MMath Master of Mathematics
 UCAS Course Code
 G103
 ALevel typical
 AAB (2017/8 entry) See All Requirements
About this course
Studying with us means that you’ll benefit from internationally recognised, researchled teaching and a high academic staff/student ratio. You’ll graduate with a deep understanding of mathematics and great career prospects (86% of our graduates were in work or study within six months), whether you specialise in pure maths, applied maths, or a mix of topics from the wide range of optional modules we offer.
This fouryear programme offers advanced study of mathematics preparing you for either further study or a career beyond university. Your lectures are complemented by smallgroup teaching that provides you with quality contact time with our world class lecturers – we were ranked 7th in the UK for the quality of our research outputs (REF 2014).
This fouryear programme offers advanced study of mathematics preparing you for either further study or a career beyond university. Your lectures are complemented by smallgroup teaching that provides you with quality contact time with our world class lecturers – we were ranked 7th in the UK for the quality of our research outputs (REF 2014).
Course Profile
Overview
This prestigious fouryear Master of Mathematics programme allows you to develop your interests in pure and applied mathematics, and in greater depth of study than a threeyear programme.
One of the advantages of studying with us is that we offer a great deal of flexibility in what you can study, enabling you to specialise in either pure or applied mathematics, or a combination of these topics. Apart from engaging in study of essential mathematical theory and technique, you will also have the opportunity to carry out a substantial research project in the final year, allowing you to experience the challenge of independent study and discovery. Furthermore this helps you to develop skills that are essential for many future career paths, including experience of report writing and oral presentation.
If you finish your studies with distinction you may want to join our active group of postgraduate students, as the programme is also excellent preparation for a career in research, either in industry or in a university. However research is just one pathway out of the wide range of challenging careers open to Master of Mathematics students.
Course Structure
The first two years run in parallel with the threeyear BSc programme, before more specialised content is covered in the third and fourth year. In these final two years you will learn advanced principles through a huge range of optional subjects, as well as undertaking an independent project.
Year 1
In the first year you will undertake a set of compulsory modules to consolidate a broad knowledge of mathematical disciplines, primarily algebra and calculus. This is supplemented by classes on the applications of mathematics, problem solving and analysis. The skills you gain from these courses will be revisited throughout the degree and should help inform your future module choices.
Year 2
The modules on offer to you are the same as those available on the BSc programme.
As you progress into your second year, you will continue to learn essential algebraic principles through compulsory modules whilst taking a selection of optional modules to suit your personal interests. The optional modules offered change each year but for instance you may choose to study the theory of special relativity or take a cryptography module to see how number theory studied elsewhere can be applied to the theory of coding. In addition, you will be introduced to mathematical software which will be invaluable in your individual fourth year MMath project.
Year 3
At this stage there are no compulsory modules and you will choose 6 modules from a range of approximately 15 offered. Each year the particular topics on offer vary to mirror the research interests of our lecturers. By this stage we anticipate that you will have found the areas of mathematics which most appeal to you, and you will use this year to focus on these topics, laying the foundations for a successful finalyear research project.
Year 4
You will undertake a substantial individual project during your final year, working under the close supervision of a lecturer whose expertise matches your subject. Each of the lecturers proposes project titles covering a very wide range of current mathematical research, but many of our students come up with their own topics in conjunction with one of our lecturers. Recent topics have ranged from â€śThe Mobius function of Finite Groupsâ€ť to â€śThe Aerodynamics of Golf Ballsâ€ť (a topic suggested by the student). The project is assessed through a written report as well as a short oral presentation to lecturers and fellow Masters students on your findings. For the remainder of your final year, you will choose from a range of Masterâ€™slevel modules that explore topics such as lie algebra, fluid structure interaction and mathematical biology. The topics on offer typically change every year.
Assessment
A variety of assessment methods are applied across the different mathematics modules, ranging from 100% coursework to 100% examination. Most mathematics modules are assessed 80% by examination and 20% by coursework. The coursework component is made up of problems set from an example sheet, to be handed in, marked and returned together with solutions. For some modules there are also programming assignments and/or class tests. In Year 4, the research project makes up onethird of the final assessment.
