MSc Pure Mathematics / Course details

Year of entry: 2024

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.

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 aims of the programme are to provide training in a range of topics related to pure mathematics, to encourage a sophisticated and critical approach to mathematics, and to prepare students who have the ability and desire to follow careers as professional mathematicians and logicians in industry or research.

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.

TitleCodeCredit ratingMandatory/optional
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
Noncommutative Algebra MATH62042 15 Optional
Representation and Characters of Groups MATH62061 15 Optional
Lie Algebras MATH62112 15 Optional
Galois Theory MATH62121 15 Optional
Algebraic Number Theory MATH62132 15 Optional
Computation and Complexity MATH63012 15 Optional
Category Theory MATH63031 15 Optional
Model theory MATH63051 15 Optional
Dynamical Systems MATH64041 15 Optional
Stochastic Calculus MATH67101 15 Optional
Brownian Motion MATH67112 15 Optional
Martingale Theory for Finance MATH67201 15 Optional
Creating a Sustainable World: Interdisciplinary Applications of the Sustainable Development Goals UCIL60312 15 Optional
Displaying 10 of 17 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.

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.


The Department of Mathematics is the largest in the UK with an outstanding research reputation and  facilities .

Disability support

Practical support and advice for current students and applicants is available from the Disability Advisory and Support Service. Email: