MMath Master of Mathematics
 ALevel typical
 AAB (2020/1 entry) See All Requirements
About this course
Our fouryear integrated Masters course is ideal if you want to take your studies to the next level and prepare to work in academia or research. Going into greater depth than our threeyear BSc programme, it’s a flexible course that allows you to specialise in either pure or applied mathematics, or a combination of the two.
In your final year you’ll take on a substantial research project. This will give you experience in independent study and help develop key career skills such as report writing and oral presentation. So you’ll not only graduate with a deep understanding of mathematics, but with great career prospects too.
At UEA you’ll also benefit from internationally recognised, researchled teaching and a high academic staff to student ratio. Lectures are complemented by small group teaching in your first year and regular workshops in later years, ensuring you get quality contact time with our worldclass lecturers.
In your final year you’ll take on a substantial research project. This will give you experience in independent study and help develop key career skills such as report writing and oral presentation. So you’ll not only graduate with a deep understanding of mathematics, but with great career prospects too.
At UEA you’ll also benefit from internationally recognised, researchled teaching and a high academic staff to student ratio. Lectures are complemented by small group teaching in your first year and regular workshops in later years, ensuring you get quality contact time with our worldclass lecturers.
Course Profile
Overview
Our prestigious fouryear Master of Mathematics degree programme will allow you to delve deeper and really develop your interests in pure and applied mathematics.
Our flexible course format will enable you to decide whether you want to focus on pure mathematics, applied mathematics, or a combination of the two. And â€“ as well as engaging in the study of essential mathematical theory and technique â€“ youâ€™ll have the opportunity to carry out a substantial research project in your final year. The project is designed to not only allow you to experience the challenge of independent study and discovery, but to also develop skills are essential to many future careers
Complete your studies with distinction you may want to join our active group of postgraduate students, as our Masters programme is also excellent preparation for a career in research â€“ either in industry or within a university. And research is just one of the many challenging career paths open to our Master of Mathematics students.
Course Structure
The first two years of our Masters course run in parallel with our threeyear BSc programme, with more specialised content being covered in your third and fourth years. 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
The first year will develop your skills in calculus and other topics which you may have covered at Alevel, such as mechanics and probability. Modules on computation, mathematical skills, and how to present mathematical arguments will encourage you to develop ways of tackling unfamiliar problems, while also providing an opportunity for group working. Modules on algebra and analysis will introduce important new concepts and ideas, which you will use in following years. In addition, youâ€™ll be introduced to mathematical software, which will be invaluable in your individual fourth year MMath project.
Year 2
As you progress into your second year, you will continue to learn essential algebraic principles through compulsory modules while also taking a selection of optional modules to suit your personal interests.
The optional modules on offer change each year but in previous years you could have chosen to study the theory of special relativity, take a module focusing on topology, or see how the mathematical theory youâ€™ve already studied can be applied to meteorology.
Year 3
By year three there are no compulsory modules. Instead youâ€™ll choose six modules from a range of approximately 15 that we offer.
The module topics vary each year, mirroring the research interests of our lecturers. By this stage we anticipate that you will have found the areas of mathematics that most appeal to you, and that youâ€™ll 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 chosen topic. Each of our lecturers will propose project titles covering a wide range of current mathematical research. Some of our students choose to devise 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). In order to be assessed, youâ€™ll submit a written report on the project, and youâ€™ll give a short oral presentation on your findings to lecturers and fellow Masters students.
Apart from your individual project, your studies will focus on Masterâ€™slevel modules that explore topics such as Lie Algebras, fluidstructure interaction, and mathematical biology. As with years two and three, the optional modules offered in your final year usually change every year.
Teaching and Learning
You will be taught by leading mathematicians in their fields. As well as teaching, our academics are actively involved in research collaborations with colleagues throughout the world, examples from which will be used to illustrate lectures and workshops. In fact, over 87% of our mathematical sciences research outputs were judged as internationally excellent or worldleading (REF 2014), so you can be sure youâ€™ll be learning in the most uptodate of environments.
New material will usually be delivered through lectures, which are complemented by online notes and workshops, where youâ€™ll focus on working through examples, either individually or in small groups, under the guidance of lecturers and mathematical teaching assistants.
In your first year youâ€™ll have around 16 or 17 hours of timetabled classes per week, comprised of approximately eleven hours of lectures, five or six hours of workshops or computer lab classes, and one tutorial.
In tutorial groups, youâ€™ll work with your academic advisor and the same six or seven students each week. Itâ€™s great way to get to know your fellow students and your academic advisor, who will be there to guide you throughout your degree.
Contact hours are similar in your second year, but with a greater emphasis on workshops, because the best way to truly understand complex mathematical theories is to work through examples with the guidance and support of your lecturers.
