MMath Master of Mathematics
 UCAS Course Code
 G103
 ALevel typical
 AAB (2017/8 entry) See All Requirements
About this course
Studying with us means that you’ll benefit from internationally recognised, researchled teaching and a high academic staff/student ratio. You’ll graduate with a deep understanding of mathematics and great career prospects (86% of our graduates were in work or study within six months), whether you specialise in pure maths, applied maths, or a mix of topics from the wide range of optional modules we offer.
This fouryear programme offers advanced study of mathematics preparing you for either further study or a career beyond university. Your lectures are complemented by smallgroup teaching that provides you with quality contact time with our world class lecturers – we were ranked 7th in the UK for the quality of our research outputs (REF 2014).
This fouryear programme offers advanced study of mathematics preparing you for either further study or a career beyond university. Your lectures are complemented by smallgroup teaching that provides you with quality contact time with our world class lecturers – we were ranked 7th in the UK for the quality of our research outputs (REF 2014).
Course Profile
Overview
This prestigious fouryear Master of Mathematics programme allows you to develop your interests in pure and applied mathematics, and in greater depth of study than a threeyear programme.
One of the advantages of studying with us is that we offer a great deal of flexibility in what you can study, enabling you to specialise in either pure or applied mathematics, or a combination of these topics. Apart from engaging in study of essential mathematical theory and technique, you will also have the opportunity to carry out a substantial research project in the final year, allowing you to experience the challenge of independent study and discovery. Furthermore this helps you to develop skills that are essential for many future career paths, including experience of report writing and oral presentation.
If you finish your studies with distinction you may want to join our active group of postgraduate students, as the programme is also excellent preparation for a career in research, either in industry or in a university. However research is just one pathway out of the wide range of challenging careers open to Master of Mathematics students.
Course Structure
The first two years run in parallel with the threeyear BSc programme, before more specialised content is covered in the third and fourth year. In these final two years you will learn advanced principles through a huge range of optional subjects, as well as undertaking an independent project.
Year 1
In the first year you will undertake a set of compulsory modules to consolidate a broad knowledge of mathematical disciplines, primarily algebra and calculus. This is supplemented by classes on the applications of mathematics, problem solving and analysis. The skills you gain from these courses will be revisited throughout the degree and should help inform your future module choices.
Year 2
The modules on offer to you are the same as those available on the BSc programme.
As you progress into your second year, you will continue to learn essential algebraic principles through compulsory modules whilst taking a selection of optional modules to suit your personal interests. The optional modules offered change each year but for instance you may choose to study the theory of special relativity or take a cryptography module to see how number theory studied elsewhere can be applied to the theory of coding. In addition, you will be introduced to mathematical software which will be invaluable in your individual fourth year MMath project.
Year 3
At this stage there are no compulsory modules and you will choose 6 modules from a range of approximately 15 offered. Each year the particular topics on offer vary to mirror the research interests of our lecturers. By this stage we anticipate that you will have found the areas of mathematics which most appeal to you, and you will use this year to focus on these topics, laying the foundations for a successful finalyear research project.
Year 4
You will undertake a substantial individual project during your final year, working under the close supervision of a lecturer whose expertise matches your subject. Each of the lecturers proposes project titles covering a very wide range of current mathematical research, but many of our students come up with their own topics in conjunction with one of our lecturers. Recent topics have ranged from â€śThe Mobius function of Finite Groupsâ€ť to â€śThe Aerodynamics of Golf Ballsâ€ť (a topic suggested by the student). The project is assessed through a written report as well as a short oral presentation to lecturers and fellow Masters students on your findings. For the remainder of your final year, you will choose from a range of Masterâ€™slevel modules that explore topics such as lie algebra, fluid structure interaction and mathematical biology. The topics on offer typically change every year.
Assessment
A variety of assessment methods are applied across the different mathematics modules, ranging from 100% coursework to 100% examination. Most mathematics modules are assessed 80% by examination and 20% by coursework. The coursework component is made up of problems set from an example sheet, to be handed in, marked and returned together with solutions. For some modules there are also programming assignments and/or class tests. In Year 4, the research project makes up onethird of the final assessment.
