This prestigious four-year Master of Mathematics programme allows greater depth of study than is possible in a three-year course. The third year of the programme is spent learning Mathematics at a North American University.
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 progessional career, including report writing skills and oral presentation skills. Spending a year abroad advertises to potential employers qualities of independence, self-organisation, and an ability to adapt to new cultures and a foreign environment. 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.
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.
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 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.
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.
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.
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:
(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.
(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.
(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.
(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:
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 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.
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.
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.
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.
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.
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
Compulsory Study (120 credits)
Students must study the following modules for 120 credits:
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.
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:
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.
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:
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.
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.
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).
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
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.
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?
Zermelo-Fraenkel set theory. The Axiom of Choice and equivalents. Cardinality, countability, and uncountability. Trees, Combinatorial set theory. Advanced topic: Infinite Ramsey theory.
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.
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.
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.
Year Abroad
Applicants for the Master of Mathematics programme have the opportunity to apply for a programme with a year abroad in North America or Australia.
Experiencing a Year Abroad as part of your degree programme is a once-in-a-lifetime opportunity, as well as providing you with the opportunity to experience a different culture, study exciting branches of mathematics in a different culture or to learn a second language. The first two years of the programme are spent at UEA with the third year spent at one of our exchange partners overseas. Students return to UEA for the fourth and final year. Employers really value students who have opted for a Year Abroad as part of their studies, recognising valued qualities such as adaptability, flexibility and independence.
It may be possible to transfer to a Year Abroad programme after you have started your studies at UEA, however this is subject to the availability of places and therefore cannot be guaranteed. Students on an exchange programme will be expected to pay 15% of their annual tuition fee to UEA during their year abroad and we will pay the overseas university.
We are constantly reviewing our exchange agreements with our overseas partners and as such the destination Universities are subject to change. Potential destinations include:
A*AA (A* in Mathematics) or A*AB (A* in Mathematics, A in Further Mathematics)
International Baccalaureate:
35 points overall including 7 in Higher Level Maths
Scottish Highers:
AAAA including grade A in Advanced Higher Mathematics
Scottish Advanced Highers:
AAA including grade A in Mathematics
Irish Leaving Certificate:
AAAAAA including grade A in Mathematics
Access Course:
See below
HND:
Please contact institution for further information
European Baccalaureate:
90% overall including 90% 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 the 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.
Year Abroad Fees
For Home/EU students opting for a Year Abroad the tuition fee is currently £1,350. The Year Abroad tuition fee will be subject to an annual increase. International Students are required to pay 25% of their annual tuition fee to UEA during their year Abroad and will be calculated based on the current tuition fee for that year.
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
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:
This prestigious four-year Master of Mathematics programme allows greater depth of study than is possible in a three-year course. The third year of the programme is spent learning Mathematics at a North American University.
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.