In your final two years your formal contact hours will be slightly reduced as you become more independent, but there will be increased emphasis on using the office hours of your lecturers for individual feedback and guidance.
Individual Study
Your final year project will of course best exemplify your independent study but, to succeed at universitylevel mathematics, youâ€™ll need to spend at least as much time on individual study as you spend in classes and workshops throughout your four years. Working through your lecture notes and trying the exercises set will be vital to really understanding the mathematics.
We offer a wide range of feedback to our students. Each lecturer has at least two office hours available each week, giving you the chance to discuss the material in more detail or to get facetoface feedback on exercises youâ€™ve attempted.
Prior to undertaking formal coursework (which will contribute to your module mark), youâ€™ll submit answers to questions based on similar material for comments from the lecturer. The feedback you receive will then help with your coursework.
Assessment
We employ a variety of assessment methods; the method we use is determined by the module in question. They range from 100% coursework to 100% examination, with most Mathematics modules combining 80% examination and 20% coursework.
The coursework component will be made up of problems set from an example sheet, which will be handed in, marked and returned, together with the solutions. For some modules there are also programming assignments and/or class tests.
Study abroad or Placement Year
Depending on your academic progress, you may be able to transfer onto our Masters of Mathematics with a Year Abroad programme at the end of year one.
After the course
Study with us and youâ€™ll graduate with a deep understanding of mathematics â€“ and with great career prospects. The experience of previous students suggests that completing a substantial project dissertation report, and a n oral presentation, are viewed very positively by prospective employers.
You could choose to enter one of the professions traditionally associated with mathematics, such as accountancy, banking and finance, statistics and data analysis, and secondary or higher education. Or you could follow other graduates into roles in which logicalthinking and problemsolving are important capabilities. These include information technology, engineering, logistics and distribution, central or local government, as well as other business areas. Many of our graduates also choose to continue their studies by going on to a higher degree.
Career destinations
Example of careers that you could enter include:
 Secondary school teacher
 Cyber Security consultant
 Mathematical modeller in industry
 Accountant
 Data Scientist
 Actuary
Course related costs
Please see Additional Course Fees for details of other courserelated costs.
Course Modules 2020/1
Students must study the following modules for 120 credits:
Name  Code  Credits 

ALGEBRA 1 Algebra plays a key role in pure mathematics and its applications. We will provide you with a thorough introduction and develop this theory from first principles. In the first semester, we consider linear algebra and in the second semester, we move on to group theory. In the first semester, we develop the theory of matrices, mainly (though not exclusively) over the real numbers. The material covers matrix operations, linear equations, determinants, eigenvalues and eigenvectors, diagonalization and geometric aspects. We conclude with the definition of abstract vector spaces. At the heart of group theory in Semester 2 is the study of symmetry and the axiomatic development of the theory. The basic concepts are subgroups, Lagrange's theorem, factor groups, group actions and the Isomorphism Theorem.  MTHA4006Y  20 
CALCULUS AND MULTIVARIABLE CALCULUS In this module you will study: (a) Complex numbers. (b) Vectors. (c) Differentiation; power series. (d) Integration: applications, curve sketching, area, arclength. (e) First and secondorder, constantcoefficient 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.  MTHA4008Y  30 
COMPUTATION AND MODELLING Computation and modelling are essential skills for the modern mathematician. While many applied problems are amenable to analytic methods, many require some numerical computation to complete the solution. The synthesis of these two approaches can provide deep insight into highly complex mathematical ideas. This module will introduce you to the art of mathematical modelling, and train you in the computer programming skills needed to perform numerical computations. A particular focus is classical mechanics, which describes the motion of solid bodies. Central to this is Newton's second law of motion, which states that a mass will accelerate at a rate proportional to the force imposed upon it. This leads to an ordinary differential equation to be solved for the velocity and position of the mass. In the simplest cases the solution can be constructed using analytical methods, but in more complex situations, for example motion under resistance, numerical methods may be required. Iterative methods for solving nonlinear algebraic equations are fundamental and will also be studied. Further examples drawn from pure mathematics and statistics demonstrate the power of modern computational techniques.  MTHA4007Y  20 
MATHEMATICAL SKILLS The unit provides you with a thorough introduction to some systems of numbers commonly found in Mathematics: natural numbers, integers, rational numbers, modular arithmetic. It also introduces you to common set theoretic notation and terminology and a precise language in which to talk about functions. There is emphasis on precise definitions of concepts and careful proofs of results. Styles of mathematical proofs you will discuss include: proof by induction, direct proofs, proof by contradiction, contrapositive statements, equivalent statements and the role of examples and counterexamples. In addition, this unit will also provide you with an introduction to producing mathematical documents using Latex, and an introduction to solving mathematical problems computationally using both Symbolic Algebra packages and Excel.  MTHA4001A  20 
