Overview
- Degree awarded
- Master of Science
- Duration
- 1 year
- Entry requirements
-
The entry requirement to the programmes is normally a good honours degree in mathematics or a mathematically-related discipline or an equivalent overseas qualification in a mathematical subject.
- How to apply
-
As there is high demand for this course we operate a staged admissions process with selection deadlines throughout the year.
Due to the competition for places, we give preference to students with grades above our minimum entry requirements. If we make you an offer, you will have 3 weeks in which to accept. Any offers not accepted within 3 weeks will be withdrawn so that an offer can be made to another candidate.
Please find more information in our Application and Selection section .
- Sustainable Development Goals
Find out how this course aligns to the UN Sustainable Development Goals, including learning which relates to:
- Goal 4: Quality education
Course options
| Full-time | Part-time | Full-time distance learning | Part-time distance learning | |
|---|---|---|---|---|
| MSc | Y | Y | N | N |
Course description
This one year taught postgraduate programme leads to the degree of MSc in Pure Mathematics. The programme is suitable not only for students who wish to improve their background knowledge prior to applying to undertake a PhD by research, but also for students who wish to enhance their knowledge of postgraduate-level abstract mathematics. The MSc comprises of the taught component, running from the start of the academic year in September until the end of the second semester in late Spring, followed by the dissertation component running from June until September.
During the taught component of the course, you will normally take six units together with a research skills and project unit. You may choose exclusively pure topics, or a mixture of pure mathematics units and mathematical logic units. In the research skills and project unit you will first complete a mini-project to improve mathematical writing skills, and then undertake a project. The project is normally an expository account of a piece of mathematics and you will write this under the guidance of a supervisor. The taught component comprises of conventional lectures supported by examples classes, project work and independent learning via reading material.
We supervise projects and dissertations in a variety of areas of pure mathematics and beyond. These include (but are not limited to): noncommutative algebra, representation theory, algebraic geometry, group theory, category theory, logic, number theory, ergodic theory, dynamical systems, geometric group theory, combinatorics, semigroups, differential geometry, and also subjects connected to probability.
After successfully completing the taught component, you will prepare a dissertation on an advanced topic in pure mathematics or mathematical logic, normally of current or recent research interest, chosen in consultation with your supervisor.
You can also take the programme part-time, over a period of two years. There is some flexibility in the precise arrangements for this programme, but you would normally attend two lecture courses each semester for three semesters before commencing work on your dissertation.
Within two weeks from the start of the academic year, students in this programme can opt to change to the Mathematical Logic Pathways leading to the degree of MSc in Pure Mathematics and Mathematical Logic.
Open days
Fees
For entry in the academic year beginning September 2025, the tuition fees are as follows:
-
MSc (full-time)
UK students (per annum): £14,000
International, including EU, students (per annum): £34,500 -
MSc (part-time)
UK students (per annum): £7,000
International, including EU, students (per annum): £14,000
Further information for EU students can be found on our dedicated EU page.
Policy on additional costs
All students should normally be able to complete their programme of study without incurring additional study costs over and above the tuition fee for that programme. Any unavoidable additional compulsory costs totalling more than 1% of the annual home undergraduate fee per annum, regardless of whether the programme in question is undergraduate or postgraduate taught, will be made clear to you at the point of application. Further information can be found in the University's Policy on additional costs incurred by students on undergraduate and postgraduate taught programmes (PDF document, 91KB).
Scholarships/sponsorships
Across our institution we offer a number of postgraduate taught scholarships and awards to outstanding UK and international students each year. We are one of the Martingale Foundation's newest university partners. The Martingale Foundation helps provide access to postgraduate mathematics study for UK students facing financial barriers by offering fully-funded MSc and PhD programmes. Information about eligibility is available via the Martingale Foundation website and applications will open on 13 August 2025. The deadline to apply is Sunday 19 October 2025. For more information about scholarships, see the Department ofMathematics Fees and funding page orvisit the University of Manchester funding for master's courses website for more information.