Course Modules 2017/8
Students must study the following modules for 120 credits:
Name  Code  Credits 

CALCULUS AND MULTIVARIABLE CALCULUS (a) Complex numbers. (b) Vectors. (c) Differentiation. Taylor and Maclaurin series. (d) Integration: Applications: curve sketching, areas, arc length. (e) Firstorder, secondorder, constant coefficient ordinary differential equations. Reduction of order. Numerical solutions using MAPLE. Partial derivatives, chain rule. (f) Line integrals. Multiple integrals, including change of coordinates by Jacobians. Green's theorem in the plane. (g) Euler type and general linear ODEs. (h) Divergence, gradient and curl of a vector field. Scalar potential and path independence of line integral. Divergence and Stokes' theorems. (i) Introduction to Matlab.  MTHA4005Y  40 
LINEAR ALGEBRA In the first semester we develop the algebra of matrices: Matrix operations, linear equations, determinants, eigenvalues and eigenvectors, diagonalization and geometric aspects. This is followed in the second semester by vectors space theory: Subspqaces, basis and dimension, linear maps, ranknullity theorem, change of basis and the characteristic polynomial.  MTHA4002Y  20 
MATHEMATICAL PROBLEM SOLVING, MECHANICS AND MODELLING STUDENTS FROM YEARS 2 OUTSIDE SCHOOL OF MATHEMATICS CAN TAKE THIS MODULE IF THEY HAVE ALREADY TAKEN MTHA4005Y, MTHB4006Y OR ENV4015Y AND HAVE NOT TAKEN MTHB4007B. The first part of the module is about how to approach mathematical problems (both pure and applied) and write mathematics. It aims to promote accurate writing, reading and thinking about mathematics, and to improve students' confidence and abilities to tackle unfamiliar problems. The second part of the module is about Mechanics. It includes discussion of Newton's laws of motion, particle dynamics, orbits, and conservation laws. This module is reserved for students registered in the School of Mathematics or registered on the Natural Sciences programme.  MTHA4004Y  20 
REAL ANALYSIS This module is concerned with the mathematical notion of a limit. We will see the precise definition of the limit of a sequence of real numbers and learn how to prove that a sequence converges to a limit. After studying limits of infinite sequences, we move on to series, which capture the notion of an infinite sum. We then learn about limits of functions and continuity. Finally, we will learn precise definitions of differentiation and integration and see the Fundamental Theorem of Calculus.  MTHA4003Y  20 
SETS, NUMBERS AND PROBABILITY Basic settheoretic notation, functions. Proof by induction, arithmetic, rationals and irrationals, the Euclidean algorithm. Styles of proof. Elementary set theory. Modular arithmetic, equivalence relations. Countability. Probability as a measurement of uncertainty, statistical experiments and Bayes' theorem. Discrete and continuous distributions. Expectation. Applications of probability: Markov chains, reliability theory.  MTHA4001Y  20 
Students must study the following modules for 80 credits:
Name  Code  Credits 

ALGEBRA We introduce groups and rings, which together with vector spaces are the most important algebraic structures. At the heart of group theory in Semester I is the study of symmetry and the axiomatic development of the theory, groups appear in many parts of mathematics. The basic concepts are subgroups, Lagrange's theorem, factor groups, group actions and the Isomorphism Theorem. In Semester II we introduce rings, using the Integers as a model and develop the theory with many examples related to familiar concepts such as substitution and factorisation. Important examples of commutative rings are fields, domains, polynomial rings and their quotients.  MTHA5003Y  20 
ANALYSIS This module covers the standard basic theory of the complex plane. The areas covered in the first semester, (a), and the second semester, (b), are roughly the following: (a) Continuity, power series and how they represent functions for both real and complex variables, differentiation, holomorphic functions, CauchyRiemann equations, Moebius transformations. (b) Topology of the complex plane, complex integration, Cauchy and Laurent theorems, residue calculus.  MTHA5001Y  20 
DIFFERENTIAL EQUATIONS AND APPLIED METHODS You'll gain a solid understanding in the following areas: Ordinary Differential Equations: solution by reduction of order; variation of parameters for inhomogeneous problems; series solution and the method of Frobenius. Legendre's and Bessel's equations: Legendre polynomials, Bessel functions and their recurrence relations; Fourier series; Partial differential equations (PDEs): heat equation, wave equation, Laplace's equation; solution by separation of variables. Method of characteristics for hyperbolic equations; the characteristic equations; Fourier transform and its use in solving linear PDEs; Dynamical Systems: equilibrium points and their stability; the phase plane; theory and applications.  MTHA5004Y  20 
FLUID DYNAMICS  THEORY AND COMPUTATION (a) Hydrostatics, compressibility. Kinematics: velocity, particle path, streamlines. Continuity, incompressibility, streamtubes. Dynamics: Material derivative, Euler's equations, vorticity and irrotational flows. Velocity potential and streamfunction. Bernoulli's equation for unsteady flow. Circulation: Kelvin's Theorem, Helmholtz's theorems. Basic water waves. (b) Computational methods for fluid dynamics; Euler's method and RungeKutta methods and their use for computing particle paths and streamlines in a variety of twodimensional and threedimensional flows; numerical computation and flow visualisation using Matlab; convergence, consistency and stability of numerical integration methods for ODEs. (c) Theory of Irrotational and Incompressible Flows: velocity potential, Laplace's Equation, sources and vortices, complex potential. Force on a body and the Blasius theorem. Method of images and conformal mappings.  MTHA5002Y  20 
Students will select 20  40 credits from the following modules:
Name  Code  Credits 

MATHEMATICAL STATISTICS It introduces the essential concepts of mathematical statistics deriving the necessary distribution theory as required. In consequence in addition to ideas of sampling and central limit theorem, it will cover estimation methods and hypothesistesting. Some Bayesian ideas will be also introduced.  CMP5034A  20 