PROBABILITY Probability is the study of the chance of events occurring. It has important applications to understand the likelihood of multiple events happening together and therefore to rational decisionmaking. This module will give you an introduction to the modern theory of probability developed from the seminal works of the Russian mathematician A.N. Kolmogorov in 1930s. Kolmogorov's axiomatic theory describes the outcomes (events) of a random experiment as mathematical sets. Using set theory language you will be introduced to the concept of random variables, and consider different examples of discrete random variables (like binomial, geometric and Poisson random variables) and continuous random variables (like the normal random variable). In the last part of the module you will explore two applications of probability: reliability theory and Markov chains. Aside of the standard lectures and workshop sessions, there will be two computerlab sessions of (2 hours each) where you will apply probability theory to specific everyday life case studies. The only prerequisites for this module are a basic knowledge of set theory and of calculus that you would have acquired during the Autumn semester. If you have done probability or statistic at Alevel you will rediscover its contents now taught using a proper and more elegant mathematical formalism.  MTHA4001B  10 
REAL ANALYSIS We will explore the mathematical notion of a limit and 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 
Students must study the following modules for 80 credits:
Name  Code  Credits 

ALGEBRA II The module offers an introduction to vector space theory in the first semester followed by ring theory in the second semester. For vector spaces you will learn about subspaces, basis and dimension, linear maps, ranknullity theorem, change of basis and the characteristic polynomial. This is followed by an introduction to rings using integers as a model. We develop the theory with many examples related to familiar concepts such as substitution and factorisation. Important examples of commutative rings include fields, domains, polynomial rings and their quotients.  MTHA5008Y  20 
COMPLEX ANALYSIS This is a course in analysis. It is an introduction to the classical theory of the complex plain  MTHA5006Y  20 
DIFFERENTIAL EQUATIONS AND APPLIED METHODS (a) 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. (b) Method of characteristics for hyperbolic equations; the characteristic equations; Fourier transform and its use in solving linear PDEs; (c) Dynamical Systems: equilibrium points and their stability; the phase plane; theory and applications.  MTHA5004Y  20 
INVISCID FLUID FLOW This module introduces some of the fundamental physical concepts and mathematical theory needed to analyse the motion of a fluid, with the focus predominantly on inviscid, incompressible motions. You will examine methods for visualising flow fields, including the use of particle paths and streamlines. You will study the dynamical theory of fluid flow taking Newton's laws of motion as its point of departure, and the fundamental set of equations comprising conservation of mass and Euler's equations will be discussed. The reduction to Laplace's equation for irrotational flow will be demonstrated, and Bernoulli's equation is derived as a first integral of the equation of motion. Having established the basic theory, the way is set for a broader discussion of flow dynamics including everyday practical examples. Vector calculus will cover divergence, gradient, curl of vector field, the Laplacian, scalar potential and pathindependence of line integral, surface integrals, divergence theorem and Stokes' theorem. Computational fluid dynamics will also be studied.  MTHA5007Y  20 
Students will select 20  40 credits from the following modules:
Name  Code  Credits 

COMBINATORICS AND FURTHER LINEAR ALGEBRA Combinatorics is one of the most applicable and accessible part of mathematics, yet it is also full of challenging problems. We shall cover many basic combinatorial concepts including counting arguments (enumerative combinatorics) and Ramsey theory. Linear Algebra underpins much of modern mathematics and is the key to many applications. We will introduce bilinear forms and symmetric operators on vector spaces leading to the diagonalization of linear maps and the spectral theorem. This theorem is key to many applications in statistics and physics. Other topics covered will include polynomials of linear maps, the CayleyHamilton theorem and the Jordan normal form of a matrix.  MTHF5031Y  20 
MATHEMATICAL MODELLING Mathematical modelling is concerned with how to convert real problems, such as those arising in industry or other sciences, into mathematical equations, and then solving them and using the results to better understand, or make predictions about, the original problem. This topic 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 nondimensionalising, 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. We will consider population modelling, chaos, and aerodynamics.  MTHF5032Y  20 
MATHEMATICAL STATISTICS This module 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.  CMP5034A  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. You'll study the basic theory, data acquisition and interpretation methods of seismic, electrical, gravity and magnetic surveys. A wide range of applications are covered, including archaeological geophysics, energy resources and geohazards. Highly valued by employers, this module features guest lecturers from industry who explain the latest 'stateoftheart' applications and give you unique insight into real world situations. Students doing this module are normally expected to have a good mathematical ability, notably in calculus and algebra.  ENV5004B  20 
DYNAMICS AND VIBRATION You will build on the introductory material you gained in first year engineering mechanics. 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, energy methods, 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 
