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 researchactive 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 1You undertake a 20,000word 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 1This module will cover topics including:
 Iterative methods for linear systems: Jacobi and GaussSeidel, 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 nonconvenx 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, LindelöfPicard 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 Astability)
 RungeKutta methods: one step methods, predictorcorrector 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 1You will cover the following areas:
 symmetrickey cryptosystems
 hash functions and message authentication codes
 publickey cryptosystems
 complexity theory and oneway 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 1You 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 1In this module, you cover:
 Banach spaces, Banach fixedpoint theorem, Baire's theorem
 bounded linear operators and on Banach spaces, continuous linear functionals, BanachSteinhaus uniform boundedness principle
 open mapping and closed graph theorems, HahnBanach theorem
 Hilbert spaces, orthogonal expansions, Riesz representation theorem.
 Galois Theory
15 credits
Autumn Teaching, Year 1A 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 rulerandcompass 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 1The 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
Topics include: fullrank 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.
Autumn Teaching, Year 1  Mathematical Fluid Mech
15 credits
Autumn Teaching, Year 1The 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 NavierStokes 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 1You will be introduced to objectoriented 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 1Topics include: Secondorder 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 1You 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 1After 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 1Topics that will be covered in this module include:
 Topological spaces
 Base and subbase
 Separation axioms
 Continuity
 Metrisability
 Completeness
 Compactness and Coverings
 Total Boundedness
 Lebesgue numbers and Epsilonnets
 Sequential Compactness
 ArzelaAscoli Theorem
 Montel's theorem
 Infinite Products
 Box and Product Topologies
 Tychonov Theorem
 BanachAlaoglu theorem.
 Advanced Partial Differential Equations
15 credits
Spring Teaching, Year 1You 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 secondorder elliptic, parabolic, and hyperbolic equations (LaxMilgram 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 1Topics covered include:
 Introduction to errorcorrecting 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 1Topics 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 1On 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
 HopfRinow theorem
 Hadmard's theorem
 Geodescis and Jacobi fields
 BonnetMeyer and Synge theorems
 LaplaceBeltrami operator
 Heat kernels and index theorem.
 Dynamical Systems
15 credits
Spring Teaching, Year 1 General dynamical systems: semiflow, stability and attraction, omegalimit set, global attractor
 Ordinary Differential Equations: Linear systems, Lyapunov function, linearised systems around fixed points, twodimensional
systems, periodic orbit  Discrete systems (iterations): Linear systems, linearised systems around fixed points, chaos
 Financial Invest & Corp Risk Analysis
15 credits
Spring Teaching, Year 1In 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, MonteCarlo 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 1You will study valuation, options, asset pricing models, the BlackScholes 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 1Topics include: partial differential equations (and methods for their solution) and how they arise in realworld problems in industry and finance. For example: advection/diffusion of pollutants, pricing of financial options.
 Measure and Integration
15 credits
Spring Teaching, Year 1In this module, you cover:
 countably additive measures, sigmaalgebras, 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
Topics include: logistic regression, fitting and interpretation. Survival times; KaplanMeier estimate, logrank test, Cox proportional hazard model. Designing medical research. Clinical trials; phases IIV, randomised doubleblind controlled trial, ethical issues, sample size, early stopping. Observational studies: prospective/retrospective, longitudinal/crosssectional. Analysis of categorical data; relative risk, odds ratio; McNemar's test, metaanalysis (MantelHaenszel method). Diagnostic tests; sensitivity and specificity; receiver operating characteristic. Standardised mortality rates.
Spring Teaching, Year 1  Monte Carlo Simulations
15 credits
Spring Teaching, Year 1The module will cover topics including:
 Introduction to R
 Pseudorandom number generation
 Generation of random variates
 Variance reduction
 Markovchain Monte Carlo and its foundations
 How to analyse Monte Carlo simulations
 Application to physics: the Ising model
 Application to statistics: goodnessoffit tests
 Numerical Solution of Partial Differential Equations
15 credits
Topics covered include: variational formulation of boundary value problems; function spaces; abstract variational problems; LaxMilgram Theorem; Galerkin method; finite element method; examples of finite elements; and error analysis.
Spring Teaching, Year 1  Optimal Control of Partial Differential Equations
15 credits
Spring Teaching, Year 1You 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 linearquadratic 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 semilinear elliptic control problems will also be considered.
 Perturbation theory and calculus of variations
15 credits
Spring Teaching, Year 1The 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 1Topics 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.
 Poisson processes:
 Density and distribution of intoevent time.
 Pooled Poisson process.
 Breaking down a Poisson process.
 Applications of the Poisson process, eg birthanddeath processes, the Kolmogorov equations.
 Renewal processes
 The ordinary renewal process.
 The equilibrium renewal process.
 The compound renewal process.
 Applications of renewal processes, queues.
 Wiener process
 Definition and properties
 Introduction to stochastic integrals
 Introduction to stochastic differential equations.
