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PhD Pure Mathematics / Overview

Year of entry: 2024

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The standard academic entry requirement for this PhD is an upper second-class (2:1) honours degree in a discipline directly relevant to the PhD (or international equivalent) OR any upper-second class (2:1) honours degree and a Master’s degree at merit in a discipline directly relevant to the PhD (or international equivalent).

Other combinations of qualifications and research or work experience may also be considered. Please contact the admissions team to check.

Full entry requirements

Apply online

In your application you’ll need to include:

• The name of this programme
• Your research project title (i.e. the advertised project name or proposed project name) or area of research
• Your proposed supervisor’s name
• If you already have funding or you wish to be considered for any of the available funding
• A supporting statement (see 'Advice to Applicants for what to include)
• Details of your previous university level study
• Names and contact details of your two referees.

Programme options

Programme description.

The The Department of Mathematics has an outstanding research reputation. The research facilities include one of the finest libraries in the country, the John Rylands University Library. This library has recently made a very large commitment of resources to providing comprehensive online facilities for the free use of the University's research community. Postgraduate students in the Department benefit from direct access to all the Library electronic resources from their offices.

Many research seminars are held in the Department on a weekly basis and allow staff and research students to stay in touch with the latest developments in their fields. The Department is one of the lead partners in the MAGIC project and research students can attend any of the postgraduate courses offered by the MAGIC consortium.

For entry in the academic year beginning September 2024, the tuition fees are as follows:

• PhD (full-time) UK students (per annum): Band A £4,786; Band B £7,000; Band C £10,000; Band D £14,500; Band E £24,500 International, including EU, students (per annum): Band A £28,000; Band B £30,000; Band C £35,500; Band D £43,000; Band E £57,000
• PhD (part-time) UK students (per annum): Band A £2393; Band B £3,500; Band C £5,000; Band D £7,250; Band E 12,250 International, including EU, students (per annum): Band A £14,000; Band B £15,000; Band C £17,750; Band D £21,500; Band E £28,500

Further information for EU students can be found on our dedicated EU page.

The programme fee will vary depending on the cost of running the project. Fees quoted are fully inclusive and, therefore, you will not be required to pay any additional bench fees or administration costs.

All fees for entry will be subject to yearly review and incremental rises per annum are also likely over the duration of the course for Home students (fees are typically fixed for International students, for the course duration at the year of entry). For general fees information please visit the postgraduate fees page .

Always contact the Admissions team if you are unsure which fees apply to your project.

Scholarships/sponsorships

There are a range of scholarships, studentships and awards at university, faculty and department level to support both UK and overseas postgraduate researchers.

To be considered for many of our scholarships, you’ll need to be nominated by your proposed supervisor. Therefore, we’d highly recommend you discuss potential sources of funding with your supervisor first, so they can advise on your suitability and make sure you meet nomination deadlines.

For more information about our scholarships, visit our funding page or use our funding database to search for scholarships, studentships and awards you may be eligible for.

Contact details

Our internationally-renowned expertise across the School of Natural Sciences informs research led teaching with strong collaboration across disciplines, unlocking new and exciting fields and translating science into reality.  Our multidisciplinary learning and research activities advance the boundaries of science for the wider benefit of society, inspiring students to promote positive change through educating future leaders in the true fundamentals of science. Find out more about Science and Engineering at Manchester .

Programmes in related subject areas

Use the links below to view lists of programmes in related subject areas.

• Mathematics

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Mathematics PhD

Key information.

• 95%  of our research overall in Mathematical Sciences was assessed to be world leading or internationally excellent  (REF 2021)  
• analysis and partial differential equations
• geometry and topology
• mathematical physics
• mathematical biology
• numerical analysis and scientific computing
• probability and statistics.

My PhD work may soon inform marketing campaigns of our industrial partners. This experience will make me a strong candidate in the job market for data analysts. ” Shane Black Mathematics PhD

We understand that deciding where and what to study is a very important decision. We’ll make all reasonable efforts to provide you with the courses, services and facilities described in this prospectus. However, if we need to make material changes, for example due to government or regulatory requirements, or unanticipated staff changes, we’ll let you know as soon as possible.

Masters and P h D events

Meet us on campus or online

Book your place

Entry requirements

• UK requirements
• International requirements

Please select your country from the list.

Philippines

Saudi arabia, south africa, south korea, switzerland, united arab emirates, my country is not listed.

If your country is not listed, you need to contact us and find out the qualification level you should have for this course. Contact us

English language requirements

Ielts (academic).

Standard level (6.0 overall, including at least 6.0 in each component).

IELTS scores are valid for two years from the test date. You cannot combine scores from more than one sitting of the test. Your score must be valid when you begin your Sussex course.  Find out more about IELTS

We accept IELTS One Skills Retake.

We do not accept IELTS Online.

Check full details of our English Language requirements and find out more about some of the alternative English language qualifications listed below

Alternative English language qualifications

Proficiency tests, cambridge advanced certificate in english (cae).

169 overall, including at least 162 in each skill.

We would normally expect the CAE test to have been taken within two years before the start of your course.

You cannot combine scores from more than one sitting of the test.  Find out more about Cambridge English: Advanced

Cambridge Certificate of Proficiency in English (CPE)

We would normally expect the CPE test to have been taken within two years before the start of your course.

You cannot combine scores from more than one sitting of the test.  Find out more about Cambridge English: Proficiency

LanguageCert International ESOL SELT

Standard level (International ESOL SELT B2 with a minimum of 36 in each component)

LanguageCert International ESOL scores are valid for two years from the test date. Your score must be valid when you begin your Sussex course. Find out more about LanguageCert SELT

We only accept LanguageCert when taken at SELT Test Centres. We do not accept the online version.

Pearson PTE Academic

Standard level (59 overall, including at least 59 in all four skills)

PTE (Academic) scores are valid for two years from the test date. You cannot combine scores from more than one sitting of the test. Your score must be valid when you begin your Sussex course. Find out more about Pearson (PTE Academic)

We do not accept the PTE Academic Online test.

TOEFL (iBT)

Standard level 80 overall, including at least 19 in Listening, 19 in Reading, 21 in Speaking, 21 in Writing.

TOEFL (iBT) scores are valid for two years from the test date. You cannot combine scores from more than one sitting of the test. Your score must be valid when you begin your Sussex course. Find out more about TOEFL (iBT)

We do not accept TOEFL (iBT) Home Edition.

The TOEFL Institution Code for the University of Sussex is 9166.

English language qualifications

As/a-level (gce).

Grade C or above in English Language.

Hong Kong Advanced Level Examination (HKALE)/ AS or A Level: grade C or above in Use of English.

GCE O-level

Grade C or above in English.

Brunei/Cambridge GCE O-level in English:  grades 1-6.

Singapore/Cambridge GCE O-level in English:  grades 1-6.

GCSE or IGCSE

Grade C or above in English as a First Language (Grade 4 or above in GCSE from 2017).

Grade B or above in English as a Second Language.

Ghana Senior Secondary School Certificate

If awarded before 1993:  grades 1-6 in English language.

If awarded between 1993 and 2005:  grades A-D in English language.

Hong Kong Diploma of Secondary Education (HKDSE)

 Level 4, including at least 3 in each component in English Language.

Indian School Certificate (Standard XII)

The Indian School Certificate is accepted at the grades below when awarded by the following examination boards:

Central Board of Secondary Education (CBSE) – English Core only:  70%

Council for Indian School Certificate Examinations (CISCE) - English:  70% 

International Baccalaureate Diploma (IB)

English A or English B at grade 5 or above.

