Mathematics PhD/iPhD/MPhil/MSc (Research)

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The School of Mathematics & Statistics combines world-leading research expertise in pure and applied mathematics and statistics in areas such as mathematical biology, fluid dynamics, geometry and topology and environmental statistics.

PhD: 3-4 years full-time; 6-8 years part-time; Thesis of Max 80,000 words
MSc (Research): 1-2 years full-time; 2-3 years part-time;
MPhil: 2-3 years full-time; 3-4 years part-time;
IPhD: 4 years full-time;

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Research projects

Mathematics thesis topics

Overview

With a sizeable complement of academic staff and postgraduate students, the School of Mathematics and Statistics is one of the largest in the UK.

Our research interests cover several areas of Pure and Applied Mathematics. These areas are not mutually exclusive and there are considerable benefits from interactions between the different areas that enhance the research environment.

All our research areas are highly rated internationally and most members of the School have ongoing collaborations with mathematicians overseas and elsewhere in the UK. Many overseas mathematicians spend periods in Glasgow working with members of the School.

There are several series of research seminars with invited speakers from the UK and overseas. There is also a regular postgraduate seminar where our PhD students can develop their presentational skills. All this helps to generate a lively and mutually supportive research environment, which has led to the award of coveted prizes and competitive fellowships for several of our younger staff.

Research areas

Study options

	full-time (years)	part-time (years)
Phd	3-4	6-8
Integrated PhD	4	n/a
MSc (Res)	1-2	2-3
MPhil	2-3	3-4

Integrated PhD programme (4 years)

Our PhD with Integrated Study in Mathematical Sciences is a four-year PhD programme in the School of Mathematics and Statistics.

Completion of taught Masters level courses in the first nine months will provide you with a valuable introduction to academic topics and research methods, whilst providing key training in the critical evaluation of research data.

Upon successful completion of the taught component, you will progress to your research degree. You will submit a thesis to be examined by the end of your fourth year.

Entry requirements

PhD programmes

2.1 Honours degree or equivalent

Required documentation

Applicants should submit:

Transcripts/degree certificate
Two references
CV
Name of potential Supervisor

Integrated PhD programmes

2.1 Honours degree or international equivalent in a relevant subject area

English language requirements

For applicants from non-English speaking countries, as defined by the UK Government, the University sets a minimum English Language proficiency level.

International English Language Testing System (IELTS) Academic and Academic Online (not General Training)

6.5 with no subtests under 6.0
IELTS One Skill Retake Accepted
Tests must have been taken within 2 years 5 months of start date. Applicants must meet the overall and subtest requirements using a single test.

Common equivalent English language qualifications for entry to this programme

TOEFL (ibt, mybest or athome)

90 overall with Reading 20; Listening 19; Speaking 19; Writing 21
Tests must have been taken within 2 years 5 months of start date. Applicants must meet the overall and subtest requirements, this includes TOEFL mybest.

Pearsons PTE Academic

59 with minimum 59 in all subtests
Tests must have been taken within 2 years 5 months of start date. Applicants must meet the overall and subtest requirements using a single test.

Cambridge Proficiency in English (CPE) and Cambridge Advanced English (CAE)

176 overall, no subtest less than 169
Tests must have been taken within 2 years 5 months of start date. Applicants must meet the overall and subtest requirements using a single test.

Oxford English Test

7 overall with no subtest less than 6
Tests must have been taken within 2 years 5 months of start date. Applicants must meet the overall and subtest requirements using a single test.

LanguageCert Academic SELT

70 overall with no subtest less than 60
Tests must have been taken within 2 years 5 months of start date. Applicants must meet the overall and subtest requirements using a single test.

Password Skills Plus

6.5 overall with no subtest less than 6.0
Tests must have been taken within 2 years 5 months of start date. Applicants must meet the overall and subtest requirements using a single test.

Trinity College Tests

Integrated Skills in English II & III & IV: ISEII Distinction with Distinction in all sub-tests
Tests must have been taken within 2 years 5 months of start date. Applicants must meet the overall and subtest requirements using a single test.

University of Glasgow Pre-sessional courses

Tests are accepted for 2 years following date of successful completion.

Alternatives to English Language qualification

Degree from majority-English speaking country (as defined by the UKVI including Canada if taught in English)
- students must have studied for a minimum of 2 years at Undergraduate level, or 9 months at Master's level, and must have completed their degree in that majority-English speaking country within the last 6 years.
Undergraduate 2+2 degrees from majority-English speaking country (as defined by the UKVI including Canada if taught in English)
- students must have completed their final two years study in that majority-English speaking country within the last 6 years.

For international students, the Home Office has confirmed that the University can choose to use these tests to make its own assessment of English language ability for visa applications to degree level programmes. The University is also able to accept UKVI approved Secure English Language Tests (SELT) but we do not require a specific UKVI SELT for degree level programmes. We therefore still accept any of the English tests listed for admission to this programme.

