MSc Pure Mathematics

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.

Apply online

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 .

• 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.

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.

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.

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 universities 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

*The Graduate Market in 2024