EDUCATIONAL PSYCHOLOGY This module will provide you with an introduction to key areas of psychology with a focus on learning and teaching in education. By the end of the module you should be able to:  Discuss the role of perception, attention and memory in learning;  Compare and contrast key theories related to learning, intelligence, language, thinking and reasoning;  Critically reflect on key theories related to learning, intelligence, language, thinking and reasoning in the practical context;  Discuss the influence of key intrapersonal, interpersonal and situational factors on pupils learning and engagement in educational settings.  EDUB5012A  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 
INTRODUCTORY MACROECONOMICS The aim of this module is to introduce students to the economic way of reasoning, and to apply these to a variety of real world macroeconomic issues. Students will begin their journey by learning how to measure macroeconomic aggregates, such as GDP, GDP growth, unemployment and inflation. The module will establish the foundations to conduct rigorous Macroeconomics analysis, as students will learn how to identify and characterise equilibrium on the goods market and on the money market. The module will also introduce students to policymaking, exploring and evaluating features and applications of fiscal and monetary policy. Students will grow an appreciation of the methods of economic analysis, such as mathematical modelling, diagrammatic representation, and narrative. The discussion of theoretical frameworks will be enriched by real world applications, and it will be supported by an interactive teaching approach.  ECO4006Y  20 
METEOROLOGY I The weather affects everyone and influences decisions that are made on a daily basis around the world. From whether to hang your washing out on a sunny afternoon to which route a commercial aircraft takes as it travels across the ocean, weather plays a vital role. With that in mind, what actually causes the weather we experience? In this module you'll learn the fundamentals of the science of Meteorology. You'll concentrate on the physical process that allow moisture and radiation to transfer through the atmosphere and how they ultimately influence our weather. The module contains both descriptive and mathematical treatments of radiation balance, thermodynamics, dynamics, boundary layers, weather systems and the water cycle. The module is assessed through a combination of one piece of coursework and an exam and is designed in a way that allows those with either mathematical or descriptive abilities to do well. A reasonable mathematical competence is essential, including basic understanding of differentiation and integration.  ENV5008A  20 
PROGRAMMING FOR NONSPECIALISTS The purpose of this module is to give you a solid grounding in the essential features of programming. 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. You will explore the energy, mechanics and 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. You will study Plate Tectonics 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. You will also explore geological time  the 4.6 billion year record of changing conditions on the planet  and how geological maps can be used to understand Earth history. This course provides you with an introduction to geological materials  rocks, minerals and sediments  and to geological resources and natural hazards.  ENV4005A  20 
Students will select 60  120 credits from the following modules:
Name  Code  Credits 

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 
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 tangent spaces and the first and second fundamental forms, Gaussian curvature, and further topics.  MTHE6030A  20 
DYNAMICAL OCEANOGRAPHY The ocean is an important component of the Earth's climate system. This module covers mathematically modelling of the largescale ocean circulation and oceanic wave motion. This module builds upon the techniques in fluid dynamics and differential equations that you developed in year two. It then uses these techniques to explain some interesting phenomena in the ocean that are relevant to the real world. We begin by examining the effects of rotation on fluid flows. This naturally leads to the important concept of geostrophy, which enables ocean currents to be inferred from measurements of the sea surface height or from vertical profiles of seawater density. Geostrophy also plays a key role in the development of a model for the global scale circulation of abyssal ocean. The role of the wind in driving the ocean will be examined. This enables us to model the largescale circulation of the ocean including the development of oceanic gyres and strong western boundary currents, such as the Gulf Stream. The module concludes by examining the role of waves, both at the sea surface and internal to the ocean. The differences between wave motion at midlatitudes and the Equator are examined, as is the roll of the Equator as a waveguide. The equatorial waves that you will study are intimately linked with the El Nino phenomenon that affects the climate throughout the globe.  MTHE6007B  20 
FINANCIAL MATHEMATICS The Mathematical Modelling of Finance is a relatively new area of application of mathematics yet it is expanding rapidly and has great importance for world financial markets. The module is concerned with the valuation of financial instruments known as derivatives. Introduction to options, futures and the noarbitrage principle. Mathematical models for various types of options are discussed. We consider also Brownian motion, stochastic processes, stochastic calculus and Ito's lemma. The BlackScholes partial differential equation is derived and its connection with diffusion brought out. It is applied and solved in various circumstances.  MTHE6026B  20 
GROUPS AND ALGEBRA This module is about further topics in algebra. It builds on the knowledge obtained on groups, rings and vector spaces in the first two years. Groups can be studied directly, or via objects called algebras (which have the structures of both rings and vector spaces). On the other hand, algebras can also be studied in their own right. Some of these concepts will be explored in this module.  MTHE6033A  20 
