Undergraduate Degrees

MMath Master of Mathematics ( G103 )

UCAS Course Code:: G103
Duration:: 4 years
Attendance:: Full Time
Award:: Degree of Master of Mathematics
School of Study:: Mathematics
Brochure:: School of Mathematics Undergraduate Brochure (PDF)
Typical A-Level Offer:: A*AB (A* in Mathematics) or A*BB (A* in Mathematics, B in Further Mathematics)

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Also offered with a year in North America (G102), and a year in Australia (G106), this prestigious four-year Master of Mathematics programme allows greater depth of study than a three-year programme.

A special feature is a research-led, individually supervised project in the final year. This programme extends mathematical knowledge to a higher level than the three year BSc Programme (G100). It further consolidates and strengthens the employability skills needed for a professional career, including report writing skills and oral presentation skills. The programme is also excellent preparation for a career in research, either in industry or in a University. The first three years of study run parallel with the BSc programme (G100) enabling students to transfer between the programmes subject to academic performance. In the first year you will study the main strands of algebra and calculus, along with statistics and computing for mathematicians. A greater degree of flexibility is offered in Years 2 and 3 enabling you to choose options best suited to your growing interests. In the final year, one-third of your time will be spent undertaking an individual research project, enabling you to experience the challenge of independent study and the thrill of discovery. The remaining two-thirds of the final year will be spent studying a range of Master’s level units alongside our postgraduate students. Progression on this programme is subject to academic performance each year and students who do not meet the required standard may be required to transfer to the three-year BSc programme.

Course Organiser:Dr. Mark Blyth

Mathematics is an exciting and challenging subject that plays a central role in many aspects of modern life. When you listen to a CD, watch a weather forecast, use a mobile phone, or surf the internet, you are benefiting from sophisticated mathematical ideas.

Mathematics provides the language and techniques to handle the problems from many disciplines. Mathematics is also studied for its own sake: it has a beauty and structure of its own, built upon thousands of years of invention and discovery.

Mathematics is often demanding but it can also be fun, especially when you are learning in good company. At UEA you will be lectured by, and get to know, world-authorities in many branches of Mathematics research. UEA is a modern institution and we pride ourselves on our friendliness. Students come here from across the UK and from overseas. Their company will enrich your time and studies through firm friendships and lasting attachments.

The School of Mathematics at UEA is recognised internationally for its strong research and teaching. The School of Mathematics has achieved an excellent performance in each of the last Research Assessment Exercises, dating back to 1996. We have strong research links and collaboration with mathematicians throughout Europe, Israel, Russia, the United States and Australia. Our teaching is highly regarded by our graduating students. In the National Student Survey we have been consistently in the top six mathematics departments in the country.

If you finish your studies with distinction you may want to join our active group of postgraduate students and study for a PhD degree. Research is just one of the wide range of careers open to a mathematician. The span of professions ranges from business communications to flying jets; from modelling and industrial design to interpreting the economy; from charting a business' fortunes to forecasting the weather.

Amongst other things, our graduates finish with a wider critical imagination and a deeper knowledge of our very beautiful subject and its applications. A Mathematics degree will launch you towards many new professional worlds.

Compulsory Study (120 credits)

Students must study the following modules for 120 credits:

Name	Code	Credits
CALCULUS AND MULTIVARIABLE CALCULUS	MTH-1A5Y	40
This module is incompatible with MTH-1B2Y, ENV-1A61 AND ENV-1A62 (a) Complex numbers. (b) Differentiation and integration. Taylor and MacLaurin series. Applications: curve sketching, areas, arc length. (c) First order, second order constant coefficient ordinary differential equations. Reduction of order. Numerical solutions using MAPLE. Partial derivatives, chain rule. (d) Vectors. (e) Line integrals. Multiple integrals, including change of co-ordinates by Jacobians. Green's theorem in the plane. (f) Euler type and general linear ODEs. Phase plane, direction fields, limit cycles, period doubling and chaos. (g) Divergence, gradient and curl of a vector field. Scalar potential and path independence of line integral. Divergence and Stokes' theorems. Students must have A-level Mathematics Grade ‘B’ or above or equivalent.
LINEAR ALGEBRA	MTH-1A2Y	20
Linear equations and matrices (including geometric aspects); Determinants. Eigenvalues and eigenvectors, Diagonalization. Vector spaces and linear transformations. Real inner product spaces. Students must have A-level Mathematics Grade 'B' or above or equivalent.
MATHEMATICAL PROBLEM SOLVING, MECHANICS AND MODELLING	MTH-1A4Y	20
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. Students must have A-level Mathematics Grade ‘B’ or above or equivalent.
REAL ANALYSIS	MTH-1A3Y	20
Sequences and series, tests for convergence. Limits, continuity, differentiation, Riemann integration, Fundamental Theorem. Students must have A-level Mathematics Grade 'B' or above or equivalent.
SETS, NUMBERS AND PROBABILITY	MTH-1A1Y	20
Basic set-theoretic 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. Students must have A-level Mathematics Grade 'B' or above or equivalent.

Compulsory Study (80 credits)

Students must study the following modules for 80 credits:

Name	Code	Credits
ALGEBRA	MTH-2C3Y	20
(a) Vector space, basis and dimension. Linear maps, rank-nullity. Matrices, change of basis, minimal and characteristic polynomial. Diagonalization. Inner product on Rn, Gram-Schmidt process, examples from algebra and analysis. (b) Revision of basic concepts. Cosets, Lagrange's theorem. Normal subgroups and factor groups. First isomorphism theorem. Rings, elementary properties and examples of commutative rings. Ideals, quotient rings. Polynomial rings and construction of finite fields. Unique Factorization in rings.
ANALYSIS	MTH-2C1Y	20
(a) Continuity, differentiation, uniform convergence, power series and how they represent functions for both real and complex variables. (b) Topology of the complex plane, holomorphic functions, Cauchy-Riemann equations, complex integration, Cauchy and Laurent theorems, residue calculus.
DIFFERENTIAL EQUATIONS AND ALGORITHMS	MTH-2C4Y	20
(a) Differential Equations: Fourier series. Partial differential equations (PDEs): diffusion equation, wave equation, Laplace's equation. Solution by separation of variables in Cartesian and polar coordinates. Ordinary differential equations (ODEs): solution by reduction of order and variation of parameters. Series solution and the method of Frobenius. Legendre's and Bessel's equations: Legendre polynomials, Bessel functions and their recurrence relations. (b) Algorithms: An introduction to a variety of numerical methods. Solution of linear algebraic equations. Solution of nonlinear equations. Numerical integration. Numerical Solution of ODEs.
FLUIDS AND SOLIDS	MTH-2C2Y	20
(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) An introduction to continuum physics, linear elasticity as an example. The strain and stress tensors. Conservation of mass, linear momentum, angular momentum. Equilibrium equations, symmetry of stress tensor. Generalised Hooke's law. Bulk, shear and Young's moduli, Poisson's ratio. Strain energy. Boundary-value problems, Bending and torsion of a rod. Plane P and S waves.

Option A Study (20 credits)

Students will select 20 credits from the following modules:

