phd mathematics london

Mathematics MPhil/PhD

London, Bloomsbury

The department is home to many internationally renowned mathematicians. Our students go on to pursue successful careers in a variety of settings, primarily as postdoctoral researchers or in the world of finance. Excellent networking opportunities are provided by our central London location and close research links to other London universities.

UK tuition fees (2024/25)

Overseas tuition fees (2024/25), programme starts, applications accepted.

• Entry requirements

A minimum of an upper second-class UK Bachelor’s degree in a relevant discipline or an overseas qualification of an equivalent standard. Where possible, candidates are always interviewed. For overseas candidates there will be an alternative interview by telephone or Skype.

The English language level for this programme is: Level 1

UCL Pre-Master's and Pre-sessional English courses are for international students who are aiming to study for a postgraduate degree at UCL. The courses will develop your academic English and academic skills required to succeed at postgraduate level.

Further information can be found on our English language requirements page.

If you are intending to apply for a time-limited visa to complete your UCL studies (e.g., Student visa, Skilled worker visa, PBS dependant visa etc.) you may be required to obtain ATAS clearance . This will be confirmed to you if you obtain an offer of a place. Please note that ATAS processing times can take up to six months, so we recommend you consider these timelines when submitting your application to UCL.

Equivalent qualifications

Country-specific information, including details of when UCL representatives are visiting your part of the world, can be obtained from the International Students website .

International applicants can find out the equivalent qualification for their country by selecting from the list below. Please note that the equivalency will correspond to the broad UK degree classification stated on this page (e.g. upper second-class). Where a specific overall percentage is required in the UK qualification, the international equivalency will be higher than that stated below. Please contact Graduate Admissions should you require further advice.

About this degree

We offer research supervision across a broad range of pure and applied mathematics. General areas of expertise in pure mathematics include analysis, geometry, number theory and topology. In applied mathematics key areas of activity include fluid dynamics, mathematical modelling, mathematical physics, mathematical biology, applied and numerical analysis and financial mathematics.

Who this course is for

Our research degree programme is aimed at graduate students in mathematics or related sciences. Applicants will have analytical skills, and have formed a strong interest in pursuing mathematical research.

What this course will give you

The department offers a unique combination of outstanding research supervision and a rich community of students. It is sufficiently large for wide-ranging research activity but remains compact enough for academic staff to be highly accessible.

UCL’s role in the London School of Geometry and Number Theory (LSGNT) and London Taught Course Centre, as well as numerous intercollegiate seminars, ensures that students are firmly integrated into the wider mathematical community.

Some PhD projects are supervised jointly with industrial partners, or with other UCL departments or by interdisciplinary centres, with a unique critical mass of interdisciplinary activities at UCL.

The foundation of your career

Many of our students have go on to careers in financial services in the City; others have proceeded to postdoctoral research and academic careers.

Employability

Recent graduates have taken up academic posts at universities such as UCL, Imperial College London, Michigan, Sheffield, Mexico, Kyoto, California State, Others have joined the financial services industry with companies such as Barclays Capital, Schroders, Deloitte, ABN Amro and J. P. Morgan; Other graduates have become mathematics teachers and computer programmers.

A further example of employer destinations in industry would be Formula One motor racing development. Some students have summer secondments, such as two recent summer secondments at the Department of Business, Innovation and Skills.

Students closely interact with their peers from other London universities via the London Taught Course Centre, which offers a programme of advanced courses in mathematics and statistics one day a week for PhD research students in the region, as well as short intensive courses open to students from elsewhere in the UK and Europe.

You will have the chance to attend the departmental postgraduate seminar run by the students for the students, as well as other seminars both within and outside the department. You'll also have the opportunity to take part in a vigorous conferences programme.

Conferences recently hosted by the department include the Numerical Methods for MFG and related PDE Workshop, a lecture course on Regularity of Area Minimising Hypersurfaces, a conference on contact geometry and the British Applied Mathematics Colloquium, and the London Mathematical Biology Conference.

Teaching and learning

The degree is predominantly research-based and is overseen by a Principal Supervisor. Additionally all students are required to undergo training aimed at developing their presentation skills and gaining a broader knowledge of mathematics through modules (e.g. those offered by the London Taught Course Centre), seminars and conference attendance.

After 12-18 months, students are upgraded from MPhil to PhD candidature subject to assessment by a panel on the basis of a written report and oral examination. Ultimately, the student submits a thesis meeting the requirements of a UCL research degree as assessed by nominated examiners at an oral examination.

In a typical week you will meet your supervisory team for up to 2 hours. Short lecture courses, attending seminars, conferences or group meetings will amount to several additional hours per week. The majority of time is self-directed study.

Research areas and structure

Departmental research specialities fall within the two main groupings of pure and applied mathematics described below, and graduate research may be pursued within either field.

• Applied mathematics : environmental flows (including vortex dynamics, atmospheric and ocean dynamics and climate modelling); fluid mechanics (e.g. free-surface flows, polymers); industrial mathematics (e.g. inverse models, sound transmission, multi-particle interactions); mathematical biology and medicine (e.g. modelling cerebral and liver blood flow, molecular and cellular dynamics); gravitation, integrable systems; mathematical modelling; applied partial differential equations; numerical analysis and scientific computing; financial mathematics
• Pure mathematics : functional analysis; real and complex analysis; spectral theory; combinatorics; algebraic number theory; geometric topology; discrete and convex geometry; probability theory; geometric group theory; symplectic and contact topology

Research environment

The department is home to many internationally renowned mathematicians. We are delighted to be among the strongest mathematical science departments in the UK. In the Research excellence Framework 2021, UCL Mathematical Sciences was ranked 5th in the UK in terms of the number of papers ranked 3* or 4*. The expertise of our faculty covers the range of pure and applied mathematics with particular highlights including our leadership of the London School of Geometry and Number Theory which offers outstanding opportunities to early career young researchers in these fields. Numerous subject specific college seminars as well as intercollegiate seminars ensure that all PhD students have access to cutting edge research in their field.

Your primary activity in all years of study is to pursue research on your chosen research topic. This is conducted in close consultation with your primary supervisor.

During the first year you will usually take four courses from the inter-collegiate London Taught Course Centre. 

At or near the start of the second year students you will submit an upgrade report that is examined by a viva voce. On successful completion of this upgrade you will move from "MPhil" to "PhD" status.

Your primary activity in all years of study is to pursue research on your chosen research topic. This is conducted in close consultation with your primary supervisor. During the first two years you will usually take four courses from the inter-collegiate London Taught Course Centre. At or near the end of the third year students will submit an upgrade report that is examined by a viva voce. On successful completion of this upgrade you will move from MPhil to PhD status.

Accessibility

Details of the accessibility of UCL buildings can be obtained from AccessAble accessable.co.uk . Further information can also be obtained from the UCL Student Support and Wellbeing team .

Fees and funding

Fees for this course.

The tuition fees shown are for the year indicated above. Fees for subsequent years may increase or otherwise vary. Where the programme is offered on a flexible/modular basis, fees are charged pro-rata to the appropriate full-time Master's fee taken in an academic session. Further information on fee status, fee increases and the fee schedule can be viewed on the UCL Students website: ucl.ac.uk/students/fees .

Additional costs

Funded PhD places include the provision of a laptop by the department to be purchased in the first 2 years of studies. Students own the laptop and are, therefore, expected to pay the costs of insuring and backing-up their laptop. Students who leave their studies early are expected to return their laptop if already purchased.

For more information on additional costs for prospective students please go to our estimated cost of essential expenditure at Accommodation and living costs .

Funding your studies

For MPhil/PhD research at least two EPSRC doctoral training awards are normally offered each year. Approximately seven PhD teaching assistantships are also available each year. In addition, there are UCL Graduate Research Scholarships and Overseas Research Scholarships, and small departmental scholarships for which applicants are automatically considered on accepting an offer of a place.

Further opportunities for financial support are occasionally available. The department encourages and offers financial support for conference and workshop attendance.

For a comprehensive list of the funding opportunities available at UCL, including funding relevant to your nationality, please visit the Scholarships and Funding website .

CSC-UCL Joint Research Scholarship

Value: Fees, maintenance and travel (Duration of programme) Criteria Based on academic merit Eligibility: EU, Overseas

Deadlines and start dates are usually dictated by funding arrangements so check with the department or academic unit to see if you need to consider these in your application preparation. In most cases you should identify and contact potential supervisors before making your application. For more information see our How to apply page.

Please note that you may submit applications for a maximum of two graduate programmes (or one application for the Law LLM) in any application cycle.

Choose your programme

Please read the Application Guidance before proceeding with your application.

Year of entry: 2024-2025

Got questions get in touch.

Mathematics

[email protected]

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MPhil/PhD Mathematics

• Graduate research
• Department of Mathematics
• Application code G1ZM
• Starting 2024
• Home full-time: Open
• Overseas full-time: Open
• Location: Houghton Street, London

This programme offers the chance to undertake a substantial piece of work that is worthy of publication and which makes an original contribution to the field of mathematics within our four broad disciplines – discrete mathematics and algorithms, financial mathematics and control theory, game theory, and operations research. You will begin on the MPhil, and will need to meet certain requirements to be upgraded to PhD status.

You have a plethora of topics to choose from including combinatorics, combinatorial optimisation, computational learning theory, control theory, financial mathematics, game theory, graph theory, integer programming, mechanism design, polyhedral combinatorics, probabilistic analysis, theory of computation and algorithms, and in the applications of mathematics in areas such as inspections, network optimisation, telecommunications, transportation, and economics.