Kenya Certificate of Secondary Education

Grades A - C in English language

Malaysian Certificate of Education (SPM) 1119/GCE O-level

If taken before the end of 2008:  grades 1-6 in English Language.

If taken from 2009 onwards:  grade C or above in English Language.

The qualification must be jointly awarded by the University of Cambridge Local Examinations Syndicate (UCLES).

West African Senior School Certificate

Grades A1-C6 (1-6) in English language when awarded by the West African Examinations Council (WAEC) or the National Examinations Council (NECO).

Country exceptions

Select to see the list of exempt english-speaking countries.

If you are a national of one of the countries below, or if you have recently completed a qualification equivalent to a UK Bachelors degree or higher in one of these countries, you will normally meet our English requirement. Note that qualifications obtained by distance learning or awarded by studying outside these countries cannot be accepted for English language purposes.

You will normally be expected to have completed the qualification within two years before starting your course at Sussex. If the qualification was obtained earlier than this, we would expect you to be able to demonstrate that you have maintained a good level of English, for example by living in an English-speaking country or working in an occupation that required you to use English regularly and to a high level.

Please note that this list is determined by the UK’s Home Office, not by the University of Sussex.

List of exempt countries: 

• Antigua and Barbuda
• New Zealand
• St Kitts and Nevis
• St Vincent and the Grenadines
• The British Overseas Territories
• Trinidad and Tobago
• United Kingdom

** Canada: you must be a national of Canada; other nationals not on this list who have a degree from a Canadian institution will not normally be exempt from needing to provide evidence of English.

English language support

If you don’t meet the English language requirements for your degree, you may be able to take a pre-sessional course

• Visas and immigration

Admissions information for applicants

If your qualifications aren’t listed or you have a question about entry requirements, contact us

• How to apply

If you’d like to join us as a research student, there are two main routes:

• browse funded projects in this subject area
• browse our potential supervisors and propose your own research project.

Find out how to apply for a PhD at Sussex

Full-time and part-time study

Choose to work on your research full time or part time, to fit around your work and personal life. For details  about part-time study, contact us at  [email protected]

PhD or MPhil?

You can choose to study for a PhD or an MPhil. PhD and MPhil degrees differ in duration and in the extent of your research work.

• For a PhD, your research work makes a substantial original contribution to knowledge or understanding in your chosen field.
• For an MPhil, your work is an independent piece of research but in less depth than for a PhD. You’ll graduate with the degree title Master of Philosophy. You might be able to change to a PhD while you study for an MPhil.

Our supervisors

My PhD has been the most challenging and rewarding part of my life so far. The University of Sussex and especially my supervisor have been crucial in my development as a young professional aiming for a career in academia .” James Van Yperen   Mathematics PhD

Explore our research interests and find potential supervisors.

Dr Miroslav Chlebik

Reader in Mathematics

[email protected]

View profile of Miroslav Chlebik

Dr Masoumeh Dashti

Senior Lecturer in Mathematics

[email protected]

View profile of Masoumeh Dashti

Prof Peter Giesl

Professor of Mathematics

[email protected]

View profile of Peter Giesl

Dr Gabriel Koch

[email protected]

View profile of Gabriel Koch

Dr Konstantinos Koumatos

[email protected]

View profile of Konstantinos Koumatos

Prof Michael Melgaard

Professor of Mathematics (Analysis and Partial Differential Equations)

[email protected]

View profile of Michael Melgaard

Prof Ali Taheri

[email protected]

View profile of Ali Taheri

Prof Xavier Calmet

Professor of Physics

[email protected]

View profile of Xavier Calmet

Prof Enrico Scalas

Professor Of Statistics & Probability

View profile of Enrico Scalas

Prof Konstantin Blyuss

Professor of Applied Mathematics

[email protected]

View profile of Konstantin Blyuss

Prof Yuliya Kyrychko

[email protected]

View profile of Yuliya Kyrychko

Dr Omar Lakkis

[email protected]

View profile of Omar Lakkis

Prof Charalambos Makridakis

Professor Of Mathematics

[email protected]

View profile of Charalambos Makridakis

Prof Vanessa Styles

Head of School MPS

[email protected]

View profile of Vanessa Styles

Dr Chandrasekhar Venkataraman

Senior Lecturer In Mathematics

[email protected]

View profile of Chandrasekhar Venkataraman

Dr Antoine Dahlqvist

Senior Lecturer in Statistics and Probab

[email protected]

View profile of Antoine Dahlqvist

Dr Nicos Georgiou

[email protected]

View profile of Nicos Georgiou

Dr Nicholas Simm

Senior Research Fellow

[email protected]

View profile of Nicholas Simm

Dr Vladislav Vysotskiy

Reader in Statistics and Probability

[email protected]

View profile of Vladislav Vysotskiy

Dr Minmin Wang

Senior Lecturer

[email protected]

View profile of Minmin Wang

Funding and fees

How can i fund my course, funded projects and scholarships.

Our aim is to ensure that every student who wants to study with us is able to despite financial barriers, so that we continue to attract talented and unique individuals. Don’t miss out on scholarships – check the specific application deadlines for funding opportunities. Note that funded projects aren’t available for all our PhDs.

Up to 10 4 year EPSRC scholarships in Quantum Information Science and Technologies

Find out more

£3,000 scholarships available to environmental influencers bringing about real-world behaviour change

£800 scholarship available to reward talented organ player studying on any course at Sussex.

5 scholarships of £800 are available to reward talented musicians studying on any course at Sussex

A 4 year PhD studentship in mathematics, funded by the Royal Society.

PhD studentship in the Numerical Analysis and Scientific Computing Group

PhD studentship in the Groups of “Mathematics Applied to Biology” and “Numerical Analysis and Scientific Computing”

PhD studentship in the Groups “Analysis and Partial Differential Equations” and “Numerical Analysis and Scientific Computing”

Cash scholarships available for students who have demonstrated sporting excellence

Up to 10 scholarships for outstanding PhD students holding China Scholarship Council awards

Applying for USA Federal Student Aid?

If any part of your funding, at any time, is through USA federal Direct Loan funds, you will be registered on a separate version of this degree which does not include the possibility of distance learning which is prohibited under USA federal regulations. Find out more about American Student Loans and Federal Student Aid .

Part-time work

We advertise around 2,500 part-time jobs a year so you can make money and gain work experience. We have a special scheme to employ students on campus, wherever possible.

Find out more about careers and employability

How much does it cost?

Fees for self-funding students.

Home students: £4,786 per year for full-time students

Channel Islands and Isle of Man students: £4,786 per year for full-time students

International students: £21,500 per year for full-time students

Home PhD student fees are set at the level recommended by United Kingdom Research and Innovation (UKRI) annually, rising in line with inflation. Overseas fees are subject to an annual increase - see details on our tuition fees page

Additional costs

Note about additional costs.

Please note that all costs are best estimates based on current market values. Activities may be subject to unavoidable change in response to Government advice. We’ll let you know at the earliest opportunity. We review estimates every year and they may vary with inflation. Find out how to budget for student life .

Empirical research costs

On top of your PhD fees and living costs, you may also need to cover some research and training costs, relevant to your research project. These costs will depend on your research topic and training needs, but may include: - travel (to archives, collections or scientific facilities) - a laptop - overseas fieldwork costs (travel and accommodation, and language training) - conference costs (travel, registration fees and accommodation) - laboratory consumables and workshop materials - participant costs - transcription or translation costs - open-access publication costs. If you have a scholarship from one of the UK Research Councils, your scholarship should cover these types of costs. You'll receive details of how to claim this additional funding. If you're self funded, or if your scholarship doesn’t cover these costs, check with the Research and Enterprise Co-ordinator in your School for details of School or Doctoral School funding that may be available.