TOPICS IN APPLIED MATHEMATICS This module is an optional Year long module. It covers two topics, Lagrangian Systems and Special Relativity, one in each semester. Lagrangian Systems involves reformulation of problems in mechanics allowing solution of problems such as the osci llation of a double pendulum. Some discussion of Hamiltonian systems will also be included. Special Relativity is concerned with changes in time and space when an observer is moving at a speed close to the speed of light.  MTHF5200Y  20 
TOPICS IN PURE MATHEMATICS This module provides an introduction to two selected topics within pure mathematics. These are selfcontained topics which have not been seen before. The topics on offer for 201718 are the following. Topology: This is an introduction to pointset topology, which studies spaces up to continuous deformations and thereby generalises analysis, using only basic set theory. We will begin by defining a topological space, and will then investigate notions like open and closed sets, limit points and closure, bases of a topology, continuous maps, homeomorphisms, and subspace and product topologies. Computability: This is an introduction to the theoretical foundation of computability theory. The main question we will focus on is "which functions can in principle (i.e., given unlimited resources of space and time) be computed?". The main object of study will be certain devices known as unlimited register machines (URM's). We will adopt the point of view that a function is computable if and only if i is computable by a URM. We will identify large families of computable functions and will prove that certain naturally occurring functions are not computable.  MTHF5100Y  20 
Students will select 0  20 credits from the following modules:
Name  Code  Credits 

APPLIED GEOPHYSICS What lies beneath our feet? This module addresses this question by exploring how wavefields and potential fields are used in geophysics to image the subsurface on scales of metres to kilometres. The basic theory, data acquisition and interpretation methods of seismic, electrical, gravity and magnetic surveys are studied. A wide range of applications is covered including archaeological geophysics, energy resources and geohazards. This module is highly valued by employers in industry; guest industrial lecturers will cover the current 'stateoftheart' applications in real world situations. Students doing this module are normally expected to have a good mathematical ability, notably in calculus and algebra before taking this module (ENV4015Y Mathematics for Scientists A or equivalent).  ENV5004B  20 
APPLIED STATISTICS A This is a module designed to give students the opportunity to apply statistical methods in realistic situations. While no advanced knowledge of probability and statistics is required, we expect students to have some background in probability and statistics before taking this module. The aim is to teach the R statistical language and to cover 3 topics: Linear regression, and Survival Analysis.  CMP5017B  20 
DYNAMICS AND VIBRATION The introductory material from first year engineering mechanics is developed. An appreciation of why dynamics and vibration are important for engineering designers leads to consideration of Singledegreeoffreedom (SDOF) systems, Equation of motion, free vibration analysis, Natural frequency, undamped and damped systems and loading. Fourier series expansion and modal analysis are applied to vibration concepts: eigenfrequency, resonance, beats, critical, undercritical and overcritical damping, and transfer function. Introduction to multidegree of freedom (MDOF) systems. Applications to beams and cantilevers. MathCAD will be used to support learning.  ENG5004B  20 
ELECTROMAGNETISM, OPTICS, RELATIVITY AND QUANTUM MECHANICS This module gives an introduction to important topics in physics, with particular, but not exclusive, relevance to chemical and molecular physics. Areas covered include optics, electrostatics and magnetism and special relativity. The module may be taken by any science students who wish to study physics beyond A Level.  PHY4001Y  20 
INTRODUCTION TO BUSINESS (2) Introduction to Business aims to provide a platform for understanding the world of management and the managerial role. The module explores the business environment, key environmental drivers and functions of organisations, providing an uptodate view of current issues faced from every contemporary enterprise such as business sustainability, corporate responsibility and internationalisation. There is consideration of how organisations are managed in response to environmental drivers. To address this aspect, this module introduces key theoretical principles in lectures and seminars are designed to facilitate fundamental study skills development, teamwork and practical application of theory. No previous knowledge of business or business management is required. The general business concepts introduced in lectures are applied in a practical manner during seminars.By the end of this module, students will be able to understand and apply key concepts and analytical tools in exploring the business environment and industry structure respectively. This module is for NONNBS students only.  NBS4008Y  20 
INTRODUCTION TO FINANCIAL AND MANAGEMENT ACCOUNTING (2) This module provides a foundation in the theory and practice of accounting and an introduction to the role, context and language of financial reporting and management accounting. The module assumes no previous study of accounting. It may be taken as a standalone course for those students following a more general management pathway or to provide a foundation to underpin subsequent specialist studies in accounting. This module is for NONNBS students only.  NBS4010Y  20 
INTRODUCTORY MACROECONOMICS This is a compulsory module for all ECO students and it is a prerequisite for later economic modules. The aim of the module is to introduce you to the fundamental principles, concepts and tools of macroeconomics and to apply these to a variety of real world macroeconomic issues. There is some mathematical content  you will be required to interpret linear equations and solve simple linear simultaneous equations. The module will introduce students to core macroeconomic indicators such as income, inflation, unemployment and the stance of the balance of payments. Thus, focussing predominantly on the shortrun, the module will consider: (1) models for equilibrium in the goods market and the money market, (2) applications of such models to discuss the role of fiscal and monetary policy, (3) the tradeoff between inflation and unemployment, and (4) the role of expectations in macroeconomic analysis.  ECO4006Y  20 