Name	Code	Credits
COMBINATORICS	MTH-2G40	10
BEFORE TAKING THIS MODULE YOU MUST TAKE MTH-1C17 OR EQUIVALENT 1. Colouring Things: Graphs, Colourings, chromatic numbers, and Ramsey Theory. 2. Counting Things: Binomial coefficients, Inclusion-Exclusion formula, Compositions and partitions.
CRYPTOGRAPHY	MTH-2G27	10
Cryptography is the science of keeping secrets secret. Throughout history there are numerous examples of use of cryptography. For instance, Caesar himself used to send encrypted messages to his generals using the now-called Caesar cypher. Nowadays, with the development of internet, the need for efficient ways to communicate private data has never been greater._In this course, we will first give a brief account of cryptography through history, we will then introduce some results in number theory which are essential to cryptography and finally, we will study some of the most famous cryptosystems (such as RSA). MTH-1C36 is not a prerequisite or co-requisite but is recommended.
MATHEMATICAL MODELLING	MTH-2G47	10
BEFORE TAKING THIS MODULE YOU MUST TAKE MTH-1C27 OR MTH-1B2Y This module will look at techniques of mathematical modelling, examining how mathematics can be applied to a variety of real problems and give insight in various areas. The topics will include approximation and non-dimensionalising, and discussion of how a mathematical model is created. We will then apply this theory to a variety of models such as traffic flow as well as examples of problems arising in industry.
MATHEMATICS MINIPROJECT	MTH-2M01	10
This module is reserved for students registered in the School of Mathematics only. A second year project on a mathematical topic. Assessment will be by written project and poster presentation.
MATHEMATICS MINIPROJECT	MTH-2M02	10
This module is reserved for students registered in the School of Mathematics only. A second year project on a mathematical topic. Assessment will be by written project and poster presentation.
QUANTUM MECHANICS	MTH-2G50	10
The motion of very small systems such as atoms does not satisfy the equations of classical mechanics. For example an electron orbiting a nucleus can only have certain discrete energy levels. In quantum mechancis the motion of a particle is described by a wave function which describes the probability of the particle having a certain energy. Topics addressed in this module include: Wave Functions, Schrodinger's Equation, Uncertainty Principle, Wave Scattering, Harmonic Oscillators.
STATISTICAL METHODS	CMPC2S11	20
This is a first course in statistics. It introduces the essential ideas of statistics deriving the necessary distribution theory as required. The aim of the course is to discuss the essential concepts in statistics rather than just to give a list of techniques for specific problems. The focus will be on developing ideas in distribution theory and inference based on the likelihood function. In consequence in addition to ideas of sampling and limit laws, it will cover maximum likelihood estimation and inference based on the likelihood ratio. If possible some Bayesian ideas will be introduced. While this course deals with concepts we shall aim to show how these are motivated by real problems More...

Free Choice Study (20 credits)

Students will select modules worth 20 credits from the course catalogue with the approval of their School

Option A Study (100 credits)

Students will select 100 credits from the following modules:

Name	Code	Credits
ADVANCED STATISTICS	CMPC3C12	20
This module covers three topics in statistical theory. For this year they are Regression and Linear Model, Generalised Models and Non-parametric Methods. The first two topics consider both the theory and practice of statistical model fitting and students will be expected to analyse real data. The third topic is chosen to be a contrasting one. Non-parametric methods are a vital part of the statisticians armoury and cheap computing makes such techniques very powerful. We look at the traditional permutation based methods as well as the empirical distribution function. More...
ASYMPTOTIC ANALYSIS	MTH-3E37	20
This 20 credit module provides introduction to asymptotic analysis of algebraic equations, ordinary and partial differential equations and integrals. Asymptotic analysis is an important tool in almost all branches of science and engineering. This analysis provides useful but approximate solutions and formulae with an accuracy which is well understood and controllable. The course covers asymptotic expansions, divergent asymptotic series, local approximations, regular and singular perturbations of solutions, asymptotic formulae, Laplace and Fourier integrals, method of strained coordinates, method of multiple scales, matched asymptotic expansions, matching rules.
DYNAMICAL OCEANOGRAPHY	MTH-3E48	20
This course applies fluid dynamics to the study of the circulation of the oceans. Topics studied include: geostrophic flow, Ekman layers, wind driven circulation, western boundary currents (e.g. the Gulf Steam), abyssal circulation, Rossby waves, Kelvin waves, Equatorial dynamics, Southern Ocean dynamics.
ELECTRICITY AND MAGNETISM	MTH-3E74	20
The behaviour of electric and magnetic fields is fundamental to many features of life we take for granted yet the underlying equations are surprisingly compact and elegant. We will begin with an historical overview of electrodynamics to see where the governing equations (Maxwell's) come from. We will then use these equations as axioms and apply them to a variety of situations including electro- and magneto-statics problems and then time-dependent problems (eg electromagnetic waves). We shall also consider how the equations change in an electromagnetic media and look at some simple examples.
FREE SURFACE FLOWS	MTH-3D77	20
Inviscid jets; stability analysis; infinite jet; semi-infinite jet; one-dimensional approximations; viscous jets; similarity solutions and breakup. Drops; satellite droplets. Uniform and nonuniform inviscid liquid sheets; temporal instability, convective/absolute instability. Viscous liquid sheets, waves on liquid sheets. Numerical simulations.
GALOIS THEORY	MTH-3E21	20
The module leads to a proof of the insolubility of quintic equations. Amongst the topics covered are field extensions, normality and separability. The Galois correspondence and Galois groups. The existence and uniqueness of finite fields and transcendence.
GRAPH THEORY	MTH-3E23	20
Graphs are among the simplest mathematical structures: sets of points which may or may not be linked by edges. Not surprisingly such structures are fundamental in many parts of science. We give a thorough introduction to the topological, combinatorial and algebraic properties of graphs.
HISTORY OF MATHEMATICS	MTH-3D71	20
Origins of Counting and Mathematical thinking, the uses and devices of Mathematics in early civilisations. Mathematics as pillar of Greek culture, philosophy and science with particular reference to work of Euclid, Archimedes and Apollonius. The decline of Mathematics in the Dark and Middle Ages with reawakening of interest in Europe through applications in Astronomy, Navigation, Art and Commerce. The Scientific Revolution, the work of Isaac Newton, the conceptual development and logical formulation of the Calculus. The postmodern approach to Algebra and Geometry in the early 19th Century, the concept of Relativity. Students will need some mathematical knowledge to attempt the module.
NUMBER THEORY	MTH-3E56	20
This module will be assessed by 100% examination, but you may also be informally assessed by coursework and/or project. The module will begin with a topic that occupied the ancient Greeks and continues to occupy us today, namely the study of Diophantine equations. After discovering some algebraic techniques to solve these equations, we will proceed to the study of elliptic curves. The viewpoint here is one of combining geometry and algebra to study equations. The course will end with an introduction to the Riemann zeta function and the Riemann hypothesis. The latter is one of the oldest unsolved problems in mathematics, and is worth a million dollars!
SET THEORY	MTH-3E18	20
Zermelo-Fraenkel set theory. The Axiom of Choice and equivalents. Cardinality, countability, and uncountability. Trees, Combinatorial set theory.
STATISTICAL MECHANICS	MTH-3E64	20
In principle, the laws of classical and quantum mechanics provide a complete description to allow us to predict the microscopic state of a system. However, for a large class of systems consisting of many degrees of freedom (e.g. molecules in a gas), it is completely impractical nor even necessary to adopt such a detailed description. Rather, it is typically sufficient to seek a macroscopic formulation that is related to the microscopic properties of the problem. This is what we commonly do, for example, when modelling the dynamics of fluids as functions of the macroscopic variables such as pressure, temperature, and density. The course will begin by using very elementary concepts of probability theory to derive macroscopic thermodynamic properties such as temperature from the microscopic properties of individual atoms or molecules. At very low temperatures, quantum effects begin to play an important role. By extending our analysis to such systems, we are able to predict the existence of a new state of matter known as a Bose-Einstein condensate which was first produced in the Laboratory as recently as 1995. The tools of statistical mechanics are useful in many branches of applied mathematics. While the module is self-contained, it is strongly recommended that students also take MTH-2G50 which will reinforce a number of the concepts used here.

Free Choice Study (20 credits)

Students will select modules worth 20 credits from the course catalogue with the approval of their School

By the end of Year 4 students MUST have completed at least 120 credits of Master's level modules.

Option A Study (40 credits)

Students will select 40 credits from the following modules:

Name	Code	Credits
MATHEMATICS PROJECT	MTH-MA9Y	40
Reserved for courses G102, G103 and G106. A fourth year project on a mathematical topic that is a compulsory part of some Master of Mathematics degrees.
MMATH PROJECT	CMPSMM1Y	40
ONLY AVAILABLE TO STUDENTS REGISTERED ON MMATH IN SCHOOL OF MATHEMATICS This unit is modelled on the Mathematics MMath project unit MTH-MA9Y, 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. More...