• Living costs

Find out typical living costs for studying at Sussex

Find out about our terms and conditions

Explore our campus

Experience Sussex life in our virtual tour.

Start your virtual tour

PhD Information Sessions

Visit campus and chat to staff and students. Book your place

Online PhD Sessions

Join a live webchat. Book your place

International

Meet us in your country

Course enquiries

+44 (0)1273 876787

Send us a message

Admissions enquiries

If you haven’t applied yet:

+44 (0)1273 876762 mps-pgrsupport@​sussex.ac.uk

Find out about the Department of Mathematics

After you’ve applied:

+44 (0)1273 877773 [email protected]

Find out how to apply

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Mathematics and Statistics

The School of Mathematics and Statistics has an active research programme covering a wide range of topics in the mathematical sciences, with weekly seminars, and several workshops and conferences throughout the year. It is home to a number of research fellows, visiting researchers and full- and part-time research students.

The main period for PhD student recruitment in the School is between October and March (for study commencing in the following October), although opportunities occasionally arise at other times of the year. Applicants are strongly encouraged to apply for projects specified by potential supervisors, rather than proposing their own. 

The School of Mathematics and Statistics provides a friendly and flexible working environment, where diversity is celebrated and welcomed. The School is active in challenging injustice and promoting equitable treatment for those from marginalised or under-represented groups and holds an Athena Swan Silver award for its work in promoting gender equality. We value diversity and welcome applications from candidates with protected characteristics.

• EPSRC PhD studentships are available
• Other full-time and part-time studentships also available
• Annual travel allowance of £1,250 for funded studentships
• International applicants welcomed to a diverse PhD student group
• Friendly, supportive School community

Most of our full-time research students are based at our Milton Keynes campus; for details of residence requirements for different modes of study see Full-time study and Part-time study .

• Access to research computing cluster
• All full-time students are allocated a desk and a computer within the school
• Access to advanced mathematical and statistical courses through the London Taught Course Centre (LTCC) and the Academy for PhD Training in Statistics (APTS)
• School of Mathematics and Statistics

Find your research topic

Explore specific areas of research, current and prospective projects, entry requirements, fees and funding, available supervisors, how to apply and contact details for advice.

Applied mathematics and theoretical physics

History of mathematics

Mathematical biology

Mathematics education

Pure mathematics

Related topics

Consider linked topics from other research areas.

Cold atoms for quantum technology

Complexity and design

Computational social science

Energy and sustainability

Physics education

Smart energy systems

Nothing can replace the thrill and satisfaction you get when you finally solve a mathematical problem after several attempts. I also like the fact that my research is multidisciplinary in the sense that it is not just about the mathematics alone, but also about the physics of the problem in question as well.

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Study Postgraduate

Phd in mathematics (2024 entry).

Course code

30 September 2024

3-4 years full-time

Qualification

Mathematics Institute

University of Warwick

Explore our PhD in Mathematics

The PhD in Mathematics offers an intellectually stimulating and dynamic research course. Study at the University of Warwick's Mathematics Institute, an international centre of research excellence, ranked 3rd for research power and 3rd for the number of 4* research outputs in REF 2021 (amongst UK universities).

Course overview

Mathematics at Warwick covers the full spectrum of mathematics and its applications. The Mathematics Postgraduate Degrees are appropriate for students with a strong and broad mathematical background who wish to engage in advanced mathematical techniques and attack mathematical research problems in their postgraduate work.

All students are required to undergo training in Year One and are encouraged to make use of further training opportunities available in subsequent years. Training ranges from gaining a broader knowledge of mathematics through taught modules, seminars and workshops, to enhancing your professional and transferrable skills. Our PhD students undertake high quality original research and are being well-prepared for a career, either in academia or elsewhere.

Teaching and learning

Students are required to complete a series of modules in their first year (from a very wide selection of bespoke modules), with assessment including an oral examination component. Upon the successful completion of these modules, students are required to complete a research project before being formally upgraded to a PhD at the end of the first year.

Training will be supplemented with attendance to seminars, cohort building activities, and additional transferable skills training.

General entry requirements

Minimum requirements.

First Class Honours undergraduate integrated Master's (4-year) degree from a UK university in Mathematics or a science degree with high mathematical content, or the equivalent qualification and grade from a non-UK university.

Alternatively, applicants who have a Bachelor's degree AND a Distinction in a postgraduate Master's degree would be considered.

English language requirements

You can find out more about our English language requirements Link opens in a new window . This course requires the following:

• IELTS overall score of 6.5, minimum component scores not below 6.0

International qualifications

We welcome applications from students with other internationally recognised qualifications.

For more information, please visit the international entry requirements page Link opens in a new window .

Additional requirements

There are no additional entry requirements for this course.

Our research

The mathematics department covers a wide range of research areas in mathematics and its applications.

You may also wish to explore the research interest of current Warwick academics .

Find a supervisor

The 'Find A Supervisor' link below will allow you to explore the research interests of academics within the department. Please include in your application the names of potential supervisors, with interests aligned with yours, or people you would like to work with.

The mathematics department, unlike some other departments, does not require students to make any arrangements with any potential supervisors before applying, though of course you are welcome to contact them directly and discuss your interests and any potential projects they may offer.

Tuition fees

Tuition fees are payable for each year of your course at the start of the academic year, or at the start of your course, if later. Academic fees cover the cost of tuition, examinations and registration and some student amenities.

Find your research course fees

Fee Status Guidance

The University carries out an initial fee status assessment based on information provided in the application and according to the guidance published by UKCISA. Students are classified as either Home or Overseas Fee status and this can determine the tuition fee and eligibility of certain scholarships and financial support.

If you receive an offer, your fee status will be stated with the tuition fee information. If you believe your fee status has been incorrectly classified you can complete a fee status assessment questionnaire (follow the instructions in your offer) and provide the required documentation for this to be reassessed.

The UK Council for International Student Affairs (UKCISA) provides guidance to UK universities on fees status criteria, you can find the latest guidance on the impact of Brexit on fees and student support on the UKCISA website .

Additional course costs

Please contact your academic department for information about department specific costs, which should be considered in conjunction with the more general costs below, such as:

• Core text books
• Printer credits
• Dissertation binding
• Robe hire for your degree ceremony

Scholarships and bursaries

Scholarships and financial support

Find out about the different funding routes available, including; postgraduate loans, scholarships, fee awards and academic department bursaries.

Mathematics Funding Opportunities

Find out more about the various funding opportunities that are available in our department.

Living costs

Find out more about the cost of living as a postgraduate student at the University of Warwick.

Mathematics at Warwick

Our challenging Mathematics degrees will harness your strong mathematical ability and commitment, enabling you to explore your passion for mathematics.

Find out more about us on our website Link opens in a new window

Our courses

• Interdisciplinary Mathematics (Diploma plus MSc)
• Interdisciplinary Mathematics (MSc)
• Mathematics (Diploma plus MSc)
• Mathematics (MSc)
• Mathematics (PhD)

How to apply

The application process for courses that start in September and October 2024 will open on 2 October 2023.

For research courses that start in September and October 2024 the application deadline for students who require a visa to study in the UK is 2 August 2024. This should allow sufficient time to complete the admissions process and to obtain a visa to study in the UK.

