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The programme

The CDT in Mathematics of Random Systems is a partnership between three world-class departments in the area of probabilistic modelling, stochastic analysis and their applications: the Oxford Mathematical Institute, the Oxford Department of Statistics and the Department of Mathematics at Imperial College London. It aims to train the next generation of academic and industry experts in stochastic modelling, advanced computational methods and data science.

The CDT offers a 4-year comprehensive training programme at the frontier of scientific research in probability, stochastic analysis, stochastic modelling, stochastic computational methods as well as applications in physics, mathematical finance, biology, healthcare and data science. 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 PhD thesis in years two to four.

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.

Course structure: 4-year PhD programme focused on research

Year 1

Term 1: Students follow mandatory coursework involving

Foundations: (2 weeks in Oxford, Sept -Oct)

  • Foundations of Stochastic Analysis

8 hours  Prof. Ben Hambly (University of Oxford)

  • Foundations of Data Science

16 hours  Prof. Mihai Cucuringu (University of Oxford)

  • Function Spaces and Distribution Theory

8 hours  Prof. GuiQiang Chen (University of Oxford)

  • Tutorials in Stochastic analysis and Data Science

Dr Renyuan Xu (Univerity of Oxford)

Four advanced core courses in Term 1 at Oxford and Imperial (Oct-Dec):


Advanced Topics in Stochastic Analysis

Dr Andreas Sojmark 
(Imperial College London)

Advanced Topics in Data Science: Deep Learning

 Prof Jared Tanner  
(University of Oxford)

Advanced topics in Stochastic Processes

Prof. Xue-Mei Li  
(Imperial College London)


Simulation Methods and Stochastic Algorithms

Prof. Mike Giles  
(University of Oxford)

Course structure: 4-year PhD programme focused on research

Year 1

Term 1

Four 8-hour introductory courses in the first 2 weeks:
  • Foundations of Stochastic Analysis
  • Foundations of Data Science
  • Function spaces and Distributions
  • Programming in Python
Four advanced Core courses in Term 1 (Oct-Dec):
  • Advanced topics in Stochastic Analysis
  • Advanced Topics in Data Science: Deep Learning
  • Foundations of Stochastic Analysis
  • Simulation methods and stochastic algorithms

The Term 1 courses are followed by 2 elective courses at Oxford or Imperial College London.

Term 2

Supervised research project

Students begin work on research with their supervisors by January. View a list of supervisors associated with the CDT. After the end of the Spring term students will attend a Spring Retreat where they will present their work.

Term 3

Term 3 will begin with an intensive group project for two weeks. Students will continue working on their projects and will submit by the end of August. There will be also a CDT annual Summer School in which all students will participate.

Years 2, 3 & 4

Supervised research culminating in a PhD thesis.


Centre staff

CDT Director

CDT co-directors

Management Committee members



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

Find out more about funding opportunities >>


 You must apply to Imperial if your intended main supervisor is based at Imperial

In your application:

  • Applications should be submitted to the programme: PhD in Mathematics of Random Systems - G1ZR.

  • Two referees email address (at least one academic) - we cannot accept private email addresses such as Gmail, Yahoo, Hotmail, etc. They must be academic/professional email addresses.

Click here to go to the general Imperial College application guidance pages


Minimum Entry Requirements

Academic requirements:

  • Masters qualification & (2:1) good upper-second honours* Bachelor's degree in Mathematics, Physics or other related subjects


  • (2:1) good upper-second honours* in a 4-year undergraduate degree with integrated master's

*see country index for equivalence



Applicants meeting the selection criteria will be invited for an interview, either in person or via Skype. Successful applicants will receive funding for the duration of their 4-year studentship.

English language requirement

All Imperial applicants must also show that they have a sufficient  level of written and spoken English to meet the demands of our challenging academic environment.

Find out more about our English language requirements for postgraduate study.

Please note that there are no deadline when applying at Imperial

 The CDT is between Imperial College London and the University of Oxford, but candidates must make separate applications to both institutions if they wish their application to be considered in both places.


Contact us

For more information on the CDT or the application process please contact us: Lydia.noa@imperial.ac.uk