Over the course of the years, the Department organises a number of personal development workshops for PhD students, designed to provide tailored support for specific areas of interest, such as careers, impact, and final year processes. Crucially, we have close ties with other departments at LSE, such as Statistics, Finance, Economics and Management, and we are an integral part of the mathematical community of the University of London.

All research students in the Department are provided with some funding each year to encourage and support their research activities, such as conference attendance and purchasing books and technology. Additional research funds are also available, upon application.

Programme details

For more information about tuition fees and entry requirements, see the fees and funding and assessing your application sections.

Entry requirements

Minimum entry requirements for mphil/phd mathematics.

Merit in a taught master's degree (or equivalent) in a related discipline and a 2:1 degree or equivalent in mathematics. 

Competition for places at the School is high. This means that even if you meet our minimum entry requirement, this does not guarantee you an offer of admission. 

If you have studied or are studying outside of the UK then have a look at our  Information for International Students  to find out the entry requirements that apply to you.

LSE values diversity and strives to promote equality at all levels. We strongly encourage applications from women, ethnic minorities, and members of other groups under-represented in higher education.

Assessing your application

Making an application.

We carefully consider each application on an individual basis, taking into account all the information presented on your application form, including your:

- academic achievement (including existing and pending qualifications) - CV - statement of academic purpose - outline research proposal - sample of written work - references

In addition to the general guidelines on application documents available  here , you can find specific guidelines for some of the application documents required as part of your application for the MPhil/PhD Mathematics programme below.  

Academic Achievement Provide detailed transcripts, with individual marks for all courses on your undergraduate and postgraduate degree programmes you have completed, and any available/provisional marks obtained in your current degree programme.

CV - Provide details of your education history. - Provide details of any employment history or other professional experience, including internships or volunteering activities. - Mention any relevant prior research experience, such as thesis work, research projects.    - If relevant, mention any career breaks or career changes, for example due to caring responsibilities.

Statement of Academic Purpose (1 page) - Explain your motivation for doing a PhD. - Explain your current career goals and aspirations and clarify how the PhD programme might help you realise them.  

Outline Research Proposal (1-2 pages) Many applicants will have little or no prior experience of research and therefore we do not expect a fully developed research proposal. The following is a recommendation of what to address, in a concise manner, in the research proposal. - Explain which overall research area you are interested in and explain why.  - Provide an example of one or two research papers that you have read or open problems you have heard about (in your proposed research area) and explain why you found them interesting. - Clarify who you see as potential supervisors and explain why.  - Explain how your training and skills are suitable for conducting research in your area of interest. For example, provide specific examples of related courses you have taken, and any research, internship, or work experiences that are relevant to your research area of interest. - If applicable, describe how any dissertation work from your BSc or MSc is relevant to your planned PhD research (be aware that this research will most likely be different).

Sample of Written Work (at least 5 pages) Submit something that showcases your mathematical writing. This could for example be a thesis, a project report, or some detailed exercise solutions. We like to see a writing sample that contains both mathematical details and plain text in which you discuss/interpret/explain the mathematical results. You can submit more than one writing sample if you only have short pieces of written work.

References You will need to nominate two referees. Academic referees are preferred, i.e., people who have taught you at university level.

If you can find a referee who can specifically comment on your research potential and your academic background in your chosen research area, that would be helpful. If you have any previous research experience, you could ask supervisors/project partners for a reference letter. An academic reference from your current degree programme where you already took exams are usually most helpful. If you have not taken any exams in your current programme yet, you can also ask for reference letters from previous degrees.

The referees will be asked to provide a reference letter and answer a selection of multiple-choice questions in which they will need to provide an assessment of your academic performance/potential etc. and research potential. --------------

Completed applications are sent to the Department after they are processed by the Graduate Admissions Office. In the Department, the numbers and quality of competing applications and the availability of an appropriate supervisor are considered. If your application is shortlisted for consideration, an interview will be arranged with the appropriate members of staff by telephone or video conferencing software. Once all interviews have been conducted, the Department will decide on who to accept and who to offer funding. If your application is received before the deadline, we aim to notify you about the outcome by the end of Winter Term.

You may also have to provide evidence of your English proficiency. You do not need to provide this at the time of your application to LSE, but we recommend that you do see our  English language requirements  for further information.

When to apply

The application deadline for this programme is 23 May 2024 . However, to be considered for any LSE funding opportunity, you must have submitted your application and all supporting documents by the funding deadline. See the fees and funding section for more details.

Fees and funding

Every research student is charged a fee in line with the fee structure for their programme. The fee covers registration and examination fees payable to the School, lectures, classes and individual supervision, lectures given at other colleges under intercollegiate arrangements and, under current arrangements, membership of the Students' Union. It does not cover living costs or travel or fieldwork.

Tuition fees 2024/25 for MPhil/PhD Mathematics

Home students: £4,829 for the first year (provisional) Overseas students: £22,632 for the first year

The fee is likely to rise over subsequent years of the programme. The School charges home research students in line with the level of fee that the Research Councils recommend. The fees for overseas students are likely to rise in line with the assumed percentage increase in pay costs (ie, 4 per cent per annum).

The Table of Fees shows the latest tuition amounts for all programmes offered by the School.

The amount of tuition fees you will need to pay, and any financial support you are eligible for, will depend on whether you are classified as a home or overseas student, otherwise known as your fee status. LSE assesses your fee status based on guidelines provided by the Department of Education.

Further information about fee status classification.

Scholarships, studentships and other funding

The School recognises that the  cost of living in London  may be higher than in your home town or country, and we provide generous scholarships each year to home and overseas students.

This programme is eligible for  LSE PhD Studentships and  Economic and Social Research Council (ESRC) funding . Selection for the PhD Studentships and ESRC funding is based on receipt of an application for a place – including all ancillary documents, before the funding deadline.

Funding deadline for LSE PhD Studentships: 15 January 2024

In addition to our needs-based awards, LSE also makes available scholarships for students from specific regions of the world and awards for students studying specific subject areas.  Find out more about financial support.

In addition, students on this programme are eligible for the Department of Mathematics' PhD Prize for Outstanding Academic Performance , which is an annual award for the best PhD performance from a student completing in the previous academic year.

External funding 

There may be other funding opportunities available through other organisations or governments and we recommend you investigate these options as well. 

Further information

Fees and funding opportunities

Information for international students

LSE is an international community, with over 140 nationalities represented amongst its student body. We celebrate this diversity through everything we do.  

If you are applying to LSE from outside of the UK then take a look at our Information for International students . 

1) Take a note of the UK qualifications we require for your programme of interest (found in the ‘Entry requirements’ section of this page). 

2) Go to the International Students section of our website. 

3) Select your country. 

4) Select ‘Graduate entry requirements’ and scroll until you arrive at the information about your local/national qualification. Compare the stated UK entry requirements listed on this page with the local/national entry requirement listed on your country specific page.

Programme structure and courses

In addition to progressing with your research, you are expected to take the listed training and transferable skills courses. You may take courses in addition to those listed and should discuss this with your supervisor. At the end of your second year (full-time), you will need to satisfy certain requirements, and if you meet these, will be retroactively upgraded to PhD status.

Training courses – Compulsory (not examined) Courses designed for research in Mathematics need to be chosen in consultation with your lead supervisor. Discrete Mathematics and Algorithms, Operations Research and Game Theory students will attend four courses organised by the London Taught Course Centre .

There are separate arrangements for students in Financial Mathematics, where courses are provided by the London Graduate School in Mathematical Finance . You also have the option of attending or auditing LSE Taught Masters modules, where appropriate.

Transferable skills courses – Compulsory (not examined) Mathematics: Seminar on Combinatorics, Games and Optimisation Research Student Seminar – you must attend and make presentations

Second year

Transferable skills courses – Compulsory (not examined) Mathematics Seminar Research Student Seminar - you must attend and make presentations.

Transferable skills courses – Compulsory (not examined) Mathematics Seminar Research Student Seminar - you must attend and make presentations.

Fourth year

Transferable skills courses– Compulsory (not examined) Mathematics Seminar Research Student Seminar - you must attend and make presentations.

For the most up-to-date list of optional courses please visit the relevant School Calendar page .  

You must note, however, that while care has been taken to ensure that this information is up to date and correct, a change of circumstances since publication may cause the School to change, suspend or withdraw a course or programme of study, or change the fees that apply to it. The School will always notify the affected parties as early as practicably possible and propose any viable and relevant alternative options. Note that the School will neither be liable for information that after publication becomes inaccurate or irrelevant, nor for changing, suspending or withdrawing a course or programme of study due to events outside of its control, which includes but is not limited to a lack of demand for a course or programme of study, industrial action, fire, flood or other environmental or physical damage to premises.  

You must also note that places are limited on some courses and/or subject to specific entry requirements. The School cannot therefore guarantee you a place. Please note that changes to programmes and courses can sometimes occur after you have accepted your offer of a place. These changes are normally made in light of developments in the discipline or path-breaking research, or on the basis of student feedback. Changes can take the form of altered course content, teaching formats or assessment modes. Any such changes are intended to enhance the student learning experience. You should visit the School’s  Calendar , or contact the relevant academic department, for information on the availability and/or content of courses and programmes of study. Certain substantive changes will be listed on the  updated graduate course and programme information page.