How to apply for a postgraduate research course  

After you’ve applied

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Admissions statement

See Warwick’s postgraduate admissions policy.

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Ask questions and engage with Warwick.

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Postgraduate fairs.

Throughout the year we attend exhibitions and fairs online and in-person around the UK. These events give you the chance to explore our range of postgraduate courses, and find out what it’s like studying at Warwick. You’ll also be able to speak directly with our student recruitment team, who will be able to help answer your questions.

Join a live chat with our staff and students, who are here to answer your questions and help you learn more about postgraduate life at Warwick. You can join our general drop-in sessions or talk to your prospective department and student services.

Departmental events

Some academic departments hold events for specific postgraduate programmes, these are fantastic opportunities to learn more about Warwick and your chosen department and course.

See our online departmental events

Warwick Talk and Tours

A Warwick talk and tour lasts around two hours and consists of an overview presentation from one of our Recruitment Officers covering the key features, facilities and activities that make Warwick a leading institution. The talk is followed by a campus tour which is the perfect way to view campus, with a current student guiding you around the key areas on campus.

Connect with us

Learn more about Postgraduate study at the University of Warwick.

We may have revised the information on this page since publication. See the edits we have made and content history .

Why Warwick

Discover why Warwick is one of the best universities in the UK and renowned globally.

9th in the UK (The Guardian University Guide 2024) Link opens in a new window

67th in the world (QS World University Rankings 2024) Link opens in a new window

6th most targeted university by the UK's top 100 graduate employers Link opens in a new window

(The Graduate Market in 2024, High Fliers Research Ltd. Link opens in a new window )

About the information on this page

This information is applicable for 2024 entry. Given the interval between the publication of courses and enrolment, some of the information may change. It is important to check our website before you apply. Please read our terms and conditions to find out more.

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Mathematics MPhil, PhD

In Pure Mathematics our two main fields are functional analysis and geometric algebra. In Applied Mathematics our research is predominantly in fluid mechanics, astrophysics and cosmology.

You are currently viewing course information for entry year:

Start date(s):

• September 2024
• January 2025

We invite MPhil and PhD proposals in any of our research areas.

As a research postgraduate in the School of Mathematics, Statistics and Physics you'll work under the supervision of an expert in your chosen field.

Within each field of Pure Mathematics there are multiple subgroups. In analysis, one subgroup concentrates on operator theory and function theory, the other on Banach algebras, cohomology and modules. In algebra there are subgroups devoted to the study of infinite groups, and finite classical groups and their geometries.

Our Applied Mathematics staff have research interests in:

• astrophysical and geophysical fluid dynamics
• quantum matter
• mathematical biology and archaeology
• cosmology and quantum gravity

Lists of example projects in Pure and Applied Mathematics are also available.

We run research seminars in algebra and geometries, analysis, and applied mathematics . Our postgraduate students also get the opportunity to lead seminars.

Specialist courses are offered through the MAGIC distance learning consortium , sponsored in part by the Engineering and Physical Sciences Research Council (EPSRC).

We're part of:

• the North British Functional Analysis Seminar
• the North British Geometric Group Theory Seminar
• Algebra and Representation Theory in the North, funded by the London Mathematical Society and the Edinburgh Mathematical Society
• the Joint Quantum Centre with Durham University

Important information

We've highlighted important information about your course. Please take note of any deadlines.

Please rest assured we make all reasonable efforts to provide you with the programmes, services and facilities described. However, it may be necessary to make changes due to significant disruption, for example in response to Covid-19.

View our  Academic experience page , which gives information about your Newcastle University study experience for the academic year 2023-24.

See our  terms and conditions and student complaints information , which gives details of circumstances that may lead to changes to programmes, modules or University services.

Related courses

Qualifications explained.

Find out about the different qualification options for this course.

An MPhil is available in all subject areas. You receive research training and undertake original research leading to the completion of a 40,000 - 50,000 word thesis.

Find out about different types of postgraduate qualifications

A PhD is a doctorate or doctoral award. It involves original research that should make a significant contribution to the knowledge of a specific subject. To complete the PhD you will produce a substantial piece of work (80,000 – 100,000 words) in the form of a supervised thesis. A PhD usually takes three years full time.

How you'll learn

As a Mathematics PhD or MPhil student you'll be supported by your supervision team. You'll also go through a research training analysis to identify any skills that you need to develop.

Depending on your modules, you'll be assessed through a combination of:

We offer a wide range of projects for the thesis. These will be provided by our academics. You can also propose your own topic.

Our mission is to help you:

• stay healthy, positive and feeling well
• overcome any challenges you may face during your degree – academic or personal
• get the most out of your postgraduate research experience
• carry out admin and activities essential to progressing through your degree
• understand postgraduate research processes, standards and rules

We can offer you tailored wellbeing support, courses and activities.

You can also access a broad range of workshops covering:

• research and professional skills
• careers support
• health and safety
• public engagement
• academic development

Find out more about our postgraduate research student support

Your development

Faculty of science, agriculture and engineering (sage) researcher development programme .

Each faculty offers a researcher development programme for its postgraduate research students. We have designed your programme to help you:

• perform better as a researcher
• boost your career prospects
• broaden your impact

You'll build your transferable skills and increase your confidence. You'll do this through workshops and activities. You’ll cover:

• techniques for effective research
• methods for better collaborative working
• essential professional standards and requirements

Your programme is flexible. You can adapt it to meet your changing needs as you progress through your doctorate.

Doctoral training and partnerships

There are opportunities to undertake your PhD at Newcastle within:

• a Centre for Doctoral Training (CDT)
• a Doctoral Training Partnership (DTP)

Being part of a CDT or DTP has many benefits. They combine research expertise and training of many leading universities and academic schools. You’ll study alongside a cohort of interdisciplinary PhD students.

PhDs are usually funded. All opportunities available are in the fees and funding section of each PhD course page. The following centres/partnerships may have PhD opportunities available in your subject area:

• Centre for Doctoral Training in Cloud Computing for Big Data
• EPSRC Aura Centre for Doctoral Training in Offshore Wind Energy and the Environment
• Discovery Medicine North - MRC DiMeN Doctoral Training Partnership
• Sustainable Electric Propulsion Centre for Doctoral Training

Your future

Our careers service.

Our award-winning Careers Service is one of the largest and best in the country, and we have strong links with employers. We provide an extensive range of opportunities to all students through our ncl+ initiative.

Visit our Careers Service website

Quality and ranking

All professional accreditations are reviewed regularly by their professional body

From 1 January 2021 there is an update to the way professional qualifications are recognised by countries outside of the UK

Check the government’s website for more information .

Fees and funding

Tuition fees for 2024 entry (per year), home fees for research degree students.

For 2024-25 entry, we will be aligning our standard Home research fees with those set by UK Research and Innovation (UKRI) . The standard fee will be confirmed in Spring 2024 by UKRI. The Home tuition fees for this course will be updated after this confirmation. 

If your studies last longer than one year, your tuition fee may increase in line with inflation.

Depending on your residency history, if you’re a student from the EU, other EEA or a Swiss national, with settled or pre-settled status under the EU Settlement Scheme, you’ll normally pay the ‘Home’ tuition fee rate and may be eligible for Student Finance England support.

EU students without settled or pre-settled status will normally be charged fees at the ‘International’ rate and will not be eligible for Student Finance England support.

If you are unsure of your fee status, check out the latest guidance here .

Scholarships

We support our EU and international students by providing a generous range of Vice-Chancellor's automatic and merit-based scholarships. See  our   searchable postgraduate funding page  for more information.  

