Mathematics MSc

From geometry, analysis, partial differential equations and mathematical physics to fluid dynamics, meteorology and modelling in life sciences – our MSc offers you an extraordinary range of research opportunities that lie at the heart of tackling the key scientific questions of our age.

Why Surrey?

In the 2008 Research Assessment Exercise, 70 per cent of our research in mathematics was rated in the top categories as either ‘world leading’ or ‘internationally excellent’. This metric puts us fifth equal in applied mathematics.

Programme overview

Our programme is for you if you want to continue your mathematical studies beyond the level reached in a BSc degree (or equivalent). Our Mathematics MSc provides you with opportunities to deepen and broaden your knowledge and engage in a significant research project under the supervision of a member of the Department of Mathematics. The programme is particularly appropriate if you are considering either an academic career or a research career in an area of business or industry where high levels of mathematical expertise are valued.

During the first two semesters, you will take a range of taught modules from an extensive list of options.  Students will discuss their choices of options with tutors to ensure that their selections are coherent and appropriate to their backgrounds and ambitions. The taught modules are followed by an extended research project conducted over the summer under the supervision of a member of the Department, culminating in the writing of a dissertation.  

This MSc reflects and benefits from the strong research activities of the Department of Mathematics. The taught modules and dissertation topics are closely aligned with the interests of the Department’s four research groups: Biosystems; Dynamical Systems & Partial Differential Equations; Fields, Strings & Geometry; and Fluid Mechanics & Meteorology.   

Module overview

During the first two semesters, students on this programme will take eight modules from those offered by the Department of Mathematics from the lists below. At least six of the modules must be taken from the Level 7 list. Students may not take a Level 6 module that overlaps significantly with a module taken during their undergraduate studies. Each student will be assigned a tutor to provide advice on their choices of modules, taking into account their academic background and their ambitions for the future. Each year the Department will typically offer five to seven modules from the Level 6 list and eight to ten from the Level 7 list. These lists are subject to revision.

During the summer, students undertake an extensive research project under the supervision of a member of the Department of Mathematics. The topic of the dissertation will typically be aligned with the interests of one or more of the Department’s four research groups: Biosystems; Dynamical Systems & Partial Differential Equations; Fields, Strings & Geometry; Fluid Mechanics & Meteorology.

Module list

Level 6 Modules

Credits

Numerical Solution of PDEs

15

Quantum Mechanics

15

Manifolds and Topology

15

Mathematics of Weather

15

Graphs and Networks

15

Level 7 Modules

Credits

Functional Analysis and PDEs

15

Quantum Field Theory

15

General Topology

15

Advanced Techniques in Mathematics

15

Lie Algebras

15

Nonlinear Wave Equations

15

Nonlinear Patterns

15

Geometric Mechanics

15

Representation Theory

15

Relativity

15

Ecological and Epidemiological Modelling 15

Dissertation

60

Level 6 modules

Numerical Solution of PDEs

Partial differential equations (PDEs) may be used to model many physical and biological processes.  Although there are some analytical solutions available for PDEs, many PDEs cannot be easily solved by hand and computational techniques play an important role in understanding and interpreting the behaviour of a given PDE. In this module some numerical methods for solving PDEs are examined, including underlying theory and their application.

Quantum Mechanics

You will be encouraged to develop an understanding of the mechanics governing the quantum world, and master the basic tools needed for its qualitative and quantitative description. On this module you will study the birth of quantum mechanics, Hilbert spaces and Dirac notation, alongside the uncertainty principle and wave functions of quantum mechanics.

Manifolds and Topology

This module will expand your knowledge of functions, vector fields and differential forms on manifolds, and will provide you with a foundation for the study of global features via the de Rham cohomology.

Mathematics of Weather

Mathematics plays a central role in the development and analysis of models for weather prediction, and this module will introduce you to topics including descriptions of fluid motion, governing equations, quasi-geostrophic theory in meteorology, vorticity dynamics and linear barotropic waves.

Graphs and Networks

Graph theory is a branch of pure mathematics with strong links to other areas of mathematics such as combinatorics, algebra, topology, probability, optimisation and numerical analysis. It also has well developed applications to a wide range of other disciplines such as operational research, chemistry, systems biology, statistical mechanics and quantum field theory. This module provides an introduction to both theory and applications that emphasises both breadth and interconnectedness.

Level 7 modules

Quantum Field Theory

Ordinary Quantum Mechanics describes extraordinarily well the microscopic world of atoms and molecules, but it has problems when it comes to the description of the ultra-energetic processes going on in particle accelerators, where particles can be created and annihilated during the collisions. When the energies are extremely high and the particle velocities approach the speed of light, Einstein's theory of Special Relativity must be taken into account. The theory that was born from the union of Quantum Mechanics and Special Relativity was called Quantum Field Theory. 

This module will present the physical motivations and the mathematical formalism of Quantum Field Theory, starting from the scalar particle to reach the description of electron and positrons via the famous Dirac Equation. Interacting fields and Feynman rules will be introduced, and a small project at the end will take a short detour into one of the favourite modern applications of the theory of quantum fields to elementary particles.

General Topology

This module provides a self-contained, rigorous, formal treatment of basic topics in point set topology which is an important subject in modern mathematics. You will encounter abstract, general mathematical arguments and techniques. Proofs, rigorous arguments and the power of generalisation in mathematics are all central to the module.