INTRODUCTORY MICROECONOMICS This is a compulsory module for all ECO students and it is a prerequisite for later economic modules. The aim of the module is to introduce you to the fundamental principles, concepts and tools of microeconomics. The aim of the module is apply these to a variety of real world economic issues. There is some mathematical content  you will be required to interpret linear equations, solve simple linear simultaneous equations and use differentiation. The module is primarily concerned with: (1) the ways individuals and households behave in the economy; (2) the analysis of firms producing goods and services; (3) how goods and services are traded or otherwise distributed  often but not exclusively through markets; and (4) the role of government as provider and/or regulator.  ECO4005Y  20 
METEOROLOGY I This module is designed to give a general introduction to meteorology, concentrating on the physical processes in the atmosphere and how these influence our weather. The module contains both descriptive and mathematical treatments of radiation balance, fundamental thermodynamics, dynamics, boundary layers, weather systems and meteorological hazards. The assessment is designed to allow those with either mathematical or descriptive abilities to do well; however a reasonable mathematical competence is essential, including a basic understanding of differentiation and integration.  ENV5008A  20 
PROGRAMMING FOR NONSPECIALISTS The purpose of this module is to give the student a solid grounding in the essential features programming using the Java programming language. The module is designed to meet the needs of the student who has not previously studied programming.  CMP5020B  20 
UNDERSTANDING THE DYNAMIC PLANET Understanding of natural systems is underpinned by physical laws and processes. This module explores energy, mechanics, physical properties of Earth materials and their relevance to environmental science using examples from across the Earth's differing systems. The formation, subsequent evolution and current state of our planet are considered through its structure and behaviour  from the planetary interior to the dynamic surface and into the atmosphere. Plate Tectonics is studied to explain Earth's physiographic features  such as mountain belts and volcanoes  and how the processes of erosion and deposition modify them. The distribution of land masses is tied to global patterns of rock, ice and soil distribution and to atmospheric and ocean circulation. We also explore geological time  the 4.6 billion year record of changing conditions on the planet  and how geological maps can used to understand Earth history. This course provides an introduction to geological materials  rocks, minerals and sediments  and to geological resources and natural hazards.  ENV4005A  20 
Students must study the following modules for credits:
Name  Code  Credits 

Students will select 80  120 credits from the following modules:
Name  Code  Credits 

ADVANCED MATHEMATICAL TECHNIQUES We provide techniques for a wide range of applications, while stressing the importance of rigor in developing such techniques. The calculus of Variations includes techniques for maximising integrals subject to constraints. A typical problem is the curve described by a heavy chain hanging under the effect of gravity. We develop techniques for algebraic and differential equations. This includes asymptotic analysis. This provides approximate solutions when exact solutions can not be found an6d when numerical solutions are difficult. Integral transforms are useful for solving problems including integrodifferential equations. This unit will include illustration of concepts using numerical investigation with MAPLE.  MTHD6032B  20 
ADVANCED STATISTICS This module covers two topics in statistical theory: Linear and Generalised Linear models and also includes Stochastic processes. The first two topics consider both the theory and practice of statistical model fitting and students will be expected to analyse real data using R. Stochastic processes including the random walk, Markov chains, Poisson processes, and birth and death processes.  CMP6004A  20 
CRYPTOGRAPHY Cryptography is the science of coding and decoding messages to keep them secure, and has been used throughout history. While previously only a few people in authority used cryptography, the internet and ecommerce mean that we now all have transactions that we want to keep secret. The speed of modern computers means messages encrypted using techniques from just a few decades ago can now be broken in seconds; thus the methods of encryption have also become more sophisticated. In this module, we will explore the mathematics behind some of these methods, notably RSA and Elliptic Curve Cryptogrphy.  MTHD6025A  20 
DYNAMICAL METEOROLOGY Dynamical meteorology is a core subject on which weather forecasting and the study of climate and climate change are based. This module applies fluid dynamics to the study of the circulation of the Earth's atmosphere. The fluid dynamical equations and some basic thermodynamics for the atmosphere are introduced. These are then applied to topics such as geostrophic flow, thermal wind and the jet streams, boundary layers, gravity waves, the Hadley circulation, vorticity and potential vorticity, Rossby waves, and equatorial waves. Emphasis will be placed on fluid dynamical concepts as well as on finding analytical solutions to the equations of motion.  MTHD6018B  20 
FERMAT'S LAST THEOREM This module looks at the Mathematics developed in attempts to prove Fermat's Last Theorem: that there are no natural number solutions to xn+yn=zn when n>2, This begins with Fermat's method of infinite descent, together with the property that any integer can be factorized uniquely into primes. However, to go beyond very small values of n, we must look at extensions of the integers, where unique factorization fails. Everntually, using tools from Abstract Algebra (rings and ideals) we will see Kummer's proof for socalle regular primes n.  MTHD6024B  20 
FLUID DYNAMICS Fluid dynamics has wide ranging applications across nature, engineering, and biology. From understanding the behaviour of ocean waves and weather, designing efficient aircraft and ships, to capturing blood flow, the ability the understand and predict how fluids (liquids and gasses) behave is of fundamental importance. This Module considers mathematical models of fluids, particularly including viscosity (or stickiness) of a fluid. Illustrated by practical examples throughout, we develop the governing differential NavierStokes equations, and then consider their solution either finding exact solutions, or using analytical techniques to obtain solutions in certain limits (for example low viscosity or high viscosity).  MTHD6020A  20 