What you're paying for

Tuition fees include the costs of:

• matriculation
• registration
• tuition (or supervision)
• library access
• examination
• re-examination

Find out more about:

• living costs
• tuition fees

If you are an international student or a student from the EU, EEA or Switzerland and you need a visa to study in the UK, you may have to pay a deposit.

You can check this in the How to apply section .

If you're applying for funding, always check the funding application deadline. This deadline may be earlier than the application deadline for your course.

For some funding schemes, you need to have received an offer of a place on a course before you can apply for the funding.

Search for funding

Find funding available for your course

Entry requirements

The entrance requirements below apply to 2024 entry.

Qualifications from outside the UK

English language requirements, admissions policy.

This policy applies to all undergraduate and postgraduate admissions at Newcastle University. It is intended to provide information about our admissions policies and procedures to applicants and potential applicants, to their advisors and family members, and to staff of the University.

Download our admissions policy (PDF: 201KB) Other policies related to admissions

Credit transfer and Recognition of Prior Learning

Recognition of Prior Learning (RPL) can allow you to convert existing relevant university-level knowledge, skills and experience into credits towards a qualification. Find out more about the RPL policy which may apply to this course

• How to apply

Using the application portal

The application portal has instructions to guide you through your application. It will tell you what documents you need and how to upload them.

You can choose to start your application, save your details and come back to complete it later.

If you’re ready, you can select Apply Online and you’ll be taken directly to the application portal.

Alternatively you can find out more about applying on our applications and offers pages .

Open days and events

You'll have a number of opportunities to meet us throughout the year including:

• campus tours
• on-campus open days
• virtual open days

Find out about how you can visit Newcastle in person and virtually

Overseas events

We regularly travel overseas to meet with students interested in studying at Newcastle University.

Visit our events calendar for the latest events

• Get in touch

Questions about this course?

If you have specific questions about this course you can contact:

Postgraduate Secretary School of Mathematics, Statistics and Physics Telephone: +44 (0) 191 208 6960 Email: [email protected]

For more general enquiries you could also complete our online enquiry form.

Fill in our enquiry form

Our Ncl chatbot might be able to give you an answer straight away. If not, it’ll direct you to someone who can help.

You'll find our Ncl chatbot in the bottom right of this page.

Keep updated

We regularly send email updates and extra information about the University.

Receive regular updates by email

Chat to a student

Chat online with current students with our Unibuddy platform.

Social media

Get involved with the School of Mathematics, Statistics and Physics.

Additional information

As a research postgraduate in the School of Mathematics, Statistics and Physics you will be working under the supervision of an expert in your chosen field. To help you identify a topic and potential supervisor, we encourage you to find out more about our staff specialisms .

• How You'll Learn
• Your Development
• Your Future
• Quality and Ranking
• Fees and Funding
• Entry Requirements
• Open days & events

Department of Mathematics

PhD and MPhil in Mathematics

Year of entry: 2024/25  ( see 2023/24 entry )

Be part of our vision to advance mathematical knowledge and understanding through impactful research.

Through our research we aim to create new applications and techniques that benefit the mathematics community and society in general. Our connections across the University, and with industrial partners and policymakers, will enable you to exchange ideas and build connections through your research. Our department provides a healthy span of research areas in pure and applied mathematics and statistics in a supportive environment for early career researchers.

Your research

Your research will culminate in a thesis on a topic agreed between you and your supervisor.  Your thesis must contain a substantial piece of research which includes some original work. This could include new ideas, or original commentary on material which is currently considered to be at the forefront of mathematical knowledge. 

Work on your thesis is guided by regular meetings with your supervisor.  You'll be assessed wholly on the basis of your thesis, although your degree will normally include six 10-hour graduate-level courses provided by the MAGIC consortium graduate school.

At the end of your degree, you'll have up to 12 months to finish writing up your research.

Assessment for the award of the degree of either PhD or MPhil will be on the basis of your thesis and an oral (viva voce) examination. The expectation of the Department of Mathematics is that a thesis submitted for the PhD degree will typically consist of between 100 and 200 A4 sized pages and a thesis submitted for the MPhil degree will typically consist of between 70 and 120 A4 sized pages.

[email protected] +44 (0)1904 323 097

Related links

• Research degree funding
• Accommodation
• International students
• Life at York
• How to apply

Impactful research

100% of our departmental research outputs received the highest ratings (3* and 4*) in the latest Research Excellence Framework (2021).

Bespoke employability training

Our dedicated support team will help you present yourself at your best for the next step of your career.

Top 20 UK research department

according to the Times Higher Education ranking of the Research Excellence Framework (REF) 2021.

Explore Mathematics funding for postgraduate researchers and wider postgraduate support.

Supervision

You'll be assigned a supervisor who will guide your work throughout your time with us. We'll match your research interests to their area of expertise.

Training and support

Throughout your course you'll have a supervisor to support you and guide your research. 

Work on your thesis is monitored by regular meetings of the Thesis Advisory Panel (at least once every six months for a full-time student and once a year for part-time students). The panel will review the progress of your research and provide additional advice and guidance.

You'll be taught and supervised by staff who themselves produce internationally renowned research. There is a supportive atmosphere among the graduate students and staff are on hand to give you the help you need.

Course location

This course is run by the Department of Mathematics.

The Department of Mathematics is located in James College on Campus West. 

Entry requirements

To apply for these courses you should hold, or expect to hold, an undergraduate degree in which mathematics has formed a substantial part of the course, with a 2:1 or first-class honours (or overseas equivalent). Assessment of your application will include consideration of your full academic record, including progress on courses you are still studying.

English language requirements

If English is not your first language you must provide evidence of your ability.

Check your English language requirements

Apply for the MPhil

Apply for the PhD

Take a look at the supporting documents you may need for your application.

Find out more about how to apply .

You don't need to provide a formal research proposal, but you should include a short statement on the area(s) of mathematics you wish to work in. In the personal statement section of the application form you should tell us about why you want to undertake a research degree. You should also include details of any relevant experience you have, such as a summer project or a topic that you have researched on your own.

There isn't a deadline for applying to join a research programme. If you're an International student, it's best to apply at least three months prior to your intended start date to avoid any delays in applying for your accommodation and/or visa. For both Home and International students, if you wish to be considered for Departmental funding, the main round of funding will be allocated in early March, with shortlisting and interviews taking place during February. Other sources of funding may have their own deadlines.

Identify a supervisor

Before applying, please look at the lists of academic staff in each of our research groups to see if there is a prospective supervisor working in an area which relates to your own research interests. You're welcome to email a prospective supervisor informally to find out more about their research or to ask if they might be considering taking on a postgraduate researcher.

Find a supervisor

As part of your application, you'll be invited to an interview (either face-to-face or online). If your first language is not English, you should be fluent enough to speak confidently about your intended area of research and discuss your mathematical background and interests with a panel of academics.

Careers and skills

Our dedicated careers team offers specific support, including a programme of professional researcher development and careers workshops and 1:1 career support sessions. These will help to build up your employability portfolio and improve your skills and experience outside of your research work.

Career opportunities

Our graduates have gone on to work in a wide range of sectors and with well-known employers including:

• PricewaterhouseCoopers
• BAE Systems
• NHS Digital

Discover York

We offer a range of campus accommodation to suit you and your budget, from economy to deluxe.

Discover more about our researchers, our facilities, and why York is the perfect choice for your research degree.

Graduate Research School

Connect with researchers across all disciplines to get the most out of your research project.