UN Sustainable Development Goals
The 17 United Nations Sustainable Development Goals (SDGs) are the world's call to action on the most pressing challenges facing humanity. At The University of Manchester, we address the SDGs through our research and particularly in partnership with our students.
Led by our innovative research, our teaching ensures that all our graduates are empowered, inspired and equipped to address the key socio-political and environmental challenges facing the world.
To illustrate how our teaching will empower you as a change maker, we've highlighted the key SDGs that our courses address.
Goal 4: Quality education
Ensure inclusive and equitable quality education and promote lifelong learning opportunities for all
Contact details
- Department
- Department of Mathematics
- Contact name
- Postgraduate Admissions Team
- Telephone
- +44 (0)161 529 3043
- pgt-maths@manchester.ac.uk
- Website
- https://www.maths.manchester.ac.uk/
- School/Faculty
-
Our internationally-renowned expertise across the School of Natural Sciences informs research led teaching with strong collaboration across disciplines, unlocking new and exciting fields and translating science into reality. Our multidisciplinary learning and research activities advance the boundaries of science for the wider benefit of society, inspiring students to promote positive change through educating future leaders in the true fundamentals of science. Find out more about Science and Engineering at Manchester .
Courses in related subject areas
Use the links below to view lists of courses in related subject areas.
Entry requirements
Academic entry qualification overview
English language
All applicants will need to demonstrate competency in English language. Applicants who do not already possess an acceptable English Language qualification will need to take a recognised test and attain the required English Language score:
- IELTS: at least 6.5 overall with no sub-test below 6.0.
- TOFEL iBT: at least 90 overall with no sub-test below 20. We do not accept 'MyBestScore'.
- Pearson PTE: at least 70 overall with no sub-test below 65.
Further information on language requirements can be found on our website .
Pre-sessional English
We will consider applicants who do not meet these scores but you may be required to complete a pre-sessional English language course at the University of Manchester prior to the start of the course.
To be considered for a pre-sessional English language course for this programme we require the following minimum IELTS (Academic) scores:
- 6 Week Pre-Sessional Course: Minimum 6.0 overall with no sub-test below 5.5.
If you have not yet completed your current academic study and are interested in studying a pre-sessional course, you must hold an IELTS for UKVI (Academic) test certificate.
English language test validity
Other international entry requirements
Application and selection
How to apply
As there is high demand for this course we operate a staged admissions process with selection deadlines throughout the year.
Due to the competition for places, we give preference to students with grades above our minimum entry requirements. If we make you an offer, you will have 3 weeks in which to accept. Any offers not accepted within 3 weeks will be withdrawn so that an offer can be made to another candidate.
Please find more information in our Application and Selection section .
Staged admissions
As there is high demand for this course we operate a staged admissions process with selection deadlines throughout the year.Due to the competition for places, we give preference to students with grades above our minimum entry requirements.
If we make you an offer, you will have 3 weeks in which to accept. Any offers not accepted within 3 weeks will be withdrawn so that an offer can be made to another candidate.
Stage 1: Application received by 08 November 2024; Decision by 10 January 2025.
Stage 2: Application received by 03 January 2025; Decision by 07 March 2025.
Stage 3: Application received by 28 February 2025; Decision by 18 April 2025.
Stage 4: Application received by 23 May 2025; Decision by 20 June 2025.
You need to ensure that you submit your supporting documents with your application as it may delay us processing your application before the decision deadline.
Whilst we aim to give you a decision on your application by the deadline date, in some instances due to the competition for places and the volume of applications received, it may be necessary to roll your application forward to the next deadline date. If this is the case we will let you know after the deadline date.
Applications received after our final selection deadline will be considered at our discretion if places are still available.
Please note: All places are subject to availability and if you apply at one of the later stages, some courses may already be closed. We therefore recommend that you apply early in the cycle to secure your place with us.
Applicants who are made a conditional offer of a place must demonstrate that they have met all the conditions of their offer by 31 July 2025.
Advice to applicants
- Latest transcripts of study showing all modules completed including credit weighting and grades achieved (and English translation if applicable).