NUMBER THEORY Number Theory is the study of arithmetical properties of the integers: properties of, and patterns in, prime numbers, integer solutions of equations with integer coefficients, etc. Gauss called Number Theory "the queen of mathematics" and, following on from work of Fermat and Euler, is responsible for the emergence of Number Theory as a central subject in modern mathematics. Since then, Number Theory has developed in many directions, including Algebraic, Analytic and Probabilistic Number Theory, Diophantine Geometry and has found surprising applications in modern life (notably in Cryptography). In this module, building on first year material on prime factorization and basic congruences, and second year material on groups, rings and fields, you will study various aspects of Number Theory, including certain diophantine equations, polynomial congruences and the famous theorem of Quadratic Reciprocity.  MTHE6035B  20 
PARTIAL DIFFERENTIAL EQUATIONS Partial Differential Equations (PDEs) are ubiquitous in applied mathematics. They arise in many models of physical systems where there is coupling between the variation in space and time, or more than one spatial dimension. Examples include fluid flows, electromagnetism, population dynamics, and the spread of infectious diseases. It is therefore important to understand the theory of PDEs, as well as different analytic and numerical methods for solving them. This module will provide you with an understanding of the different types of PDE, including linear, nonlinear, elliptic, parabolic and hyperbolic; and how these features affect the required boundary conditions and solution techniques. We will study different methods of analytical solution (such as greens functions, boundaryintegral methods, similarity solutions, and characteristics); as well as appropriate numerical methods (with topics such as implicit versus explicit schemes, convergence and stability). Examples and applications will be taken from a variety of fields.  MTHE6034A  20 
QUANTUM MECHANICS This module covers the laws of physics described by quantum mechanics that govern the behaviour of microscopic particles. The module will focus on nonrelativitic quantum mechanics that is described by the Schrodinger equation. Timedependent and timeindependent solutions will be presented in different contexts including an application to the hydrogen atom. Approximation schemes will also be discussed, with particular emphasis on variational principles, WKB approximation.  MTHE6032A  20 
SET THEORY This module is concerned with foundational issues in mathematics and provides the appropriate mathematical framework for discussing 'sizes of infinity'. On the one hand we shall cover concepts such as ordinals, cardinals, and the ZermeloFraenkel axioms with the Axiom of Choice. On the other, we shall see how these ideas come up in other areas of mathematics, such as graph theory and topology. Familiarity with and a taste for mathematical proofs will be assumed. Therefore, second year Analysis is a desired prerequisite.  MTHE6003B  20 
WAVES You will gain an introduction to the theory of waves. You will study aspects of linear and nonlinear waves using analytical techniques and Hyperbolic Waves and Water Waves will also be covered. It requires some knowledge of hydrodynamics and multivariable calculus. The module is suitable for those with an interest in Applied Mathematics.  MTHE6031B  20 
Students will select 20  60 credits from the following modules:
Name  Code  Credits 

HISTORY OF MATHEMATICS We will trace the development of mathematics from prehistory to the high cultures of ancient Egypt, Mesopotamia, and the Indus Valley civilisation, through Islamic mathematics, and on to mathematical modernity, through a selection of topics. We trace the rise of calculus and algebra, from the time of Ancient Greek and Indian mathematicians, up to the era of Newton and Leibniz. Other topics are also discussed. We will explore mathematical practice and conceptual developments in different historical and geographical settings.  MTHA6002A  20 
MATHEMATICS PROJECT This module is reserved for 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. The focus of the project is on independent study  you will have the opportunity to undertake research in an area which is interesting to you. You will write an indepth report on your chosen project, in the mathematical typesetting language LaTeX. There will also be a short oral presentation.  MTHA6005Y  20 
MODELLING ENVIRONMENTAL PROCESSES Our aim 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, the practicals being designed to illustrate the solution of problems using the methods covered in lectures. We will guide you through the solution of a model of an environmental process of your 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 you to the study of the teaching and learning of mathematics with particular focus to secondary and post compulsory level. In this module, you will explore theories of learning and teaching of mathematical concepts typically included in the secondary and post compulsory curriculum. Also, you will learn about knowledge related to mathematical teaching. If you are interested in mathematics teaching as a career or interested in mathematics education as a research discipline, then this module will equip you with the necessary knowledge and skills.  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. You'll study the basic theory, data acquisition and interpretation methods of seismic, electrical, gravity and magnetic surveys. A wide range of applications are covered, including archaeological geophysics, energy resources and geohazards. Highly valued by employers, this module features guest lecturers from industry who explain the latest 'stateoftheart' applications and give you unique insight into real world situations. Students doing this module are normally expected to have a good mathematical ability, notably in calculus and algebra.  ENV5004B  20 
