MPhil/PhD Mathematics

  • Graduate research
  • Department of Mathematics
  • Application code G1ZM
  • Starting 2020
  • UK/EU 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 Michaelmas Term 2020 
Information on how LSE will deliver teaching and learning in Michaelmas term can be found here.

Programme details

Key facts

MPhil/PhD Mathematics
Start date 30 September 2020
Application deadline 19 June 2020. 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 UK/EU: £4,435 (for the first year)
Overseas: £19,368 (for the first year)
Financial support LSE PhD Studentships (deadlines 10 January and 27 April 2020)
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.

Assessing your application

Informal enquiries - Discrete Mathematics & Algorithms, Operations Research, and Game Theory

Prior to submitting a formal application, prospective students are encouraged to informally enquire about the MPhil/PhD programme. Enquiries can be about making a formal application within the area of your research interests and about the availability of potential supervisors.

If you would like to make an informal enquiry, please email Enfale Farooq, the Departmental Research Manager, with some information about your background (a CV or similar) and a brief statement telling us about your motivation to undertake a PhD, detailing what areas of mathematics you find especially engaging and important.

Please do not contact potential supervisors directly, unless instructed to do so by the Departmental Research Manager.

Financial Mathematics & Control Theory

Please follow the procedure outlined in the 'making an application' section below to submit a formal application. Please email Enfale Farooq, the Departmental Research Manager for queries related to the application process. 

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)
- statement of academic purpose
- references
- CV
- outline research proposal
- sample of written work.

See further information on supporting documents

Applications are sent to the Department as 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 appropriate members of staff by telephone or Skype at a range of times offered by the Department. You will be notified of the outcome as soon as possible after the interview.  However, the whole process may take several months.

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 19 June 2020. 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.

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. You will be assigned to:

-  A principal supervisor with requisite knowledge in your chosen field

- An appropriate second supervisor. Where appropriate, a second or joint supervisor may be appointed from another department, institute or programme.

Before submitting a formal application to Graduate Admissions, you should follow the Department’s preferred informal application process and potential supervisor contact guidelines, which vary according to your topic.

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.


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

Student stories

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

Nóra Frankl - MPhil/PhD Mathematics 2016-present


Nóra currently holds an MSc in Mathematics from Loránd Eötvös University, Budapest; studying for a PhD in Mathematics (G1ZM)

Written in June 2017

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.

Written in September 2016

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.

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.

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 2020/21 for MPhil/PhD Mathematics

UK/EU students: £4,435 for the first year (provisional)
Overseas students: £19,368 for the first year

The fee is likely to rise over subsequent years of the programme. The School charges UK/EU 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 (UK/EU) or overseas student, otherwise known as your fee status. LSE assesses your fee status based on guidelines provided by the Department of Education.

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 over £13 million in 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: 10 January 2020. 
Funding deadline for the second round of LSE PhD Studentships: 27 April 2020.

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

Frequently Asked Questions

Can I teach an undergraduate class in the Department?

All mathematics MPhil/PhD students are eligible to apply for teaching. Further details will be provided on your arrival. Those funded by LSE Studentships are required to undertake class teaching for the Department as part of the conditions of the Scholarship, amounting to a 14% value of their stipend.

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

Request a prospectus

  • Name
  • Address

Register your interest

  • Name

Speak to Admissions

Content to be supplied