MPhil/PhD Mathematics

  • Graduate research
  • Department of Mathematics
  • Application code G1ZM
  • Starting 2021
  • Home full-time: Closed
  • Overseas full-time: Closed
  • 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. 

Teaching and learning in 2021 

LSE is committed to offering you the best possible teaching and learning experience within the constraints of the ongoing COVID-19 pandemic. 

Our expectation for the 2021-22 academic year is that all LSE students will be in London and studying on campus, where we will provide flexible teaching and learning which blends both in-person and online elements. This flexible approach has been informed by our student and academic community and builds upon the innovations and improvements we have put in place over the past year. If, due to events outside of our reasonable control, such as the COVID-19 pandemic, we have to make any changes to the delivery of the programme in the 2021/22 academic year, we will provide as much notice as is reasonably practicable by updating this page and sending an email to all offer holders/students. 

For more information about LSE's teaching plans for 2021 and our Coronavirus FAQs for prospective students please visit our website.

Programme details

Key facts

MPhil/PhD Mathematics
Start date 27 September 2021
Application deadline 27 May 2021. However please note the funding deadlines
Duration Three to four years full-time (minimum two). We do not normally offer part-time study
Tuition fee Home students: £4,500 for the first year 
Overseas students: £20,136 for the first year
Financial support LSE PhD Studentships deadline is 17 December 2020. We have a second deadline on 29 April 2021 (subject to available funding). All applicants will be considered for LSE PhD Studentships, please adhere to the deadlines.
Minimum entry requirement Merit in a taught master’s degree in a relevant discipline
GRE/GMAT requirement None
English language requirements Research (see 'Assessing your application')
Location  Houghton Street, London

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.

- 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.

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 Lent 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 27 May 2021. 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 2021/22 for MPhil/PhD Mathematics

Home students: £4,500 for the first year
Overseas students: £20,136 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).

Fee status

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 graduate students from the UK, the EU and outside the EU.

This programme is eligible for LSE PhD Studentships. Selection for the PhD Studentships  is based on receipt of an application for a place – including all ancillary documents, before the funding deadline.

Funding deadline for first round of LSE PhD Studentships: 17 December 2020. 
Funding deadline for the second round of LSE PhD Studentships (subject to available funding): 29 April 2021.

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. 

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

Home: £4,517 (for the first year) - provisional
Overseas: £20,136 (for the first year)

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.

First year

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.

Third year

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 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


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 a PC within the Department of Mathematics’ PhD study rooms.  These areas provide 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 and 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 a specific course you are taking. 

Disability and Wellbeing Service – the staff 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, arranging exam adjustments and run groups and workshops. 

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

LSE Faith Centre – 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 9 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 future 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 it’s 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, offer one-to-one sessions with study advisers who can help you with reading, making notes, writing, research and exam revision, and provide 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 - 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 - 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 advocates and advisers– we have a School Senior Advocate for Students and an Adviser to Women Students who can help with academic and pastoral matters. 

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Student stories

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

Nóra Frankl - MPhil/PhD Mathematics 2016-2020


Nóra currently holds an MSc in Mathematics from Loránd Eötvös University, Budapest; she graduated with a PhD in Mathematics in 2020.

What are you currently researching?
I am mostly interested in discrete geometry, which includes combinatorial questions about geometric objects. Sometimes I also think about purely combinatorial questions, for example I am currently working on a question about partitioning edge coloured hypergraphs into monochromatic cycles.

Why did you choose this area of study?
I like combinatorics and geometry, and this area is a mixture of these two.

What do you hope to do career-wise, long term?
I would like to stay in academia and do research.

Can you provide any advice to prospective students about the most effective way to approach research and keep stress levels down?
Of course, this varies from individual to individual and from area to area, but there are some things that can be useful in general. Set realistic expectations: you should not anticipate finding results quickly. It is a slow procedure. For me the recipe is to try to be happy even with small results: don’t let failure disappoint you too greatly. I think it is also good to not separate weekdays and weekends too much; when you have ideas and feel motivated, don't stop for the weekend, but treat yourself to much-needed rest days later.

What resources are available at LSE to help young researchers? 
There are several funds at both School and Departmental level.  Mathematicians need whiteboards – we’re lucky to have many in our PhD office, plus all the basic provisions we could ever need (stationery, printing, equipment, etc.).  Our PhD Office itself is a really good, productive environment to work in, where we can focus solidly on our research but also collaborate and share thoughts. The Department as a whole, alongside the PhD Academy and our Research Manager, assist with the essential practicalities of PhD study.  The Department invites key visitors to present at our seminar series. Crucially, we have a fantastic coffee machine in the Department :-)

In a few words, what is the best thing about studying at LSE?
Everyone is very nice; I am a valued member of the Department.

