Mathematics MPhil, PhD
In Pure Mathematics our two main fields are functional analysis and geometric algebra. In Applied Mathematics our research is predominantly in fluid mechanics, astrophysics and cosmology.
You are currently viewing course information for entry year:
Start date(s):
- September 2025
- January 2026
- April 2026
Overview
We invite MPhil and PhD proposals in any of our research areas.
As a research postgraduate in the School of Mathematics, Statistics and Physics you'll work under the supervision of an expert in your chosen field.
Within each field of Pure Mathematics there are multiple subgroups. In analysis, one subgroup concentrates on operator theory and function theory, the other on Banach algebras, cohomology and modules. In algebra there are subgroups devoted to the study of infinite groups, and finite classical groups and their geometries.
Our Applied Mathematics staff have research interests in:
- astrophysical and geophysical fluid dynamics
- quantum matter
- mathematical biology and archaeology
- cosmology and quantum gravity
To help you identify a topic and potential supervisor, we encourage you to find out more about our staff specialisms.
Lists of example projects in Pure and Applied Mathematics are also available.
We run research seminars in algebra and geometries, analysis, and applied mathematics. Our postgraduate students also get the opportunity to lead seminars.
Specialist courses are offered through the MAGIC distance learning consortium, sponsored in part by the Engineering and Physical Sciences Research Council (EPSRC).
We're part of:
- the North British Functional Analysis Seminar
- the North British Geometric Group Theory Seminar
- Algebra and Representation Theory in the North, funded by the London Mathematical Society and the Edinburgh Mathematical Society
- the Joint Quantum Centre with Durham University
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Important information
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Please rest assured we make all reasonable efforts to provide you with the programmes, services and facilities described. However, it may be necessary to make changes due to significant disruption, for example in response to Covid-19.
View our Academic experience page, which gives information about your Newcastle University study experience for the academic year 2024-25.
See our terms and conditions and student complaints information, which gives details of circumstances that may lead to changes to programmes, modules or University services.
Qualifications explained
Find out about the different qualification options for this course.
An MPhil is available in all subject areas. You receive research training and undertake original research leading to the completion of a 40,000 - 50,000 word thesis.
Find out about different types of postgraduate qualifications
A PhD is a doctorate or doctoral award. It involves original research that should make a significant contribution to the knowledge of a specific subject. To complete the PhD you will produce a substantial piece of work (80,000 – 100,000 words) in the form of a supervised thesis. A PhD usually takes three years full time.
Find out about different types of postgraduate qualifications
How you'll learn
As a Mathematics PhD or MPhil student you'll be supported by your supervision team. You'll also go through a research training analysis to identify any skills that you need to develop.
Depending on your modules, you'll be assessed through a combination of:
- Thesis
- Viva
We offer a wide range of projects for the thesis. These will be provided by our academics. You can also propose your own topic.
Our mission is to help you:
- stay healthy, positive and feeling well
- overcome any challenges you may face during your degree – academic or personal
- get the most out of your postgraduate research experience
- carry out admin and activities essential to progressing through your degree
- understand postgraduate research processes, standards and rules
We can offer you tailored wellbeing support, courses and activities.
You can also access a broad range of workshops covering:
- research and professional skills
- careers support
- wellbeing
- health and safety
- public engagement
- academic development
Find out more about our postgraduate research student support
Your development
Faculty of Science, Agriculture and Engineering (SAgE) researcher development programme
Each faculty offers a researcher development programme for its postgraduate research students. We have designed your programme to help you:
- perform better as a researcher
- boost your career prospects
- broaden your impact
Through workshops and activities, it will build your transferable skills and increase your confidence.
You’ll cover:
- techniques for effective research
- methods for better collaborative working
- essential professional standards and requirements
Your programme is flexible. You can adapt it to meet your changing needs as you progress through your doctorate.
Doctoral training and partnerships
There are opportunities to undertake your PhD at Newcastle within a:
- Centre for Doctoral Training (CDT)
- Doctoral Training Partnership (DTP)
Being part of a CDT or DTP has many benefits:
- they combine research expertise and training of a number of leading universities, academic schools and academics.
