Mathematics of Random Systems: Analysis, Modelling and Algorithms (CDT)

The course is full-time and requires attendance in Oxford. Full-time students are subject to the University's residency 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.

As a graduate student, you will have access to the University's wide range of 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, as well as guidance on what technology to bring with you as a new student at Oxford.

The number of places and average number of applicants for this course are shown below. For a breakdown of admission statistics by department, please refer to our published graduate admissions statistics.

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.

The requirements described below are specific to this course and apply only in the year of entry that is shown. You can use our guidance to help you evaluate whether your application is likely to be competitive.

We know that contextual factors can make it difficult for candidates 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:

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.

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.

^*Changes to the TOEFL iBT test are being introduced on 21 January 2026. The University will not accept TOEFL tests taken from that date to meet the English language condition until a review of the revised test has been completed. Our Application Guide provides full details of the tests we accept.

^†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 Completing your application 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 Completing your application 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.

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.

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 'Supervision' in the Course details 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.

Details of college-specific funding opportunities can also be found on many individual college websites. To access this information, first select a college from the list of colleges that accept students for this course. Next, navigate to the Contact details section of the college page, where a direct link to the college's funding information will usually be provided. 

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.

Fees for the 2026-27 academic year at the University of Oxford

The fees for this course are charged on an annual basis.

What do course fees cover?

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 costs information below.

How long do I need to pay 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 fees will usually increase annually, as explained in the University’s Terms and Conditions.

Graduate students who have reached the end of their standard period of fee liability will be required to pay a University continuation charge and/or a college continuation charge.

The University continuation charge, per term for entry in 2026-27 is £656, please be aware that this will increase annually. For part-time students, the termly charge will be half of the termly rate payable by full-time students.

If a college continuation charge applies (not applicable for non-matriculated courses) it will be between £150 and £500, as explained in our information about continuation charges. Please contact your college for more details, including information about whether your college's continuation charge is applied at a different rate for part-time study.

Where can I find more information about fees?

Our fees and other charges pages provide further information, including details about:

• course fees and fee liability;
• how your fee status is determined;
• changes to fees and other charges; and
• continuation charges.

Information about how much fees and other costs will usually increase each academic year is set out in the University's Terms and Conditions.

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 2026-27 academic year, the range of likely living costs for a single, full-time student is between £1,405 and £2,105 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 (if dependant visa eligibility criteria are met).

Further information about living costs

The current economic climate and periods of high national inflation in recent years make it harder to estimate potential changes to the cost of living over the next few years. For study in Oxford beyond the 2026-27 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.

A breakdown of likely living costs for one month during the 2026-27 academic year are shown below. These costs are based on a single, full-time graduate student, with no dependants, living in Oxford.

For information about how these figures have been calculated as well as tables showing the likely living costs for nine and twelve months, please refer to the living costs page of our website.

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. 

Our guide to getting started provides general advice on how to prepare for and start your application, including advice 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.

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.

Please refer to our guidance on how to identify eligible courses offered by MPLS and Medical Sciences departments.

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 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 2026-27 academic year). Our Application Guide provides instructions for entering your application fee waiver code.

You do not need to contact the department before you apply but you are encouraged to visit the relevant departmental webpages to read any further information about your chosen course.

This course is taking part in initiatives to improve the selection procedure for graduate applications, to ensure that all candidates are assessed fairly.

Contextual 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.

You can start or return to an application using the Apply button on this page. As you complete the form, please refer to the requirements in the Completing your application section and consult our Application Guide for advice.

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.

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) whom you would like to supervise your research. Otherwise, leave this field blank.

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 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.

The course is currently closed to applications and it is not possible to submit a contextual statement. 

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.

If possible, please ensure that the word count is clearly displayed on the document.

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.

Advice about contacting the department can be found in the Before you apply section of this page.

Help and guidance on your application is available from our comprehensive Application Guide.