Supervision, progression and assessment

Supervision.

Supervisors are selected during the application process, where we take into account the information and preferences you mention in your application. You will be assigned to:

-  One or two principal supervisor(s) with requisite knowledge in your chosen field. Most of your day-to-day supervision will be with the principal supervisor(s). If the research project or your interests shift during your time in the Department, it is possible to change principal supervisor(s). - If there is only one principal supervisor, an appropriate second supervisor will be appointed. There will always be a principal supervisor from the Mathematics Department. Where appropriate, a second or joint supervisor may be appointed from another department or institution.

Progression and assessment

You are initially registered for the MPhil, and will be able to upgrade to PhD registration during your second year, dependent on satisfactory progress. Progress is assessed regularly by your supervisors, in consultation with the Doctoral Programme Director, on the basis of the extent to which the agreed research goals have been achieved. Any upgrade is dependent on the successful completion of a Major Review, the date of which is determined by the Doctoral Programme Director in consultation with the lead supervisor.

By the end of your first year you will be required to present a more detailed project proposal. The proposal, which should illustrate your command of the theoretical and empirical literature related to your topic, will be a clear statement of the theoretical and methodological approach you will take. It will include a draft outline and work plan, which should identify any periods of fieldwork necessary to your research. This should demonstrate the coherence and feasibility of the proposed research and thesis.

Study facilities

Students are provided with their own workspace and Windows PC within the Department of Mathematics’ PhD study room.  This area was recently renovated, and has been modernised to become a professional, purposeful, and relaxed work environment. Students are thus offered a supportive environment within a community of scholars and are well-placed to pursue a career building on their research accomplishments. 

In addition to the space provided in Columbia House, a dedicated Postgraduate Common Room is available to students in 32 Lincoln's Inn Fields.  Students will also find the  PhD Academy  useful, a dedicated space and services hub for doctoral candidates.

Students will have access to the comprehensive facilities of the  LSE Library  and to the libraries of other colleges of the University of London. They will also benefit from the IT and other facilities available at the School.

Student support and resources

We’re here to help and support you throughout your time at LSE, whether you need help with your academic studies, support with your welfare and wellbeing or simply to develop on a personal and professional level.

Whatever your query, big or small, there are a range of people you can speak to who will be happy to help.  

Department librarians   – they will be able to help you navigate the library and maximise its resources during your studies. 

Accommodation service  – they can offer advice on living in halls and offer guidance on private accommodation related queries.

Class teachers and seminar leaders  – they will be able to assist with queries relating to specific courses. 

Disability and Wellbeing Service  – they are experts in long-term health conditions, sensory impairments, mental health and specific learning difficulties. They offer confidential and free services such as  student counselling,  a  peer support scheme  and arranging  exam adjustments.  They run groups and workshops.  

IT help  – support is available 24 hours a day to assist with all your technology queries.   

LSE Faith Centre  – this is home to LSE's diverse religious activities and transformational interfaith leadership programmes, as well as a space for worship, prayer and quiet reflection. It includes Islamic prayer rooms and a main space for worship. It is also a space for wellbeing classes on campus and is open to all students and staff from all faiths and none.   

Language Centre  – the Centre specialises in offering language courses targeted to the needs of students and practitioners in the social sciences. We offer pre-course English for Academic Purposes programmes; English language support during your studies; modern language courses in nine languages; proofreading, translation and document authentication; and language learning community activities.

LSE Careers  ­ – with the help of LSE Careers, you can make the most of the opportunities that London has to offer. Whatever your career plans, LSE Careers will work with you, connecting you to opportunities and experiences from internships and volunteering to networking events and employer and alumni insights. 

LSE Library   –   founded in 1896, the British Library of Political and Economic Science is the major international library of the social sciences. It stays open late, has lots of excellent resources and is a great place to study. As an LSE student, you’ll have access to a number of other academic libraries in Greater London and nationwide. 

LSE LIFE  – this is where you should go to develop skills you’ll use as a student and beyond. The centre runs talks and workshops on skills you’ll find useful in the classroom; offers one-to-one sessions with study advisers who can help you with reading, making notes, writing, research and exam revision; and provides drop-in sessions for academic and personal support. (See ‘Teaching and assessment’). 

LSE Students’ Union (LSESU)  – they offer academic, personal and financial advice and funding.  

PhD Academy   – this is available for PhD students, wherever they are, to take part in interdisciplinary events and other professional development activities and access all the services related to their registration. 

Sardinia House Dental Practice   – this   offers discounted private dental services to LSE students.  

St Philips Medical Centre  – based in Pethwick-Lawrence House, the Centre provides NHS Primary Care services to registered patients.

Student Services Centre  – our staff here can answer general queries and can point you in the direction of other LSE services.  

Student advisers   – we have a  Deputy Head of Student Services (Advice and Policy)  and an  Adviser to Women Students  who can help with academic and pastoral matters.

Student life

As a student at LSE you’ll be based at our central London campus. Find out what our campus and London have to offer you on academic, social and career perspective. 

Student societies and activities

Your time at LSE is not just about studying, there are plenty of ways to get involved in  extracurricular activities . From joining one of over 200 societies, or starting your own society, to volunteering for a local charity, or attending a public lecture by a world-leading figure, there is a lot to choose from. 

The campus 

LSE is based on one  campus  in the centre of London. Despite the busy feel of the surrounding area, many of the streets around campus are pedestrianised, meaning the campus feels like a real community. 

Life in London 

London is an exciting, vibrant and colourful city. It's also an academic city, with more than 400,000 university students. Whatever your interests or appetite you will find something to suit your palate and pocket in this truly international capital. Make the most of career opportunities and social activities, theatre, museums, music and more. 

Want to find out more? Read why we think  London is a fantastic student city , find out about  key sights, places and experiences for new Londoners . Don't fear, London doesn't have to be super expensive: hear about  London on a budget . 

Student stories

To read all our Alumni Stories,  see our webpage here .

Quick Careers Facts for the Department of Mathematics

Median salary of our PG students 15 months after graduating: £39,500

• Financial and Professional Services              
• Information, Digital Technology and Data            
• Accounting and Auditing              
• Real Estate, Environment and Energy 
• Advertising, Marketing, PR, Media, Entertainment, Publishing and Journalism

Top 5 sectors our students work in:

The data was collected as part of the Graduate Outcomes survey, which is administered by the Higher Education Statistics Agency (HESA). Graduates from 2020-21 were the fourth group to be asked to respond to Graduate Outcomes. Median salaries are calculated for respondents who are paid in UK pounds sterling and who were working in full-time employment.

Students who successfully complete the programme often embark on an academic career. 

Further information on graduate destinations for this programme

Support for your career

Many leading organisations give careers presentations at the School during the year, and LSE Careers has a wide range of resources available to assist students in their job search. Find out more about the  support available to students through LSE Careers .

Frequently Asked Questions

Can i or must i teach as a mphil/phd student in the department.

All mathematics MPhil/PhD students are usually expected to undertake some class teaching for the Department. You will be paid separately for this. Further details will be provided on your arrival. 

Will I receive any additional funding to support conference attendance, book purchases, etc.?

Each registered PhD student in the Department is entitled to claim up to £500 per academic year towards their research expenses relating directly to your studies, such as the purchase of books or conference attendance. All claims must be accompanied by full receipts. 

Can I apply to start in the Winter Term (January) or Spring Term (April)?

Under execptional circumstances, starting in January may be permissable.  Starting in the Spring Term is not permitted.

I am already enrolled in a PhD programme at another university and I would like to transfer to your PhD programme. How do I do that?

LSE does not accept transfer of credits. All MPhil/PhD applicants, regardless of previous academic experience, are required to complete a formal application. Previous research will be considered, but all students are initially registered as MPhil students by the School, are upgraded to PhD status according to the Department's standard policy and are required to fulfil the School's minimum registration requirements.

Can I apply to study part-time?

We will consider applications for part-time registrations in the PhD programme, subject to visa regulations. Applicants with personal circumstances such as caring responsibilities who may otherwise not pursue a PhD may consider this route. We emphasise that studying for a PhD requires a serious commitment of regular periods of time and concentration. Pursuing a PhD while holding full-time employment is discouraged.

We would need to see evidence that an applicant:

• Would be available to participate in activities that are essential to becoming an independent researcher (e.g. attend seminars, go to conferences, follow taught courses in their first year(s), etc.)
• Can find mutual times to work with their proposed supervisor
• Can spend sufficient time on their PhD research

Find out more about LSE

Discover more about being an LSE student - meet us in a city near you, visit our campus or experience LSE from home. 

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Come on a guided campus tour, attend an undergraduate open day, drop into our office or go on a self-guided tour.  Find out about opportunities to visit LSE . 

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Student Marketing, Recruitment and Study Abroad travels throughout the UK and around the world to meet with prospective students. We visit schools, attend education fairs and also hold Destination LSE events: pre-departure events for offer holders.  Find details on LSE's upcoming visits . 

How to apply

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Course type

Qualification, university name, phd mathematics in london.

19 degrees at 10 universities in London.

Customise your search

Select the start date, qualification, and how you want to study

Related subjects:

• PhD Mathematics
• PhD Applied Mathematics
• PhD General Mathematics
• PhD Mathematics for Specific Applications
• PhD Operational Research (OR)
• PhD Pure Mathematics
• PhD Statistics
• PhD Statistics, Probability and Operational Research

• Course title (A-Z)
• Course title (Z-A)
• Price: high - low
• Price: low - high

PhD/MPhil Mathematics

City, university of london.

