The course comprises 180 credits, split across 120 credits of taught modules and a 60-credit research project.
This consists of taught modules of which students must take up to 120 credits worth. Central to the course are three pairs of modules each consisting of an autumn and a spring module. Students must choose at least one such pair of modules. Each pair provides a substantial foundation in analysis, algebra (in particular group theory) and number theory, respectively.
Students must take a 120 credits from the group listed under 'Modules' below. This must include both modules from at least one of the following pairs:
- Foundations of Advanced Analysis and Further Topics in Analysis
- Advanced Group Theory and Combinational Group Theory
- Higher Number Theory and Algebraic Number Theory
During the summer period, you will conduct an independent research project under the supervision of academic staff, which is worth 60 credits.
The MSc Pure Mathematics is offered on a full-time basis over one year and is designed for students with a degree in Mathematics with a substantial component in pure mathematics.
Students should have a strong interest in pure mathematics and specifically they should have a good background in at least two to three of the following subject areas: algebra, number theory, group theory or analysis.
Modules are mainly delivered through lectures and example and/or problem classes for smaller groups. You will typically be assessed by a combination of examination, coursework and a class test.
Specific prerequisites and recommended books, where appropriate, are listed below for all the taught modules on the course.
Foundations of Advanced Analysis
You should have a good background in real analysis.
- Sutherland; Metric and Topological Spaces
Advanced Group Theory
Basic knowledge in algebra and group theory.
- J B Fraleigh; A First Course in Abstract Algebra
- W Ledermann & A J Weir; Introduction to group theory (2nd edition, Longman Mathematical Series)
Good math background in algebra and commutative ring theory.
- W. Fulton; Algebraic Curves
- M Atiyah, R Macdonald; Introduction to Commutative Algebra
A good first mathematical course in complex analysis and solid background in real analysis as covered in J W Brown; Complex variables and applications.
- L V Ahlfors; Complex analysis: an introduction to the theory of analytic functions of one complex variable
Higher Number Theory
A solid maths back ground in basic number theory (factorisation, Diophantine equations, classical theorems, multiplicative arithmetic functions, perfect numbers and Mersenne numbers).
- K Rosen; Elementary number theory and its applications
- K Ireland, M Rosen; A Classical Introduction to Modern Number Theory
- F Gouvêa; p-adic numbers: an introduction
Further Topics in Analysis
A solid background in metric and topological spaces covering completeness etc. as covered in Foundations of Advanced Analysis and a solid knowledge of linear algebra.
- Bollobás, Béla; Linear analysis: an introductory course
Algebraic Number Theory
A solid background in advanced number theory, algebra, rings and modules and Galois theory.
- S Lang; Algebraic Number Theory
Combinatorial Group Theory
A solid background in group theory.
- D L Johnson; Presentations of Groups