Ewan Davies - MPhil/PhD Mathematics 2013-2017

Ewan Davies 200

Ewan Davies was a student of the MPhil/PhD in Mathematics who joined the Department in October 2013 under the supervision of Jozef Skokan and Peter Allen.  He successfully completed his studies in October 2017.  His research interests lie in combinatorics, particularly extremal graph theory and probabilistic combinatorics, as well as the intersection of these areas with other fields such as statistical physics and number theory.  During his time at LSE, amongst many other activities, Ewan contributed extensively to the department, through committees and teaching, was awarded grants to facilitate his research visits and gave many talks around the world.

I started my PhD at LSE after spending four years in Cambridge for a combined undergraduate and masters in mathematics. I wanted to retain the freedom and intellectual rigour of university life, but also move to a different city and discover new and exciting aspects of life outside work. A mathematics PhD in London was ideal for this; pure mathematics is a rigorous and highly distilled form of problem solving that I find exceptionally rewarding, and London is a near-limitless trove of opportunities to explore.

My work isn’t tied to a specific title or single unifying idea, I have enjoyed working on a variety of projects which are broadly from the same branch of mathematics, but use different techniques and ideas. This is great for motivation, there’s often something appealing to work on and I’m not pressured to make everything fit some central theme. Recently I’ve been focusing on a new method for optimising the observable properties of certain probability distributions that link combinatorics and statistical physics. With a few simple mathematical tricks I have been answering a variety of questions in combinatorics using ideas from statistical mechanics. I’m essentially analysing the average behaviour of a physical system with the property that any possible state of the system occurs with a probability proportional to its energy. Selecting an interesting system and the right definition of energy yields a variety of mathematical applications and I hope to spend the final year of my PhD trying to develop a general theory based on the early successful examples of the technique.

The atmosphere in the department at LSE is excellent; people are friendly, supportive and approachable. When I joined I was jokingly told, “we might not be the best maths department in the world, but we probably are the friendliest”. This succinctly captures the slightly British sense of humour and light-hearted environment that I’ve enjoyed being a part of. It’s also rather too modest, I frequently work with world-leading academics and feel very positive about the quality of the research I’m able to do here. After my PhD I hope to continue in academia with postdoctoral research, and I feel the high quality of the mathematics department at LSE is extremely beneficial for my goals. 

Barnaby Roberts - MPhil/PhD Mathematics 2013-2017


Barnaby Roberts was a student of the MPhil/PhD in Mathematics who joined the Department in October 2013 under the supervision of Peter Allen and Jozef Skokan.  He successfully completed his studies in September 2017.  His research interests lie in discrete mathematics, particularly Graph Theory. In his fourth, final year, Barnaby wrote this commentary about his time at LSE.
Written in March 2017 

Whilst I enjoyed undergraduate maths I didn’t want to dedicate so much time to maths without doing some of my own research.  Once I decided to pursue a PhD in Graph Theory I decided I wanted to go to a university where there were more than one academic in that area.  LSE was one of just a few such institutions in the UK.  In fact, LSE has a large and very active group of researchers in Graph Theory, Combinatorics and Discrete Mathematics.

I have loved research which, as well as being a good intellectual challenge, is also a surprisingly sociable activity.  Discussing ideas with fellow PhD students and other academics is a really invigorating experience and the atmosphere at LSE makes collaborations really easy to get involved in.  At LSE, my supervisors have been very flexible in allowing me to choose my own projects whilst also offering guidance and suggesting fruitful directions of study.  I have not only worked with other members of LSE but also with various people I have met at conferences and with invited guests who have visited LSE to give a seminars (we have a very active, engaging seminar series in Combinatorics, Games and Optimisation).

There are many aspects to a PhD beyond research.  Presenting work, attending conferences and teaching are all part of it too.  All three of those seemed a little daunting at first but quickly became really enjoyable.  Learning to present work well and similarly to teach maths clearly are both good challenges.  They are also very transferrable skills.  From being at LSE I have attended conferences across the world.  A particular highlight was spending 6 weeks in Brazil working with mathematicians in Rio and Sao Paulo.  This was made possible by funding accessible through LSE.


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 Lent Term (January) or Summer Term (April)?

Under execptional circumstances, starting in January may be permissable.  Starting in the Summer 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 do not normally offer MPhil/PhDs on a part-time basis but, on rare occasions, this may be viable.  

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

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