MATHEMATICAL BIOLOGY Mathematics finds wideranging applications in biological systems: including population dynamics, epidemics and the spread of diseases, enzyme kinetics, some diffusion models in biology including Turing instabilities and pattern formation, and various aspects of physiological fluid dynamics.  MTHD6021A  20 
MATHEMATICAL LOGIC The subject analyses symbolically the way in which we reason formally, particularly about mathematical structures. The ideas have applications to other parts of Mathematics, as well as being important in theoretical computer science and philosophy. We give a thorough treatment of predicate and propositional logic and an introduction to model theory.  MTHD6015A  20 
THEORY OF FINITE GROUPS Group theory is the mathematical study of symmetry. The modern treatment of this is group actions and these are a central theme of this course. We will begin with permutation groups, group actions and the orbitstabilizer theorem with many applications. This is followed by a discussion of the Sylow theorems, the class equations and an elementary theory of pgroups. Further topics include the theorem of Jordan and Hoelder, solvable groups and simple. Simplicity of finite and infinite alternating groups.  MTHD6014A  20 
Students will select 0  40 credits from the following modules:
Name  Code  Credits 

HISTORY OF MATHEMATICS We trace the development of mathematics from prehistory to the high cultures of old Egypt, Mesopotamia and the Valley of Ind, through Islamic mathematics onto the mathematical modernity through a selection of results from the present time. We present the rise of calculus from the first worsk of the Indian and Greek mathematicians differentiation and integration through at the time of Newton and Leibniz. We discuss mathematical logic, the ideas of propositions, the axiomatisation of mathematics, and the idea of quantifiers. Our style is to explore mathematical practice and conceptual developments in different historical and geographic contexts.  MTHA6002B  20 
MATHEMATICS PROJECT This module is reserved for third year students who have completed an appropriate number of mathematics modules at levels 4 and 5. It is a project on a mathematical topic supervised by a member of staff within the school, or in a closely related school. Assessment will be by written project and oral presentation.  MTHA6005Y  20 
MODELLING ENVIRONMENTAL PROCESSES The aim of the module is to show how environmental problems may be solved from the initial problem, to mathematical formulation and numerical solution. Problems will be described conceptually, then defined mathematically, then solved numerically via computer programming. The module consists of lectures on numerical methods and computing practicals (using Matlab); the practicals being designed to illustrate the solution of problems using the methods covered in lectures. The module will guide students through the solution of a model of an environmental process of their own choosing. The skills developed in this module are highly valued by prospective employers.  ENV6004A  20 
THE LEARNING AND TEACHING OF MATHEMATICS The aim of the module is to introduce students to the study of the teaching and learning of mathematics with particular focus to secondary and post compulsory level; to explore theories of learning and teaching of mathematical concepts typically included in the secondary and post compulsory curriculum and to explore mathematics knowledge for teaching. This module is recommended for anyone interested in Mathematics teaching as a career or, indeed, for anyone interested in mathematics education as a research discipline.  EDUB6014A  20 
Students will select 0  20 credits from the following modules:
Name  Code  Credits 

APPLIED GEOPHYSICS What lies beneath our feet? This module addresses this question by exploring how wavefields and potential fields are used in geophysics to image the subsurface on scales of metres to kilometres. The basic theory, data acquisition and interpretation methods of seismic, electrical, gravity and magnetic surveys are studied. A wide range of applications is covered including archaeological geophysics, energy resources and geohazards. This module is highly valued by employers in industry; guest industrial lecturers will cover the current 'stateoftheart' applications in real world situations. Students doing this module are normally expected to have a good mathematical ability, notably in calculus and algebra before taking this module (ENV4015Y Mathematics for Scientists A or equivalent).  ENV5004B  20 
APPLIED STATISTICS A This is a module designed to give students the opportunity to apply statistical methods in realistic situations. While no advanced knowledge of probability and statistics is required, we expect students to have some background in probability and statistics before taking this module. The aim is to teach the R statistical language and to cover 3 topics: Linear regression, and Survival Analysis.  CMP5017B  20 
MATHEMATICAL STATISTICS It introduces the essential concepts of mathematical statistics deriving the necessary distribution theory as required. In consequence in addition to ideas of sampling and central limit theorem, it will cover estimation methods and hypothesistesting. Some Bayesian ideas will be also introduced.  CMP5034A  20 
METEOROLOGY I This module is designed to give a general introduction to meteorology, concentrating on the physical processes in the atmosphere and how these influence our weather. The module contains both descriptive and mathematical treatments of radiation balance, fundamental thermodynamics, dynamics, boundary layers, weather systems and meteorological hazards. The assessment is designed to allow those with either mathematical or descriptive abilities to do well; however a reasonable mathematical competence is essential, including a basic understanding of differentiation and integration.  ENV5008A  20 
OCEAN CIRCULATION This module gives you an understanding of the physical processes occurring in the basinscale ocean environment. We will introduce and discuss large scale global ocean circulation, including gyres, boundary currents and the overturning circulation. Major themes include the interaction between ocean and atmosphere, and the forces which drive ocean circulation. You should be familiar with partial differentiation, integration, handling equations and using calculators. Shelf Sea Dynamics is a natural followon module and builds on some of the concepts introduced here. We strongly recommend that you also gain oceanographic fieldwork experience by taking the 20credit biennial Marine Sciences fieldcourse.  ENV5016A  20 