Course Modules 2018/9
Students must study the following modules for 120 credits:
Name  Code  Credits 

CALCULUS AND MULTIVARIABLE CALCULUS (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. (g) Vector calculus: divergence, gradient, curl of vector field. The Laplacian. Scalar potential and pathindependence of line integral. (h) Surface integrals, Divergence Theorem and Stokes' Theorem. Operators in orthogonal curvilinear coordinates. (i) Introduction to Matlab.  MTHA4005Y  40 
LINEAR ALGEBRA In the first semester we develop the algebra of matrices: Matrix operations, linear equations, determinants, eigenvalues and eigenvectors, diagonalisation and geometric aspects. This is followed in the second semester by vectors space theory: Subspaces, basis and dimension, linear maps, ranknullity theorem, change of basis and the characteristic polynomial.  MTHA4002Y  20 
MATHEMATICAL PROBLEM SOLVING, MECHANICS AND MODELLING This module comprises two parts: andquot;Mathematical Problem Solvingandquot; and andquot;Mechanics and Modellingandquot;. Being able to tackle unfamiliar problems using existing knowledge is an essential part of mathematics and a key transferable skill. Equally important is being able to express mathematical ideas in written and verbal form. In the first part of this module you will acquire these skills through collaborative group work on a number of example problems covering different areas of mathematics. The module will promote accurate reading, writing, and thinking about mathematics, and will also improve your confidence and ability to tackle unfamiliar problems. Newtonian mechanics provides a basic description of how particles and rigid bodies move in response to applied forces. In the second part of the module you will study Newton's laws of motion and how they can be applied to particle dynamics, vibrations, motion in polar coordinates, and conservation laws.  MTHA4004Y  20 
REAL ANALYSIS You 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 
SETS, NUMBERS AND PROBABILITY You will explore basic settheoretic notation, functions, proof by induction, arithmetic, rationals and irrationals, the Euclidean algorithm and the styles of proof. Elementary set theory, modular arithmetic, equivalence relations and countability are also covered during this module. You will study probability as a measurement of uncertainty, statistical experiments and Bayes' theorem as well as discrete and continuous distributions. Expectation. Applications of probability: Markov chains, reliability theory.  MTHA4001Y  20 
Students must study the following modules for 80 credits:
Name  Code  Credits 

ALGEBRA This module will introduce groups and rings. Together with vector spaces these are the most important structures in modern algebra. At the heart of group theory in Semester I is the study of symmetry and the axiomatic development of the theory. Groups appear in many parts of mathematics. The basic concepts are subgroups, Lagrange's theorem, factor groups, group actions and the First Isomorphism Theorem. In Semester II we introduce rings, using the Integers as a model and we will develop the theory with many examples related to familiar concepts such as substitution and factorisation. Important examples of commutative rings are fields, domains, polynomial rings and their quotients.  MTHA5003Y  20 
ANALYSIS You will study the standard basic theory of the complex plane. In the first semester, you will study within the areas of continuity, power series and how they represent functions for both real and complex variables, differentiation, holomorphic functions, CauchyRiemann equations, Moebius transformations. In the second semester, you will study within the areas of topology of the complex plane, complex integration, Cauchy and Laurent theorems, residue calculus.  MTHA5001Y  20 
DIFFERENTIAL EQUATIONS AND APPLIED METHODS You'll gain a solid understanding in the following areas: Ordinary Differential Equations: solution by reduction of order; variation of parameters for inhomogeneous problems; series solution and the method of Frobenius. Legendre's and Bessel's equations: Legendre polynomials, Bessel functions and their recurrence relations; Fourier series; Partial differential equations (PDEs): heat equation, wave equation, Laplace's equation; solution by separation of variables. Method of characteristics for hyperbolic equations; the characteristic equations; Fourier transform and its use in solving linear PDEs; Dynamical Systems: equilibrium points and their stability; the phase plane; theory and applications.  MTHA5004Y  20 
FLUID DYNAMICS  THEORY AND COMPUTATION 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.  MTHA5002Y  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, using the results to better understand, or make predictions about, the original problem. You 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, including approximation and nondimensionalising, and discussion of how a mathematical model is created. You will then apply this theory to a variety of models, such as traffic flow, as well as examples of problems arising in industry.  MTHF5032Y  
MATHEMATICAL STATISTICS Learn the essential concepts of mathematical statistics, deriving the necessary distribution theory as required. Additionally, you'll explore ideas of sampling and central limit theorem, covering estimation methods and hypothesistesting, with the introduction of some Bayesian ideas.  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 from 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. Assessment: Coursework 100%  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, aspect of chemical physics, basic quantum mechanics and special relativity. The module will involve both lectures and workshops, where you will develop analytical thinking and problem solving skills. The module may be taken by any science students who wish to study physics beyond A Level.  PHY4001Y  20 