CHILDREN, TEACHERS AND MATHEMATICS This module will introduce you to key issues in mathematics education, particularly those that relate to the years of compulsory schooling. Specifically in this module we: Introduce the mathematics curriculum and pupils' perception of, and difficulties with, key mathematical concepts; Discuss public and popular culture perceptions of mathematics, mathematical ability and mathematicians as well as address ways in which these perceptions can be modified; Outline and discuss specific pedagogical actions (focused on challenge and motivation) that can be taken as early as possible during children's schooling and can provide a solid basis for pupils' understanding and appreciation of mathematics. By the end of the module you will be able to gain understanding of key curricular, pedagogical and social issues that relate to the teaching and learning of mathematics, a crucial subject area in the curriculum; Reflect on pedagogical action that aims to address those issues, particularly in the years of compulsory schooling; Be informed and able to consider the potential of pursuing a career in education, either as a teacher, educational professional or researcher in education with particular specialisation in the teaching and learning of mathematics.  EDUB6006A  20 
CLIMATE SYSTEMS What sets the mean global temperature of the world? Why are some parts of the world arid whilst others at the same latitudes are humid? This module aims to provide you with an understanding of the processes that determine why the Earth's climate (defined, for example, by temperature and moisture distribution) looks like it does, what the major circulation patterns and climate zones are and how they arise. You will study why the climate changes in time over different timescales, and how we use this knowledge to understand the climate systems of other planets. This module is aimed at you if you wish to further your knowledge of climate, or want a base for any future study of climate change, such as the Meteorology/Oceanography.  ENV6025B  20 
COMBINATORICS AND FURTHER LINEAR ALGEBRA Combinatorics is one of the most applicable and accessible part of mathematics, yet it is also full of challenging problems. We shall cover many basic combinatorial concepts including counting arguments (enumerative combinatorics) and Ramsey theory. Linear Algebra underpins much of modern mathematics and is the key to many applications. We will introduce bilinear forms and symmetric operators on vector spaces leading to the diagonalization of linear maps and the spectral theorem. This theorem is key to many applications in statistics and physics. Other topics covered will include polynomials of linear maps, the CayleyHamilton theorem and the Jordan normal form of a matrix.  MTHF5031Y  20 
EDUCATIONAL PSYCHOLOGY This module will provide you with an introduction to key areas of psychology with a focus on learning and teaching in education. By the end of the module you should be able to:  Discuss the role of perception, attention and memory in learning;  Compare and contrast key theories related to learning, intelligence, language, thinking and reasoning;  Critically reflect on key theories related to learning, intelligence, language, thinking and reasoning in the practical context;  Discuss the influence of key intrapersonal, interpersonal and situational factors on pupils learning and engagement in educational settings.  EDUB5012A  20 
FINANCIAL ACCOUNTING What are the rules that dictate how company accounts should be prepared and why do those rules exist? This is the essence of this module. Whilst company directors may wish to present the financial condition of a business in the best possible light, rules have been developed to protect investors and users of the accounts from being misled. You'll develop knowledge and skills in understanding and applying accounting standards when preparing financial statements. You'll also prepare and analyse statements of both individual businesses and groups of companies. Large UK companies report using International Financial Reporting Standards and these are the standards that you'll use. You'll begin by preparing basic financial statements and progress, preparing accounts of increasing complexity by looking at topics including goodwill, leases, cashflow statements, foreign currency transactions, financial instruments and group accounts. You'll also deepen your analytical skills through ratio analysis. You'll learn through a mixture of lectures, seminars and selfstudy, and be assessed by coursework and final examination. On successful completion of this module, you'll have acquired significant technical skills in both the preparation and analysis of financial statements. This will give you a strong basis from which to build should you wish to study advanced financial accounting or are planning on a career in business or accounting.  NBS5002Y  20 
KNOWLEDGE SCIENCE AND PROOF FOR SECOND YEARS Epistemology examines what knowledge is. Science is concerned with the acquisition of secure knowledge, and philosophy of science considers what counts as science, what objects the scientist knows about, and what methods can be used to attain such knowledge; logic uses formal tools to investigate different forms of reasoning deployed to acquire knowledge. You will be given an opportunity to explore a selection of these areas of philosophy, through teaching informed by recent and ongoing research: which ones will be explored on this occasion will be selected in the light of the lecturers' current research interests and their general appeal.  PPLP5175B  20 
MATHEMATICAL MODELLING Mathematical modelling is concerned with how to convert real problems, such as those arising in industry or other sciences, into mathematical equations, and then solving them and using the results to better understand, or make predictions about, the original problem. This topic 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 nondimensionalising, 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. We will consider population modelling, chaos, and aerodynamics.  MTHF5032Y  20 
MATHEMATICAL STATISTICS This module 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.  CMP5034A  20 