Option B Study (20 credits)

Students will select 20 credits from the following modules:

Name	Code	Credits
SLOW VISCOUS FLOW	MTH-ME84	20
This module will be assessed by 100% examination, but you may also be informally assessed by coursework and/or project. Introduction to Stokes Flow, basic properties, and theorems. Solution via Papkovich-Neuber potentials. Integral representations. Slender-body theory. Lubrication theory and extensional flow equations. Pugs and Slugs in pipe flow.
TOPOLOGY	MTH-ME88	20
RESERVED FOR STUDENTS REGISTERED IN THE SCHOOL OF MATHEMATICS Topology is the mathematical study of properties which are preserved under continuous transformation. In the first section we generalise concepts from analysis (distance, open and closed sets, continuity) to give some precise mathematical sense to this. In the remaining sections we introduce methods which ‘approximate’ the analytic situation (continuous maps between topological spaces) by an algebraic problem (homomorphisms between groups). The surprising outcome is that one obtains deep results in analysis which often admit no other style of proof. Two examples of results which we will come across are the Brouwer fixed point theorem (a continuous map from the unit disc to itself has a fixed point); and the Borsuk - Ulam theorem (paraphrased as saying that at any given time, there are two points on the Earth’s surface which have both the same temperature and the same pressure).

Option C Study (60 credits)

Students will select 60 credits from the following modules:

