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.
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.
Research will be supervised by CDT faculty from the Mathematical Institute or the Department of Statistics. A list of supervisors may be found on the CDT website. The allocation of graduate supervision for this course is the responsibility of the Mathematical Institute and it is not always possible to accommodate the preferences of incoming graduate students to work with a particular member of staff. Students interact with their research supervisor through periodic meetings and participation in seminars and working groups throughout the duration of their doctoral studies.
The outcome of the research project will be presented in the form of a doctoral thesis which, if successfully defended, will lead to the award of the DPhil degree.
Students will be initially admitted to the status of Probationer Research Student (PRS). Within around 15 months of your course starting you will be expected to apply for transfer of status from Probationer Research Student to DPhil status.
A successful transfer of status from PRS to DPhil status will require completion of assessed work to a satisfactory level for the four core and three elective courses. You will be required to acquire transferable skills as part of your training and to complete six days of training prior to transfer of status. Students who are successful at transfer will also need to apply for and gain confirmation of DPhil status within around 39 months of admission, to show that your work continues to be on track.
Both milestones involve submission of written work and an interview with two assessors (other than your supervisor) and therefore provide important experience for the final oral examination.
You will be expected to teach at least one set of classes before transfer of status and at least two additional sets before confirmation of status.
You will be expected to submit an original thesis after three or, at most, four years from the date of admission. To be successfully awarded a DPhil in Mathematics you will need to defend your thesis orally (viva voce) in front of two appointed examiners.
The CDT in Mathematics of Random Systems will aim to provide postdoctoral research opportunities in the UK and abroad through the CDT's international network of academic partners, as well as industry placement opportunities through our numerous industry partners.
Changes to this course and your supervision
The University will seek to deliver this course in accordance with the description set out in this course page. However, there may be situations in which it is desirable or necessary for the University to make changes in course provision, either before or after registration. The safety of students, staff and visitors is paramount and major changes to delivery or services may have to be made in circumstances of a pandemic (including Covid-19), epidemic or local health emergency. In addition, in certain circumstances, for example due to visa difficulties or because the health needs of students cannot be met, it may be necessary to make adjustments to course requirements for international study.
Where possible your academic supervisor will not change for the duration of your course. However, it may be necessary to assign a new academic supervisor during the course of study or before registration for reasons which might include illness, sabbatical leave, parental leave or change in employment.
Other courses you may wish to consider
If you're thinking about applying for this course, you may also wish to consider the courses listed below. These courses may have been suggested due to their similarity with this course, or because they are offered by the same department or faculty.
All graduate courses offered by the Mathematical Institute
Other courses suggested by the department
Entry requirements for entry in 2022-23
Proven and potential academic excellence
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.
If your degree is not from the UK or another country specified above, visit our International Qualifications page for guidance on the qualifications and grades that would usually be considered to meet the University’s minimum entry requirements.
GRE General Test scores
No Graduate Record Examination (GRE) or GMAT scores are sought.
Other qualifications, evidence of excellence and relevant experience
- Research experience in the proposed research area may be an advantage.
- Publications are not expected.
If your ability to meet the entry requirements has been affected by the COVID-19 pandemic (eg you were awarded an unclassified/ungraded degree) or any other exceptional personal circumstance (eg other illness or bereavement), please refer to the guidance on extenuating circumstances in the Application Guide for information about how to declare this so that your application can be considered appropriately.
English language requirement
This course requires proficiency in English at the University's standard level. If your first language is not English, you may need to provide evidence that you meet this requirement. The minimum scores required to meet the University's standard level are detailed in the table below.
|Test||Minimum overall score||Minimum score per component|
|IELTS Academic (Institution code: 0713)||7.0||6.5|
TOEFL iBT, including the 'Home Edition'
(Institution code: 0490)
*Previously known as the Cambridge Certificate of Advanced English or Cambridge English: Advanced (CAE)
†Previously known as the Cambridge Certificate of Proficiency in English or Cambridge English: Proficiency (CPE)
Your test must have been taken no more than two years before the start date of your course. Our Application Guide provides further information about the English language test requirement.
You will be required to supply supporting documents with your application, including references and an official transcript. See 'How to apply' for instructions on the documents you will need and how these will be assessed.