INTRODUCTION TO BUSINESS (2) How are businesses organised and managed? This module helps nonNorwich Business School students explore the dynamic and everchanging world of business and provides insights into the managerial role. You'll explore the business environment, key environmental drivers and the basic functions of organisations. There will be a review of how organisations are managed in response to various environmental drivers. You will consider some of the current issues faced by every organisation, such as business sustainability, corporate responsibility and internationalisation. This module is designed to provide an overview of the corporate world for nonbusiness specialists, so no previous knowledge of business or business management is required for this module. General business concepts are introduced in lectures and applied in a practical manner during seminars. By the end of this module, you will be able to understand and apply key business concepts and employ a number of analytical tools to help explore the business environment, industry structure and business management. You will be assessed through a range of assignments, for example an individual piece of coursework, group work and an exam. Therefore, the module reinforces fundamental study skills development through a combination of academic writing, presentational skills, teamwork and the practical application of theory. Core business theory is introduced in lectures and applied practically with the use of examples in seminars. By the end of this module you will be able to understand and apply key business concepts and a range of analytical tools to explore the business environment. Introduction to Business facilitates study skills development that is essential across all 3 years of the undergraduate degree by developing academic writing, presentation, team working and communication skills effectively.  NBS4008Y  20 
INTRODUCTION TO FINANCIAL AND MANAGEMENT ACCOUNTING (2) It is vital that everyone working in business has an understanding of accounting data in order that financial information can be used to add value to the organisation. You'll be provided with a foundation in the theory and practice of accounting and an introduction to the role, context and language of financial reporting and management accounting. The module assumes no previous study of accounting. You'll begin with building a set of accounts from scratch so that you will be able to analyse and provide insight form the major financial statements. You'll also look at management decision making tools such as costing, budgeting and financial decision making. You will be required to actively participate in your learning both in lectures and seminars. The module employs a learn by doing approach.  NBS4010Y  20 
INTRODUCTORY MACROECONOMICS This module will introduce you to the economic way of reasoning, exploring how to apply this to a variety of real world macroeconomic issues. You'll begin your journey by learning how to measure macroeconomic aggregates, such as GDP, GDP growth, unemployment and inflation. Establishing the foundations to conduct rigorous Macroeconomics analysis, you'll learn how to identify and characterise equilibrium on the goods market and on the money market. You'll examine policymaking, exploring and evaluating features and applications of fiscal and monetary policy, and grow an appreciation of the methods of economic analysis, such as mathematical modelling, diagrammatic representation, and narrative. Discussion of theoretical frameworks will be enriched by real world applications and supported by an interactive teaching approach.  ECO4006Y  20 
INTRODUCTORY MICROECONOMICS Forming a foundation for subsequent economic modules, this module will introduce you to the fundamental principles, concepts and tools of microeconomics and show you how to apply these to a variety of real world economic issues. There is some mathematical content  you will be required to interpret linear equations, solve simple linear simultaneous equations and use differentiation. The module is primarily concerned with: 1) the ways individuals and households behave in the economy 2) the analysis of firms producing goods and services 3) how goods and services are traded or otherwise distributed  often but not exclusively through markets 4) the role of government as provider and/or regulator.  ECO4005Y  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, although 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 using the Java programming language. The module is designed to meet the needs of the student who has not previously studied programming.  CMP5020B  20 
UNDERSTANDING THE DYNAMIC PLANET Understanding of natural systems is underpinned by physical laws and processes. 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 must study the following modules for credits:
Name  Code  Credits 

Students will select 80  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 gives an introduction to ideas of differential geometry. Key examples will be curves and surfaces embedded in 3dimensional Euclidean space. We will start with curves and will study the curvature and torsion, building up to the fundamental theorem of curve theory. From here we move on to more advanced topics including surfaces.  MTHE6030A  20 