You will conduct world class research for Mathematics at City in topics such as representation theory, mathematical physics or applied Read more...

• 2 years Full time degree: £4,770 per year (UK)
• 3 years Part time degree: £2,390 per year (UK)

Mathematics PhD

Royal holloway, university of london.

About us Academic staff in the Department of Mathematics carry out pioneering research which is making an impressive impact on the world Read more...

• 4 years Full time degree: £4,786 per year (UK)

Mathematical Sciences Integrated PhD

Brunel university london.

Research profile Our research-active academics are involved in cutting-edge research covering a range of topics including applied Read more...

• 4 years Full time degree

Statistical Science MPhil/PhD

Ucl (university college london).

The demand for numerate graduates exceeds the supply in most areas. Many new and existing opportunities – in industry, medicine, Read more...

• 3 years Full time degree: £6,035 per year (UK)
• 5 years Part time degree: £2,930 per year (UK)

Queen Mary University of London

The School of Mathematical Sciences at QMUL is home to a thriving community of postgraduate research students currently numbering Read more...

• 3 years Full time degree: £4,786 per year (UK)
• 6 years Part time degree: £2,393 per year (UK)

University of West London

This PhD in Mathematics course allows you to use theoretical, applied, and computational research methods to solve a wide range of Read more...

• 4 years Full time degree: £3,995 per year (UK)
• 6 years Part time degree: £2,000 per year (UK)
• 3 years Full time degree
• 6 years Part time degree

Mathematics MPhil/PhD

We offer research supervision across a broad range of pure and applied mathematics. General areas of expertise in pure mathematics include Read more...

You should ensure that you have a realistic plan to secure sufficient funding to complete the research and writing-up process within the Read more...

Smart Power Networks PhD

Research profile Our research focuses on the development of algorithms to improve distribution efficiency, and strategies to allow mass Read more...

• 3 years Full time degree: £4,712 per year (UK)

Mathematics and Statistics PhD

Birkbeck, university of london.

An PhD is an advanced postgraduate research degree that requires original research and the submission of a substantial dissertation of Read more...

• 4 years Full time degree: £4,712 per year (UK)
• 7 years Part time degree: £2,500 per year (UK)

Imperial College London

A research degree is a very individual experience, more so than an undergraduate degree. While the overarching structure will be identical Read more...

• 5 years Part time degree: £2,393 per year (UK)

Pure Mathematics Research MPhil/PhD

King's college london, university of london.

We have a wide range of research opportunities in the three groups that make up the Pure section of the Department of Mathematics, namely Read more...

• 3 years Full time degree: £6,936 per year (UK)
• 6 years Part time degree: £3,468 per year (UK)

MPhil/PhD Statistics

London school of economics and political science, university of london.

This programme offers the chance to undertake a substantial piece of work that is worthy of publication and which makes an original Read more...

• 3 years Full time degree: £4,829 per year (UK)

Statistics Research MPhil/PhD

Our department has a large number of active and internationally renowned researchers and postdoctoral research fellows. The Statistics Read more...

MPhil/PhD Mathematics

Biostatistics and health informatics research md(res)/mphil/phd.

Our PhD programme is designed to train and guide students for a research-intensive career in the academia or industry. Our aim is to Read more...

• 3 years Full time degree: £7,950 per year (UK)
• 6 years Part time degree: £3,975 per year (UK)

MPhil/PhD Data, Networks and Society

Media and communications research is developing rapidly, both theoretically and methodologically, in keeping with the vast expansion in the Read more...

Applied Mathematics Research MPhil/PhD

Description Our department has a large number of active and internationally renowned researchers and postdoctoral research fellows. The Read more...

Course type:

• Full time PhD
• Part time PhD

Qualification:

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Key information.

Duration: 4 years full time

Institution code: R72

Campus: Egham

UK fees * : £4,786

International/EU fees ** : £19,700

Academic staff in the Department of Mathematics carry out pioneering research which is making an impressive impact on the world stage. In the most recent Research Excellence Framework (REF 2021) 96% of research output is rated world-leading and internationally excellent.

The department has 20 staff performing research in a number of areas of pure, applied and applicable mathematics, probability and statistics, and information security.

The main research interests in the department can be grouped into the following areas

• Discrete Mathematics and its Applications
• Number Theory
• Quantum Dynamics
• Statistics and Probability.

From time to time, we make changes to our courses to improve the student and learning experience. If we make a significant change to your chosen course, we’ll let you know as soon as possible.

Research facilities and environment

PhD students have access to excellent computing facilities in the Department. In addition, staff members hold workshops and discussion meetings in a variety of areas on a regular basis.

There are weekly seminars from national and international speakers.

PhD researchers also benefit from Royal Holloway’s access to world-class research and library facilities in London and to advanced postgraduate courses in their research field shared with other University of London Colleges through the London Taught Course Centre.

Once the research has been successfully completed the student must write and submit a final report in the form of a PhD research thesis. This will be evaluated by at least two experts and the student will be invited to attend an oral examination where they must satisfactorily defend their thesis.

Entry requirements

The minimum entry requirement for an MPhil or an MPhil leading to a PhD degree is the equivalent of a UK Upper Second Class Honours degree in an appropriate subject, although in many cases a Masters (or MSci) level qualification will also be expected. Candidates must also be demonstrably proficient in English.

English language requirements

All teaching at Royal Holloway is in English. You will therefore need to have good enough written and spoken English to cope with your studies right from the start.

The scores we require

• IELTS: 6.5 overall. Writing 7.0. No other subscore lower than 5.5.
• Pearson Test of English: 61 overall. Writing 69. No other subscore lower than 51.
• Trinity College London Integrated Skills in English (ISE): ISE III.
• Cambridge English: Advanced (CAE) grade C.
• TOEFL ib: 88 overall, with Reading 18 Listening 17 Speaking 20 Writing 26.

Country-specific requirements

For more information about country-specific entry requirements for your country please see  here .

Our PhD students have a high employability rate.  Our Mathematics PhD students either continue on the academic route by taking up Post-Doctoral research positions at other institutions or move, for example, into the Financial Sector. Many of the skills acquired by Mathematics PhD students are in demand outside of Academia.

Fees & funding

Home (UK) students tuition fee per year*: £4,786

EU and international students tuition fee per year**: £19,700

Other essential costs***: There are no single associated costs greater than £50 per item on this course

…How do I pay for it? Find out more about   funding options,   including loans, grants,   scholarships   and bursaries. 

* and ** These tuition fees apply to students enrolled on a full-time basis in the academic year 2024/25.

* Please note that for research courses, we adopt the minimum fee level recommended by the UK Research Councils for the Home   tuition fee. Each year, the fee level is adjusted in line with inflation (currently, the measure used is the Treasury GDP deflator). Fees displayed here are therefore subject to change and are usually confirmed in the spring of the year of entry.   For more information on the Research Council Indicative Fee please see the   UKRI website.

** This figure is the fee for EU and international students starting a degree in the academic year 2024/25.   

Royal Holloway reserves the right to increase all postgraduate tuition fees annually, based on the UK’s Retail Price Index (RPI). Please therefore be aware that tuition fees can rise during your degree (if longer than one year’s duration), and that this also means that the overall cost of studying the course part-time will be slightly higher than studying it full-time in one year. For further information, please see our  terms and conditions .

***   These estimated costs relate to studying this particular degree at Royal Holloway during the 2024/25 academic year and are included as a guide. Costs, such as accommodation, food, books and other learning materials and printing, have not been included. 

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Discover world-class research at Royal Holloway.

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Find about our decision-making processes and the people who lead and manage Royal Holloway today.

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Mathematics and Statistics

Application options include:

Course Overview

An MPhil/PhD is an advanced postgraduate research degree that requires original research and the submission of a substantial dissertation of 60,000 to 100,000 words. At Birkbeck, you are initially registered on an MPhil and you upgrade to a PhD after satisfactory progress in the first year or two. You need to find a suitable academic supervisor at Birkbeck, who can offer the requisite expertise to guide and support you through your research. Find out more about undertaking a research degree at Birkbeck .

Our MPhil/PhD degree in Mathematics and Statistics aims to train you to conduct research of a high academic standard and to make original contributions to the subject.

The programme involves coursework (where suitable) and research training, but its major component is the preparation of a substantial research thesis. The thesis should demonstrate a sound understanding of the main issues in the area and add to existing knowledge.

Research interests in mathematics and statistics include: mathematical finance, in particular the analysis of risk and numerical computation; mathematical physics and partial differential equations; approximation theory and numerical analysis; probability and stochastic processes, pure and applied; applied statistics and multivariate analysis; covariance modelling for repeated measures and longitudinal data; medical statistics; combinatorics, algebra and designs.

Key information

Mathematics and statistics mphil/phd: 7 years part-time, on campus, starting 2024-25.

• October 2024
• January 2025

Mathematics and Statistics MPhil/PhD: 4 years full-time, on campus, starting 2024-25

Find another course:

• Birkbeck is  one of the world’s leading research-intensive institutions . Our cutting-edge scholarship informs public policy, achieves scientific advances, supports the economy, promotes culture and the arts, and makes a positive difference to society.
• Birkbeck’s research excellence was  confirmed in the most recent Research Excellence Framework  with 83% of our research rated world-leading or internationally excellent.