 Dissertation (Mathematics)
Entry requirements
An upper secondclass (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 presessional 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
Sussex Graduate Scholarship (2017)
Open to Sussex students who graduate with a first or upper secondclass degree and offered a fulltime place on a Sussex Masters course in 2017
Application deadline:
1 August 2017
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
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
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
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
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 nonmutually exclusive areas of:
 Analysis and Partial Differential Equations
Dr Filippo Cagnetti
Senior Lecturer in Mathematics
F.Cagnetti@sussex.ac.ukResearch interests: Calculus of Variations, Partial Differential Equations
Dr Miroslav Chlebik
Reader in Mathematics
M.Chlebik@sussex.ac.ukResearch interests: Calculus of Variations, Computational Complexity, Geometric Analysis, Measure Theory, Partial Differential Equations
Dr Masoumeh Dashti
Lecturer in Mathematics
M.Dashti@sussex.ac.ukResearch interests: Fluid Mechanics (Continuum), Inverse Problems, Partial Differential Equations
Dr Peter Giesl
Reader in Mathematics
P.A.Giesl@sussex.ac.ukResearch interests: Biomechanics, Dynamical Systems, Numerical Analysis
Dr Gabriel Koch
Senior Lecturer in Mathematics
G.Koch@sussex.ac.ukResearch interests: Partial Differential Equations
Dr Konstantinos Koumatos
Lecturer in Mathematics
K.Koumatos@sussex.ac.ukProf Michael Melgaard
Professor of Mathematics (Analysis and Partial Differential Equations)
M.Melgaard@sussex.ac.ukResearch interests: Analysis, Mathematics, Nonlinear partial differential equations, Partial Differential Equations, Quantum dynamics, Quantum Many Body Theory, Quantum mechanics, Spectral Theory
Dr Mariapia Palombaro
Senior Lecturer in Mathematics
M.Palombaro@sussex.ac.ukResearch interests: Mathematics
Dr Ali Taheri
Reader In Mathematics
A.Taheri@sussex.ac.ukResearch interests: Calculus of Variations, Geometric Analysis, Harmonic Analysis, Partial Differential Equations, Real Analysis, Topology
Dr Qi Tang
Reader in Mathematics
Q.Tang@sussex.ac.ukResearch interests: Stochastic integraldifferential equations
 Geometry and Topology
Dr Roger Fenn
Associate Tutor
R.A.Fenn@sussex.ac.ukProf James Hirschfeld
Tutorial Fellow in Mathematics
JWPH@sussex.ac.uk  Mathematics Applied to Biology
Dr Konstantin Blyuss
Senior Lecturer In Mathematics
K.Blyuss@sussex.ac.ukResearch interests: Applied Mathematics, Epidemiology, Immunology, Mathematical and Computational Biology, Mathematical Biology, Mathematical modelling, Nonlinear Dynamics and Chaos
Dr Istvan Kiss
Reader In Mathematics
I.Z.Kiss@sussex.ac.ukResearch interests: Dynamical Systems, Mathematical Biology, Network Theory and Complexity, Stochastic Processes
Dr Yuliya Kyrychko
Reader in Mathematics
Y.Kyrychko@sussex.ac.ukResearch interests: Applied Mathematics, Delay Differential Equations, Feedback control, Mathematical modelling, Networks of coupled systems, Nonlinear Dynamics and Chaos, Synchronisation
Prof Anotida Madzvamuse
Professor of Mathematical&ComputationalBiology'RSW Research Merit Award Holder'
A.Madzvamuse@sussex.ac.ukResearch interests: computational biology, Coupled bulksurface models, Dynein transport models, evolving surface finite element, Keratin spatiotemporal models, Mathematical Biology, Mathematical modelling, moving grid finite element, Optimal control of Geometric PDES, Parameter Identification, Pattern Formation, Reactiondiffusion, Scientific Computing
 Numerical Analysis and Scientific Computing
Dr Bertram Duering
Reader in Mathematics
B.During@sussex.ac.ukResearch interests: Applied Mathematics, Financial Mathematics, Modelling, Numerical Analysis, Optimal Control, Partial Differential Equations
Dr Max Jensen
Senior Lecturer In Mathematics
M.Jensen@sussex.ac.ukResearch interests: Financial Mathematics, Numerical Analysis, Optimal Control, Partial Differential Equations
Dr Omar Lakkis
Senior Lecturer
O.Lakkis@sussex.ac.ukResearch interests: Applied Mathematics, Computational Methods and Tools, Mathematics, Nonlinear partial differential equations, Numerical Analysis, Stochastic PDEs
Prof Charalambos Makridakis
Professor Of Mathematics
C.Makridakis@sussex.ac.ukResearch interests: Multiscale Modelling, Numerical Analysis for Differential Equations
Dr Vanessa Styles
Reader In Mathematics
V.Styles@sussex.ac.ukResearch interests: Computational Partial Differential Equations, Mathematical and Computational Biology, Numerical Analysis, Partial Differential Equations
 Probability and Statistics
Dr Andrew Duncan
Lecturer in Statistics and Probability
Andrew.Duncan@sussex.ac.ukDr Nicos Georgiou
Senior Lecturer
N.Georgiou@sussex.ac.ukResearch interests: Applied Probability, Probability Theory
Dr Sabine Jansen
Lecturer in Statistics and Probability
S.C.Jansen@sussex.ac.ukProf Enrico Scalas
Professor Of Statistics & Probability
E.Scalas@sussex.ac.ukResearch interests: Econophysics, Financial Mathematics, Mathematical Statistics, Monte Carlo simulations, Probability Theory, Statistical Mechanics, Stochastic Processes
Dr Dimitrios Tsagkarogiannis
Senior Lecturer
D.Tsagkarogiannis@sussex.ac.ukResearch interests: Probability, Statistical Mechanics
Dr Vladislav Vysotskiy
Reader in Statistics and Probability
V.Vysotskiy@sussex.ac.uk
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 parttime work while you study. Find out more about career development and parttime 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 AlMuhtadee Billar College, Brunei Darussalam
Life at Sussex
Contact us

Course enquiries
+44 (0)1273 873254
mps@sussex.ac.uk 
Admissions enquiries
If you haven’t applied yet:
+44 (0)1273 876787
pg.enquiries@sussex.ac.ukAfter you’ve applied:
+44 (0)1273 877773
pg.applicants@sussex.ac.uk