars, for research group meetings and study groups, and to attend workshops at ICMS.