Meet us online or on campus

Find out all you need to know about applying to York

Scholarships

Find scholarships to support your studies

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Course type

Qualification, university name, distance learning postgraduate mathematics.

11 degrees at 6 universities in the UK.

Customise your search

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

Related subjects:

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

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

PhD Computing and Mathematics

University of wolverhampton.

• 4 years Distance without attendance degree: £4,712 per year (UK)
• 4 years Full time degree: £4,712 per year (UK)
• 8 years Part time degree: £2,356 per year (UK)

Statistics for Clinical Trials MSc

Ucl (university college london).

• 1 year Distance without attendance degree
• 2 years Distance without attendance degree
• Advanced Clinical Trials Statistics- Core
• Further Trial Designs and Outcomes (15 Credits) - Core
• Health Economics in Clinical Trials- Core
• Statistical Coding in Clinical Trials- Core
• Meta Analysis in Clinical Trials- Core
• View all modules

Mathematics PhDs and Mphils (Distance Learning)

University of portsmouth.

• 6 years Distance without attendance degree: £2,356 per year (UK)

Operational Research & Logistics PhDs and MPhils (Distance Learning)

Mathematics by distance learning (graduate certificate), birkbeck, university of london.

• 1 year Distance without attendance degree: £3,800 per year (UK)

Postgraduate Diploma in Mathematics

Open university.

• 2 years Distance without attendance degree: £2,520 per year (UK)

Statistics with Financial Mathematics MSc

University of sheffield.

• 2 years Distance without attendance degree: £6,035 per year (UK)
• 1 year Full time degree: £12,070 per year (UK)
• Bayesian Statistics and Computational Methods (30 Credits) - Core
• Stochastic Processes and Finance (20 Credits) - Core
• Financial Mathematics (10 Credits) - Core
• Time Series (15 Credits) - Core
• Machine Learning (15 Credits) - Core

Postgraduate Certificate in Mathematics

• 1 year Distance without attendance degree: £2,520 per year (UK)

Statistics Graduate Certificate

• 9 months Distance without attendance degree: £4,023 per year (UK)
• Mathematical Methods for Statistics (20 Credits) - Core
• Probability and Probability Distributions (20 Credits) - Core
• Basic Statistics (20 Credits) - Core

MSc in Mathematics

• 2 years Distance without attendance degree: £3,780 per year (UK)
• Dissertation in mathematics (M840) (30 Credits) - Core

Statistics MSc

• Medical Statistics (15 Credits) - Core
• Sampling Theory and Design of Experiments (15 Credits) - Core
• The Statistician's Toolkit (30 Credits) - Core

Course type:

• Distance learning

Qualification:

Related subjects:.

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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Mathematics

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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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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. 

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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 

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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. 

Experience LSE from home

Webinars, videos, student blogs and student video diaries will help you gain an insight into what it's like to study at LSE for those that aren't able to make it to our campus.  Experience LSE from home . 

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 . 

LSE visits you

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

Virtual Graduate Open Day

Register your interest

Related programmes, mphil/phd statistics.

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PhD opportunities

Why study with us?

Join a department with a long and established track record of world-leading mathematics research. We offer an exceptional learning environment in which to work on your PhD and grow as a researcher.

Fees and funding

The University allocates around 150 entry awards each year in PhD studentships and bursaries, so there are many ways to access PhD funding.

How we support you

You'll receive support from our Department as well as the Doctoral and Researcher College, which is the University of Reading's hub for all doctoral activity. 

Life in the Department

You'll join a large, inclusive community, and have opportunities to present your research in workshops and at conferences. 

Our academics have a wide range of expertise across the breadth of pure and applied mathematics, which they bring to their doctoral supervision.

Our research

98% of our research is world leading or internationally excellent and 100% of our research impact has been classed ‘outstanding’ or ‘very considerable’ (Research Excellence Framework 2021, combining 4* and 3* submissions – Mathematical Sciences).

Take the next step

• How to apply
• Get a prospectus
• Ask us a question
• Learn about the Doctoral and Researcher College

• Find a course
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• Postgraduate study
• MPhil/PhD research
• Short courses
• Entry requirements
• Financial support

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Mathematics

Graduate Certificate, Graduate Diploma

Application options include:

Course Overview

Our Graduate Diploma and Graduate Certificate in Mathematics provide you with an opportunity to extend and refresh your skills and background knowledge in mathematics, whether you are looking to progress to further postgraduate study, have particular interests in this area, or simply wish to complement your previous mathematical education.

On these mathematics courses, you will gain crucial skills in understanding and applying core mathematics results from areas such as algebra, calculus and analysis. You will also learn the importance of rigorous mathematical arguments and gain understanding of key mathematical concepts that are the basis of postgraduate study in mathematics.

Designed to be as flexible as possible, on both of these courses you will have a choice of modules taken from our  BSc Mathematics . You will meet with the course director before the start of the academic year and decide on a suitable course of study, based on your interests and experience.

Both the Graduate Diploma and Graduate Certificate are undergraduate-level qualifications that will prepare you for postgraduate study. They typically take one to two years to complete and are made up of two, three or four modules at final-year undergraduate degree level (worth 60, 90 or 120 credits).

Graduate Certificate : this course is also available to study online by distance learning with a January start. We have specifically developed the course materials and content to meet the needs of distance learners to offer you the flexibility you need to combine study with work.

Discover the career opportunities available by taking Mathematics (Graduate Certificate, Graduate Diploma).

Key information and modules

Mathematics graduate certificate: 1 year part-time, on campus, starting october 2024.

Central London

Mathematics by Distance Learning: January start Graduate Certificate: 1 year part-time, online, starting January 2025

Distance learning

Mathematics Graduate Diploma: 1 year full-time, on campus, starting October 2024

Mathematics graduate diploma: 2 years part-time, on campus, starting october 2024.

Find another course:

• Designed for students with mathematical ability and a first degree in a quantitative subject.
• An ideal way to refresh and extend your existing knowledge, as preparation for further graduate study, or as a stand-alone course.
• Modules are designed and led by research-active mathematicians with expertise in areas such as algebra, combinatorics and numerical analysis.
• Allow you to follow your passion learning more about the areas of mathematics that interest you most.
• Copies of the recommended texts for each module will be available in the  Birkbeck Library . The library also provides excellent facilities for private study, several computer workstation rooms plus a range of electronic resources, including electronic textbooks and journal access.

Birkbeck makes all reasonable efforts to deliver educational services, modules and programmes of study as described on our website. In the event that there are material changes to our offering (for example, due to matters beyond our control), we will update applicant and student facing information as quickly as possible and offer alternatives to applicants, offer-holders and current students.

Entry Requirements

A second-class honours degree (2:2 or above) in a quantitative discipline, such as science or economics, or a joint degree containing some mathematics.

In exceptional circumstances, candidates without a first degree in a quantitative discipline may be admitted, provided they have equivalent-level qualifications or professional experience that convinces the admissions team that the course is suitable for them.

Applications are reviewed on their individual merits and your professional qualifications and/or relevant work experience will be taken into consideration positively. We actively support and encourage applications from mature learners.

On your application form, please list all your relevant qualifications and experience, including those you expect to achieve.

Apply now  to secure your place. The earlier you apply, the sooner your application can be considered and you can enrol. You do not need to have completed your current qualification to start your application.

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 and foundation programmes to help you improve your English language skills and get your place at Birkbeck.

Visit the International section of our website to find out more about our  English language entry requirements and relevant requirements by country .

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.

