Mathematics of Random Systems: Analysis, Modelling and Algorithms (CDT)
About the course
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.
You will participate in a comprehensive doctoral training course in stochastic analysis, probability theory, stochastic modelling, computational methods and applications arising in biology, physics, quantitative finance, and data science. The course 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 the following foundation areas:
- Stochastic analysis: foundations and new directions
- Stochastic partial differential equations
- Stochastic computational methods and optimal control
and application areas:
- Randomness and universal behaviour in physical systems
- Stochastic modelling and data-driven modelling in finance
- Mathematical and algorithmic challenges in data science
- Mean-field models and agent-based modelling
In your first year, you will follow four courses matching your area of interest, and choose a main research topic and a research supervisor. This research project will then be expected to evolve into your DPhil thesis in years two to four.
Throughout the four years of the course, you will participate in various CDT activities, including CDT social events, 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 and finance 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.
The department offers extensive support to students, from 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.
Attendance
The course is full-time and requires attendance in Oxford. Full-time students are subject to the University's Residence requirements.
Provision exists for students on some courses to undertake their research in a ‘well-founded laboratory’ outside of the University. This may require travel to and attendance at a site that is not located in Oxford. Where known, existing collaborations will be outlined on this page. Please read the course information carefully, including the additional information about course fees and costs.
Resources to support your study
As a graduate student, you will have access to the University's wide range of world-class resources including libraries, museums, galleries, digital resources and IT services.
The Bodleian Libraries is the largest library system in the UK. It includes the main Bodleian Library and libraries across Oxford, including major research libraries and faculty, department and institute libraries. Together, the Libraries hold more than 13 million printed items, provide access to e-journals, and contain outstanding special collections including rare books and manuscripts, classical papyri, maps, music, art and printed ephemera.
The University's IT Services is available to all students to support with core university IT systems and tools, as well as many other services and facilities. IT Services also offers a range of IT learning courses for students, to support with learning and research.
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, you will be based in a cohort study room in the Andrew Wiles Building. In years two to four, you will be allocated an office that you will share with three or six other students.
You will have your 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.
Supervision
Research will be supervised by CDT faculty from the Mathematical Institute.
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.
You will have the opportunity to interact with your research supervisor through periodic meetings and participation in seminars and working groups throughout the duration of your doctoral studies.
Assessment
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. You will be required to acquire transferable skills as part of your training amounting to 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 two sets of classes before transfer of status and at least three 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.
Graduate destinations
After completion of the programme, graduates will be equipped to take up postdoctoral research opportunities in the UK and abroad 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 if a pandemic, epidemic or local health emergency occurs. 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.
For further information please see our page on changes to courses and the provisions of the student contract regarding changes to courses.
Entry requirements for entry in 2025-26
Proven and potential academic excellence
The requirements described below are specific to this course and apply only in the year of entry that is shown. You can use our interactive tool to help you evaluate whether your application is likely to be competitive.
We know that factors such as socio-economic circumstances and school performance can make it difficult for students to demonstrate their full potential. This course is taking part in an initiative to use contextual data to help us to better understand your achievements in the context of your individual background. For further details, please refer to the information about improving access to graduate study in the How to apply section of this page.
Please be aware that any studentships that are linked to this course may have different or additional requirements and you should read any studentship information carefully before applying. Contextual data may also be used in the assessment of studentships.
Degree-level qualifications
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 bachelor's degree from the USA, the minimum overall GPA that is normally required to meet the undergraduate-level requirement is 3.8 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) | 100 | Listening: 22 Reading: 24 Speaking: 25 Writing: 24 |
| C1 Advanced* | 185 | 176 |
| C2 Proficiency† | 185 | 176 |
*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.
References
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.
Supporting documents
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 will take place online via an online platform such as Teams.
It is expected that interviews will take place around three to five weeks after an application deadline.
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:
Financial Declaration
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)
This course may require you to obtain an ATAS certificate before you can apply for a visa/immigration permission. If you are offered a place, the academic department will confirm whether an ATAS certificate is required. If so, they will also send you the information you need to apply for one. You can apply for ATAS whilst your offer is conditional and before the Confirmation of Acceptance for Studies (CAS) is issued. Further information about ATAS is available on the student visa webpages.
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.
Mathematics
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 cover the spectrum of pure and applied mathematics with researchers working in fields including:
- algebra
- geometry
- topology
- logic
- number theory
- combinatorics
- analysis
- mathematical physics
- mathematical finance
- mathematical modelling
- mathematical biology networks
- numerical analysis.
The Mathematical Institute is proud to have received an Athena SWAN silver award renewal in 2021, reflecting its commitment to promoting diversity and to creating a working environment in which students and staff alike can achieve their full potential.
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 institute’s home is the purpose-built Andrew Wiles Building, opened in 2013. This provides ample teaching facilities for lectures, classes and seminars. The Mathematical Institute provides six lecture theatres and six classrooms.
Graduate students have access to the department common room, where members of the department regularly gather for coffee and other social occasions, and the mezzanine level of the Andrew Wiles Building houses a café and teaching spaces.
Funding
For entry in the 2025-26 academic year, the collegiate University expects to offer over 1,000 full or partial graduate scholarships across a wide range of graduate courses.