PROGRAMMING FOR NONSPECIALISTS The purpose of this module is to give the student a solid grounding in the essential features programming using the Java programming language. The module is designed to meet the needs of the student who has not previously studied programming.  CMP5020B  20 
SHELF SEA DYNAMICS AND COASTAL PROCESSES The shallow shelf seas that surround the continents are the oceans that we most interact with. They contribute a disproportionate amount to global marine primary production and CO2 drawdown into the ocean, and are important economically through commercial fisheries, offshore oil and gas exploration, and renewable energy developments (e.g. offshore wind farms). This module explores the physical processes that occur in shelf seas and coastal waters, their effect on biological, chemical and sedimentary processes, and how they can be harnessed to generate renewable energy.  ENV5017B  20 
TOPICS IN APPLIED MATHEMATICS This module is an optional Year long module. It covers two topics, Lagrangian Systems and Special Relativity, one in each semester. Lagrangian Systems involves reformulation of problems in mechanics allowing solution of problems such as the osci llation of a double pendulum. Some discussion of Hamiltonian systems will also be included. Special Relativity is concerned with changes in time and space when an observer is moving at a speed close to the speed of light.  MTHF5200Y  20 
TOPICS IN PURE MATHEMATICS This module provides an introduction to two selected topics within pure mathematics. These are selfcontained topics which have not been seen before. The topics on offer for 201718 are the following. Topology: This is an introduction to pointset topology, which studies spaces up to continuous deformations and thereby generalises analysis, using only basic set theory. We will begin by defining a topological space, and will then investigate notions like open and closed sets, limit points and closure, bases of a topology, continuous maps, homeomorphisms, and subspace and product topologies. Computability: This is an introduction to the theoretical foundation of computability theory. The main question we will focus on is "which functions can in principle (i.e., given unlimited resources of space and time) be computed?". The main object of study will be certain devices known as unlimited register machines (URM's). We will adopt the point of view that a function is computable if and only if i is computable by a URM. We will identify large families of computable functions and will prove that certain naturally occurring functions are not computable.  MTHF5100Y  20 
Students must study the following modules for credits:
Name  Code  Credits 

Students will select 40 credits from the following modules:
Please note that CMP6004A Advanced Statistics or equivalent is a prerequisite for CMP7017Y.
Name  Code  Credits 

MATHEMATICS DISSERTATION Reserved for courses G102, G103 and G106. A fourth year dissertation on a mathematical topic that is a compulsory part of some Master of Mathematics degrees.  MTHA7029Y  40 
MMATH PROJECT ONLY AVAILABLE TO STUDENTS REGISTERED ON MMATH IN SCHOOL OF MATHEMATICS. This module is modelled on the Mathematics MMath project module MTHMA9Y. However, in this case it consists of a supervised dissertation on a topic in the general area of probability or statistics. It may involve some computation, this will depend on the topic chosen.  CMP7017Y  40 
Students will select 20 credits from the following modules:
Name  Code  Credits 

DIFFERENTIAL GEOMETRY This module will give an introduction to ideas of differential geometry. Key examples will be curves and surfaces embedded in 3dimensional Euclidean space. We will start with curves and will study the curvature and torsion, building up to the fundamental theorem of curve theory. From here we move on to more advanced topics including surfaces.  MTHD7030B  20 
QUANTUM FLUIDS Macroscopic Wavefunction for a Superfluid, Nonlinear Schrodinger Equation for Wavefunction, Madelung transformation and fluid equations of motion, Integral identities for Energy and Momentum, Travelling plane Wave and Vortex Solutions, Vortex Dynamics in 3D, BiotSavart Law, Extensions to BoseEinstein condensates and Superfluid Liquid Helium.  MTHD7027B  20 
Students will select 60 credits from the following modules:
Name  Code  Credits 

ADVANCED MATHEMATICAL TECHNIQUES WITH ADVANCED TOPICS This unit provides a selection of techniques applicable to mathematical problems in a wide range of applications, while at the time stressing the importance of rigor in developing such techniques. Topics to be studied include calculus of variation, asymptotic analysis, Green's functions and Integral transforms. There will be in depth study of other aspects of asymptotic theory, including Matched Asymptotic Expansions and the WKB approximation. This unit will include illustration of concepts using numerical investigation with MAPLE.  MTHD7032B  20 
CRYPTOGRAPHY WITH ADVANCED TOPICS Cryptography is the science of coding and decoding messages to keep them secure, and has been used throughout history. While previously only a few people in authority used cryptography, the internet and ecommerce mean that we now all have transactions that we want to keep secret. The speed of modern computers means messages encrypted using techniques from just a few decades ago can now be broken in seconds; thus the methods of encryption have also become more sophisticated. In this module, we will explore the mathematics behind some of these methods, notably RSA and Elliptic Curve Cryptogrphy.  MTHD7025A  20 
DYNAMICAL METEOROLOGY WITH ADVANCED TOPICS Dynamical meteorology is a core subject on which weather forecasting and the study of climate and climate change are based. This module applies fluid dynamics to the study of the circulation of the Earth's atmosphere. The fluid dynamical equations and some basic thermodynamics for the atmosphere are introduced. These are then applied to topics such as geostrophic flow, thermal wind and the jet streams, boundary layers, gravity waves, the Hadley circulation, vorticity and potential vorticity, Rossby waves, and equatorial waves. Emphasis will be placed on fluid dynamical concepts as well as on finding analytical solutions to the equations of motion. Advanced Topic: Advanced Rossby wave propagation.  MTHD7018B  20 