DYNAMICAL OCEANOGRAPHY The ocean is an important component of the Earth's climate system. You will cover mathematical modelling of the largescale ocean circulation and oceanic wave motion. You will build upon the techniques in fluid dynamics and differential equations that you developed in year two. You will then use 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. You will conclude 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 
ELECTRICITY AND MAGNETISM 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 a 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 magnetostatics problems and then timedependent problems (eg electromagnetic waves). We shall also consider how the equations change in an electromagnetic media and look at some simple examples.  MTHE6010A  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. You will be introduced to options, futures and the noarbitrage principle. Mathematical models for various types of options are also discussed. We consider 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 
FLUID STRUCTURE INTERACTION Think of a fish swimming in river or a long container ship vibrating in sea waves. This may give you a clue about fluidstructure interaction (FSI), where a "structure" (fish or ship) moves interacting with a "fluid" (water and/or air). The flow of the fluid is changed by the moving structure which in turn is affected by the fluid loads. The fluid loads depend on the structure motions, and the structure motions depend on the fluid loads. A fluid and a structure cannot be considered separately in the problems you will study in this module. Their motions are coupled. The problems of fluidstructure interaction become even more complex if the structure is deformable. You will study interesting and practical FSI problems from ship hydrodynamics and offshore/coastal engineering, including wave interaction with coastal structures, underwater motions of rigid bodies, water impact onto elastic surfaces and others. The problems will be formulated and methods of their analysis will be presented. The module covers mathematical models of liquid motion and motions of rigid and elastic bodies, coupled problems of FSI and methods to find solutions to such problems. The mathematical techniques include method of separating variables, methods of analytic function theory, and methods of asymptotic analysis.  MTHE6013B  20 
REPRESENTATION THEORY This module gives an introduction the area of representation theory. It introduces you to algebras, representations, modules and related concepts. Important theorems of the module are the JordanHoelder and ArtinWedderburn Theorems.  MTHD6016B  20 
SEMIGROUP THEORY This module introduces you to Semigroup Theory. Semigroups are algebraic objects which generalize groups. They are of interests because they arise naturally in many parts of mathematics, for example, whenever we are composing functions, multiplying matrices, or considering homomorphisms between objects, there are semigroups underlying our mathematics. You will study a class of algebraic objects called semigroups. A semigroup is an algebraic structure consisting of a set together with an associative binary operation. For example, every group is a semigroup, but the converse is far from being true. Semigroups are ubiquitous in pure mathematics: whenever we are composing functions, multiplying matrices, or considering homomorphisms between objects, there are semigroups underlying our mathematics. Finite semigroups are also of importance in the theory of finite automata (an area of theoretical computer science). You will cover the fundamentals of semigroup theory, with the focus on using Green's relations to study their underlying structure. Topics covered will include: definition of semigroups and monoids with examples, idempotents, maximal subgroups, ideals and Rees quotients, Green's relations and regular semigroups, 0simple semigroups, principal factors, Rees matrix semigroups and the Rees theorem.  MTHE6011A  20 
SET THEORY Understand the foundational issues in mathematics and learn the appropriate mathematical framework for discussing 'sizes of infinity'. You will study concepts such as ordinals, cardinals, and the ZermeloFraenkel axioms with the Axiom of Choice. You will also explore 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, and second year Analysis is a desired prerequisite. Set theory plays a dual role in mathematics. It provides a manageable foundation to mathematics and it is itself a sophisticated area of mathematics. The foundational role of set theory consists in providing a reasonable set of assumptions (axioms) which enable us to construct most mathematical objects, and from which most mathematics can be derived by proving theorems based on these axioms. You will explore this system of axioms, known as ZFC (ZermeloFraenkel Axioms with the Axiom of Choice), and demonstrate how it can be used to build the foundations of mathematics. You will participate in discussions around some background foundational issues, including Godel's Incompleteness Theorems and the notion of consistency (these issues will be discussed without proofs), alongside some alternatives to ZFC. You will understand the complete development of the general theory of ordinals and, along with it, be introduced to the methods of transfinite induction and recursion. Armed with these tools, you will be able to see how set theory provides the right framework for studying infinite sets. Examples of such sets are the set of all natural numbers, the set of all rationals, and the set of all real numbers. It turns out that there is a very natural way to assign a notion of size to such sets, providing us with more information than just 'infinite'. According to this notion (cardinality), the first two of the above sets have the same size, which is strictly smaller than that of the third. You will learn how to construct concrete examples of infinite objects in mathematics, such as infinite graphs, almost disjoint families, topological spaces, and groups, and study some of their properties. Finally, if we have time, the limitations of ZFC will be briefly discussed as well as criteria for extending ZFC in a sensible way.  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 unit is suitable for those with an interest in Applied Mathematics.  MTHE6031A  20 
