MSc
1 year full time
Starts September 2017

Mathematics

Gain an understanding of advanced mathematics, concentrating on pure, applied and numerical mathematics. This MSc allows you to choose the mathematical topics that best fit your tastes and aspirations.

Mathematics at Sussex plays an important role in the current development of areas as diverse as:

  • analysis and partial differential equations
  • geometry and topology
  • mathematical physics
  • mathematics applied to biology
  • numerical analysis and scientific computing
  • probability and statistics.

This course is for you if you:

  • are interested in Mathematics research and plan to pursue further studies
  • intend to work in industry
  • want to improve your mathematical education for professional reasons.
The Department of Mathematics has a community feel – the tutors here take a real interest in your work.”Stephen Ashton
Mathematics MSc

Key facts

  • 97% of our research output was rated world leading, internationally excellent or internationally recognised in the 2014 Research Excellence Framework (REF).
  • You’ll benefit from our collaborative links with other departments in the UK and overseas.
  • We foster an intellectually stimulating environment in which you are encouraged to develop your own research interests with the support of our faculty.

How will I study?

In the autumn and spring terms, you choose from a range of core modules and options.

In the summer term, you work on your MSc dissertation. You can choose from a wide range of dissertation topics. You’ll be supervised by research-active faculty members.

What will I study?

  • Module list

    Core modules

    Core modules are taken by all students on the course. They give you a solid grounding in your chosen subject and prepare you to explore the topics that interest you most.

    • Dissertation (Mathematics)

      60 credits
      All Year Teaching, Year 1

      You undertake a 20,000-word dissertation from a wide choice of topics, taken under the supervision of a faculty member. This includes personal tutorial hours, where you and your supervisor discuss progress.

    Options

    Alongside your core modules, you can choose options to broaden your horizons and tailor your course to your interests.

    • Advanced Numerical Analysis

      15 credits
      Autumn Teaching, Year 1

      This module will cover topics including:

      • Iterative methods for linear systems: Jacobi and Gauss-Seidel, conjugate gradient, GMRES and Krylov methods
      • Iterative methods for nonlinear systems: fixed point iteration, Newton's method and Inexact Newton
      • Optimisation: simplex methods, descent methods, convex optimisation and non-convenx optimisation
      • Eigenvalue problems: power method, Von Mises method, Jacobi iteration and special matrices
      • Numerical methods for ordinary differential equations: existence of solutions for ODE's, Euler's method, Lindelöf-Picard method, continuous dependence and stability of ODE's
      • Basic methods: forward and backward Euler, stability, convergence, midpoint and trapezoidal methods (order of convergence, truncation error, stability convergence, absolute stability and A-stability)
      • Runge-Kutta methods: one step methods, predictor-corrector methods, explicit RK2 and RK4 as basic examples, and general theory of RK methods such as truncation, consitency, stability and convergence 
      • Linear multistep methods: multistep methods, truncation, consistency, stability, convergence, difference equaitons, Dahlquist's barriers, Adams family and backward difference formulas
      • Boundary value problems in 1d, shooting methods, finite difference methods, convergence analysis, Galerkin methods and convergence analysis
    • Cryptography

      15 credits
      Autumn Teaching, Year 1

      You will cover the following areas: 

      • symmetric-key cryptosystems
      • hash functions and message authentication codes
      • public-key cryptosystems
      • complexity theory and one-way functions
      • primality and randomised algorithms
      • random number generation
      • elliptic curve cryptography
      • attacks on cryptosystems
      • quantum cryptography
      • cryptographic standards.
    • Financial Mathematics

      15 credits
      Autumn Teaching, Year 1

      You will study generalized cash flows, time value of money, real and money interest rates, compound interest functions, quations of value, loan repayment schemes, investment project evaluation and comparison, bonds, term structure of interest rates, some simple stochastic interest rate models and project writing.

    • Functional Analysis

      15 credits
      Autumn Teaching, Year 1

      In this module, you cover:

      • Banach spaces, Banach fixed-point theorem, Baire's theorem
      • bounded linear operators and on Banach spaces, continuous linear functionals, Banach-Steinhaus uniform boundedness principle
      • open mapping and closed graph theorems, Hahn-Banach theorem
      • Hilbert spaces, orthogonal expansions, Riesz representation theorem.
    • Galois Theory

      15 credits
      Autumn Teaching, Year 1

      A quadratic equation in one variable has a formula for its solutions. So do cubic and quartic equations, whereas a general quintic has no such formula. The theory of field equations and its connection to the theory of groups explains this.

