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:
- Stochastic analysis: foundations and new directions
- Stochastic partial differential equations
- Random combinatorial structures: trees, graphs, networks, branching processes
- Stochastic computational methods and optimal control
- Random dynamical systems and ergodic theory
and five application areas:
- Randomness and universal behaviour in physical systems
- Stochastic modelling and data-driven modelling in finance
- Mathematical modelling in biology and healthcare
- Mathematical and algorithmic challenges in data science
- 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. It is not a requirement to contact potential supervisors prior to applying to the CDT. CDT students choose their research project and supervisor by the end of their first term, but you can indicate a preference to work with a CDT faculty member at the time of application if you have one.
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 five days of training prior to transfer of status. Students who are successful at transfer will also be expected to apply for and gain confirmation of DPhil status within nine terms of admission, to verify that their 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, 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.
Entry requirements for entry in 2024-25
Proven and potential academic excellence
As a minimum, applicants should hold or be predicted to achieve the following UK qualifications or their equivalent:
- 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.
English language proficiency
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.
Declaring extenuating circumstances
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.
You will need to register three referees who can give an informed view of your academic ability and suitability for the course. The How to apply section of this page provides details of the types of reference that are required in support of your application for this course and how these will be assessed.
You will be required to supply supporting documents with your application. The How to apply section of this page provides details of the supporting documents that are required as part of your application for this course 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, by telephone or video link such as Teams.
It is expected that interviews will take place around three to five weeks after an application deadline.
How your application is assessed
Your application will be assessed purely on your proven and potential academic excellence and other entry requirements published under that heading.
References and supporting documents submitted as part of your application, and your performance at interview (if interviews are held) will be considered as part of the assessment process. Whether or not you have secured funding will not be taken into consideration when your application is assessed.
An overview of the shortlisting and selection process is provided below. Our 'After you apply' pages provide more information about how applications are assessed.
Shortlisting and selection
Students are considered for shortlisting and selected for admission without regard to age, disability, gender reassignment, marital or civil partnership status, pregnancy and maternity, race (including colour, nationality and ethnic or national origins), religion or belief (including lack of belief), sex, sexual orientation, as well as other relevant circumstances including parental or caring responsibilities or social background. However, please note the following:
- socio-economic information may be taken into account in the selection of applicants and award of scholarships for courses that are part of the University’s pilot selection procedure and for scholarships aimed at under-represented groups;
- country of ordinary residence may be taken into account in the awarding of certain scholarships; and
- protected characteristics may be taken into account during shortlisting for interview or the award of scholarships where the University has approved a positive action case under the Equality Act 2010.
Initiatives to improve access to graduate study
This course is taking part in a continuing pilot programme to improve the selection procedure for graduate applications, in order to ensure that all candidates are evaluated fairly.
For this course, socio-economic data (where it has been provided in the application form) will be used to contextualise applications at the different stages of the selection process. Further information about how we use your socio-economic data can be found in our page about initiatives to improve access to graduate study.
If you wish, you may submit an additional contextual statement (using the instructions in the How to apply section of this page) to provide further information on your socio-economic background or personal circumstances in support of your application. Further information about how your contextual statement will be used can be found in our page about initiatives to improve access to graduate study.
Processing your data for shortlisting and selection
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.
Other factors governing whether places can be offered
The following factors will also govern whether candidates can be offered places:
- the ability of the University to provide the appropriate supervision for your studies, as outlined under the 'Supervision' heading in the About section of this page;
- the ability of the University to provide appropriate support for your studies (eg through the provision of facilities, resources, teaching and/or research opportunities); and
- minimum and maximum limits to the numbers of students who may be admitted to the University's taught and research programmes.
Offer conditions for successful applications
If you receive an offer of a place at Oxford, your offer will outline any conditions that you need to satisfy and any actions you need to take, together with any associated deadlines. These may include academic conditions, such as achieving a specific final grade in your current degree course. These conditions will usually depend on your individual academic circumstances and may vary between applicants. Our 'After you apply' pages provide more information about offers and conditions.
In addition to any academic conditions which are set, you will also 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 Student visa (under the Student Route). 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.
Mathematics has been studied in Oxford since the University was first established in the 12th century. The Mathematical Institute aims to preserve and expand mathematical culture through excellence in teaching and research.
The Mathematical Institute offers a wide range of graduate courses, including both taught master’s courses and research degrees. Research and teaching covers the spectrum of pure and applied mathematics with researchers working in fields including:
- number theory
- mathematical physics
- mathematical finance
- mathematical modelling
- mathematical biology
- numerical analysis.