METEOROLOGY I The weather affects everyone and influences decisions that are made on a daily basis around the world. From whether to hang your washing out on a sunny afternoon to which route a commercial aircraft takes as it travels across the ocean, weather plays a vital role. With that in mind, what actually causes the weather we experience? In this module you'll learn the fundamentals of the science of Meteorology. You'll concentrate on the physical process that allow moisture and radiation to transfer through the atmosphere and how they ultimately influence our weather. The module contains both descriptive and mathematical treatments of radiation balance, thermodynamics, dynamics, boundary layers, weather systems and the water cycle. The module is assessed through a combination of one piece of coursework and an exam and is designed in a way that allows those with either mathematical or descriptive abilities to do well. A reasonable mathematical competence is essential, including 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.  ENV5016B  20 
PROGRAMMING FOR NONSPECIALISTS The purpose of this module is to give you a solid grounding in the essential features of programming. The module is designed to meet the needs of the student who has not previously studied programming.  CMP5020B  20 
SCIENCE COMMUNICATION You will gain an understanding of how science is disseminated to the public and explore the theories surrounding learning and communication. You will investigate science as a culture and how this culture interfaces with the public. Examining case studies in a variety of different scientific areas, alongside looking at how information is released in scientific literature and subsequently picked up by the public press, will give you an understanding of science communication. You will gain an appreciation of how science information can be used to change public perception and how it can sometimes be misinterpreted. You will also learn practical skills by designing, running and evaluating a public outreach event at a school or in a public area. If you wish to take this module you will be required to write a statement of selection. These statements will be assessed and students will be allocated to the module accordingly.  BIO6018Y  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). You will explore 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. You will develop new skills during this module that will support careers in the offshore oil and gas industry, renewable energy industry, environmental consultancy, government laboratories (e.g. Cefas) and academia. The level of mathematical ability required to take this module is similar to Ocean Circulation and Meteorology I. You should be familiar with radians, rearranging equations and plotting functions.  ENV5017A  20 
WEATHER APPLICATIONS  ENV5009B  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 You will complete a fourth year dissertation on a mathematical topic that is a compulsory part of some Master of Mathematics degrees.  MTHA7029Y  40 
MMATH PROJECT This module is modelled on the Mathematics MMath project module MTHA7029Y. 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 80 credits from the following modules:
Name  Code  Credits 

DIFFERENTIAL GEOMETRY WITH ADVANCED TOPICS 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 tangent spaces and the first and second fundamental forms, Gaussian curvature, and further topics, including the advanced topics for 4th year students.  MTHE7030A  20 
DYNAMICAL OCEANOGRAPHY WITH ADVANCED TOPICS The ocean is an important component of the Earth's climate system. This module covers mathematically modelling of the largescale ocean circulation and oceanic wave motion. This module builds upon the techniques in fluid dynamics and differential equations that you developed in previous years of study. It then uses these techniques to explain some interesting phenomena in the ocean that are relevant to the real world. We begin by examining the effects of rotation on fluid flows. This naturally leads to the important concept of geostrophy, which enables ocean currents to be inferred from measurements of the sea surface height or from vertical profiles of seawater density. Geostrophy also plays a key role in the development of a model for the global scale circulation of abyssal ocean. The role of the wind in driving the ocean will be examined. This enables us to model the largescale circulation of the ocean including the development of oceanic gyres and strong western boundary currents, such as the Gulf Stream. The module concludes by examining the role of waves, both at the sea surface and internal to the ocean. The differences between wave motion at midlatitudes and the Equator are examined, as is the roll of the Equator as a waveguide. The equatorial waves that you will study are intimately linked with the El Nino phenomenon that affects the climate throughout the globe. The advanced topic is a study of barotropic and baroclinic instability.  MTHE7007B  20 
FINANCIAL MATHEMATICS WITH ADVANCED TOPICS The Mathematical Modelling of Finance is a relatively new area of application of mathematics yet it is expanding rapidly and has great importance for world financial markets. The module is concerned with the valuation of financial instruments known as derivatives. Introduction to options, futures and the noarbitrage principle. Mathematical models for various types of options are discussed. We consider also Brownian motion, stochastic processes, stochastic calculus and Ito's lemma. The BlackScholes partial differential equation is derived and its connection with diffusion brought out. It is applied and solved in various circumstances. Further advanced topics may include American options or stochastic interest rate models.  MTHE7026B  20 
GROUPS AND ALGEBRA WITH ADVANCED TOPICS This module is about further topics in algebra. It builds on the knowledge obtained on groups, rings and vector spaces in the first two years. Groups can be studied directly, or via objects called algebras (which have the structures of both rings and vector spaces). On the other hand, algebras can also be studied in their own right. Some of these concepts will be explored in this module.  MTHE7033A  20 
