MSc in Mathematics and Foundations of Computer Science
About the course
The MSc in Mathematics and Foundations of Computer Science, run by the Mathematical Institute and the Department of Computer Science, is a taught, full-time course focusing on the interface between pure mathematics and theoretical computer science.
The course is suitable for those who wish to pursue research in pure mathematics (especially algebra, number theory, combinatorics, general topology and their computational aspects), mathematical logic, or theoretical computer science. It is also suitable for students wishing to enter industry with an understanding of mathematical and logical design and concurrency.
The mathematical side of the course concentrates on areas where computers are used, or which are relevant to computer science, namely algebra, general topology, number theory, combinatorics and logic.
Examples from the computing side include computational complexity, concurrency, computational learning theory, and quantum computing.
It is intended that a major feature of this course is that you should gain a broad knowledge and understanding over a wide range of material.
Course structure
An overview of the course structure is provided below. Details of the optional elements of the course are provided in the Course components section of this page.
You will take a minimum of five optional lecture courses from across the two departments, usually representing around 16 hours of lectures and associated classes. The lecture courses will be divided into schedule I (basic) and schedule II (advanced). The majority of lecture courses will be given in the first two terms.
You will write a dissertation on a topic related to the course material during the third term and the summer.
Attendance
The course is full-time and requires attendance in Oxford. Full-time students are subject to the University's Residence requirements.
The course runs from the beginning of October through to the end of September, including the dissertation. Apart from the dissertation, around 75% of the course comprises taught content and 25% is self-directed learning.
Resources to support your study
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 Mathematical Institute provides IT support and the department's Whitehead Library, where students will find an extensive range of books and journals. A shared study room with desktop computers is located in the Mathematical Institute for MSc in Mathematics and Foundations of Computer Science students.
Graduate students have access to the department common room, where graduate students regularly gather for coffee and other social occasions and the mezzanine level of the Andrew Wiles Building houses a café and teaching spaces.
The Department of Computer Science Library contains books, monographic series, journals, technical reports and past theses covering the main research interests of the department. It is principally for use by graduate students and staff. The department has kitchens on each floor and a central common room where you can meet informally. There is an active social committee organising events for staff, students and families.
Supervision
The allocation of graduate supervision for this course is the responsibility of the Mathematical Institute and/or the Department of Computer Science and it is not always possible to accommodate the preferences of incoming graduate students to work with a particular member of staff. Under exceptional circumstances a supervisor may be found outside the Mathematical Institute and/or the Department of Computer Science.
You will be assigned an initial supervisor on arrival in Oxford whose role is to act as an academic during the course. When you start work on your dissertation, you will find a dissertation supervisor, who is usually not the same as your initial supervisor. Students typically have around eight meetings with their dissertation supervisor, mainly during Trinity term, but possibly continuing into July. The exact arrangements are made mutually.
Assessment
Each lecture course taken from the course option list will receive an assessment upon its completion by means of a take-home assessment (mini-project), taken between terms.
You will be required to pass five option courses, including at least two taken from the schedule II level.
It is possible, with the permission of the Course Director, to substitute one written assignment with an appropriate course of study from outside the published list which need not be examined by written assignment. For example, you may request permission to take a course assessed by examination, in place of one mini-project.
During Trinity term and over the summer, you will complete a dissertation on a topic agreed with your supervisor. The dissertation must be related to the course material.
You will be required to submit your dissertation proposals early in Trinity term. The dissertation submission date is around the beginning of September. The dissertation will be marked by your supervisor as well as a second marker, and the final mark will be based on their reports as well as a short compulsory viva, which is expected to take place in September.
Graduate destinations
Graduates typically pursue careers in academia or the technology sector. Quite a high proportion of students on the course are interested in continuing study at research degree level.
Changes to this course
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.
Course components
Compulsory study
The course includes a compulsory dissertation on a topic related to the course material.
Options
You will take a minimum of five optional lecture courses from across the two departments. The lecture courses will be divided into schedule I (basic) and schedule II (advanced).
The following list of optional courses is indicative. Not all options may be offered every year and new courses may be added to this list for 2026-27 entry.