Students will select 0  40 credits from the following modules:
Name  Code  Credits 

HISTORY OF MATHEMATICS You 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. You will explore the rise of calculus and algebra from the time of Greek and Indian mathematicians, up to the era of Newton and Leibniz. We also discuss other topics, such as mathematical logic: ideas of propositions, axiomatisation and quantifiers. Our style is to explore mathematical practice and conceptual developments, in different historical and geographical settings.  MTHA6002A  20 
MATHEMATICS PROJECT This module is reserved for third year students who have completed an appropriate number of mathematics modules at levels 4 and 5. It is a project on a mathematical topic supervised by a member of staff within the school, or in a closely related school. 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 The aim of the module is to show how environmental problems may be solved from the initial problem, to mathematical formulation and numerical solution. Problems will be described conceptually, then defined mathematically, then solved numerically via computer programming. The module consists of lectures on numerical methods and computing practicals; the practicals being designed to illustrate the solution of problems using the methods covered in lectures. The module will guide students through the solution of a model of an environmental process of their own choosing. The skills developed in this module are highly valued by prospective employers.  ENV6004A  20 
THE LEARNING AND TEACHING OF MATHEMATICS This module will introduce you to the study of the teaching and learning of mathematics with a particular focus on secondary and post compulsory level. You'll also explore theories of learning and teaching of mathematical concepts typically included in the secondary and post compulsory curriculum, and study mathematics knowledge for teaching. If you're 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. Assessment: Written Assignment 40% 3000 words Mini Project 60% 4500 words  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 or Climate Change degrees.  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. Assessment: Coursework 100%  EDUB5012A  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, using the results to better understand, or make predictions about, the original problem. You 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, including approximation and nondimensionalising, and discussion of how a mathematical model is created. You will then apply this theory to a variety of models, such as traffic flow, as well as examples of problems arising in industry.  MTHF5032Y  
MATHEMATICAL STATISTICS Learn the essential concepts of mathematical statistics, deriving the necessary distribution theory as required. Additionally, you'll explore ideas of sampling and central limit theorem, covering estimation methods and hypothesistesting, with the introduction of some Bayesian ideas.  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, although 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. You should be familiar with partial differentiation, integration, handling equations and using calculators. Shelf Sea Dynamics is a natural followon module and builds on some of the concepts introduced here. We strongly recommend that you also gain oceanographic fieldwork experience by taking the 20credit biennial Marine Sciences field course.  ENV5016A  20 
PROGRAMMING FOR NONSPECIALISTS The purpose of this module is to give you a solid grounding in the essential features of programming using the Java programming language. The module is designed to meet the needs of the student who has not previously studied programming.  CMP5020B  20 
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, looking at how information is released in scientific literature and how this is subsequently picked up by the public press will provide you with an understanding of the importance 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.  ENV5017B  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 ONLY AVAILABLE TO STUDENTS REGISTERED ON MMATH IN SCHOOL OF MATHEMATICS. This module is modelled on the Mathematics MMath project module MTHMA9Y. However, in this case it consists of a supervised dissertation on a topic in the general area of probability or statistics. It may involve some computation, this will depend on the topic chosen.  CMP7017Y  40 
Students will select 80 credits from the following modules:
Name  Code  Credits 

DIFFERENTIAL GEOMETRY WITH ADVANCED TOPICS This module gives 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 other topics, including surfaces, and 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. In this module, you will cover mathematical modelling of the largescale ocean circulation and oceanic wave motion. You will build 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. You will conclude 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 