NUMBER THEORY WITH APPLICATIONS IN CRYPTOGRAPHY Number Theory is the study of arithmetical properties of the integers: properties of, and patterns in, prime numbers, integer solutions of equations with integer coefficients, etc. Gauss called Number Theory "the queen of mathematics" and, following on from work of Fermat and Euler, is responsible for the emergence of Number Theory as a central subject in modern mathematics. Since then, Number Theory has developed in many directions, including Algebraic, Analytic and Probabilistic Number Theory, Diophantine Geometry and has found surprising applications in modern life (notably in Cryptography). In this module, building on first year material on prime factorization and basic congruences, and second year material on groups, rings and fields, you will study various aspects of Number Theory, including certain diophantine equations, polynomial congruences and the famous theorem of Quadratic Reciprocity. The Advanced Topics will be on applications of Number Theory in Cryptography.  MTHE7035B  20 
PARTIAL DIFFERENTIAL EQUATIONS WITH ADVANCED TOPICS Partial Differential Equations (PDEs) are ubiquitous in applied mathematics. They arise in many models of physical systems where there is coupling between the variation in space and time, or more than one spatial dimension. Examples include fluid flows, electromagnetism, population dynamics, and the spread of infectious diseases. It is therefore important to understand the theory of PDEs, as well as different analytic and numerical methods for solving them. This module will provide you with an understanding of the different types of PDE, including linear, nonlinear, elliptic, parabolic and hyperbolic; and how these features affect the required boundary conditions and solution techniques. We will study different methods of analytical solution (such as greens functions, boundaryintegral methods, similarity solutions, and characteristics); as well as appropriate numerical methods (with topics such as implicit versus explicit schemes, convergence and stability). Examples and applications will be taken from a variety of fields.  MTHE7034A  20 
QUANTUM MECHANICS WITH QUANTUM FLUIDS This module covers the laws of physics described by quantum mechanics that govern the behaviour of microscopic particles. The module will focus on nonrelativitic quantum mechanics that is described by the Schrodinger equation. Timedependent and timeindependent solutions will be presented in different contexts including an application to the hydrogen atom. Approximation schemes will also be discussed, with particular emphasis on variational principles, WKB approximation. Extensions of this content to describe quantum fluids such as ultracold Bose gases and superfluids in terms of the GrossPitaevskii equation will also be presented.  MTHE7032A  20 
SET THEORY WITH ADVANCED TOPICS ZermeloFraenkel set theory. The Axiom of Choice and equivalents. Cardinality, countability, and uncountability. Trees, Combinatorial set theory. Advanced topic: Constructibility.  MTHE7003B  20 
WAVES WITH ADVANCED TOPICS You will gain an introduction to the theory of waves. You will study aspects of linear and nonlinear waves using analytical techniques, and Hyperbolic Waves and Water Waves will also be covered. It requires some knowledge of hydrodynamics and multivariable calculus. The module is suitable for those with an interest in Applied Mathematics.  MTHE7031B  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 or ABB with an A in the Extended Project, including an A in Mathematics or ABB including an A in Mathematics and a B in Further Mathematics. Science Alevels must include a pass in the practical element.
 International Baccalaureate 33 points including Higher Level 6 in Mathematics.
 Scottish Highers AAAAA including a B in Advanced Higher Mathematics.
 Scottish Advanced Highers BBC including a B in Mathematics.
 Irish Leaving Certificate 4 subjects at H2, 2 subjects at H3, including H2 in 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 credits in Mathematics at Distinction. Please note that an interview will be required.
 BTEC DDD alongside grade A in Alevel Mathematics. Excludes BTEC Public Services, BTEC Uniformed Services and BTEC Business Administration
 European Baccalaureate 80% overall including 85% in Mathematics.
Entry Requirement
General Studies and Critical Thinking are not accepted.
If you do not meet the academic requirements for direct entry, you may be interested in one of our Foundation Year programmes.
Mathematics with a Foundation Year
Students for whom English is a Foreign language
Applications from students whose first language is not English are welcome. We require evidence of proficiency in English (including writing, speaking, listening and reading):
 IELTS: 6.5 overall (minimum 5.5 in all components)
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 yet meet the English language requirements for this course, INTO UEA offer a variety of English language programmes which are designed to help you develop the English skills necessary for successful undergraduate study:
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 Physical Sciences and Engineering
 International Foundation in Mathematics and Actuarial Sciences
Interviews
Most applicants will not be called for an interview and a decision will be made via UCAS Track. However, for some applicants an interview will be requested. Where an interview is required the Admissions Service will contact you directly to arrange a 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 on your UCAS application.
Intakes
The annual intake is in September each year.
Alternative Qualifications
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.
GCSE Offer
You are required to have Mathematics and English Language at a minimum of Grade C or Grade 4 or above at GCSE.
Course Open To
UK and overseas applicants.
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 application 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 is sent to UCAS so that they can process it and send it to your chosen universities and colleges.
The Institution code for the University of East Anglia is E14.
Further Information
Please complete our Online Enquiry Form to request a prospectus and to be kept up to date with news and events at the University.
Tel: +44 (0)1603 591515
Email: admissions@uea.ac.uk
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