Schedule I (basic)
- Algebraic Topology
- Algebraic Number Theory
- Analytic Number Theory
- Analytic Topology
- Categories, Proofs, and Processes
- Category Theory
- Computer-Aided Formal Verification
- Godel’s Incompleteness Theorems
- Graph Theory
- Information Theory
- Integer Programming
- Introduction to Quantum Information
- Lambda Calculus and Types
- Model Theory
- Quantum Processes and Computation
- Topology and Groups
Schedule II
- Additive Combinatorics
- Applied Category Theory (directed reading course)
- Algebraic Geometry
- Automata, Logic and Games
- Axiomatic Set Theory
- Combinatorics
- Computational Algebraic Topology
- Classical and quantum compositional distributional meaning (directed reading course)
- Distributed processes, types programming
- Elliptic Curves
- Foundations of Self-Programming Agents
- Geometric Deep Learning
- Geometric Group Theory
- Homological Algebra
- Infinite Groups
- Introduction to Schemes
- Low-dimensional Topology and Knot Theory
- Networks
- Probabilistic Combinatorics
- Topological Groups (directed reading course)
Entry requirements for entry in 2026-27
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 a subject with significant mathematical content.
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 3.7 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
- Publications are not expected.
English language proficiency
This course requires proficiency in English at the University's higher 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 higher level are detailed in the table below.
| Test | Minimum overall score | Minimum score per component |
|---|---|---|
| IELTS Academic (Institution code: 0713) | 7.5 | 7.0 |
| TOEFL iBT* including the 'Home Edition' (Institution code: 0490) | 110 | Listening: 22 Reading: 24 Speaking: 25 Writing: 24 |
| C1 Advanced† | 191 | 185 |
| C2 Proficiency‡ | 191 | 185 |
| Oxford Test of English Advanced | 165 | 155 |
*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.
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
Interviews may be held as part of the admissions process, at the discretion of the Admissions Panel and the Supervisory Committee.
If you are shortlisted for interview you will usually be notified within one month of the application deadline. Where applications are still accepted after the final standard University deadline, you will be informed whether or not you are invited for interview shortly after applications close. In both cases you should expect to receive one to two weeks’ notice of an interview and it is expected that interviews will take place around five to six weeks after an application deadline.
If invited you can expect to be interviewed by at least two people. Interviews are held online.
The major part of the interview will be the technical interview in which you will be asked questions on material relevant to the course. In addition, you will be asked why you would like to undertake the course and there will be opportunity for you to ask questions (although these questions are not taken into account when assessing interview performance).
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.
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.
Funding
For entry in the 2026-27 academic year, the collegiate University expects to offer over 1,100 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 institute's website.
Costs
Annual course fees
The fees for this course are charged on an annual basis.
Fees for the 2026-27 academic year at the University of Oxford
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.
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; and
- changes to fees and other 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.
Additional costs
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 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.
| Lower range | Upper range | |
|---|---|---|
| Food | £315 | £545 |
| Accommodation | £825 | £990 |
| Personal items | £160 | £310 |
| Social activities | £50 | £130 |
| Study costs | £35 | £90 |
| Other | £20 | £40 |
| Total | £1,405 | £2,105 |
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.
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.
The following colleges accept students on the MSc in Mathematics and Foundations of Computer Science:
Before you apply
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.
Application fee waivers
An application fee of £75 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.
Do I need to contact anyone before I apply?
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.
If you have any questions about the course, you are welcome to make contact with the Course Director. You will be allocated a supervisor by the department on your arrival, so there is no need to contact potential supervisors.
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 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.
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.
Referees:
Three overall, of which at least two must be 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.
It is recommended that you use at least two academic referees, who can comment directly on your academic work. You may also use up to one professional reference.
Your references will support intellectual ability, academic achievement, motivation and commitment to pursue the chosen course to a successful conclusion.
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:
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.
Your statement should focus on your motivation for wishing to undertake the course rather than personal achievements, interests and aspirations.
This will be assessed for your reasons for applying; evidence of motivation for and understanding of the proposed area of study; the ability to present a reasoned case in English; and commitment to the subject, beyond the requirements of the degree course.
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.