ELECTRICITY AND MAGNETISM WITH ADVANCED TOPICS 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 magnetostatics problems and then timedependent problems (eg electromagnetic waves). We shall also consider how the equations change in an electromagnetic media and look at some simple examples. The advanced topic will be on nonlinear models of magnetic materials.  MTHE7010A  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. You will be introduced to options, futures and the noarbitrage principle. Mathematical models for various types of options are also discussed. We consider 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 
FLUID STRUCTURE INTERACTION WITH ADVANCED TOPICS Think of a fish swimming in river or a long container ship vibrating in sea waves. This may give you a clue about fluidstructure interaction (FSI), where a "structure" (fish or ship) moves interacting with a "fluid" (water and/or air). The flow of the fluid is changed by the moving structure which in turn is affected by the fluid loads. The fluid loads depend on the structure motions, and the structure motions depend on the fluid loads. A fluid and a structure cannot be considered separately in the problems you will study in this module. Their motions are coupled. The problems of fluidstructure interaction become even more complex if the structure is deformable. You will study interesting and practical FSI problems from ship hydrodynamics and offshore/coastal engineering, including wave interaction with coastal structures and very large floating structures, underwater motions of rigid bodies, water impact onto elastic surfaces and others. The problems will be formulated and methods of their analysis will be presented. The module covers mathematical models of liquid motion and motions of rigid and elastic bodies, coupled problems of FSI and methods to find solutions to such problems. The mathematical techniques include method of separating variables, methods of analytic function theory, variational inequalities and methods of asymptotic analysis. The advanced part of the module will consider problems with unknown (in advance) contact region between water and the surface of the structure. In such problems, the area of the body surface, where the fluid loads are applied, should be determined as part of the solution. You will study water entry problem, ship slamming and water wave impact problems by advanced mathematical techniques.  MTHE7013B  20 
REPRESENTATION THEORY WITH ADVANCED TOPICS This module gives an introduction the area of representation theory. It introduces you to algebras, representations, modules and related concepts. Important theorems of the module are the JordanHoelder and ArtinWedderburn Theorems.  MTHD7016B  20 
SEMIGROUP THEORY WITH ADVANCED TOPICS This module introduces you to Semigroup Theory. Semigroups are algebraic objects which generalize groups. They are of interests because they arise naturally in many parts of mathematics, for example, whenever we are composing functions, multiplying matrices, or considering homomorphisms between objects, there are semigroups underlying our mathematics. You will study a class of algebraic objects called semigroups. A semigroup is an algebraic structure consisting of a set together with an associative binary operation. For example, every group is a semigroup, but the converse is far from being true. Semigroups are ubiquitous in pure mathematics: whenever we are composing functions, multiplying matrices, or considering homomorphisms between objects, there are semigroups underlying our mathematics. Finite semigroups are also of importance in the theory of finite automata (an area of theoretical computer science). You will cover the fundamentals of semigroup theory, with the focus on using Green's relations to study their underlying structure. Topics covered will include: definition of semigroups and monoids with examples, idempotents, maximal subgroups, ideals and Rees quotients, Green's relations and regular semigroups, 0simple semigroups, principal factors, Rees matrix semigroups and the Rees theorem. In the advanced topic you will learn about an important finiteness property in semigroup theory called residual finiteness.  MTHE7011A  20 
SET THEORY WITH ADVANCED TOPICS You will explore foundational issues in mathematics and 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. Main topics covered include: 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 considered. This module requires some knowledge of hydrodynamics and multivariable calculus. The unit is suitable for those with an interest in Applied Mathematics.  MTHE7031A  20 
Disclaimer
Whilst the University will make every effort to offer the modules listed, changes may sometimes be made arising from the annual monitoring, review and update of modules and regular (fiveyearly) review of course programmes. Where this activity leads to significant (but not minor) changes to programmes and their constituent modules, there will normally be prior consultation of students and others. It is also possible that the University may not be able to offer a module for reasons outside of its control, such as the illness of a member of staff or sabbatical leave. In some cases optional modules can have limited places available and so you may be asked to make additional module choices in the event you do not gain a place on your first choice. Where this is the case, the University will endeavour to inform students.Further Reading

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