Entry Requirements

First- or upper second-class honours degree in a relevant subject. In many instances, an MSc will be preferable. Applicants should submit a research proposal which is in line with the research interests of our academic staff.

English language requirements

If English is not your first language or you have not previously studied in English, our usual requirement is the equivalent of an International English Language Testing System (IELTS Academic Test) score of 6.5, with not less than 6.0 in each of the sub-tests.

If you don't meet the minimum IELTS requirement,  we offer pre-sessional English courses, foundation programmes and language support services  to help you improve your English language skills and get your place at Birkbeck.

Visa and funding requirements

If you are not from the UK and you do not already have residency here, you may need to apply for a visa.

The visa you apply for varies according to the length of your course:

• Courses of more than six months' duration: Student visa
• Courses of less than six months' duration: Standard Visitor visa

International students who require a Student visa should apply for our full-time courses as these qualify for Student visa sponsorship. If you are living in the UK on a Student visa, you will not be eligible to enrol as a student on Birkbeck's part-time courses (with the exception of some modules).

For full information, read our visa information for international students page .

Please also visit the international section of our website to find out more about relevant visa and funding requirements by country .

Please note students receiving US Federal Aid are only able to apply for in-person, on-campus programmes which will have no elements of online study.

Mathematics and Statistics MPhil/PhD: 7 years part-time or 4 years full-time, on campus, starting in academic year 2024-25

Academic year 2024–25, starting october 2024, january 2025, april 2025.

Part-time home students: £2,539 per year Full-time home students: £4,786 per year Part-time international students : £7,525 per year Full-time international students: £14,885 per year

Students are charged a tuition fee in each year of their course. Tuition fees for students continuing on their course in following years may be subject to annual inflationary increases. For more information, please see the College Fees Policy .

If you’ve studied at Birkbeck before and successfully completed an award with us, take advantage of our Lifelong Learning Guarantee to gain a discount on the tuition fee of this course.

Fees and finance

PhD students resident in England can apply for government loans of over £26,000 to cover the cost of tuition fees, maintenance and other study-related costs.

Flexible finance: pay your fees in monthly instalments at no extra cost . Enrol early to spread your costs and reduce your monthly payments.

We offer a range of studentships and funding options to support your research.

Discover the financial support available to you to help with your studies at Birkbeck.

International scholarships

We provide a range of scholarships for eligible international students, including our Global Future Scholarship. Discover if you are eligible for a scholarship .

Our research culture

As a research student in mathematics and statistics, you will have access to a wide range of study resources, including the University of London seminar programme in probability and statistics, excellent library facilities close by in Bloomsbury, and the taught courses and project component of our MSc Applied Statistics programmes.

To ensure that we have an appropriate supervisor for your area of research, you should contact the course team to discuss it before submitting your application.

Recent research topics include:

• Non-associative algebras and normal ideals
• Canonical auto and cross correlations of multivariate time series
• Dimension and measure defined by infinite Bernoulli convolutions
• Some Markov decision models for pest control
• Aspects of estimation in linear and non-linear time series models
• Inventory renewal time series and their ARMA equivalents
• Some statistical aspects of the estimation of fire losses
• The use of tensor algebras in population genetics.

Extensive computing facilities include PCs and UNIX platforms and generic courses and workshops are offered by the College.

Read more about  our vibrant research culture .

Follow these steps to apply to an MPhil/PhD research degree at Birkbeck:

1. Check that you meet the entry requirements, including English language requirements, as described on this page.

2. Find a potential supervisor for your MPhil/PhD research. You can look at the Find a Supervisor area on this page for an overview, or  search our Experts’ Database  or  browse our staff pages  for more in-depth information. You may also find it helpful to view the research projects of our current students.

3. Contact the academic member of staff - or the department they teach in - for an informal discussion about your research interests and to establish if they are willing and able to supervise your research. (Please note: finding a potential supervisor does not guarantee admission to the research degree, as this decision is made using your whole application.)  Find out more about the supervisory relationship and how your supervisor will support your research .

4. Draft a research proposal. This needs to demonstrate your knowledge of the field, the specific research questions you wish to pursue, and how your ideas will lead to the creation of new knowledge and understanding.  Find out more about writing a research proposal .

5. Apply directly to Birkbeck, using the online application link on this page. All research students are initially registered on an MPhil and then upgrade to a PhD after making sufficient progress.

Find out more about the application process, writing a research proposal and the timeframe .

Application deadlines and interviews

You will need to submit a research proposal with your application.

You can apply at any time during the year. Entry months for the programme are October, January and April of each year.

If you wish to apply for funding, you will need to apply by certain deadlines. Consult the websites of relevant bodies for details.

Apply for your course

Apply for your course using the apply now button in the key information section .

Finding a supervisor

A critical factor when applying for postgraduate study in mathematics and statistics is the correlation between the applicant’s intellectual and research interests and those of one or more potential supervisors.

Find out more about the research interests of our academic staff:

• Brad Baxter, BA, PhD : approximation theory; numerical analysis; mathematical finance; theory and algorithms of radial basis functions.
• Anthony Brooms, BSc, MSc, PhD : stochastic processes; stochastic order results; stochastic games, with applications to models of service systems; optimisation and control.
• Swati Chandna, BSc, MSc, PhD : statistical analysis of network data; time series in the frequency domain; speech signal processing; boot-strap methods for time series; saptio-temporal analysis.
• Simon Hubbert, PhD : approximation theory, optimisation and mathematical finance.
• Professor Steven Noble, MSc, DPhil : combinatorics, particularly graph polynomials.
• Professor Maura Paterson, BSc, PhD : information security; combinatorics.
• Ilaria Peri, PhD : mathematical finance; quantitative finance; risk and performance measures; financial risk; backtesting.
• Richard Pymar, MA, MMath, PhD : probability theory, particularly interacting particle systems, mixing times, random walks (in random environment).

Related courses

• Computer Science and Information Systems (MPhil/PhD)

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Mathematics PhD

Course detail, entry requirements.

• Fees & funding
• Study & career progression

This PhD in Mathematics course allows you to use theoretical, applied, and computational research methods to solve a wide range of problems ranging from theoretical to the applied sector. Our academics have extensive experience and knowledge to support you throughout the course.

The focus of the program is on substantial research on core areas of mathematics leading to a PhD dissertation, allowing you to develop your skills in presenting and teaching mathematics and its applications. The doctoral offers an opportunity for you to obtain high level research skills and significantly deepen your knowledge in the area of Mathematics.

We invite applications for doctoral research in various mathematics topic areas, including:

• Nonlinear dynamics and chaos
• Applications of mathematics in electrical or civil engineering
• Educational mathematics
• Gauge theory
• Special geometries with torsion
• Exceptional holonomy
• Stochastic differential equations and modelling
• Financial mathematics

See a list of potential PhD supervisors and read about their expertise, in the 'Supervisors' section lower down the page.

Select your desired study option, then pick a start date to see relevant course information:

Start date:

If your desired start date is not available, try selecting a different study option.

Why study Mathematics with us?

What our students say…

The staff members that I encountered were warm, welcoming and supportive of my studies. The relatively small size of the University’s postgraduate school created a close family/communal environment for both staff and students. This provided a good support system as I could quickly grow acquainted with the postgraduate team and other Doctoral research candidates.

The Faringdon Centre for Non-Destructive Testing and Remote Sensing

The Centre carries out research and consultancy work on the applications of non-destructive testing methods and techniques.

World-leading Research

The University of West London has been recognised by the Government's Research Excellence Framework (REF) for its exceptional research work.

With academic staff with extensive professional experience within a vast array of disciplines, we provide a stimulating and supportive environment where you will benefit from:

• peer feedback and discussion
• a series of master-classes and lectures from industry figures
• support by a supervisor and second supervisor suited to your project.

About PhD study

This course is available for you to study either on a full-time or part-time basis and you have the flexibility to switch should you need to.

A PhD is founded on independent research.  You will undertake a systematic and in-depth exploration of your chosen topic to produce a substantial body of knowledge and make an original and important contribution to the subject area.  

The support provided by your supervisory team will be vital to your student experience and scholarly advancement.  You and your supervisors will have regular one-to-one meetings which will provide you with opportunities to develop your research topic and discuss your progress.

School of Computing and Engineering's Research Centres and Groups

Our School is closely affiliated with  The Faringdon Centre for Non-Destructive Testing , as well as the research groups below:

• Bio inspired modelling and technology
• Sustainable civil and structural engineering

The Faringdon Centre for Non-Destructive Testing explores new avenues of research into the development, within this context, the Centre carries out research and consultancy work on the applications of non-destructive testing methods and techniques.

The Bio inspired modelling and technology group develop methods and computational tools for modelling and simulation to understand various complex systems and tasks such as learning and intelligence,  their applications to system design and artificial intelligence.

The Sustainable civil and structural engineering group has established connections with the construction industry and benefits from highly qualified researchers, including professionally qualified Civil, Structural, Highway, Geotechnical and Water Engineers; Architects and Mathematicians. 

Our research record

View our  academic journal 'New Vistas'   to see the work of students and academics who are making an impact both locally and globally through their research findings.

Based in the heart of Ealing, west London, you can make use of the excellent transport links to travel to the the capital or further afield.

London is well known for its concentration of high-technology industry including many of the big names in technology and computing companies, alongside digital media, computer games, and electronic commerce.