      The syllabus will include:

      • Consideration of the historic problems
      • Quadratic equations, complex roots of 1, cubic equations, quartic equations
      • Insolvability of the quintic
      • Ruler and compass constructions, squaring the circle, duplicating the cube
      • Field extensions
      • Applications to ruler-and-compass constructions
      • Normal extensions
      • Application to finite fields, splitting fields
      • Galois group of polynomials
      • Application to x5 - 1 = 0
      • Fundamental Theorem of Galois Theory
      • Galois group for cubic polynomial
      • Solutions of equations in radicals and soluble groups
    • Introduction to Mathematical Biology

      15 credits
      Autumn Teaching, Year 1

      The module will introduce you to the concepts of mathematical modelling with applications to biological, ecological and medical phenomena. The main topics will include:

      • Continuous populations models for single species;
      • Discrete population models for single species;
      • Phase plane analysis;
      • Interacting populations (continuous models);
      • Enzyme kinetics;
      • Dynamics of infectious diseases and epidemics.
    • Linear Statistical Models

      15 credits
      Autumn Teaching, Year 1

      Topics include: full-rank model (multiple and polynomial regression), estimation of parameters, analysis of variance and covariance; model checking; comparing models, model selection; transformation of response and regressor variables; models of less than full rank (experimental design), analysis of variance, hypothesis testing, contrasts; simple examples of experimental designs, introduction to factorial experiments; and use of a computer statistical package to analyse real data sets.
    • Mathematical Fluid Mech

      15 credits
      Autumn Teaching, Year 1

      The aim of this module is to provide an introduction to fluid mechanics, regarded from the perspective of the mathematical analysis of underlying PDE models. As such the course is at the interface between pure and applied mathematics.

      The mdoule focuses on the basic equations of fluid dynamics, namely the Navier-Stokes and Euler equations. These are the equations governing the motion of fluids, such as water or air.

      The module starts with the derivation of the basic conservation laws. Some simple cases of solutions are analyzed in detail and then a general existence theory in bounded and unbounded domain is obtained, based on energy methods.

    • Object Oriented Programming

      15 credits
      Autumn Teaching, Year 1

      You will be introduced to object-oriented programming, and in particular to understanding, writing, modifying, debugging and assessing the design quality of simple Java applications.

      You do not need any previous programming experience to take this module, as it is suitable for absolute beginners.

    • Partial Differential Equations

      15 credits
      Autumn Teaching, Year 1

      Topics include: Second-order Partial Differential Equations: wave equation, heat equation, Laplace equation. D'Alembert's solution, separation of variables, Duhamel's principle, energy method, Maximum principle, Green's identities.

    • Probability Models

      15 credits
      Autumn Teaching, Year 1

      You cover topics including:

      • short revision of probability theory
      • expectation and conditional expectation
      • convergence of random variables, in particular laws of large numbers, moment generating functions, and central limit theorem
      • stochastic processes in discrete time in particular Markov chains, including random walk, martingales in discrete time, Doob's optional stopping theorem, and martingale convergence theorem.
    • Programming in C++

      15 credits
      Autumn Teaching, Year 1

      After a review of the basic concepts of the C++ language, you are introduced to object oriented programming in C++ and its application to scientific computing. This includes writing and using classes and templates, operator overloading, inheritance, exceptions and error handling. In addition, Eigen, a powerful library for linear algebra is introduced. The results of programs are displayed using the graphics interface dislin.

