Pure Mathematics The University of Manchester

Overview

The MSc in Pure Mathematics at The University of Manchester offers a comprehensive one-year taught postgraduate programme tailored for individuals seeking to expand their knowledge in advanced mathematics. This course is particularly beneficial for students aiming to strengthen their foundation before embarking on a PhD by research or those who desire to deepen their understanding of abstract mathematical concepts. The programme consists of a taught component that runs from the beginning of the academic year in September until the conclusion of the second semester in late Spring, followed by a dissertation component extending from June to September.

During the taught section, students typically engage in six units alongside a research skills and project unit. Participants have the flexibility to focus solely on pure mathematics topics or to combine these with mathematical logic units. The research skills and project unit includes a mini-project aimed at enhancing mathematical writing abilities, followed by a major project, which usually entails creating an expository account of a mathematical concept under the supervision of a faculty member. Instruction is delivered through traditional lectures, supplemented by example classes, project work, and independent study, allowing for a well-rounded educational experience.

Syllabus

The course units for the MSc in Pure Mathematics include:

• Dissertation in Pure Mathematics and Mathematical Logic
• MSc Pure Mathematics Research and Project Skills
• Measure Theory and Ergodic Theory
• Differentiable Manifolds
• Algebraic Topology
• Riemann Surfaces
• Lie Algebras
• Galois Theory
• Graph Theory
• Representation Theory
• Computation and Complexity
• Category Theory
• Model Theory
• Dynamical Systems
• Stochastic Calculus
• Brownian Motion
• Martingale Theory
• Creating a Sustainable World: Interdisciplinary Applications of the Sustainable Development Goals

Careers 

Graduates of the MSc in Pure Mathematics are well-prepared for a variety of career paths. The programme equips students with strong analytical skills applicable in numerous sectors. Alumni have successfully pursued roles such as Teachers, Research Associates, Software Engineers, and Chief Financial Officers. Notable employers of graduates include Oracle, Alliance Manchester Business School, Scottish Life, AT&T Labs, and the NHS.