Performance at interview
Technical interviews are normally held as part of the admissions process.
If invited you can expect to be interviewed by at least two people and for the interview to last around 30 minutes. The interview may take place face-to-face or by telephone or Skype.
It is expected that interviews will take place around three to five weeks after an application deadline.
Any offer of a place is dependent on the University’s ability to provide the appropriate supervision for your chosen area of work. Please refer to the ‘About’ section of this page for more information about the provision of supervision for this course.
How your application is assessed
Your application will be assessed purely on academic merit and potential, according to the published entry requirements for the course. The After you apply section of this website provides further information about the academic assessment of your application, including the potential outcomes. Please note that any offer of a place may be subject to academic conditions, such as achieving a specific final grade in your current degree course. These conditions may vary depending upon your individual academic circumstances.
Students are considered for shortlisting and selected for admission without regard to gender, marital or civil partnership status, disability, race, nationality, ethnic origin, religion or belief, sexual orientation, age or social background. Whether you have secured funding will not be taken into consideration when your application is assessed.
Admissions panels and assessors
All recommendations to admit a student involve the judgement of at least two members of the academic staff with relevant experience and expertise, and must also be approved by the Director of Graduate Studies or Admissions Committee (or equivalent within the department).
Admissions panels or committees will always include at least one member of academic staff who has undertaken appropriate training.
After an offer is made
If you receive an offer of a place at Oxford, your offer letter will give full details of your offer and any academic conditions, such as achieving a specific final grade in your current degree course. In addition to any academic conditions which are set, you will be required to meet the following requirements:
If you are offered a place, you will be required to complete a Financial Declaration in order to meet your financial condition of admission.
Disclosure of criminal convictions
In accordance with the University’s obligations towards students and staff, we will ask you to declare any relevant, unspent criminal convictions before you can take up a place at Oxford.
Academic Technology Approval Scheme (ATAS)
Some postgraduate research students in science, engineering and technology subjects will need an Academic Technology Approval Scheme (ATAS) certificate prior to applying for a Tier 4 visa. Further information can be found on our Tier 4 (General) Student visa page. For some courses, the requirement to apply for an ATAS certificate may depend on your research area.
The home of the Mathematical Institute is the purpose-built Andrew Wiles Building, opened in 2013. This provides ample teaching facilities for lectures, classes and seminars. In year one, students are based in a cohort study room in the Andrew Wiles Building. In years two to four, each student is allocated an office that they will share with three or six other students. Each student has their own desk with a computer. The Mathematical Institute provides IT support, and students can use the department's Whitehead Library, with an extensive range of books and journals. Students will be expected to travel to visit Imperial College London, and travel costs will be covered by the CDT. At Imperial students will be provided access to library facilities and to a dedicated working space where "hot-desks" will be available.
In addition to the common room, where graduate students regularly gather for coffee and other social occasions, there is also a café in the Andrew Wiles Building.
The department offers extensive support to students, from regular skills training and career development sessions to a variety of social events in a welcoming and inclusive atmosphere. You will have the opportunity to interact with fellow students and other members of your research groups, and more widely across the department. The department aims to offer excellent supervision and provide a stimulating research environment.
The University expects to be able to offer around 1,000 full or partial graduate scholarships across the collegiate University in 2022-23. You will be automatically considered for the majority of Oxford scholarships, if you fulfil the eligibility criteria and submit your graduate application by the relevant December or January deadline. Most scholarships are awarded on the basis of academic merit and/or potential.
For further details about searching for funding as a graduate student visit our dedicated Funding pages, which contain information about how to apply for Oxford scholarships requiring an additional application, details of external funding, loan schemes and other funding sources. Please ensure that you visit individual college websites for details of college-specific funding opportunities using the links provided on our college pages.
Further information about funding opportunities for this course can be found on the department's website.
Annual fees for entry in 2022-23
Annual Course fees
Further details about fee status eligibility can be found on the fee status webpage.
Course fees are payable each year, for the duration of your fee liability (your fee liability is the length of time for which you are required to pay course fees). For courses lasting longer than one year, please be aware that fees will usually increase annually. For details, please see our guidance on changes to fees and charges.
