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Mathematics of Random Systems: Analysis, Models and Algorithms (EPSRC CDT) Doctoral Programme

Mathematics of Random Systems: Analysis, Models and Algorithms (EPSRC CDT) Doctoral Programme

Key information

Qualification type

Doctoral Programme

Subject areas

Mathematics (General) Craft Design & Technology Systems Analysis Algorithms

Course type


Course Summary

The Centre for Doctoral Training (CDT) in Mathematics of Random Systems is a four-year doctoral programme that offers academically outstanding students training in the areas of probabilistic modelling and stochastic analysis at Imperial and Oxford.

The Mathematics of Random Systems CDT offers a comprehensive four-year doctoral training course in stochastic analysis, probability theory, stochastic modelling, computational methods and applications arising in biology, physics, quantitative finance, healthcare and data science. It provides solid training in core skills related to probability theory, stochastic modelling, data analysis, stochastic simulation, optimal control and probabilistic algorithms.

Research topics focus on five Foundation areas:

1. Stochastic analysis: foundations and new directions
2. Stochastic partial differential equations
3. Random combinatorial structures: trees, graphs, networks, branching processes
4. Stochastic computational methods and optimal control
5. Random dynamical systems and ergodic theory

and five application areas:

6. Randomness and universal behaviour in physical systems
7. Stochastic modelling and data-driven modelling in finance
8. Mathematical modelling in biology and healthcare
9. Mathematical and algorithmic challenges in data science
10. Mean-field models and agent-based modelling

In the first year, students follow four Core courses on Foundation areas and three elective courses, and choose a main research topic and a research supervisor. This research project will then be expected to evolve into a DPhil thesis in years two to four. Progress will be assessed at approximately 15 months (transfer of status) and after 39 months (confirmation of status). These assessments involve the submission of written work and an oral examination.

Throughout the four years of the course, students will participate in various CDT activities with their cohort, including a CDT spring retreat, the annual summer school as well as regular seminars, workshops and training in transferrable skills such as communication, ethics and team-working.

The CDT has multiple industry partners in the areas of data analytics, finance and healthcare who provide funding for DPhil projects linked to their areas of activity. Candidates with an interest in industry-related research projects are encouraged to apply. Industry-funded DPhil projects provide students with the opportunity to actively engage with our industry partners through collaborative research.

Different course options

Study mode

Full time


4 years

Start date


Tuition fees

UK fees
Course fees for UK / EU students

For this course (per year)


Average for all Postgrad courses (per year)


International fees
Course fees for non-UK / EU students

For this course (per year)


Average for all Postgrad courses (per year)


Entry requirements

As a minimum, applicants should hold or be predicted to achieve the equivalent of the following UK qualifications: a first-class undergraduate degree with honours in mathematics or a related discipline. A previous master's degree is not required, although the requirement for a first-class undergraduate degree with honours may be alternatively demonstrated by strong performance in a master's degree. For applicants with a degree from the USA, the minimum GPA sought is 3.7 out of 4.0.