    • Topology and Advanced Analysis

      15 credits
      Autumn Teaching, Year 1

      Topics that will be covered in this module include:

      • Topological spaces
      • Base and sub-base
      • Separation axioms
      • Continuity
      • Metrisability
      • Completeness
      • Compactness and Coverings
      • Total Boundedness
      • Lebesgue numbers and Epsilon-nets
      • Sequential Compactness
      • Arzela-Ascoli Theorem
      • Montel's theorem
      • Infinite Products
      • Box and Product Topologies
      • Tychonov Theorem
      • Banach-Alaoglu theorem.
    • Advanced Partial Differential Equations

      15 credits
      Spring Teaching, Year 1

      You will be introduced to modern theory of linear and nonlinear Partial Differential Equations. Starting from the theory of Sobolev spaces and relevant concepts in linear operator theory, which provides the functional analytic framework, you will treat the linear second-order elliptic, parabolic, and hyperbolic equations (Lax-Milgram theorem, existence of weak solutions, regularity, maximum principles), e.g., the potential, diffusion, and wave equations that arise in inhomogeneous media.

      The emphasis will be on the solvability of equations with different initial/boundary conditions, as well as the general qualitative properties of their solutions. They then turn to the study of nonlinear PDE, focusing on calculus of variation.

    • Coding Theory

      15 credits
      Spring Teaching, Year 1

      Topics covered include: 

      • Introduction to error-correcting codes. The main coding theory problem. Finite fields.
      • Vector spaces over finite fields. Linear codes. Encoding and decoding with a linear code.
      • The dual code and the parity check matrix. Hamming codes. Constructions of codes.
      • Weight enumerators. Cyclic codes. MDS codes.
    • Continuum Mechanics

      15 credits
      Spring Teaching, Year 1

      Topics include: 

      • Kinematics: Eulerian and Lagrangian descriptions, velocity, acceleration, rate of change of physical quantities, material derivatives, streamlines.
      • Deformation: stress and strain tensors, Hooke's law, equilibrium equations.
      • Conservation laws for mass, momentum and energy.
      • Phase/group velocities of travelling wave solutions.
      • Models of fluid and solid mechanics.
    • Differential Geometry

      15 credits
      Spring Teaching, Year 1

      On this module, we will cover:

      • Manifolds and differentiable structures
      • Lie derivatives
      • Parallel transport
      • Riemannian metrics and affine connections
      • Curvature tensor
      • Sectional curvature
      • Scalar curvature
      • Ricci curvature
      • Bianchi identities
      • Schur's lemma
      • Complete manifolds
      • Hopf-Rinow theorem
      • Hadmard's theorem
      • Geodescis and Jacobi fields
      • Bonnet-Meyer and Synge theorems
      • Laplace-Beltrami operator
      • Heat kernels and index theorem.
    • Dynamical Systems

      15 credits
      Spring Teaching, Year 1

      • General dynamical systems: semiflow, stability and attraction, omega-limit set, global attractor
      • Ordinary Differential Equations: Linear systems, Lyapunov function, linearised systems around fixed points, two-dimensional
        systems, periodic orbit
      • Discrete systems (iterations): Linear systems, linearised systems around fixed points, chaos
    • Financial Invest & Corp Risk Analysis

      15 credits
      Spring Teaching, Year 1

      In this module, we introduce the three main risk concepts in the investment and corporate risk management field: market risk (times series), credit risk (financial rating) and operational risk (evaluation and reporting techniques), using Basel Regulations as guidelines.

      We then introduce the mathematical tools required to quantify, describe and analyse these risks quantitatively (including graphic representation, bootstrapping, calculation of transition matrices, ARCH/GARCH models, VaR, Monte-Carlo simulation)

      We also introduce some programming tools in Excel and MatLab on how to deal with these problems.

    • Financial Portfolio Analysis

      15 credits
      Spring Teaching, Year 1

      You will study valuation, options, asset pricing models, the Black-Scholes model, Hedging and related MatLab programming. These topics form the most essential knowledge for you if you intend to start working in the financial fields. They are complex application problems. Your understanding of mathematics should be good enough to understand the modelling and reasoning skills required. The programming element of this module makes complicated computations manageable and presentable.

    • Mathematical Models in Finance and Industry

      15 credits
      Spring Teaching, Year 1

      Topics include: partial differential equations (and methods for their solution) and how they arise in real-world problems in industry and finance. For example: advection/diffusion of pollutants, pricing of financial options.