Name	Code	Credits
ADVANCED STATISTICS	CMPC3C12	20
This module covers three topics in statistical theory. For this year they are Regression and Linear Model, Generalised Models and Non-parametric Methods. The first two topics consider both the theory and practice of statistical model fitting and students will be expected to analyse real data. The third topic is chosen to be a contrasting one. Non-parametric methods are a vital part of the statisticians armoury and cheap computing makes such techniques very powerful. We look at the traditional permutation based methods as well as the empirical distribution function. More...
ASYMPTOTIC ANALYSIS	MTH-3E37	20
This 20 credit module provides introduction to asymptotic analysis of algebraic equations, ordinary and partial differential equations and integrals. Asymptotic analysis is an important tool in almost all branches of science and engineering. This analysis provides useful but approximate solutions and formulae with an accuracy which is well understood and controllable. The course covers asymptotic expansions, divergent asymptotic series, local approximations, regular and singular perturbations of solutions, asymptotic formulae, Laplace and Fourier integrals, method of strained coordinates, method of multiple scales, matched asymptotic expansions, matching rules.
ASYMPTOTIC ANALYSIS WITH ADVANCED TOPICS	MTH-ME37	20
This 20 credit module provides introduction to asymptotic analysis of algebraic equations, ordinary and partial differential equations and integrals. Asymptotic analysis is an important tool in almost all branches of science and engineering. This analysis provides useful but approximate solutions and formulae with an accuracy which is well understood and controllable. The course covers asymptotic expansions, divergent asymptotic series, local approximations, regular and singular perturbations of solutions, asymptotic formulae, Laplace and Fourier integrals, method of strained coordinates, method of multiple scales, matched asymptotic expansions, matching rules. Advanced topic: Hydrodynamic models, Asymptotic analysis of fluid flows.
DYNAMICAL OCEANOGRAPHY	MTH-3E48	20
This course applies fluid dynamics to the study of the circulation of the oceans. Topics studied include: geostrophic flow, Ekman layers, wind driven circulation, western boundary currents (e.g. the Gulf Steam), abyssal circulation, Rossby waves, Kelvin waves, Equatorial dynamics, Southern Ocean dynamics.
DYNAMICAL OCEANOGRAPHY WITH ADVANCED TOPICS	MTH-ME48	20
This course applies fluid dynamics to the study of the circulation of the oceans. Topics studied include: geostrophic flow, Ekman layers, wind driven circulation, western boundary currents (e.g. the Gulf Steam), abyssal circulation, Rossby waves, Kelvin waves, Equatorial dynamics, Southern Ocean dynamics. Advanced topic: Baroclinic instability.
ELECTRICITY AND MAGNETISM	MTH-3E74	20
The behaviour of electric and magnetic fields is fundamental to many features of life we take for granted yet the underlying equations are surprisingly compact and elegant. We will begin with an historical overview of electrodynamics to see where the governing equations (Maxwell's) come from. We will then use these equations as axioms and apply them to a variety of situations including electro- and magneto-statics problems and then time-dependent problems (eg electromagnetic waves). We shall also consider how the equations change in an electromagnetic media and look at some simple examples.
ELECTRICITY AND MAGNETISM WITH ADVANCED TOPICS	MTH-ME74	20
BEFORE TAKING THIS MODULE YOU MUST TAKE MTH-2C4Y OR TAKE ENV-2A22 OR EQUIVALENT The behaviour of electric and magnetic fields is fundamental to many features of life we take for granted yet the underlying equations are surprisingly compact and elegant. We will begin with an historical overview of electrodynamics to see where the governing equations (Maxwell's) come from. We will then use these equations as axioms and apply them to a variety of situations including electro- and magneto-statics problems and then time-dependent problems (eg electromagnetic waves). We shall also consider how the equations change in an electromagnetic media and look at some simple examples. Further advanced topics will come from examining the equations in dielectrics and magnetic materials. Advanced topic will be an introduction to Magneto-Hydro Dynamics (MHD).
FREE SURFACE FLOWS	MTH-3D77	20
Inviscid jets; stability analysis; infinite jet; semi-infinite jet; one-dimensional approximations; viscous jets; similarity solutions and breakup. Drops; satellite droplets. Uniform and nonuniform inviscid liquid sheets; temporal instability, convective/absolute instability. Viscous liquid sheets, waves on liquid sheets. Numerical simulations.
FREE SURFACE FLOWS WITH ADVANCED TOPICS	MTH-MD77	20
Inviscid jets; stability analysis; infinite jet; semi-infinite jet; one-dimensional approximations; viscous jets; similarity solutions and breakup. Drops; satellite droplets. Uniform and nonuniform inviscid liquid sheets; temporal instability, convective/absolute instability. Viscous liquid sheets, waves on liquid sheets. Numerical simulations. Advanced Topic: Computational methods for free surface flows (Level set method, VOF).
GALOIS THEORY	MTH-3E21	20
The module leads to a proof of the insolubility of quintic equations. Amongst the topics covered are field extensions, normality and separability. The Galois correspondence and Galois groups. The existence and uniqueness of finite fields and transcendence.
GALOIS THEORY WITH ADVANCED TOPICS	MTH-ME21	20
Polynomials and irreducibility: field extensions: algebraic, transcendental, normal, separable, splitting fields: field automorphisms, Galois group, Fundamental Theorem of Galois Theory: applications to constructability and roots of polynomial equations. Advanced topic: the inverse Galois problem
GRAPH THEORY	MTH-3E23	20
Graphs are among the simplest mathematical structures: sets of points which may or may not be linked by edges. Not surprisingly such structures are fundamental in many parts of science. We give a thorough introduction to the topological, combinatorial and algebraic properties of graphs.
GRAPH THEORY WITH ADVANCED TOPICS	MTH-ME23	20
Graphs are among the simplest mathematical structures: sets of points which may or may not be linked by edges. Not surprisingly such structures are fundamental in many parts of science. We give a thorough introduction to the topological, combinatorial and algebraic properties of graphs. Advanced topic: strongly regular graphs.
HISTORY OF MATHEMATICS	MTH-3D71	20