Credits and accredited prior learning (APL)

If you have studied at university, you may have accumulated credits through the modules you studied. It may be possible to transfer these credits from your previous study to Birkbeck or another institution.

Mathematics by Distance Learning: January start Graduate Certificate: 1 year part-time, online, starting in academic year 2024-25

Academic year 2024–25, starting january 2025.

Part-time home students: £3,800 per year Part-time international students : £6,610 per year

Mathematics Graduate Certificate: 1 year part-time, on campus, starting in academic year 2024-25

Academic year 2024–25, starting october 2024, mathematics graduate diploma: 1 year full-time or 2 years part-time, on campus, starting in academic year 2024-25.

Part-time home students: £3,800 per year Full-time home students: £7,600 per year Part-time international students : £6,610 per year Full-time international students: £13,220 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.

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 .

At Birkbeck, most of our courses are taught in the evening and all of our teaching is designed to support students who are juggling evening study with work and other commitments. We actively encourage innovative and engaging ways of teaching, to ensure our students have the best learning experience.

Teaching may include formal lectures, seminars, and practical classes and tutorials. Formal lectures are used in most degree programmes to give an overview of a particular field of study. They aim to provide the stimulus and the starting point for deeper exploration of the subject during your own personal reading. Seminars give you the chance to explore a specific aspect of your subject in depth and to discuss and exchange ideas with fellow students. They typically require preparatory study.

In addition, you will have access to pastoral support via a named Personal Tutor.

Methods of teaching on this course

Lectures and seminars. Examinations are held in May and June. You will work on your project throughout the course, and submit the final dissertation in September (at the end of your second year if studying part time).

Mathematics by Distance Learning Graduate Certificate : pre-recorded online lectures, online self-assessment quizzes with automated marking/feedback, live-streamed examples classes, Moodle (our virtual learning environment) discussion boards and virtual 'office hours'.

Teaching hours

Our evening hours are normally between 6pm and 9pm (6-7.30pm and 7.30-9pm). Some programmes also offer teaching during the day and this will be clearly signposted to you where it is available.

On our taught courses, you will have scheduled teaching and study sessions each year. Scheduled teaching sessions may include lectures, seminars, workshops or laboratory work. Depending on the modules you take, you may also have additional scheduled academic activities, such as tutorials, dissertation supervision, practical classes, visits and field trips. On our taught courses, the actual amount of time you spend in the classroom and in contact with your lecturers will depend on your course, the option modules you select and when you undertake your final-year project (if applicable).

Alongside your contact hours, you will also undertake assessment activities and independent learning outside of class. The amount of time you need to allocate to study both for taught sessions (this might include online sessions and/or in-person sessions) and personal study will depend on how much you are studying during the year and whether you are studying full time or part time.

Birkbeck’s courses are made up of modules and allocated ‘credit’. One credit is equivalent to ten hours of learning time. Modules are usually in 15, 30 or 60 credit units. A 15-credit module will mean around 150 hours of learning, including taught sessions and independent study or group work. This is spread out over the whole period of that module and includes the time you spend on any assessments, including in examinations, preparing and writing assessments or engaged in practical work as well as any study support sessions to help you in your learning.

On our distance-learning and blended-learning courses, discussion, collaboration and interaction with your lecturers and fellow students is encouraged and enabled through various learning technologies.

Timetables are usually available from September onwards and you can access your personalised timetable via your My Birkbeck Profile online (if you have been invited to enrol).

Indicative class size

Class sizes vary, depending on your course, the module you are undertaking, and the method of teaching. For example, lectures are presented to larger groups, whereas seminars usually consist of small, interactive groups led by a tutor.

Independent learning

On our taught courses, much of your time outside of class will be spent on self-directed, independent learning, including preparing for classes and following up afterwards. This will usually include, but is not limited to, reading books and journal articles, undertaking research, working on coursework and assignments, and preparing for presentations and assessments.

Independent learning is absolutely vital to your success as a student. Everyone is different, and the study time required varies topic by topic, but, as a guide, expect to schedule up to five hours of self-study for each hour of teaching.

Study skills and additional support

Birkbeck offers study and learning support to undergraduate and postgraduate students to help them succeed. Our Learning Development Service can help you in the following areas:

• academic skills (including planning your workload, research, writing, exam preparation and writing a dissertation)
• written English (including structure, punctuation and grammar)
• numerical skills (basic mathematics and statistics).

Our Disability and Dyslexia Service can support you if you have additional learning needs resulting from a disability or from dyslexia.

Our Counselling Service can support you if you are struggling with emotional or psychological difficulties during your studies.

Our Mental Health Advisory Service can support you if you are experiencing short- or long-term mental health difficulties during your studies.

Assessment is an integral part of your university studies and usually consists of a combination of coursework and examinations, although this will vary from course to course - on some of our courses, assessment is entirely by coursework. The methods of assessment on this course are specified below under 'Methods of assessment on this course'. You will need to allow time to complete coursework and prepare for exams.

Where a course has unseen written examinations, these may be held termly, but, on the majority of our courses, exams are usually taken in the Summer term, during May to June. Exams may be held at other times of the year as well. In most cases, exams are held during the day on a weekday - if you have daytime commitments, you will need to make arrangements for daytime attendance - but some exams are held in the evening. Exam timetables are published online.

Find out more about assessment at Birkbeck, including guidance on assessment, feedback and our assessment offences policy.

Methods of assessment on this course

Each module will have a daytime examination at the end of the year. There will also be regular assessed coursework, usually contributing 20% of the marks for the module. Normally this will consist of two to four take-home exercise sets.

Mathematics by Distance Learning Graduate Certificate : online quizzes, short problem-based assignments submitted and marked online, and formal examinations taken in person at an assessment centre near you.

Careers and employability

Graduates can pursue career paths in the financial sector, actuarial profession, IT and computing, teaching and academia. Possible professions include:

• statistician
• chartered accountant
• corporate investment banker
• investment analyst
• quantity surveyor.

We offer a comprehensive careers service - Careers and Enterprise - your career partner during your time at Birkbeck and beyond. At every stage of your career journey, we empower you to take ownership of your future, helping you to make the connection between your experience, education and future ambitions.

You apply directly to Birkbeck for this course, using the online application link.

You will need to prove your identity when you apply - read more about suitable forms of identification .

When to apply

You are strongly advised to apply now, to ensure there are still places on your chosen course and to give you enough time to complete the admissions process, to arrange funding and to enrol.

You don't need to complete your current programme of study before you apply - Birkbeck can offer you a place that is conditional on your results.

You will also receive information about subject-specific induction sessions over the summer.

Help and advice with your application

Get all the information you need about the application, admission and enrolment process at Birkbeck.

Our online personal statement tool will guide you through every step of writing the personal statement part of your application.

Apply for your course

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

Related courses

• Finance (MSc)
• Banking and Finance (MSc)

Course structure

Course structure listing, course structure and modules for mathematics by distance learning: january start graduate certificate: 1 year part-time, online, starting january 2025.

You will study four compulsory modules to a total of 60 credits.

• Abstract Algebra 1
• Abstract Algebra 2
• Advanced Calculus
• Real Analysis

Course structure and modules for Mathematics Graduate Certificate: 1 year part-time, on campus, starting October 2024

You must complete modules worth a total of 60 credits, consisting of two 30-credit modules at Level 6 (final-year undergraduate level).

Indicative option modules - on campus

• Advanced Mathematical Methods
• Algebra and Analysis
• Calculus 3: Transforms & Models
• Finite Mathematics

Indicative option modules - online

Course structure and modules for mathematics graduate diploma: 1 year full-time or 2 years part-time, on campus, starting october 2024.

