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Mathematics Research MPhil/PhD (Applied Mathematics, Pure Mathematics)

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  • RAE: According to the RAE assessment over 65 per cent of the research in the Department is internationally excellent or world-leading in terms of originality, significance and rigour. This puts the Department in the top quarter of all UK Mathematics Departments and near the top in London.

  • Research income: Approximately £2m per annum.

  • Current number of academic staff: 40 permanent, 10 fixed-term

  • Current number of research students: Approximately 65.

  • Research grants: Researchers from our department currently hold research grants from BBSRC, EPSRC, STFC, Royal Society, Leverhulme Trust, London Mathematical Society and the European Comission. Our grants include studentships for postgraduate research students.

  • Joint PhDs available: Exciting opportunities to gain a joint PhD with the University of Hong Kong and the Humboldt University of Berlin.

Key information

Duration Full-time: 3-4 years; Part-time: 6-8 years.

Study mode Full-time, Part-time

Further details

Awarding institution King's College London/King's and HKU for joint programme

Faculty Faculty of Natural & Mathematical Sciences

Department Department of Mathematics



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Course detail


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

Joint PhD programme
Exciting opportunities are now available to undertake a joint PhD programme with the University of Hong Kong or the Humboldt University of Berlin.

Course study environment

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

Postgraduate training

Carrying out research is learned in apprenticeship mode as PhD student works with a supervisor. Our PhD students receive various forms of training during their period of research, eg attending courses in the London Taught Courses Centre, attendance at EPSRC summer schools; provision of advanced lecture courses; College training courses for graduates who will give tutorial teaching to undergraduates; weekly seminars in the area of your research; frequent research group meetings; attendance at national and international conference and research meetings. Communication skills are developed by: preparing and presenting seminars in the department, assisted by your supervisor; apprenticeship in writing papers and, in due course, the PhD thesis. Students also have the opportunity to give tutorials (with training, see above) to undergraduates.

Head of Department

Profressor Steven Gilmour

Contact for information

Contact the Admissions Office • Before you apply: via our Enquiry Form (www.kcl.ac.uk/study/pg/contacts.aspx#admissions) • After applying: use the messaging service at apply.kcl.ac.uk Postgraduate Officer, Admissions Office Tel: +44 (0)20 7848 1648

Course website


Entry requirements

Entry requirements

Maths Research entry requirements
Minimum UK requirements
  • Financial Maths
  •   Bachelor’s degree with 1st class or 2:1 honours. Those applying for the joint degree are encouraged to contact an academic at King's to develop research links with the partner institution. Candidates may also be interviewed.
  • Disordered Systems
  •   Bachelor’s degree with 1st class or 2:1 honours. Those applying for the joint degree are encouraged to contact an academic at King's to develop research links with the partner institution.
  • Theoretical Physics
  •   Bachelor’s degree with 1st class or 2:1 honours. A good MMath, MSci or master's degree with high grades in modules that relate to the chosen research area will strengthen the application. Candidates may also be interviewed at the Department's open day or afterwards.
  • Pure Maths
  •   MMath, MSci or Master’s degree with Merit and high grades in modules relating to the research area. Candidates may also be interviewed.
    International requirements   Visit our admissions webpages to view our International entry requirements.
    English Language requirements   Band E for 2019/20 academic year

    Band D for 2020/21 academic year onwards (i.e. from October 2020 entry)

    Visit our admissions webpages to view our English language entry requirements.


    Students applying for the joint PhD programme with Humboldt University may be required to hold a Master’s degree in order to meet the requirements of Humboldt University.

    Application procedure

    Applicants applying for the Pure Mathematics pathway should apply to the Pure Mathematics Research MPhil/PhD

    You can apply for supervision in all fields of interest of our staff members. Your application is considered and processed by the relevant admissions officers. We aim to reply within six weeks. To suitably qualified applicants, we offer opportunities to meet with prospective supervisors. Each February we hold an open day which provides information about our research activities and an opportunity to meet with relevant members of the department.

    September, January, and April start dates are available. Applicants are strongly encouraged to start their degree at beginning of the academic year in September, when the College offers a full induction programme.

    Please note that you should submit your application by 1 February if you want to be considered for a Graduate Teaching Scholarship (GTS) or other funds. You can find more information on funding processes on the PhD Funding Pages.

    Although there can be variations the selection process typically runs as follows:

    Starting in February students are selected for interview. The interviews are held in March and a first round of offers is made. If an offer is declined then the groups make second round offers until the positions are filled. Research groups tend to fill their funded PhD positions first as these are the most competitive. Therefore students are advised to apply on time to receive full consideration. Unfunded positions are rare as most supervisors will have taken on a funded student.

    If you have any further questions please contact the Admissions Tutors or the Postgraduate Admissions Team.

    ATAS  An ATAS certificate is required for successful applicants applying for this course whose nationality is outside the European Economic Area (EEA) and Switzerland. For further guidance on obtaining an ATAS certificate can be found on our International Student Advice pages.