Origins of Counting and Mathematical thinking, the uses and devices of Mathematics in early civilisations. Mathematics as pillar of Greek culture, philosophy and science with particular reference to work of Euclid, Archimedes and Apollonius. The decline of Mathematics in the Dark and Middle Ages with reawakening of interest in Europe through applications in Astronomy, Navigation, Art and Commerce. The Scientific Revolution, the work of Isaac Newton, the conceptual development and logical formulation of the Calculus. The postmodern approach to Algebra and Geometry in the early 19th Century, the concept of Relativity. Students will need some mathematical knowledge to attempt the module.
NUMBER THEORY	MTH-3E56	20
This module will be assessed by 100% examination, but you may also be informally assessed by coursework and/or project. The module will begin with a topic that occupied the ancient Greeks and continues to occupy us today, namely the study of Diophantine equations. After discovering some algebraic techniques to solve these equations, we will proceed to the study of elliptic curves. The viewpoint here is one of combining geometry and algebra to study equations. The course will end with an introduction to the Riemann zeta function and the Riemann hypothesis. The latter is one of the oldest unsolved problems in mathematics, and is worth a million dollars!
NUMBER THEORY WITH ADVANCED TOPICS	MTH-ME56	20
BEFORE TAKING THIS MODULE YOU MUST TAKE MTH-2C1Y AND MTH-2C3Y OR EQUIVALENT. This module will be assessed by 100% examination, but you may also be informally assessed by coursework and/or project. The module will begin with a topic that occupied the ancient Greeks and continues to occupy us today, namely the study of Diophantine equations. After discovering some algebraic techniques to solve these equations, we will proceed to the study of elliptic curves. The viewpoint here is one of combining geometry and algebra to study equations. The course will end with an introduction to the Riemann zeta function and the Riemann hypothesis. The latter is one of the oldest unsolved problems in mathematics, and is worth a million dollars! The advanced topic will explore the density measure of rational points on elliptic curves. In other words, can we say something about the complexity of rational points on such curves?
SET THEORY	MTH-3E18	20
Zermelo-Fraenkel set theory. The Axiom of Choice and equivalents. Cardinality, countability, and uncountability. Trees, Combinatorial set theory.
SET THEORY WITH ADVANCED TOPICS	MTH-ME18	20
Zermelo-Fraenkel set theory. The Axiom of Choice and equivalents. Cardinality, countability, and uncountability. Trees, Combinatorial set theory. Advanced topic: Infinite Ramsey theory.
SLOW VISCOUS FLOW	MTH-ME84	20
This module will be assessed by 100% examination, but you may also be informally assessed by coursework and/or project. Introduction to Stokes Flow, basic properties, and theorems. Solution via Papkovich-Neuber potentials. Integral representations. Slender-body theory. Lubrication theory and extensional flow equations. Pugs and Slugs in pipe flow.
STATISTICAL MECHANICS	MTH-3E64	20
In principle, the laws of classical and quantum mechanics provide a complete description to allow us to predict the microscopic state of a system. However, for a large class of systems consisting of many degrees of freedom (e.g. molecules in a gas), it is completely impractical nor even necessary to adopt such a detailed description. Rather, it is typically sufficient to seek a macroscopic formulation that is related to the microscopic properties of the problem. This is what we commonly do, for example, when modelling the dynamics of fluids as functions of the macroscopic variables such as pressure, temperature, and density. The course will begin by using very elementary concepts of probability theory to derive macroscopic thermodynamic properties such as temperature from the microscopic properties of individual atoms or molecules. At very low temperatures, quantum effects begin to play an important role. By extending our analysis to such systems, we are able to predict the existence of a new state of matter known as a Bose-Einstein condensate which was first produced in the Laboratory as recently as 1995. The tools of statistical mechanics are useful in many branches of applied mathematics. While the module is self-contained, it is strongly recommended that students also take MTH-2G50 which will reinforce a number of the concepts used here.
STATISTICAL MECHANICS WITH ADVANCED TOPICS	MTH-ME64	20
In principle, the laws of classical and quantum mechanics provide a complete description to allow us to predict the microscopic state of a system. However, for a large class of systems consisting of many degrees of freedom (e.g. molecules in a gas), it is completely impractical nor even necessary to adopt such a detailed description. Rather, it is typically sufficient to seek a macroscopic formulation that is related to the microscopic properties of the problem. This is what we commonly do, for example, when modelling the dynamics of fluids as functions of the macroscopic variables such as pressure, temperature, and density. The course will begin by using very elementary concepts of probability theory to derive macroscopic thermodynamic properties such as temperature from the microscopic properties of individual atoms or molecules. At very low temperatures, quantum effects begin to play an important role. By extending our analysis to such systems, we are able to predict the existence of a new state of matter known as a Bose-Einstein condensate which was first produced in the Laboratory as recently as 1995. The tools of statistical mechanics are useful in many branches of applied mathematics. While the module is self-contained, it is strongly recommended that students also take MTH-2G50 which will reinforce a number of the concepts used here.
TOPOLOGY	MTH-ME88	20
RESERVED FOR STUDENTS REGISTERED IN THE SCHOOL OF MATHEMATICS Topology is the mathematical study of properties which are preserved under continuous transformation. In the first section we generalise concepts from analysis (distance, open and closed sets, continuity) to give some precise mathematical sense to this. In the remaining sections we introduce methods which ‘approximate’ the analytic situation (continuous maps between topological spaces) by an algebraic problem (homomorphisms between groups). The surprising outcome is that one obtains deep results in analysis which often admit no other style of proof. Two examples of results which we will come across are the Brouwer fixed point theorem (a continuous map from the unit disc to itself has a fixed point); and the Borsuk - Ulam theorem (paraphrased as saying that at any given time, there are two points on the Earth’s surface which have both the same temperature and the same pressure).