- you’ll study alongside a cohort of other PhD students
- they’re often interdisciplinary
- your PhD may be funded
If there are currently opportunities available in your subject area you’ll find them when you search for funding in the fees and funding section on this course.
The following centres/partnerships below may have PhD opportunities available in your subject area in the future:
- Centre for Doctoral Training in Cloud Computing for Big Data
- EPSRC Aura Centre for Doctoral Training in Offshore Wind Energy and the Environment
- Discovery Medicine North - MRC DiMeN Doctoral Training Partnership
- Sustainable Electric Propulsion Centre for Doctoral Training
- EPSRC Centre for Doctoral Training in Geospatial Systems
Your future
Our Careers Service
Our award-winning Careers Service is one of the largest and best in the country, and we have strong links with employers. We provide an extensive range of opportunities to all students through our ncl+ initiative.
Quality and ranking
All professional accreditations are reviewed regularly by their professional body
From 1 January 2021 there is an update to the way professional qualifications are recognised by countries outside of the UK
Fees and funding
Tuition fees for 2025 entry (per year)
Home fees for research degree students
For 2024-25 entry, we have aligned our standard Home research fees with those set by UK Research and Innovation (UKRI). The standard fee was confirmed in Spring 2024 by UKRI.
For 2025-26 entry, we will be aligning our standard Home research fees with those set by UK Research and Innovation (UKRI). The standard fee will be confirmed in Spring 2025 by UKRI.
As a general principle, you should expect the tuition fee to increase in each subsequent academic year of your course, subject to government regulations on fee increases and in line with inflation.
Depending on your residency history, if you’re a student from the EU, other EEA or a Swiss national, with settled or pre-settled status under the EU Settlement Scheme, you’ll normally pay the ‘Home’ tuition fee rate and may be eligible for Student Finance England support.
EU students without settled or pre-settled status will normally be charged fees at the ‘International’ rate and will not be eligible for Student Finance England support. You will be eligible for a scholarship worth 15% off the international fee.
If you are unsure of your fee status, check out the latest guidance here.
Scholarships
We support our EU and international students by providing a generous range of Vice-Chancellor's automatic and merit-based scholarships. See our searchable postgraduate funding page for more information.
What you're paying for
Tuition fees include the costs of:
- matriculation
- registration
- tuition (or supervision)
- library access
- examination
- re-examination
- graduation
Find out more about:
If you are an international student or a student from the EU, EEA or Switzerland and you need a visa to study in the UK, you may have to pay a deposit.
You can check this in the How to apply section.
If you're applying for funding, always check the funding application deadline. This deadline may be earlier than the application deadline for your course.
For some funding schemes, you need to have received an offer of a place on a course before you can apply for the funding.
Search for funding
Find funding available for your course
Entry requirements
The entrance requirements below apply to 2025 entry.
Qualifications from outside the UK
English Language requirements
Admissions policy
This policy applies to all undergraduate and postgraduate admissions at Newcastle University. It is intended to provide information about our admissions policies and procedures to applicants and potential applicants, to their advisors and family members, and to staff of the University.
University Admissions Policy and related policies and procedures
Credit transfer and Recognition of Prior Learning
Recognition of Prior Learning (RPL) can allow you to convert existing relevant university-level knowledge, skills and experience into credits towards a qualification. Find out more about the RPL policy which may apply to this course
How to apply
Using the application portal
The application portal has instructions to guide you through your application. It will tell you what documents you need and how to upload them.
You can choose to start your application, save your details and come back to complete it later.
If you’re ready, you can select Apply Online and you’ll be taken directly to the application portal.
Alternatively you can find out more about applying on our applications and offers pages.
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Get in touch
Questions about this course?
If you have specific questions about this course you can contact:
Postgraduate Secretary
Telephone: +44 (0) 191 208 6960
Email: maths.physics.pg@ncl.ac.uk
School of Mathematics, Statistics and Physics
ncl.ac.uk/maths-physics
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