The department of Computing Science has close connections with many of these organisations via collaborative projects, staff secondments and visiting industrial staff.

Got a question?

If you would like guidance or more information about studying for a research degree, you can contact Dr Anastasia Sofroniou  or  Professor Massoud Zolgharni .

To enable you to enhance your professional profile, we support you throughout your research degree by:

• providing research seminars
• organising doctoral events and activities
• facilitating networking and collaboration opportunities
• encouraging and supporting publication and dissemination of your research
• offering opportunities to gain teaching expertise and experience.

We provide structured research training, expert supervision, and an environment where you can discuss your research with other PhD students and researchers.

We run seminars in research methods from the Graduate Centre, as well as an ongoing series of events and activities organised by Schools and Colleges. Specialist help with academic English for students for whom English is not their first language is available.

We offer access to equipment and software to aid your research investigations, including specialist development environments.

• workstations and laptops
• deep learning development servers
• RAID servers
• custom software repositories

Rami Ranger House (Postgraduate Student Centre)

Postgraduate and International Student Centre is a new focal point for the university’s postgraduate and international students, providing dedicated space for social and learning interaction.

This building, which is three storeys high, offers spaces for collaborative working, socialising, supervision and mentoring on the ground floor. The first floor has work spaces for the postgraduate support teams to use while the second floor provides guest accommodation for visiting scholars.

The Paul Hamlyn Library

The Paul Hamlyn Library provides an extensive range of books, journals and digital resources, PC and Mac workstations and a variety of study spaces. Find out more about what the  Paul Hamlyn Library has to offer .

We contribute to national and international initiatives and promote collaboration and networking opportunities. We also encourage and support you to publish and disseminate your research in academic journals and via presenting papers at conferences.

We run an annual conference for doctoral students, where you are encouraged to present a paper about your research. As well as being an opportunity to discuss your work with other students, the conference is a chance to gain valuable experience in presenting your research and participating in open discussions with academic peers.

You will also find other opportunities such as postgraduate student seminars and forums within your specific subject area.

Once you start a PhD course at UWL, you become part of our research community. You will have access to a postgraduate common room, located at our Ealing campus on St Mary’s Road, where you will meet fellow researchers from other subject disciplines offering scope for collaborations or simply to discuss ideas, allowing you to be part of a vibrant research environment.

• Requirements: UK
• Requirements: International

The minimum entry requirements for a research degree are:

• a good first degree (First Class or Upper Second Class), or equivalent qualification in a relevant field
• a Masters Degree (MA, MSc, MBA or MRes) with Merit, or equivalent postgraduate or research experience.

We look for students with:

• a passion for their chosen subject.

You will also have a well thought through and persuasive proposal.

• Competence in written and spoken English is a pre-requisite for entrance to this programme. An IELTS (International English Language Testing System) score of 6.5 (with no element under 6.0).

Fees & funding

• Funding: UK
• Funding: International

The fee above is the cost per year of your course.

If your course runs for two years or more, you will need to pay the fee for each academic year at the start of that year. If your course runs for less than two years, the cost above is for your full course and you will need to pay the full fee upfront.

Government regulation does affect tuition fees and the fees listed for courses starting in the 2025/26 academic year are subject to change.

If no fee is shown above then the fees for this course are not available yet. Please check again later for updates.

Funding your studies

Funding for postgraduate students usually comes from one or more of a range of key sources:

• research councils
• charities and trust funds, including those funded by the UK government
• higher Education institutions
• overseas governments (international students only)
• professional and career development loans
• self-funding (including family funds).

Find out more about funding opportunities. Examples of most of these types of funding are included on the postgraduate studentships website , (with the exception of funding you may be able to obtain from your employer and self-funding).

Bursaries and scholarships

We offer generous bursaries and scholarships to make sure your aspirations are your only limit. See our PhD scholarships , scholarships and bursaries .

For any overseas students, your first port of call should be grant-awarding bodies in your own country (eg The Ministry / Department of Education) and your local (or nearest) office of the British Council.

The British Council manage a small number of international studentship grants in some countries and should be able to tell you what other awards may be available to you - they also produce the Sources of funding for international students guide.

Supervisors

Dr anastasia sofroniou.

Dr Thomas Madsen

Dr Shihan Miah

Study & career progression

A PhD degree in Mathematics – the highest academic qualification, based on the advanced study and independent research, opens up an array of career opportunities both in academia and within the professional sector. 

Many students go on to pursue an academic career, following the PhD with a postdoctoral study, then a fellowship or lectureship. Others pursue professional careers in industry, engineering, government, education, finance, banking or actuarial science sectors. 

During your PhD, you will also be learning transferable core skills that apply to jobs both in and out of academia, including: 

• written and oral communication
• research and information management
• public speaking
• project management
• critical thinking
• collaboration
• analysis and problem solving
• negotiation.

By the end of your research degree, you will be able to articulately apply these skills to enhance your career path.

How to apply

• How to apply: UK
• How to apply: International

To apply for one of our research courses, click the green 'apply now' link shown below to complete an online application form. You will need to attach the following documentation to your online application form:

• research proposal outline (5000 words maximum)
• transcript of your highest qualification.

The research proposal outline, or statement of research interests, enables us to assess your suitability for higher degree work including:

• viability of the topic as a research study
• the most appropriate supervisor(s) to be appointed.

Click here  for more information on applying for a PhD.

Apply for this course

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Any questions about a course or studying at UWL? We're here to help - call us on 0800 036 8888 (option 2, Monday – Friday 10am-4pm) or email us on [email protected].

To apply for one of our research courses, click the green 'apply now' link shown below to complete an online application form.  You will need to attach the following documentation to your online application form:

• research proposal outline

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What do you want to do?

Find out about the research we do in mathematics.

• Mathematics PhD

Find a supervisor

Mode of study

3 years full-time

6 years part-time

International   £23,615

UK   £4,786

Entry requirements

Research profile.

Our research-active academics are involved in cutting-edge research covering a range of topics including applied analysis, computational mathematics, continuum mechanics and mathematical physics, financial mathematics, operational research and applied statistics.

We address problems of real biological or engineering importance and investigate the underlying mathematical and phenomenological processes. There is a strong emphasis on the development of innovative analytic, asymptotic, computational and hybrid methods. Our research also focuses on random matrix theory, quantum information theory, mathematical foundations of quantum mechanics, mesoscopic disordered systems, statistical mechanics, graph theory, matroid theory, and infinite-dimensional Riemannian geometry, algebraic geometry and orthogonal polynomials. 

Find out about the exciting research we do in this area. Browse profiles of our experts, discover the research groups and their inspirational research activities you too could be part of. We’ve also made available extensive reading materials published by our academics and PhD students.  

Learn more about research in this area.

You can explore our campus and facilities for yourself by taking our virtual tour .

Our researchers create knowledge and advance understanding, and equip versatile doctoral researchers with the confidence to apply what they have learnt for the benefit of society. Find out more about working with the Supervisory Team .

You are welcome to approach your potential supervisor directly to discuss your research interests. Search for expert supervisors for your chosen field of research.

View supervisors by research area

Applied and Numerical Analysis:

• Analysis of partial differential equations, including nonlinear PDEs of fluid mechanics and mathematical biology ( S. Mikhailov ,  M. Winter )
• Analysis and numerical implementation of boundary-domain integral and integro-differential equations ( S. Mikhailov )
• Computational modelling of problems in solid mechanics, as well as acoustic, elastic and electromagnetic wave propagation, by Finite Element and Boundary Element methods ( S. Langdon ,  M. Maischak ,  S. Shaw ,  M. Warby ,  J. Whiteman )
• Approximation of orthogonal polynomials and special functions ( I. Krasikov )
• Abstract bifurcation and singularity theory ( J. Furter )
• Fast solvers and preconditioners, error estimators and adaptive algorithms, high performance and scientific computing, software development ( S. Langdon ,  M. Maischak ,  S. Shaw )
• Theoretical and computational modelling of fatigue, damage, durability, and fracture ( S. Mikhailov )

Financial Mathematics and Operational Research:

• Financial modelling; in particular, forecasting of spreads in commodity futures prices using latent state based models/ MCMC filters ( P. Date ,  J.W. Lim )
• Applications of machine learning in financial models. ( P. Date ,  E. Boguslavskaya )
• Optimisation problems in power system transmission networks ( P. Date ,  C. Lucas )
• Modelling paradigms and stochastic optimisation applied to (financial) decision making under uncertainty and risk ( P. Date ,  D. Roman ,  C. Lucas )
• Meta heuristics for solving large combinatorial problems. ( C. Lucas )
• Preventative maintenance modelling in the face of uncertainty ( P. Date ,  C. Lucas )
• Stochastic optimal control, with applications in finance ( D. Roman ,  C. Lucas )
• Efficient simulation of Levy processes ( E. Boguslavskaya ,  J.W. Lim )

Mathematical Physics and Applied Mathematics:

• Random matrix theory and its applications ( D. Savin ,  I. Smolyarenko )
• Resonances and transport in open wave chaotic systems ( D. Savin )
• Quantum information and quantum computing ( S. Virmani )
• Algebraic geometry, birational geometry ( A.-S. Kaloghiros )
• Complex networks ( G. Rodgers ,  I. Smolyarenko )
• Statistical mechanics of complex systems and econophysics ( G. Rodgers )
• Waves in solids and fluids ( M. Greenhow ,  J. Lawrie ,  E. Nolde ,  A. Pichugin )
• Structural acoustics and diffraction theory ( M. Greenhow ,  J. Lawrie )
• Asymptotic theory of thin elastic structures ( E. Nolde  ,  A. Pichugin )
• Layout optimization of structures ( A. Pichugin )