Course fees cover your teaching as well as other academic services and facilities provided to support your studies. Unless specified in the additional information section below, course fees do not cover your accommodation, residential costs or other living costs. They also don’t cover any additional costs and charges that are outlined in the additional information below.
Following the period of fee liability, you may also be required to pay a University continuation charge and a college continuation charge. The University and college continuation charges are shown on the Continuation charges page.
There are no compulsory elements of this course that entail additional costs beyond fees (or, after fee liability ends, continuation charges) and living costs. However, please note that, depending on your choice of research topic and the research required to complete it, you may incur additional expenses, such as travel expenses, research expenses, and field trips. You will need to meet these additional costs, although you may be able to apply for small grants from your department and/or college to help you cover some of these expenses.
In addition to your course fees, you will need to ensure that you have adequate funds to support your living costs for the duration of your course.
For the 2022-23 academic year, the range of likely living costs for full-time study is between c. £1,215 and £1,755 for each month spent in Oxford. Full information, including a breakdown of likely living costs in Oxford for items such as food, accommodation and study costs, is available on our living costs page. When planning your finances for any future years of study in Oxford beyond 2022-23, you should allow for an estimated increase in living expenses of 3% each year.
All graduate students at Oxford belong to a department or faculty and a college or hall (except those taking non-matriculated courses). If you apply for a place on this course you will have the option to express a preference for one of the colleges listed below, or you can ask us to find a college for you. The Colleges section of this website provides information about the college system at Oxford, as well as factors you may wish to consider when deciding whether to express a college preference. Please note that ‘college’ and ‘colleges’ refers to all 45 of the University’s colleges, including those designated as Permanent Private Halls (PPHs).
For some courses, the department or faculty may have provided some additional advice below to help you to decide. Whatever you decide, it won’t affect how the academic department assesses your application and whether they decide to make you an offer. If your department makes you an offer of a place, you’re guaranteed a place at one of our colleges.
The following colleges accept student on the Mathematics of Random Systems CDT:
How to apply
You are welcome to contact academics involved in their preferred area of research, although this is not a necessary prerequisite to the application process. If you are unsure of who to contact, please use the contact details provided on this page and your email will be forwarded onto the relevant academic.
The set of documents you should send with your application to this course comprises the following:
Your transcripts should give detailed information of the individual grades received in your university-level qualifications to date. You should only upload official documents issued by your institution and any transcript not in English should be accompanied by a certified translation.
More information about the transcript requirement is available in the Application Guide.
A CV/résumé is compulsory for all applications. Most applicants choose to submit a document of one to two pages highlighting their academic achievements and any relevant professional experience.
Statement of purpose/personal statement:
A maximum of 1,000 words
Your statement should be written in English and explain your motivation for applying for the course at Oxford, your relevant experience and education, and the specific areas that interest you and/or you intend to specialise in.
If possible, please ensure that the word count is clearly displayed on the document.
This will be assessed for evidence of motivation for and understanding of the proposed area of study and whether a suitable supervisor can be provided.
References/letters of recommendation:
Three overall, generally academic
Whilst you must register three referees, the department may start the assessment of your application if two of the three references are submitted by the course deadline and your application is otherwise complete. Please note that you may still be required to ensure your third referee supplies a reference for consideration.
Your references should generally be academic, though up to one professional reference will be accepted.
Your references will support intellectual ability, academic achievement, motivation and your ability to work in a group.
Start or continue an application
Step 1: Read our guide to getting started, which explains how to prepare for and start an application.
Step 2: Check that you meet the Entry requirements and read the How to apply information on this page.
Step 3: Check the deadlines on this page and the deadline information in our Application Guide. Plan your time to submit your application well in advance - we recommend two or three weeks earlier.
Step 4: Check if you're eligible for an application fee waiver. Application fee waivers are available for:
- UK applicants from low-income backgrounds who meet the eligibility criteria;
- residents in a country listed as low-income by the World Bank (refer to the eligibility criteria);
- current Oxford graduate taught students applying for readmission to an eligible course; and
- additional applications to selected research courses that are closely related to your first application.
Step 5: Start your application using the relevant link below. As you complete the form, consult our Application Guide for advice at each stage. You'll find the answers to most common queries in our FAQs.