You must complete four modules worth a total of 120 credits:

• one at Level 5 or 6 (30 credits)
• three at Level 6 (30 credits each).

All Level 5 modules run every year; Level 6 modules differ each year. You should not select more than 60 credits of online modules.

With the course director’s approval, you may replace one of the 30-credit Level 6 modules with two 15-credit modules from our Graduate Certificate in Mathematics by Distance Learning . These shorter modules run for a single term.

Indicative option modules - Level 5

• Analysing Data
• Number Theory and Cryptography
• Probability Models

Indicative option modules - Level 6

• Statistics: Theory and Practice

Indicative option modules - Level 6, online

3 Distance learning PhD Programmes in Mathematics 2024

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Doctor of Philosophy

Edith cowan university.

• Joondalup, Australia
• Mount Lawley, Australia

Full time, Part time

8 semesters

Distance learning, On-Campus

A Doctor of Philosophy (PhD) is an opportunity to pursue a topic you're passionate about at the highest academic level.

Compare this program

Save this program

Doctor of Philosophy (Integrated)

The Doctor of Philosophy (Integrated) is a research degree commencing with a cohort-based foundation year of research preparation followed by an independent, supervised research project.

Doctorate in Mathematics

Atlantic international university.

• Honolulu, USA

English, Portuguese, Spanish

The Doctorate of Mathematics program helps students to understand and use mathematics in other fields of knowledge with basic mathematical skills for everyday living, and to be employed and to act in a consulting capacity on matters concerning mathematics. Career opportunities in mathematics include actuarial services, education, and in industries such as telecommunications, aerospace, and computer.

Popular study format

Popular education type

Popular locations

Distance learning PhD Programmes in Mathematics

The subject of mathematics is often paired up with other subjects such as education, statistics, finance, and computer science. This pairing can give added value in the teaching, computer programming, and financial forecasting and planning fields.

The PhD is a doctoral degree, specifically called a "doctor of philosophy" degree. This is misleading because PhD holders are not necessarily philosophers (unless they earned their degree in philosophy!). That said, PhD recipients are able to engage in thought experiments, reason about problems, and solve problems in sophisticated ways.

Online or distance learning refers to the use of electronic media and information and communication technologies (ICT) in education. With online learning, one can access education at any time and from any location with an available internet connection.

• Schools & departments

Mathematics Education PhD

Awards: PhD

Study modes: Full-time, Part-time

Funding opportunities

Programme website: Mathematics Education

Discovery Day

Join us online on 18th April to learn more about postgraduate study at Edinburgh

View sessions and register

Research profile

By joining the School of Mathematics, you will have opportunities to interact with educational research groups in Mathematics as well as cognate disciplines such as the Edinburgh Physics Education Group, and the interdisciplinary Centre for Research in Digital Education. As a research student you will be part of a vibrant and dynamic community of educators, with expertise in educational research and opportunities to develop and pursue your research goals. You can be certain of a rich academic setting with opportunities available for students to gain a breadth of knowledge from leading experts.

You will enjoy excellent facilities, ranging from one of the world’s major supercomputing hubs to generous library provision for research at the leading level, including the Noreen and Kenneth Murray Library at King’s Buildings.

Students have access to more than 1,400 computers in suites distributed across the University’s sites, many of which are open 24 hours a day. In addition, if you are a research student, you will have your own desk with desktop computer.

We provide all our mathematics postgraduates with access to software packages such as Maple, Matlab and Mathematica. Research students are allocated parallel computing time on ‘Eddie’ – the Edinburgh Compute and Data Facility. It is also possible to arrange use of the BlueGene/Q supercomputer facility if your research requires it.

Career opportunities

Graduates are expected to find employment in positions at public universities, private schools, community colleges, and vocational institutions to teach students at associates, bachelors, masters, or even doctoral level.

Due to their area of expertise, many graduates with a PhD in Mathematical Education will focus on training the next generation of teachers and educational support staff for secondary schools. 


There are many other potential career paths for holders of a PhD in mathematics, including finance and IT.

Entry requirements

These entry requirements are for the 2024/25 academic year and requirements for future academic years may differ. Entry requirements for the 2025/26 academic year will be published on 1 Oct 2024.

A UK first class honours degree, or its international equivalent, in an appropriate subject; or a UK 2:1 honours degree plus a UK masters degree, or their international equivalents; or relevant qualifications and experience.

International qualifications

Check whether your international qualifications meet our general entry requirements:

• Entry requirements by country
• English language requirements

Regardless of your nationality or country of residence, you must demonstrate a level of English language competency at a level that will enable you to succeed in your studies.

English language tests

We accept the following English language qualifications at the grades specified:

• IELTS Academic: total 6.5 with at least 6.0 in each component. We do not accept IELTS One Skill Retake to meet our English language requirements.
• TOEFL-iBT (including Home Edition): total 92 with at least 20 in each component. We do not accept TOEFL MyBest Score to meet our English language requirements.
• C1 Advanced ( CAE ) / C2 Proficiency ( CPE ): total 176 with at least 169 in each component.
• Trinity ISE : ISE II with distinctions in all four components.
• PTE Academic: total 62 with at least 59 in each component.

Your English language qualification must be no more than three and a half years old from the start date of the programme you are applying to study, unless you are using IELTS , TOEFL, Trinity ISE or PTE , in which case it must be no more than two years old.

Degrees taught and assessed in English

We also accept an undergraduate or postgraduate degree that has been taught and assessed in English in a majority English speaking country, as defined by UK Visas and Immigration:

• UKVI list of majority English speaking countries

We also accept a degree that has been taught and assessed in English from a university on our list of approved universities in non-majority English speaking countries (non-MESC).

• Approved universities in non-MESC

If you are not a national of a majority English speaking country, then your degree must be no more than five years old* at the beginning of your programme of study. (*Revised 05 March 2024 to extend degree validity to five years.)

Find out more about our language requirements:

• Academic Technology Approval Scheme

If you are not an EU , EEA or Swiss national, you may need an Academic Technology Approval Scheme clearance certificate in order to study this programme.

Fees and costs

Tuition fees, scholarships and funding, featured funding.

• School of Mathematics funding opportunities
• Research scholarships for international students

UK government postgraduate loans

If you live in the UK, you may be able to apply for a postgraduate loan from one of the UK's governments.

The type and amount of financial support you are eligible for will depend on:

• your programme
• the duration of your studies
• your tuition fee status

Programmes studied on a part-time intermittent basis are not eligible.

• UK government and other external funding

Other funding opportunities

Search for scholarships and funding opportunities:

• Search for funding

Further information

• Graduate School Administrator
• Phone: +44 (0)131 650 5085
• Contact: [email protected]
• Programme Director, Professor Chris Sangwin
• Phone: +44 (0)131 650 5966
• Contact: [email protected]
• School of Mathematics
• James Clerk Maxwell Building
• Peter Guthrie Tait Road
• The King's Buildings Campus
• Programme: Mathematics Education
• School: Mathematics
• College: Science & Engineering

Select your programme and preferred start date to begin your application.

PhD Mathematics Education - 3 Years (Full-time)

Phd mathematics education - 6 years (part-time), application deadlines.

We strongly recommend you submit your completed application as early as possible, particularly if you are also applying for funding or will require a visa. We may consider late applications if we have places available. All applications received by 22 January 2024 will receive full consideration for funding. Later applications will be considered until all positions are filled.

• How to apply

You must submit two references with your application.

Find out more about the general application process for postgraduate programmes: