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 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, with a substantial proportion of course units undertaken in areas of pure mathematics (e.g. algebra, analysis, geometry, topology, number theory, combinatorics, logic). If you have any doubts as to whether the courses you have studied thus far form a suitable basis, please contact:pgt-maths@manchester.ac.uk