    • Measure and Integration

      15 credits
      Spring Teaching, Year 1

      In this module, you cover:

      • countably additive measures, sigma-algebras, Borel sets, measure spaces
      • outer measures and Caratheodory's construction of measures
      • construction and properties of Lebesgue measure in Euclidean spaces
      • measurable and integrable functions, Lebesgue integration theory on measure spaces, L^p spaces and their properties
      • convergence theorems: monotone convergence, dominated convergence, Fatou's lemma
      • application of limit theorems to continuity and differentiability of integrals depending on a parameter
      • properties of finite measure spaces and probability theory.
    • Medical Statistics

      15 credits
      Spring Teaching, Year 1

      Topics include: logistic regression, fitting and interpretation. Survival times; Kaplan-Meier estimate, log-rank test, Cox proportional hazard model. Designing medical research. Clinical trials; phases I-IV, randomised double-blind controlled trial, ethical issues, sample size, early stopping. Observational studies: prospective/retrospective, longitudinal/cross-sectional. Analysis of categorical data; relative risk, odds ratio; McNemar's test, meta-analysis (Mantel-Haenszel method). Diagnostic tests; sensitivity and specificity; receiver operating characteristic. Standardised mortality rates.
    • Monte Carlo Simulations

      15 credits
      Spring Teaching, Year 1

      The module will cover topics including:

      • Introduction to R 
      • Pseudo-random number generation 
      • Generation of random variates 
      • Variance reduction 
      • Markov-chain Monte Carlo and its foundations 
      • How to analyse Monte Carlo simulations 
      • Application to physics: the Ising model 
      • Application to statistics: goodness-of-fit tests
    • Numerical Solution of Partial Differential Equations

      15 credits
      Spring Teaching, Year 1

      Topics covered include: variational formulation of boundary value problems; function spaces; abstract variational problems; Lax-Milgram Theorem; Galerkin method; finite element method; examples of finite elements; and error analysis.
    • Optimal Control of Partial Differential Equations

      15 credits
      Spring Teaching, Year 1

      You will be introduced to optimal control problems for partial differential equations. Starting from basic concepts in finite dimensions (existence, optimality conditions, adjoint, Lagrange functional and KKT system) you will study the theory of linear-quadratic elliptic optimal control problems (weak solutions, existence of optimal controls, adjoint operators, necessary optimality conditions, Langrange functional and adjoint as Langrangian multiplier) as well as basic numerical methods for your solution (gradient method, projected gradient method and active set strategy). The extension to semi-linear elliptic control problems will also be considered.

    • Perturbation theory and calculus of variations

      15 credits
      Spring Teaching, Year 1

      The aim of this module is to introduce you to a variety of techniques primarily involving ordinary differential equations, that have applications in various branches of applied mathematics. No particular application is emphasised.

      Topics covered include

      • Dimensional analysis and scaling:
      • physical quantities and their measurement;
      • dimensions;
      • change of units;
      • physical laws;
      • Buckingham Pi Theorem;
      • scaling.
      • Regular perturbation methods:
      • direct method applied to algebraic equations and initial value problems (IVP);
      • Poincar method for periodic solutions;
      • validity of approximations.
      • Singular perturbation methods:
      • finding approximate solutions to algebraic solutions;
      • finding approximate solutions to boundary value problems (BVP) including boundary layers and matching.
      • Calculus of Variations:
      • necessary conditions for a function to be an extremal of a fixed or free end point problem involving a functional of integral form;
      • isoperimetric problems.
    • Random processes

      15 credits
      Spring Teaching, Year 1

      Topics covered include:

      Rationalisation:
      After the introduction of the Poisson process, birth and death processes as well as epidemics models can be presented in full generality as applications of the pooled Poisson process. At the same time, the students will be introduced to the Kolmogorov equations and to the techniques for solving them. Renewal theory is needed to better understand queues, and, for this reason, it is discussed before queues.
      Modernisation:
      A modern introductory course on stochastic processes must include at least a section on compound renewal processes (with a focus on the compound Poisson process) as well as a chapter on the Wiener process and on Ito stochastic calculus. This is necessary given the importance this process has in several applications from finance to physics. Modernisation is achieved by including a new introductory chapter divided into three parts.
      1. Poisson processes:
        1. Density and distribution of into-event time.
        2. Pooled Poisson process.
        3. Breaking down a Poisson process.
        4. Applications of the Poisson process, eg birth-and-death processes, the Kolmogorov equations.
      1. Renewal processes
        1. The ordinary renewal process.
        2. The equilibrium renewal process.
        3. The compound renewal process.
        4. Applications of renewal processes, queues.
      1. Wiener process
        1. Definition and properties
        2. Introduction to stochastic integrals
        3. Introduction to stochastic differential equations.