Statistics and Data Science:

• High-dimensional Bayesian Learning ( D. Chakrabarty )
• Learning in the Absence of Training Data ( D. Chakrabarty )
• Applications of Statistics in Astronomy, Materials Science, etc. using MCMC-based inference ( D. Chakrabarty ,  C. Spire ,  K. Yu )
• Random Geometric Graphs & Networks ( D. Chakrabarty ,  B. Parker )
• Design of Experiments for Network Science ( B. Parker )
• Algorithms for Experimental Design ( B. Parker )
• Bayesian regression beyond the mean ( K. Yu )
• Weibull analysis for lifetime data analysis ( K. Yu )
• Quantile regression for big data ( K. Yu )
• Machine learning methods and application ( K. Yu ,  B. Parker )
• Nonparametric smoothing ( K. Yu )
• Advanced regression analysis of carbon emissions ( K. Yu )
• Applications of Statistics in Health Science, Biology and Genomics ( K. Yu )

While we welcome applications from student with a clear direction for their research, we are providing you with some ideas for your chosen field of research:

• Ambient Vibration-Based Calibration of Finite Element Models of Bridges, supervised by Michael Rustell
• Automatic computational fluid-dynamics, supervised by James Tyacke
• Autonomous Drone Surveys and Convolutional Neural Networks for Bridge Maintenance: A Predictive Approach Using Finite Element Analysis, supervised by Michael Rustell
• Bridging the Gap: Integrating Neural Radiance Fields and Micro-drones for Enhanced 3D Volumetric Finite Element Analysis, supervised by Michael Rustell
• Decision making for stratified medicine life cycle, supervised by Yang Yang

Research journey

This course can be studied 3 years full-time or 6 years part-time, starting in January. Or this course can be studied 3 years full-time or 6 years part-time, starting in October. Or this course can be studied 3 years full-time or 6 years part-time, starting in April.

Find out about what progress might look like at each stage of study here:  Research degree progress structure.

Research support

Excellent research support and training

The Graduate School provides a range of personal, professional and career development opportunities. This includes workshops, online training, coaching and events, to enable you to enhance your professional profile, refine your skills, and plan your next career steps as part of the Researcher Development Programme . The researcher development programme (RDP) offers workshops and seminars in a range of areas including progression, research management, research dissemination, and careers and personal development. You will also be offered a number of online, self-study courses on BBL, including Research Integrity, Research Skills Toolkit, Research Methods in Literature Review and Principles of Research Methods.

Library services

Brunel's Library is open 24 hours a day, has 400,000 books and 250,000 ebooks, and an annual budget of almost £2m. Subject information Specialists train students in the latest technology, digital literacy, and digital dissemination of scholarly outputs. As well as the physical resources available in the Library, we also provide access to a wealth of electronic resources. These include databases, journals and e-books. Access to these resources has been bought by the Library through subscription and is limited to current staff and students.

Dedicated research support staff provide guidance and training on open access, research data management, copyright and other research integrity issues.

Find out more: Brunel Library

Careers and your future

You will receive tailored careers support during your PhD and for up to three years after you complete your research at Brunel. We encourage you to actively engage in career planning and managing your personal development right from the start of your research, even (or perhaps especially) if you don't yet have a career path in mind. Our careers provision includes online information and advice, one-to-one consultations and a range of events and workshops. The Professional Development Centre runs a varied programme of careers events throughout the academic year. These include industry insight sessions, recruitment fairs, employer pop-ups and skills workshops.

In addition, where available, you may be able to undertake some paid work as we recognise that teaching and learning support duties represent an important professional and career development opportunity.

Find out more.

Following the completion of the course students may follow several career paths:

• Career path within academia starting as a Post-doc or Lecturer/Assistant Professor at a university
• Career progression within research institutions commencing as a Researcher and progressing to Senior Researcher.
• Career path within the industry as a Research Scientist, Senior Research Scientists, Financial Analyst, etc.
• Career path in secondary education as Maths teacher, Maths Subject Leader

UK entry requirements

The general University entrance requirement for registration for a research degree is normally a First or Upper Second Class Honours degree (1st or 2:1). 

An interview will be required as part of the admissions process and will be conducted by at least two academic staff members remotely via MS Teams, Zoom, or face to face.

Applicants will be required to submit a personal statement  and a research statement. Please contact your proposed supervisor, where possible, to receive feedback and guidance on your research statement before submitting it. Learn how to prepare a research statement  here .   

EU and International entry requirements

If you require a Tier 4 visa to study in the UK, you must prove knowledge of the English language so that we can issue you a Certificate of Acceptance for Study (CAS). To do this, you will need an IELTS for UKVI or Trinity SELT test pass gained from a test centre approved by  UK Visas and Immigration (UKVI) and on the Secure English Language Testing (SELT) list . This must have been taken and passed within two years from the date the CAS is made.

English language requirements

• IELTS: 6.5 (min 6 in all areas)
• Pearson: 59 (59 in all subscores)
• BrunELT : 63% (min 58% in all areas)
• TOEFL: 90 (min 20 in all) 

You can find out more about the qualifications we accept on our  English Language Requirements  page.

Should you wish to take a pre-sessional English course to improve your English prior to starting your degree course, you must sit the test at an approved SELT provider for the same reason. We offer our own BrunELT English test and have pre-sessional English language courses for students who do not meet requirements or who wish to improve their English. You can find out more information on English courses and test options through our  Brunel Language Centre .

Please check our Admissions  pages for more information on other factors we use to assess applicants. This information is for guidance only and each application is assessed on a case-by-case basis. Entry requirements are subject to review, and may change.

Fees and funding

2024/5 entry, international.

£23,615 full-time

£11,805 part-time

£4,786 full-time

£2,393 part-time

Fees quoted are per year and are subject to an annual increase.

Some courses incur  additional course related costs . You can also check our  on-campus accommodation costs  for more information on living expenses.

Brunel offers a number of funding options to research students that help cover the cost of their tuition fees, contribute to living expenses or both. Recently the UK Government made available the Doctoral Student Loans of up to £25,000 for UK and EU students and there is some funding available through the Research Councils. Many of our international students benefit from funding provided by their governments or employers. Brunel alumni enjoy tuition fee discounts of 15%.

Scholarships and bursaries

• Brunel Graduate Discount

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• School of Mathematical Sciences
• Postgraduate
• Postgraduate Research

PhD projects

The School of Mathematical Sciences invites applications for the PhD projects listed below.

Application deadlines:

Application deadlines for funded projects are listed in the tables below, but please be aware that applications will be considered on a rolling basis.

Unfunded projects are listed without application or start deadlines, and w e welcome applications from self-funded students throughout the year.

Combinatorics, Algebra & Number Theory

Complex systems, data science, statistics & probability.

• Geometry, Analysis & Gravitation

Enquiries and Further Information

For any general enquiries regarding the above PhD studentships please contact Dr Reem Yassawi , the Director of Graduate Studies, or Dr Alex Shestopaloff , the Deputy Director of Graduate Studies . For more administrative queries about the PhD programme at Queen Mary, please contact   Katie Hale , the PGR Programmes Officer .

If you have already secured funding for your PhD studies and therefore do not wish your application to be considered within the studentship competition please state this on the appropriate part of your application form.

Choosing your Research Topic

It is highly recommended that first you make up your mind in which area of mathematics you wish to work and, ideally, to even think of prospective PhD supervisors at our School. It is important that your supervisor shares your research interests such that he/she can successfully guide you in your research. Many PhD students in mathematics do not pursue targeted research projects specified at the outset. Instead, they develop an agreed programme of study in discussion with their supervisor during their first year here. This programme tends to evolve in response to what has been learned during preliminary studies.

With this in mind, the important question for a prospective student is: Are my interests aligned with those of the School? The following links provide information on the general research strengths of the School:

• Algebra and Number Theory
• Combinatorics
• Complex Systems and Networks
• Dynamical Systems and Statistical Physics
• Probability and Applications
• Statistics and Data Science

Collaborative Research 

From time to time, we have projects available which are co-sponsored by an industrial partner, or which are run jointly with colleagues in another department at Queen Mary. Recent examples of the latter include the School of Biological and Chemical Sciences, the School of Electronic Engineering and Computer Science, and the Wolfson Institute of Population Health.

Imperial College London Imperial College London

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Looking for funding?

Use our scholarships search tool to look for available scholarships. Also explore our latest funded PhD vacancies .

A PhD (Doctor of Philosophy) is the most common type of doctoral degree and the highest level of academic qualification you can achieve. 

It normally takes between three and four years of full-time work to complete. It is also possible to undertake a PhD part time, over five to six years.

The main activity of a PhD is to carry out an original research project under the direction of one or more supervisors, to be written up as a thesis.

Different routes to achieving a PhD

There are a number of ways to achieving a PhD at Imperial:

• by undertaking a course of study based on your own research proposal
• by joining a research project that comes with funding attached (known as a studentship)
• by combining it with Master's study in an integrated route that typically lasts four years

Pursuing your own research idea

To search for PhD opportunities based on your own research proposal you first need to identify a research group within Imperial whose area of expertise best matches your idea.