-
If you have not yet graduated, a list of the modules that you will be completing in the final year of your degree together with their credit weighting.
-
An official document from your university verifying your current weighted average mark if this information is not included in your transcript of study. Please note : this must be recorded as a percentage, not as a GPA grade, and must give the weighted average mark, not an arithmetic average mark.
-
We require references from two people who have knowledge of your academic ability in support of your application, although we can process your application with one academic reference. In most cases, these should be academic references, from a lecturer or professor at your last university. In some cases (for example, if your academic studies occurred some time ago), it might be more appropriate to submit recommendations from those familiar with your professional experience. If you have difficulty in identifying suitable referees you should ask for advice from the admissions team for your course. We will contact your referees directly after you submit your application and direct them to complete our online reference form.
-
Degree certificate if you have already graduated (and English translation if applicable).
-
Curriculum vitae (CV) if you graduated more than three years ago.
- Personal Statement. This should be a one-page document and, in particular, should describe why you want to pursue an MSc degree in Mathematics and what area of mathematics you find most interesting and why. It should also mention any projects/dissertation you have written or worked on, along with brief mathematical details of your work.
-
If English is not your first language, we also require proof of your English language ability. If you have already taken an English language qualification, please include your certificate with your application. We may be willing to consider your application without this document, but if we choose to make you an offer, the conditions will include IELTS (or equivalent qualification).
You must submit all these supporting documents with your application. If any of the above information is missing, we will not be able to consider your application and it may be rolled forward to the next stage or withdrawn.
How your application is considered
We consider your full academic history including which course units you have taken and the marks obtained. Even if you have met our minimum entry requirements, we will take into account your marks in relevant course units in our final decision making.
If you graduated more than three years ago, we will also consider the information contained on your CV and any relevant work experience you have to assess if you are still able to fulfil the entry criteria. For some applicants (typically those with qualifications from some years ago or where we need additional information to assess suitability for the course) you may be contacted by the programme tutor for further assessment.
Interview requirements
Overseas (non-UK) applicants
Self-funded international applicants for this course will be required to pay a deposit of £1,000 towards their tuition fees before a confirmation of acceptance for studies (CAS) is issued. This deposit will only be refunded if immigration permission is refused. We will notify you about how and when to make this payment.
Please upload a copy of your current valid passport with your application showing the photograph page with your application. For CAS purposes, this must show your full name, date of birth, nationality, passport number and the date the passport is valid until, which must be later than the date of your planned arrival in the UK, and the start date of your course.
If you have previously studied in the UK on a Tier 4 visa as an undergraduate or postgraduate student, please send a copy of your previous CAS statement to us as it will assist with the issue of your new CAS statement. This includes study in the UK on study abroad programmes and any study that you did not complete.
You cannot use your CAS to apply for a visa more than three months before the start date of your course. The Admissions Team will contact you at the appropriate time.
Your CAS number is only valid for one Tier 4 application.
Deferrals
Applications for deferred entry are not accepted for this course. If you receive an offer for 2024 entry and decide not to accept it, should you subsequently wish to be considered for 2025 entry you would be required to reapply.
Re-applications
Course details
Course description
This one year taught postgraduate programme leads to the degree of MSc in Pure Mathematics. The programme is suitable not only for students who wish to improve their background knowledge prior to applying to undertake a PhD by research, but also for students who wish to enhance their knowledge of postgraduate-level abstract mathematics. The MSc comprises of the taught component, running from the start of the academic year in September until the end of the second semester in late Spring, followed by the dissertation component running from June until September.
During the taught component of the course, you will normally take six units together with a research skills and project unit. You may choose exclusively pure topics, or a mixture of pure mathematics units and mathematical logic units. In the research skills and project unit you will first complete a mini-project to improve mathematical writing skills, and then undertake a project. The project is normally an expository account of a piece of mathematics and you will write this under the guidance of a supervisor. The taught component comprises of conventional lectures supported by examples classes, project work and independent learning via reading material.