FERMAT'S LAST THEOREM WITH ADVANCED TOPICS This module looks at the Mathematics developed in attempts to prove Fermat's Last Theorem: that there are no natural number solutions to xn+yn=zn when n>2, This begins with Fermat's method of infinite descent, together with the property that any integer can be factorized uniquely into primes. However, to go beyond very small values of n, we must look at extensions of the integers, where unique factorization fails. Everntually, using tools from Abstract Algebra (rings and ideals) we will see Kummer's proof for socalle regular primes n. Finally, we will look at a sketch of Wiles's proof of the general case.  MTHD7024B  20 
FLUID DYNAMICS WITH ADVANCED TOPICS Fluid dynamics has wide ranging applications across nature, engineering, and biology. From understanding the behaviour of ocean waves and weather, designing efficient aircraft and ships, to capturing blood flow, the ability the understand and predict how fluids (liquids and gasses) behave is of fundamental importance. This Module considers mathematical models of fluids, particularly including viscosity (or stickiness) of a fluid. Illustrated by practical examples throughout, we develop the governing differential NavierStokes equations, and then consider their solution either finding exact solutions, or using analytical techniques to obtain solutions in certain limits (for example low viscosity or high viscosity).  MTHD7020A  20 
MATHEMATICAL BIOLOGY WITH ADVANCED TOPICS Mathematics finds wideranging applications in biological systems: including population dynamics, epidemics and the spread of diseases, enzyme kinetics, some diffusion models in biology including Turing instabilities and pattern formation, and various aspects of physiological fluid dynamics.  MTHD7021A  20 
MATHEMATICAL LOGIC WITH ADVANCED TOPICS The subject analyses symbolically the way in which we reason formally, particularly about mathematical structures. The ideas have applications to other parts of Mathematics, as well as being important in theoretical computer science and philosophy. We give a thorough treatment of predicate and propositional logic and an introduction to model theory. The Advanced Topic will be Further model theory.  MTHD7015A  20 
THEORY OF FINITE GROUPS WITH ADVANCED TOPICS Group theory is the mathematical study of symmetry. The modern treatment of this is group actions and these are a central theme of this course. We will begin with permutation groups, group actions and the orbit stabilizer theorem with many applications. This is followed by a discussion of the Sylow theorems, the class equations and an elementary theory of p groups. Further topics include the theorem of Jordan and Hoelder, solvable groups and simple. Simplicity of finite and infinite alternating groups. Advanced Topic: Finite Reflection Groups.  MTHD7014A  20 
Disclaimer
Whilst the University will make every effort to offer the modules listed, changes may sometimes be made arising from the annual monitoring, review and update of modules and regular (fiveyearly) review of course programmes. Where this activity leads to significant (but not minor) changes to programmes and their constituent modules, there will normally be prior consultation of students and others. It is also possible that the University may not be able to offer a module for reasons outside of its control, such as the illness of a member of staff or sabbatical leave. In some cases optional modules can have limited places available and so you may be asked to make additional module choices in the event you do not gain a place on your first choice. Where this is the case, the University will endeavour to inform students.Further Reading

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Essential Information
Entry Requirements
 A Level AAB including A in Mathematics or ABB including A in Mathematics and B in Further Mathematics
 International Baccalaureate 33 points including HL Mathematics at 6 and one other HL subject at 6
 Scottish Advanced Highers AAB including A in Mathematics
 Irish Leaving Certificate AAAABB including A in Mathematics
 Access Course Pass the Access to HE Diploma with Distinction in 36 credits at Level 3 at Merit in 9 credits at Level 3, including 12 Level 3 credits in Mathematics
 BTEC Only accepted alongside Alevel Mathematics
 European Baccalaureate 80% overall including 85% in Mathematics
Entry Requirement
You are required to have Mathematics and English Language at a minimum of Grade C or Grade 4 or above at GCSE.
Critical Thinking and General Studies are not accepted.
UEA recognises that some students take a mixture of International Baccalaureate IB or International Baccalaureate Careerrelated Programme IBCP study rather than the full diploma, taking Higher levels in addition to A levels and/or BTEC qualifications. At UEA we do consider a combination of qualifications for entry, provided a minimum of three qualifications are taken at a higher Level. In addition some degree programmes require specific subjects at a higher level.
Students for whom English is a Foreign language
We welcome applications from students from all academic backgrounds. We require evidence of proficiency in English (including writing, speaking, listening and reading):
 IELTS: 6.5 overall (minimum 6.0 in any component)
We also accept a number of other English language tests. Please click here to see our full list.
INTO University of East Anglia
If you do not meet the academic and or English requirements for direct entry our partner, INTO University of East Anglia offers guaranteed progression on to this undergraduate degree upon successful completion of a preparation programme. Depending on your interests, and your qualifications you can take a variety of routes to this degree:
International Foundation in General Science FS1
International Foundation in Physical Sciences and Mathematics FS3
International Foundation in Mathematics with Actuarial Science FMA
Interviews
The majority of candidates will not be called for an interview and a decision will be made via UCAS Track. However, for some students an interview will be requested. You may be called for an interview to help the School of Study, and you, understand if the course is the right choice for you. The interview will cover topics such as your current studies, reasons for choosing the course and your personal interests and extracurricular activities. Where an interview is required the Admissions Service will contact you directly to arrange a convenient time.