Use the links below to search the different PhD opportunities within our academic departments, centres and institutes. This includes information about current studentships and often guidance on finding a supervisor.

Our interdisciplinary approach means our expertise often spans departmental boundaries – and so do our courses – so you may find opportunities in an unexpected area of the university.

Faculty of Engineering

• Aeronautics
• Bioengineering
• Chemical Engineering
• Civil and Environmental Engineering
• School of Design Engineering
• Earth Science and Engineering
• Electrical and Electronic Engineering
• Mechanical Engineering

Faculty of Medicine

• Department of Brain Sciences
• Department of Immunology and Inflammation
• Department of Infectious Disease
• Department of Metabolism, Digestion and Reproduction
• Department of Surgery and Cancer
• National Heart and Lung Institute
• School of Public Health

Faculty of Natural Sciences

• Life Sciences
• Mathematics
• Centre for Environmental Policy

Imperial College Business School

• Doctoral programme

Centre for Languages, Culture and Communication

• PhD in Arabic, German, Italian, Russian and Spanish Studies
• PhD in science communication studies

Global Challenge institutes

We have six Global Challenge institutes, which were created to address some of society's biggest challenges.

If you have an idea for a PhD that falls within the remit of one of our Global Challenge institutes please contact them directly to discuss before making a formal application.

• Data Science Institute
• Grantham Institute – Climate Change and the Environment
• Institute for Molecular Science and Engineering
• Institute for Security Science and Technology
• Institute of Global Health Innovation

Energy Futures Lab  does not offer PhD programmes, but does deliver the  MSc in Sustainable Energy Futures .

Joint Academy of Doctoral Studies | Imperial College London-Technical University of Munich

We have recently formed  a strategic partnership in education, research and innovation  with the Technical University of Munich, one of Germany’s most international and entrepreneurial universities, producing highly ranked research, like Imperial, in science, engineering and medicine.

As part of the partnership, Imperial and TUM have launched a 'Joint Academy of Doctoral Studies' with the aim of co-developing cross-disciplinary clusters of PhD students who will have access to world-leading academic supervisors and state-of-the art facilities at both institutions.

The first round of the programme will focus on the theme of 'Artificial Intelligence, Healthcare and Robotics'.

Find out more about the Joint Academy of Doctoral Studies and apply

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Research (MPhil / PhD) Entry Route

The University of London academic community pursues and achieves excellence in a wide range of research activities and scholarship.

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Research opportunities

MPhil and PhD opportunities are available on-campus and by arrangement through our self-governing member institutions and research institutes, including the School of Advanced Study

Many of these institutions have performed highly in the Research Excellence Framework and are consistently ranked highly for research among UK universities.

Postgraduate research is offered via distance learning through the School of Advanced Study (Opens in new window) .

Research activity

The majority of academic staff are actively engaged in research, so you will be taught by experienced and motivated researchers who are eminent in their field.

To find out more about research opportunities, you can either search our courses to see which areas of research are available, or contact a university that offers related subjects to see if they can support your proposal.

Applied Mathematics Research: Disordered Systems/Financial Mathematics/Probability MPhil/PhD

Key information.

We have a wide range of research opportunities in the Department of Mathematics. We recommend that you explore and identify research topics and academic staff in your area of interest.

You can explore potential supervisors on our research group pages . Click here for all the details on how to make an application.

If you apply for this programme you will be doing research in one of our research groups which are listed below. You can click to explore more information about them:

Disordered Systems

Financial mathematics, probability.

If you are interested in Theoretical Physics, please visit this page: Applied Mathematics Research: Theoretical Physics - King's College London (kcl.ac.uk)

Head of Department: Professor Steven Gilmour

Course intake

PhD: 8-20 full-time, 2-5 part-time per year MPhil: 5-10 full-time, 1-5 part-time per year

Our department has a large number of active and internationally renowned researchers and postdoctoral research fellows. The research groups organise regular seminars, where top-ranking scientists from around the world present new results, which our research students can witness first hand. The students also organise their own informal seminars and discussion groups. The lively environment and the exceptionally friendly atmosphere at our department contribute to the high success rate of our students. You can apply for supervision in all fields of interest of our staff members. The department provides funding for PhD students to attend suitable schools and conferences during their studies.

More than 80% of the PhD students at the department are fully funded through a number of funding schemes; the most common is departmental funding which covers tuition as well as a living stipend. In recent years, on average, 10 students per year have been admitted to a PhD programme with funding from the department.

• How to apply
• Fees or Funding

For funding opportunities please explore these pages:

• List of funding opportunities
• External funding opportunities for International students
• King’s-China Scholarship Council PhD Scholarship programme (K-CSC)

UK Tuition 2023/24

Full time tuition fees: £6,540 per year (PhD, Applied Mathematics Research: Disordered Systems/Financial Mathematics/Probability/Theoretical Physics)

Part time tuition fees: £3,270 per year (PhD, Applied Mathematics Research: Disordered Systems/Financial Mathematics/Probability/Theoretical Physics)

Full time tuition fees: £6,540 per year (MPhil/PhD, Mathematics Research)

Part Time Tuition fees: £3,270 per year (MPhil/PhD, Mathematics Research)

International Tuition Fees 2023/24

Full time tuition fees: £24,360 per year (PhD, Applied Mathematics Research: Disordered Systems/Financial Mathematics/Probability/Theoretical Physics)

Part time tuition fees: £12,180 per year (PhD, Applied Mathematics Research: Disordered Systems/Financial Mathematics/Probability/Theoretical Physics)

Full time tuition fees: £24,360 per year (MPhil/PhD, Mathematics Research)

Part Time Tuition fees: £12,180 per year (MPhil/PhD, Mathematics Research)

UK Tuition 2024/25

Full time tuition fees: £6,936 per year (PhD, Applied Mathematics Research: Disordered Systems/Financial Mathematics/Probability/Theoretical Physics)

Part time tuition fees: £3,468 per year (PhD, Applied Mathematics Research: Disordered Systems/Financial Mathematics/Probability/Theoretical Physics)

Full time tuition fees: £6,936 per year (MPhil/PhD, Mathematics Research)

Part Time Tuition fees: £3,468 per year (MPhil/PhD, Mathematics Research)

International Tuition Fees 2024/25

Full time tuition fees: £26,070 per year (PhD, Applied Mathematics Research: Disordered Systems/Financial Mathematics/Probability/Theoretical Physics)

Part time tuition fees: £13,035 per year (PhD, Applied Mathematics Research: Disordered Systems/Financial Mathematics/Probability/Theoretical Physics)

Full time tuition fees: £26,070 per year (MPhil/PhD, Mathematics Research)

Part Time Tuition fees: £13,035 per year (MPhil/PhD, Mathematics Research)

Mathematics Research with University of Hong Kong or Humboldt-Universität Zu Berlin

Full time tuition fees:

£24,360 per year (MPhil/PhD, Mathematics Research with University of Hong Kong)

£24,360 per year (MPhil/PhD, Mathematics Research with Humboldt-Universität Zu Berlin)

Part time tuition fees:

£12,180 (MPhil/PhD, Mathematics Research with Humboldt-Universität Zu Berlin)

£26,070 per year (MPhil/PhD, Mathematics Research with University of Hong Kong)

£26,070 per year (MPhil/PhD, Mathematics Research with Humboldt-Universität Zu Berlin)

£13,035 (MPhil/PhD, Mathematics Research with Humboldt-Universität Zu Berlin)

All of these fees may be subject to additional increases in subsequent years of study, in line with King's terms and conditions.

Bench fees will be applicable to the non-award research programme for visiting students.

• Study environment

You will be assigned a supervisor with whom you will work closely. You will also attend research seminars and take part in other research related activities in your research group, the department and more widely in the University of London. We do not specify fixed attendance hours, but we expect a good level of attendance, and our research students benefit from informal interaction with each other. You will be provided with access to working and storage space, as well as a laptop. On arrival you will discuss your research programme with your supervisor, and you will attend general induction sessions.

Postgraduate training

Carrying out research is learned in apprenticeship mode as PhD student works with a supervisor. Our PhD students receive various forms of training during their period of research, eg attending courses in the London Taught Courses Centre, attendance at EPSRC summer schools; provision of advanced lecture courses; College training courses for graduates who will give tutorial teaching to undergraduates; weekly seminars in the area of your research; frequent research group meetings; attendance at national and international conferences and research meetings.

Communication skills are developed by preparing and presenting seminars in the department, assisted by your supervisor; apprenticeship in writing papers and, in due course, the PhD thesis.

To build your teaching skills and experience, you are strongly encouraged to apply to become a Graduate Teaching Assistant, giving tutorials to our undergraduates (training is provided).

• Entry requirements
• Research groups

The Disordered Systems group at King's is at the forefront of research in statistical mechanics of disordered and complex systems.

King’s College has a large and thriving Financial Mathematics group, with an international reputation for research excellence. 

The Probability group in the Department of Mathematics at King's College London.

Centre for Doctoral Studies

NMES Graduate School

A supportive and engaging environment for PhD students

Funding & Scholarships for PhD students

The Centre for Doctoral Studies helps secure funding for students...

NMES Graduate School: Virtual Open Event Session One

The NMES Graduate School Virtual Open Events for prospective postgraduate...

NMES Graduate School: Virtual Open Event Session Two