    Personal statement and supporting information

    You will be asked to submit the following documents in order for your application to be considered:

    Document checklist
    Research Proposal Yes The proposal should explain in some detail precisely the field of study that you want to contribute to and current research gaps, what you want to do and how you propose to do it. For advice on how to write a winning application, please visit the following page.
    Previous Academic Study Yes A copy (or copies) of your official academic transcript(s), showing the subjects studied and marks obtained. If you have already completed your degree, copies of your official degree certificate will also be required. Applicants with academic documents issued in a language other than English, will need to submit both the original and official translation of their documents.
    Reference Yes One is reference is required, professional references will be accepted if you have completed your qualifications over five years ago.
    Other Optional You may also wish to include a CV (Resume) or evidence of professional registration as part of your application.


    Course intake

    PhD: 8-15 FT, 2-5 PT per year; MPhil: 5-10 FT, 1-5 PT per year.

    Joint PhDs - Application advice

    Applicants for the Joint PhD programme must contact the relevant departments at both universities before submitting an application in order to discuss the suitability of their topic for the joint programme and to locate potential supervisors. Applications should initially be submitted to the proposed home institution only, ie where the student will start and finish their programme. Students should note that acceptance onto the programme may take slightly longer than for single-institution PhDs because of the additional steps involved. Further details, including FAQs, can be found on the King’s Worldwide web pages.

    Applicants who choose King’s as their home institution should apply through the online system, selecting the appropriate Joint PhD option from the drop-down list. In addition to the standard supporting documentation, applicants should submit a Travel Plan form indicating how they intend to divide their time between the two partner institutions. Students must spend a specified amount of time in each institution, details of which can be found in the ‘Notes’ section of the Travel plan form.

    It is recommended that students submit applications for the Joint PhD programme by the end of March to begin the following September.

    Application closing date

    The final deadlines for applicants with Home, EU or overseas (international) fee status are detailed below. Please note that funding applications deadlines may be earlier. We will open applications for the corresponding intake in 2022 after the same intake has passed in 2021.  

    • February 2021 entry – 23rd October 2020 for international applicants and 23rd November 2020 for Home/EU applicants 

    • June 2021 entry - 12th April 2021 for international and Home/EU applicants 

    • October 2021 entry – 30th July 2021 for international/EU applicants and 27th August 2021 for Home applicants 

    • February 2022 entry – 12th November 2021 for international/EU applicants and 6th December 2021 for Home applicants 

    • June 2022 entry – 1st April 2022 for international/EU applicants and 11th April 2022 for Home applicants 

    Applications for 2022/23 academic year will open from October 2021. 

    Help and support

    If you don't have a suitable qualification for direct entry to a UK university, or if English isn't your first language, our academic preparation courses can help you get ready for study in the UK.

    Preparation courses

    Fees and funding

    Mathematics Research

    UK Tuition 2020/21

    Full time tuition fees:

    £5,550 per year (MPhil/PhD, Mathematics Research)

    Part Time Tuition fees:

    £2,780 per year (MPhil/PhD, Mathematics Research)

    UK Tuition 2021/22

    Full time tuition fees:

    £5,820 per year (MPhil/PhD, Mathematics Research)

    Part Time Tuition fees:

    £2,910 per year (MPhil/PhD, Mathematics Research)

    International Tuition Fees 2020/21

    Full time tuition fees:

    £20,820 per year (MPhil/PhD, Mathematics Research)

    Part Time Tuition fees:

    £10,410 per year (MPhil/PhD, Mathematics Research)

    International Tuition Fees 2021/22

    Full time tuition fees:

    £21,870 per year (MPhil/PhD, Mathematics Research)

    Part Time Tuition fees:

    £10,935 per year (MPhil/PhD, Mathematics Research)

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

    International Tuition Fees 2020/21

    Full time tuition fees: 

    £20,820 per year (MPhil/PhD, Mathematics Research with University of Hong Kong)

    £20,820  per year (MPhil/PhD, Mathematics Research with Humboldt-Universität Zu Berlin)

    Part time tuition fees: £10,410  (MPhil/PhD, Mathematics Research  with Humboldt-Universität Zu Berlin)

    International Tuition Fees 2021/22

    Full time tuition fees: 

    £21,870 per year (MPhil/PhD, Mathematics Research with University of Hong Kong)

    £21,870 per year (MPhil/PhD, Mathematics Research  with Humboldt-Universität Zu Berlin)

    Part time tuition fees: £10,935 (MPhil/PhD, Mathematics Research  with Humboldt-Universität Zu Berlin) 

    Applied Mathematics / Pure Mathematics Research

    International Tuition Fees 2020/21

    Full time tuition fees:  £20,820 per year

    Part time tuition fees: £10,410 per year

    International Tuition Fees 2021/22

    Full time tuition fees:  £21,870 per year

    Part time tuition fees: £10,935 per year

    EU Students starting their programme in the academic year 2021/22 will pay international tuition fees.

    These tuition fees may be subject to additional increases in subsequent years of study, in line with King’s terms and conditions.

     There may be particular research areas where bench fees may be charged.  In these cases the fee levels are set out in this document.

    Financial help and support

    Visit the fees and funding webpages to find out more about bursaries, scholarships, grants, tuition fees, living expenses, student loans and other financial help available at King's.


    Blue box with King's College London rankings. Starting with, 7th in the UK for research quality. Followed by, 6th in the UK for research power. Concluding with, 4th among multi-faculty universities for research Impact. The source is research excellence framework 2014

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