Entry requirements

An upper second-class (2.1) undergraduate honours degree or above in mathematics. Degree subjects with substantial mathematics content or joint mathematics degrees are also acceptable.

English language requirements

Lower level (IELTS 6.0, with not less than 6.0 in each section)

Find out about other English language qualifications we accept.

English language support

Don’t have the English language level for your course? Find out more about our pre-sessional courses.

Additional information for international students

We welcome applications from all over the world. Find out about international qualifications suitable for our Masters courses.

Visas and immigration

Find out how to apply for a student visa


Fees and scholarships

How much does it cost?

Fees

Home: £7,700 per year

EU: £7,700 per year

Channel Islands and Isle of Man: £7,700 per year

Overseas: £15,100 per year

Note that your fees may be subject to an increase on an annual basis.

How can I fund my course?

Postgraduate Masters loans

Borrow up to £10,280 to contribute to your postgraduate study.

Find out more about Postgraduate Masters Loans

Scholarships

Our aim is to ensure that every student who wants to study with us is able to despite financial barriers, so that we continue to attract talented and unique individuals.

Chancellor's Masters Scholarship (2017)

Open to students with a 1st class from a UK university or excellent grades from an EU university and offered a F/T place on a Sussex Masters in 2017

Application deadline:

1 August 2017

Find out more about the Chancellor's Masters Scholarship

Sussex Graduate Scholarship (2017)

Open to Sussex students who graduate with a first or upper second-class degree and offered a full-time place on a Sussex Masters course in 2017

Application deadline:

1 August 2017

Find out more about the Sussex Graduate Scholarship

Sussex India Scholarships (2017)

Sussex India Scholarships are worth £3,500 and are for overseas fee paying students from India commencing Masters study in September 2017.

Application deadline:

1 August 2017

Find out more about the Sussex India Scholarships

Sussex Malaysia Scholarships (2017)

Sussex Malaysia Scholarships are worth £3,500 and are for overseas fee paying students from Malaysia commencing Masters study in September 2017.

Application deadline:

1 August 2017

Find out more about the Sussex Malaysia Scholarships

Sussex Nigeria Scholarships (2017)

Sussex Nigeria Scholarships are worth £3,500 or £5,000 and are for overseas fee paying students from Nigeria commencing a Masters in September 2017.

Application deadline:

1 August 2017

Find out more about the Sussex Nigeria Scholarships

Sussex Pakistan Scholarships (2017)

Sussex Pakistan Scholarships are worth £3,500 and are for overseas fee paying students from Pakistan commencing Masters study in September 2017.

Application deadline:

1 August 2017

Find out more about the Sussex Pakistan Scholarships

How Masters scholarships make studying more affordable

Living costs

Find out typical living costs for studying at Sussex.


Faculty

Research in the Department focuses on the non-mutually exclusive areas of: 

“This MSc is ideal for anyone interested in theory and technique in mathematics and its use in practical applications, or in using mathematical knowledge to identify and resolve unexplained issues.” Dr Miroslav ChlebikConvenor of Mathematics MSc

Careers

Graduate destinations

100% of students from the Department of Mathematics were in work or further study six months after graduating. Recent graduates have gone on to jobs including:

  • accountant, Ernst & Young
  • graduate analyst, Invesco
  • performance analyst, Legal and General Investment Management.

(HESA EPI, Destinations of Post Graduate Leavers from Higher Education Survey 2015)

Your future career

Our graduates go on to careers in:

  • academia
  • scientific research
  • teaching
  • management
  • actuarial roles
  • financial management and analysis
  • programming
  • scientific journalism.

Working while you study

Our Careers and Employability Centre can help you find part-time work while you study. Find out more about career development and part-time work

Today the knowledge and experiences that I gained from my MSc are still central to the way I educate my students and lead a department of 18 academic staff.”Maureen Siew Fang Chong
Head of the Mathematics Department
Duli Pengiran Muda Al-Muhtadee Billar College, Brunei Darussalam

Contact us