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About the project

Postgraduate research

Mathematics PhD/iPhD/MPhil/MSc (Research)

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.

Our Online Application Form and Applicant Self Service will be unavailable from 08:00-14:00 (GMT) on Thursday 29 October for essential maintenance. We apologise for any inconvenience caused.

• 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;
• 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;
• MPhil: 2-3 years full-time; 3-4 years part-time; IPhD: 4 years full-time;
• IPhD: 4 years full-time;

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

• Algebra
• Analysis
• Continuum Mechanics
• Geometry and Topology
• Geophysical & Astrophysical Fluid Dynamics
• Integrable Systems and Mathematical Physics
• Mathematical Biology
• Number Theory

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

Our regular standard of admission is usually a 2.1 honours degree.

Required documents Applicants should submit: Academic Transcripts and Degree Certificates CV Two References

Required documents

• Academic Transcripts and Degree Certificates
• CV
• Two References

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.

Accepted English language tests

We accept a wide range of English language tests for entry to this programme. Tests must have been taken within 2 years 5 months of programme start date, and requirements must be met using a single test.

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
• We do not accept General Training

TOEFL iBT (including MyBest and Home Edition)

Tests taken up to 20 January 2026

Tests taken from 21 January 2026

• 90 Overall , no subtest lower than Reading 20; Listening 19; Speaking 19; Writing 21
• 92 Overall , no subtest lower than 4.5

Pearsons PTE Academic (test centre only)

• 65 overall with no subtest less than Reading 60; Listening 60; Speaking 65; Writing 60

Cambridge C1 Advanced and C2 Proficiency

• 176 overall, no subtest less than 169

Oxford ELLT

• 7 overall with no subtest less than 6

LanguageCert Academic SELT/Academic/Academic Online

• 70 overall with no subtest less than 60

Password Skills Plus

• 6.5 overall with no subtest less than 6.0

Trinity College Integrated Skills in English II

• 96 overall with no subtest less than 90

Kaplan Test of English

• Any two subtests at 480 or higher, and any two subtests at 450 or higher

PSI Skills for English

• B2 Pass with Merit

Duolingo English Test

• 120 overall with Writing at 120 and no subtest less than 110

Oxford Test of English Advanced

• 140 Overall with any two subtests at 126 or higher, and any two subtests at 136 or higher

Alternatives to English Language qualification

Degree from majority-English speaking country (as defined by the UKVI including Canada if taught in English)

TNE degree for UK University taught at a campus outside of the UK.

• Students must have studied for a minimum of their final year at Undergraduate level, or 9 months at Master's level, and must have completed their degree in that majority-English speaking country within 6 years of programme start.
• Students must be awarded the degree by the UK university and must have completed the degree within 6 years of programme start.

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:

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

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:

• 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.
• Pre-sessional courses
• Heriot Watt
• Kingston Upon Thames
• Middlesex University
• Manchester University
• Reading University
• Edinburgh University
• ST Andrews University
• UCL
• Durham

2027/28

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.

• UK: To be confirmed [26/27 fee was £5,238]
• International & EU: £33,708
• Fee status and policies

Alumni discount

We offer a 15% tuition fee discount to eligible self-funded alumni starting a Postgraduate Taught (PGT) Masters or Postgraduate Research (PGR) programme in the 2027/28 academic year.

This includes University of Glasgow graduates and those who have completed a Study Abroad programme, Exchange programme, International Summer School or Erasmus programme with us. This discount can be awarded alongside most University scholarships. No additional application is required.

• Full details of our Alumni Discount

Possible additional fees

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.

• 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

Funding

• The College of Science & Engineering funding opportunities

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:

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

• 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.

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 .

Required documents

Our Online Application Form and Applicant Self Service will be unavailable from 08:00-14:00 (GMT) on Thursday 29 October for essential maintenance. We apologise for any inconvenience caused.

• Academic Transcripts and Degree Certificates
• CV
• Two References

Contact us

• If you have any questions about your application before you apply: email scieng-gradschool@glasgow.ac.uk
• If you have any questions after you have submitted your application: contact our Admissions team
• Any references may be submitted by email to: pg-research-admissions@glasgow.ac.uk

International Students

• Advice on visa, immigrations and the Academic Technology Approval Scheme (ATAS) can be found at Applying for a student visa outside the UK

More information

• External collaborations

Our research environment

• Discover how we support and develop postgraduate researchers

Induction

• Getting started with PGR development: how postgraduate researchers are welcomed into our community

Postgraduate researcher blogs

• A community blog, written by and for postgraduate researchers at the University of Glasgow

Related links

• Mathematics research
• School of Mathematics & Statistics
• College of Science & Engineering

Download

• Graduate School Pocket Guide (PDF)

Research areas