Gap Year
We welcome applications from students who have already taken or intend to take a gap year. We believe that a year between school and university can be of substantial benefit. You are advised to indicate your reason for wishing to defer entry and to contact admissions@uea.ac.uk directly to discuss this further.
Intakes
The School's annual intake is in September of each year.
 A Level AAB to include an A in Mathematics. Science Alevels must include a pass in the practical element.
 International Baccalaureate 33 points including HL 6 in Mathematics and HL 6 in one other subject. If no GCSE equivalent is held, offer will include Mathematics and English requirements.
 Scottish Highers Only accepted in combination with Scottish Advanced Highers.
 Scottish Advanced Highers BBC to include a B in Mathematics. A combination of Advanced Highers and Highers may be acceptable.
 Irish Leaving Certificate AAAABB or 4 subjects at H1 and 2 subjects at H2, to include grade A or H1 in Higher Level Mathematics.
 Access Course Pass Access to HE Diploma with Distinction in 36 credits at Level 3 and Merit in 9 credits at Level 3, including 12 Level 3 credits in Mathematics. Science pathway required.
 BTEC DDM in a relevant subject plus Alevel Mathematics at Grade A. Excluding Public Services. BTEC and Alevel combinations are considered  please contact us.
 European Baccalaureate 80% overall to include at least 85% in Mathematics.
Entry Requirement
GCSE Requirements: GCSE English Language grade 4 and GCSE Mathematics grade 4 or GCSE English Language grade C and GCSE Mathematics grade C.
General Studies and Critical Thinking are not accepted.
UEA recognises that some students take a mixture of International Baccalaureate IB or International Baccalaureate Careerrelated Programme IBCP study rather than the full diploma, taking Higher levels in addition to A levels and/or BTEC qualifications. At UEA we do consider a combination of qualifications for entry, provided a minimum of three qualifications are taken at a higher Level. In addition some degree programmes require specific subjects at a higher level.
Students for whom English is a Foreign language
We welcome applications from students from all academic backgrounds. We require evidence of proficiency in English (including speaking, listening, reading and writing) at the following level:
 IELTS: 6.5 overall (minimum 6.0 in any component)
We will also accept a number of other English language qualifications. Review our English Language Equivalences here.
INTO University of East Anglia
If you do not meet the academic and/or English language requirements for this course, our partner INTO UEA offers guaranteed progression on to this undergraduate degree upon successful completion of a foundation programme. Depending on your interests and your qualifications you can take a variety of routes to this degree:
 International Foundation in Mathematics and Actuarial Sciences
 International Foundation in Physical Sciences and Engineering
INTO UEA also offer a variety of English language programmes which are designed to help you develop the English skills necessary for successful undergraduate study:
Interviews
The majority of candidates will not be called for an interview. However, for some students an interview will be requested. These are normally quite informal and generally cover topics such as your current studies, reasons for choosing the course and your personal interests and extracurricular activities.
Gap Year
We welcome applications from students who have already taken or intend to take a gap year, believing that a year between school and university can be of substantial benefit. You are advised to indicate your reason for wishing to defer entry and may wish to contact the appropriate Admissions Office directly to discuss this further.
Intakes
The School's annual intake is in September of each year.Alternative Qualifications
We encourage you to apply if you have alternative qualifications equivalent to our stated entry requirement. Please contact us for further information.
Fees and Funding
Undergraduate University Fees and Financial Support
Tuition Fees
Information on tuition fees can be found here:
Scholarships and Bursaries
We are committed to ensuring that costs do not act as a barrier to those aspiring to come to a world leading university and have developed a funding package to reward those with excellent qualifications and assist those from lower income backgrounds.
The University of East Anglia offers a range of Scholarships; please click the link for eligibility, details of how to apply and closing dates.
How to Apply
Applications need to be made via the Universities Colleges and Admissions Services (UCAS), using the UCAS Apply option.
UCAS Apply is a secure online application system that allows you to apply for fulltime Undergraduate courses at universities and colleges in the United Kingdom. It is made up of different sections that you need to complete. Your application does not have to be completed all at once. The system allows you to leave a section partially completed so you can return to it later and add to or edit any information you have entered. Once your application is complete, it must be sent to UCAS so that they can process it and send it to your chosen universities and colleges.
The UCAS code name and number for the University of East Anglia is EANGL E14.
Further Information
If you would like to discuss your individual circumstances with the Admissions Office prior to applying please do contact us:
Undergraduate Admissions Office (Mathematics)
Tel: +44 (0)1603 591515
Email: admissions@uea.ac.uk
Please click here to register your details online via our Online Enquiry Form.
International candidates are also actively encouraged to access the University's International section of our website.
Next Steps
Got a question? Just ask
We canâ€™t wait to hear from you. Just pop any questions about this course into the form below and our enquiries team will answer as soon as they can.
Admissions enquiries:
admissions@uea.ac.uk or
telephone +44 (0)1603 591515