Graduate students are an integral part of the department, interacting with each other and with academic staff as part of a vibrant community that strives to further mathematical study. As a graduate student at Oxford you will benefit from excellent resources, extensive training opportunities and supportive guidance from your supervisor or course director.
The Mathematical Institute has strong ties with other University departments including Computer Science, Statistics and Physics, teaching several courses jointly. Strong links with industrial and other partners are also central to the department.
The University expects to be able to offer over 1,000 full or partial graduate scholarships across the collegiate University in 2024-25. 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 any college-specific funding opportunities using the links provided on our college pages or below:
Please note that not all the colleges listed above may accept students on this course. For details of those which do, please refer to the College preference section of this page.
Further information about funding opportunities for this course can be found on the department's website.
Annual fees for entry in 2024-25
Annual Course fees
Further details about fee status eligibility can be found on the fee status webpage.
Information about course fees
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.
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 2024-25 academic year, the range of likely living costs for full-time study is between c. £1,345 and £1,955 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. The current economic climate and high national rate of inflation make it very hard to estimate potential changes to the cost of living over the next few years. When planning your finances for any future years of study in Oxford beyond 2024-25, it is suggested that you allow for potential increases in living expenses of around 5% each year – although this rate may vary depending on the national economic situation. UK inflationary increases will be kept under review and this page updated.
Students enrolled on this course will belong to both a department/faculty and a college. Please note that ‘college’ and ‘colleges’ refers to all 43 of the University’s colleges, including those designated as societies and permanent private halls (PPHs).
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. Before deciding, we suggest that you read our brief introduction to the college system at Oxford and our advice about expressing a college preference. For some courses, the department may have provided some additional advice below to help you decide.
You are encouraged to state no college preference when you apply in order to allow the CDT to assign your application to an appropriate college if you are accepted.
The following colleges accept student on the Mathematics of Random Systems CDT:
Before you apply
Our guide to getting started provides general advice on how to prepare for and start your application. Check the deadlines on this page and the information about deadlines in our Application Guide. If it's important for you to have your application considered under a particular deadline – eg under a December or January deadline in order to be considered for Oxford scholarships – we recommend that you aim to complete and submit your application at least two weeks in advance.
Application fee waivers
An application fee of £75 is payable per course application. Application fee waivers are available for the following applicants who meet the eligibility criteria:
- applicants from low-income countries;
- refugees and displaced persons;
- UK applicants from low-income backgrounds; and
- applicants who applied for our Graduate Access Programmes in the past two years and met the eligibility criteria.
You are encouraged to check whether you're eligible for an application fee waiver before you apply.
Readmission for current Oxford graduate taught students
If you're currently studying for an Oxford graduate taught course and apply to this course with no break in your studies, you may be eligible to apply to this course as a readmission applicant. The application fee will be waived for an eligible application of this type. Check whether you're eligible to apply for readmission.
Do I need to contact anyone before I apply?
You do not need to make contact with the department before you apply but you are encouraged to visit the relevant departmental webpages to read any further information about your chosen course.
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.
Completing your application
You should refer to the information below when completing the application form, paying attention to the specific requirements for the supporting documents.
For this course, the application form will include questions that collect information that would usually be included in a CV/résumé. You should not upload a separate document. If a separate CV/résumé is uploaded, it will be removed from your application.
If any document does not meet the specification, including the stipulated word count, your application may be considered incomplete and not assessed by the academic department. Expand each section to show further details.
Proposed field and title of research project
Under the 'Field and title of research project' please enter your proposed field or area of research if this is known. If the department has advertised a specific research project that you would like to be considered for, please enter the project title here instead.
You should not use this field to type out a full research proposal. You will be able to upload your research supporting materials separately if they are required (as described below).
If known, under 'Proposed supervisor name' enter the name of the academic(s) who you would like to supervise your research. Otherwise, leave this field blank.
Three overall, academic preferred
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.
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.
If you wish to provide a contextual statement with your application, you may also submit an additional statement to provide contextual information on your socio-economic background or personal circumstances in support of your application.
It is not necessary to anonymise this document, as we recognise that it may be necessary for you to disclose certain information in your statement. This statement will not be used as part of the initial academic assessment of applications at shortlisting, but may be used in combination with socio-economic data to provide contextual information during decision-making processes.
Please note, this statement is in addition to completing the 'Extenuating circumstances’ section of the standard application form.
You can find more information about the contextual statement on our page that provides details of the continuing pilot programme to improve the assessment procedure for graduate applications.
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.