We supervise projects and dissertations in a variety of areas of pure mathematics and beyond. These include (but are not limited to): noncommutative algebra, representation theory, algebraic geometry, group theory, category theory, logic, number theory, ergodic theory, dynamical systems, geometric group theory, combinatorics, semigroups, differential geometry, and also subjects connected to probability.
After successfully completing the taught component, you will prepare a dissertation on an advanced topic in pure mathematics or mathematical logic, normally of current or recent research interest, chosen in consultation with your supervisor.
You can also take the programme part-time, over a period of two years. There is some flexibility in the precise arrangements for this programme, but you would normally attend two lecture courses each semester for three semesters before commencing work on your dissertation.
Within two weeks from the start of the academic year, students in this programme can opt to change to the Mathematical Logic Pathways leading to the degree of MSc in Pure Mathematics and Mathematical Logic.
Aims
Coursework and assessment
The taught component is assessed by coursework, project work and by written examination.
The written exams take place at the end of January (for the first semester course units) and the end of May (for the second semester course units). The dissertation component is assessed by the quality and competence of the written dissertation.
The Postgraduate Diploma and Postgraduate Certificate exist as exit awards for students who do not pass at MSc level.
Course unit details
The taught courses cover material related to the research interests of the academic staff.
Course unit list
The course unit details given below are subject to change, and are the latest example of the curriculum available on this course of study.
| Title | Code | Credit rating | Mandatory/optional |
|---|---|---|---|
| Dissertation (60cr) Pure Mathematics and Mathematical Logic | MATH60000P | 60 | Mandatory |
| MSc Pure Mathematics Research and Project Skills | MATH61000 | 30 | Mandatory |
| Measure Theory and Ergodic Theory | MATH61021 | 15 | Optional |
| Differentiable Manifolds | MATH61061 | 15 | Optional |
| Algebraic Topology | MATH61072 | 15 | Optional |
| Riemann surfaces | MATH61131 | 15 | Optional |
| Lie Algebras | MATH62112 | 15 | Optional |
| Galois Theory | MATH62121 | 15 | Optional |
| Graph Theory | MATH62192 | 15 | Optional |
| Representation Theory | MATH62261 | 15 | Optional |
| Displaying 10 of 18 course units | |||
| Display all course units | |||
Scholarships and bursaries
Across our institution, we offer a number of postgraduate taught scholarships and awards to outstanding UK and international students each year. We are one of the Martingale Foundation's newest university partners. The Martingale Foundation helps provide access to postgraduate mathematics study for UK students facing financial barriers by offering fully-funded MSc and PhD programmes. Information about eligility can be found at the Martingale Foundation website and applications will open on 13 August 2025. The deadline to apply is Sunday 19 October 2025.
The University of Manchester is committed to widening participation in master's study, and allocates £300,000 in funding each year. Our Manchester Masters Bursaries are aimed at widening access to master's courses by removing barriers to postgraduate education for students from underrepresented groups.
For more information, see the Department of Mathematics Fees and funding page or visit the University of Manchester funding for master's courses website for more information.
If you are a sponsored student please check the requirements of your sponsorship before registering on a course. If you require further information please contact the Department.
Facilities
Disability support
Careers
Career opportunities
Our MSc programme provides our students with strong qualitative skills in a wide variety of areas of pure mathematics. We tailor the course to the interests of our individual students in order to prepare them for a broad scope of career prospects. The programme provides several opportunities for students to study advance topics in mathematics as a foundation for doctoral studies (PhD) or more applied courses.
The University of Manchester is one of the most targeted university by graduate employers*. Besides providing the necessary skills for those wishing to pursue a research and/or academic career (e.g., University Lecturer), common careers that our graduates have pursued are in the financial industry, in the computer industry, and teaching at college level.
See below some of the roles our graduates have gone on to do:
- Teacher
- Research Associate
- Software Engineer
- Chief Financial Officer
Below are also just some of the employers that our graduates now work with:
- Oracle
- Alliance Manchester Business School
- Scottish Life
- AT&T Labs
- NHS