Advanced Techniques in Mathematics

This module focuses on a range of important analytical techniques commonly used to tackle advanced applied mathematical problems. These are (i) calculus of variations, which is concerned with optimising functionals (usually integrals), (ii) orthogonal function expansions, (iii) Laplace and Fourier transforms and their applications to solving ordinary and partial differential equations, and (iv) applications of geometric singular perturbation theory which is a theory for systems of differential equations that contain a small parameter.

Lie Algebras

You will explore the definitions and properties of Lie algebras, subalgebras, ideals, homomorphisms and automorphisms. In addition, you will become familiar with standard examples and understand concepts of solvable, semi-simple and simple Lie algebras.

Nonlinear Wave Equations

You will encounter a range of techniques for studying certain types of nonlinear partial differential equations that are important in some fields of mathematics. The techniques include linearised analysis, exact solutions, stability and blow-up. One equation you will encounter is the famous Korteweg-de Vries equation which arises in modelling solitary waves in shallow water.

Nonlinear Patterns

Regular patterns arise naturally in many physical and biological systems, from hexagonal convection cells on the surface of the sun to stripes on a zebra's back. This module provides you with a basic framework for understanding the formation and evolution of these patterns using ordinary and partial differential equations and group theory.

Geometric Mechanics

You will study elements of multi-linear algebra, differential geometry and Lie group actions as well as conservation laws, Lie-Poisson structures, infinite dimensions and symplectic spaces on this module.

Representation Theory

This module introduces the theory of group representations as a systematic way of classifying objects on which a group can act.  Furthermore, it reveals how this leads to a deeper understanding of symmetry aspects of physical systems and how one can use it to simplify mathematical computations.

Relativity

The aim of this module is to describe the basics of Einstein's general theory of relativity, one of the biggest discoveries in modern physics, which describes gravitational phenomena at scales ranging from the solar system to the universe as a whole. The module will discuss Einstein’s special theory of relativity, introduce a four-dimensional space-time continuum called Minkowski space, dwell on (pseudo) Riemannian geometry, and eventually formulate Einstein's equation of gravity and discuss some of its consequences touching upon bizarre objects known as black holes.

Ecological and Epidemiological Modelling

This module introduces ideas of mathematical modelling in ecology and epidemiology. The focus will be on models described by ordinary differential equations, delay differential equations and partial differential equations. In particular, the module will consider analytical techniques for studying such models, interpreting the results and making predictions.

Functional Analysis and PDEs

This module introduces the basic concepts of functional analysis including Hilbert and Banach spaces, the associated spaces of linear functionals, weak convergence, etc. The introduced concepts are then used to give an introduction to the modern theory of partial differential equations.

Dissertation (compulsory)

Careers

Mathematics is not only central to science, technology and finance-related fields, but the logical insight, analytical skills and intellectual discipline gained from a mathematical education are highly sought after in a broad range of other areas such as law, business and management. There is also a strong demand for new mathematics teachers to meet the ongoing shortage in schools.

As well as being designed to meet the needs of future employers, our MSc programme also provides a solid foundation from which to pursue further research in mathematics or one of the many areas to which mathematical ideas and techniques are applied. 

This is a new programme and so there are no data yet on destinations of graduates. However recent graduates of Surrey’s BSc and MMath in Mathematics have proceeded to positions with employers such as BAE Systems, Lloyds TSB Group, Skandia Life, Friends Provident, Logica CMG, UniChem, Generics UK, Thames Water, the Civil Service and QinetiQ, as well as to postgraduate research programmes at Surrey and other universities.   

Related departments/schools

Related research areas

Programme leader

Professor Stephen Gourley

Find out more

General enquiries:

+44 (0)1483 681 681

Admissions enquiries:

+44-(0)1483-682-222

admissions@surrey.ac.uk

Programme facts

Type of programme:

MSc

Programme length:

  • Full-time: 12 months

Start date:

Sep 2016

Entry Requirements

At least a 2.1 BSc degree or equivalent in mathematics or a closely related discipline. This must include a sufficient mathematical preparation for the programme.

View entry requirements by country

English language requirements

IELTS minimum overall: 6.5

IELTS minimum by component: 6.0

We offer intensive English language pre-sessional courses, designed to take you to the level of English ability and skill required for your studies here.

Fees

Study mode Start date UK/EU fees Overseas fees
Full-time Sep 2016 £7,000 £18,000

Please note these fees are for the academic year 2016/2017 only. Annual fees will rise by four per cent (rounded up to the nearest £100) for each year of study.

A complete list of all fees for our Masters Programmes

Funding

Discounts for Surrey graduates

Thinking of continuing your education at Surrey? As an alumnus of Surrey you may be eligible for a ten per cent discount on our taught Masters programme fees. Learn more.

For more details

GREAT Surrey Scholarships India

For for all postgraduate taught courses starting in September 2016 within the Faculty of Engineering and Physical Sciences, the University is offering graduates from India the opportunity to apply for one of six scholarships worth £5,000 through the GREAT Scholarships - India programme. Download a flyer or read more for eligibility and to apply.

For more details

Admissions Information

Our Admissions Policy provides the basis for admissions practice across the University and gives a framework for how we encourage, consider applications and admit students.

Further information for applicants

Postgraduate Study Advice

Steps to Postgraduate Study is an official, independent guide for anyone considering a taught postgraduate course. The guide is produced by the Higher Education Funding Council for England (HEFCE), the Higher Education Funding Council for Wales, the Scottish Funding Council and the Department for Employment and Learning, Northern Ireland.

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Disclaimer

Modules listed are indicative, reflecting the information available at the time of publication. Please note that not all modules described are compulsory and may be subject to teaching availability and/or student demand.