Pre-sessional courses

The University of Glasgow accepts evidence of the required language level from the English for Academic Study Unit Pre-sessional courses. We would strongly encourage you to consider the pre-sessional courses at the University of Glasgow's English for Academic Study (EAS) Unit. Our Pre-sessional courses are the best way to bring your English up to entry level for University study. Our courses give you:

direct entry to your University programme for successful students (no need to take IELTS)
essential academic skills to help you study effectively at University
flexible entry dates so you can join the right course for your level.

For more detail on our pre-sessional courses please see:

Pre-sessional courses

We can also consider the pre-sessional courses accredited by the below BALEAP approved institutions to meet the language requirements for admission to our postgraduate taught degrees:

Heriot Watt
Kingston Upon Thames
Middlesex University
Manchester University
Reading University
Edinburgh University
ST Andrews University
UCL
Durham.

Fees and funding

Fees

2025/26

UK: £5,005
International & EU: £31,800

Prices are based on the annual fee for full-time study. Fees for part-time study are half the full-time fee.

Irish nationals who are living in the Common Travel Area of the UK, EU nationals with settled or pre-settled status, and Internationals with Indefinite Leave to remain status can also qualify for home fee status.

Fee status and policies

Alumni discount

We offer a 20% discount to our alumni on all Postgraduate Research and full Postgraduate Taught Masters programmes. This includes University of Glasgow graduates and those who have completed Junior Year Abroad, Exchange programme or International Summer School with us. The discount is applied at registration for students who are not in receipt of another discount or scholarship funded by the University. No additional application is required.

Possible additional fees

Re-submission by a research student £540
Submission for a higher degree by published work £1,355
Submission of thesis after deadline lapsed £350
Submission by staff in receipt of staff scholarship £790

Depending on the nature of the research project, some students will be expected to pay a bench fee (also known as research support costs) to cover additional costs. The exact amount will be provided in the offer letter.

Funding

View a full list of our current scholarships

Support

Our postgraduate students join a community of academic experts across a wide range of pure and applied mathematics and statistics and develop a mature understanding of fundamental theories and analytical skills applicable to many solutions.

There is a lively seminar program with members of the Schools involved in a number of networks including the North British Functional Analysis Seminar, The North British Differential Equations Seminar and the LMS Network on Classical and Quantum Integrability.

The School also welcomes many guest speakers from the UK and overseas. We hold regular postgraduate seminars, where our PhD students can develop their presentation skills, and international conferences and workshops.

Students can also attend our hugely popular week-long training course each year, which provides practically motivated training in key statistical analysis and modelling skills.

You will be part of a Graduate School which provides the highest level of support to its students.

The overall aim of our Graduate School is to provide a world-leading environment for students which is intellectually stimulating, encourages them to contribute to culture, society and the economy and enables them to become leaders in a global environment.

We have a diverse community of over 750 students from more than 50 countries who work in innovative and transformative disciplinary and interdisciplinary fields. An important part of our work is to bring our students together and to ensure they consider themselves an important part of the University’s academic community.

Being part of our Graduate School community will be of huge advantage to you in your studies and beyond and we offer students a number of benefits in addition to exceptional teaching and supervision, including:

A wide-ranging and responsive research student training programme which enables you to enhance your skills and successfully complete your studies.
Mobility scholarships of up to £4000 to enable you to undertake work in collaboration with an international partner.
A diverse programme of activities which will ensure you feel part of the wider-research community (including our biannual science slam event).
A residential trip for all new research students.
The opportunity to engage with industry-partners through training, placements and events.
Professionally accredited programmes.
Unique Masters programmes run in collaboration with other organisations.
State-of-the-art facilities including the James Watt Nanofabrication Centre and the Kelvin Nanocharacterisation Centre.
Highly-rated support for international students.

Over the last five years, we have helped over 600 students to complete their research studies and our students have gone on to take up prestigious posts in industries across the world.

Email: scieng-gradschool@glasgow.ac.uk

How to apply

Identify potential supervisors

All Postgraduate Research Students are allocated a supervisor who will act as the main source of academic support and research mentoring. You may want to identify a potential supervisor and contact them to discuss your research proposal before you apply. Please note, even if you have spoken to an academic staff member about your proposal you still need to submit an online application form.

You can find relevant academic staff members with our staff research interests search.

Gather your documents

Before applying please make sure you gather the following supporting documentation:

Final or current degree transcripts including grades (and an official translation, if needed) – scanned copy in colour of the original document.
Degree certificates (and an official translation, if needed): scanned copy in colour of the original document.
Two references on headed paper and signed by the referee. One must be academic, the other can be academic or professional. References may be uploaded as part of the application form or you may enter your referees contact details on the application form. We will then email your referee and notify you when we receive the reference. We can also accept confidential references direct to rio-researchadmissions@glasgow.ac.uk, from the referee’s university or business email account.
Research proposal, CV, samples of written work as per requirements for each subject area.