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 (five-yearly) 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. Where this is the case, the University will endeavour to inform students.

Entry Requirements

A Level:: A*AB (A* in Mathematics) or A*BB (A* in Mathematics, B in Further Mathematics)
International Baccalaureate:: 34 points overall including 7 in Higher Level Maths
Scottish Highers:: AAAB including grade A in Advanced Higher Mathematics
Scottish Advanced Highers:: AAB including grade A in Mathematics
Irish Leaving Certificate:: AAAABB including grade A in Mathematics
Access Course:: See below
HND:: Please contact institution for further information
European Baccalaureate:: 85% overall including 85% in Mathematics

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). Recognised English Language qualifications include:

IELTS: 6. overall (minimum 5.5 in any component)
TOEFL: Internet-based score of 78 overall (minimum 20 in Speaking component, 17 in Writing and Listening components and 18 in Reading components.
PTE: 55 overall (minimum 51 in any component).

If you do not meet the University's entry requirements, our INTO Language Learning Centre offers a range of university preparation courses to help you develop the high level of academic and 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 extra-curricular 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.

Special Entry Requirements

Critical Thinking and General Studies are not accepted.

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.

Pass Access to HE Diploma with Distinction in 45 credits at Level 3, including 12 Level 3 Maths credits.

GCSE Offer

Students are required to have Mathematics and English at minimum of Grade C or above at GCSE Level.

Fees and Funding

Undergraduate University Fees

We are committed to ensuring that Tuition Fees 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. Full time UK/EU students starting an undergraduate degree course in 2013 will be charged a tuition fee of £9,000. The level of fee may be subject to yearly increases. Full time International students starting an undergraduate degree course in 2013 will be charged a tuition fee of £14,400. The level of fee may be subject to yearly increases.

Scholarships and Bursaries

Home/EU - The University of East Anglia offers a range of Bursaries and Scholarships. To check if you are eligible please visit http://www.uea.ac.uk/study/undergraduate/finance/university-financial-support

International Students

The Maths courses have 1 £3,000 year one scholarship available for 2013 entry. The Scholarship deadline is 15th January 2013. Please contact the Admissions office at mth.ug.admiss@uea.ac.uk for more information.

The University offers around £1 million of Scholarships each year to support International students in their studies. Scholarships are normally awarded to students on the basis of academic merit and are usually for the duration of the period of study. Our University international pages gives you more details about preparation for studying with us, including Fees and Funding http://www.uea.ac.uk/international

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 full-time 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.