If you apply by the January deadline shown on this page and receive a course offer, your application will then be considered for Oxford scholarships. For the majority of Oxford scholarships, your application will automatically be assessed against the eligibility criteria, without needing to make a separate application. There are further Oxford scholarships available which have additional eligibility criteria and where you are required to submit a separate application. Most scholarships are awarded on the basis of academic merit and/or potential.
To ensure that you are considered for Oxford scholarships that require a separate application, for which you may be eligible, use our fees, funding and scholarship search tool to identify these opportunities and find out how to apply. Alongside Oxford scholarships, you should also consider other opportunities for which you may be eligible including a range of external funding, loan schemes for postgraduate study and any other scholarships which may also still be available after the January deadline as listed on our fees, funding and scholarship search tool.
Details of college-specific funding opportunities can also be found on individual college websites:
Please refer to the College preference section of this page to identify which of the colleges listed above accept students for this course.
For the majority of college scholarships, it doesn’t matter which college, if any, you state a preference for in your application. If another college is able to offer you a scholarship, your application can be moved to that college if you accept the scholarship. Some college scholarships may require you to state a preference for that college when you apply, so check the eligibility requirements carefully.
Further information about funding opportunities for this course can be found on the department's website.
Costs
Annual fees for entry in 2025-26
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.
Continuation charges
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.
Where can I find further information about fees?
The Fees and Funding section of this website provides further information about course fees, including information about fee status and eligibility and your length of fee liability.
Additional information
Living costs
In addition to your course fees and any additional course-specific costs, you will need to ensure that you have adequate funds to support your living costs for the duration of your course.
Living costs for full-time study
For the 2025-26 academic year, the range of likely living costs for a single, full-time student is between £1,425 and £2,035 for each month spent in Oxford. We provide the cost per month so you can multiply up by the number of months you expect to live in Oxford. Depending on your circumstances, you may also need to budget for the costs of a student visa and immigration health surcharge and/or living costs for family members or other dependants that you plan to bring with you to Oxford (assuming that dependant visa eligibility criteria are met).
Further information about living costs
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. For study in Oxford beyond the 2025-26 academic year, it is suggested that you budget for potential increases in living expenses of around 4% each year – although this rate may vary depending on the national economic situation. For further information, please consult our more detailed information about living costs, which includes a breakdown of likely living costs in Oxford for items such as food, accommodation and study costs.
College preference
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.
If you are a current Oxford student and you would like to remain at your current Oxford college, you should check whether it is listed below. If it is, you should indicate this preference when you apply. If not, you should contact your college office to ask whether they would be willing to make an exception. Further information about staying at your current college can be found in our Application Guide.
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 students on the Mathematics of Random Systems Analysis Modelling and Algorithms CDT:
Before you apply
Our guide to getting started provides general advice on how to prepare for and start your application. You can use our interactive tool to help you evaluate whether your application is likely to be competitive.
If it is important for you to have your application considered under a particular deadline – eg under the 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. Check the deadlines on this page and the information about deadlines and when to apply in our Application Guide.
Application fee waivers
An application fee of £20 is payable for each application to this course. 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.
Application fee waivers for eligible associated courses
If you apply to this course and up to two eligible courses during the same application cycle, you can request an application fee waiver so that you only need to pay one application fee. We recommend that you use your application fee waiver to apply only for eligible courses that are closely related in research area to this one.
To be considered eligible for an application fee waiver, each additional course must be:
- doctoral level eg a Doctor of Philosophy (DPhil) or Centre for Doctoral Training (CDT) course; and
- offered by one of the departments in the MPLS Division or one of the departments in the Medical Sciences Division.
If this is the first eligible course that you are applying to, you can request an application fee waiver for an additional course after you have submitted your application for this course. If you have already applied to another course that the meets the eligibility criteria shown above, you should request an application fee waiver before starting an application to this course.
Remember to state clearly in your request which course(s) you intend to apply to. If your request is successful, you will receive an application fee waiver code that is valid for this admission cycle (ie for entry in the 2025-26 academic year). Our Application Guide provides instructions for entering your application fee waiver code.
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.
Improving access to graduate study
This course is taking part in initiatives to improve the selection procedure for graduate applications, to ensure that all candidates are evaluated fairly.
Socio-economic data (where it has been provided in the application form) and your contextual statement (if you choose to provide one) will be used as part of an initiative to contextualise applications at the different stages of the selection process.
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).
Proposed supervisor
If known, under 'Proposed supervisor name' enter the name of the academic(s) whom you would like to supervise your research. Otherwise, leave this field blank.
Referees:
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.
Official transcript(s)
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.
Contextual statement
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.
Start or continue your application
You can start or return to an application using the relevant link below. As you complete the form, please refer to the requirements above and consult our Application Guide for advice.
After you've submitted your application
Your application (including the supporting documents outlined above) will be assessed against the entry requirements detailed on this course page. Whether or not you have secured funding will not be taken into consideration when your application is assessed. You can find out more about our shortlisting and selection process in our detailed guide to what happens next.
Find out how to manage your application after submission, using our Applicant Self-Service tool.