MMath Master of Mathematics

Key details

MMATH MASTER OF MATHEMATICS

Start Year

2021

Attendance

Full Time

Award

Degree of Master of Mathematics

UCAS course code

G103

Entry Requirements

AAB

Duration (years)

Our prestigious four-year 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 – as well as engaging in the study of essential mathematical theory and technique – you’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 – 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.

About

Our four-year 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 three-year 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, research-led 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 world-class lecturers.

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Course Reference Number: 1545401

Important Information

Whilst the University will make every effort to offer the courses listed, changes may sometimes be made arising from the regular review of course programmes. Where this activity leads to significant (but not minor) changes to programmes, there will normally be prior consultation of students and others. Changes may for example consist of variations to the content and method of delivery of programmes, courses and other services, to discontinue programmes, courses and other services and to merge or combine programmes or courses. The University will endeavour to keep such changes to a minimum, and will inform students.

Assessment for Year 1

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.

Structure

The first two years of our Masters course run in parallel with our three-year 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.

The first year will develop your skills in calculus and other topics which you may have covered at A-level, 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, you’ll be introduced to mathematical software, which will be invaluable in your individual fourth year MMath project.

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 world-leading (REF 2014), so you can be sure you’ll be learning in the most up-to-date of environments.

New material will usually be delivered through lectures, which are complemented by online notes and workshops, where you’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 you’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, you’ll work with your academic advisor and the same six or seven students each week. It’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 university-level mathematics, you’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 face-to-face feedback on exercises you’ve attempted.

Prior to undertaking formal coursework (which will contribute to your module mark), you’ll submit answers to questions based on similar material for comments from the lecturer. The feedback you receive will then help with your coursework.

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Assessment for Year 2

Structure

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 you’ve already studied can be applied to meteorology.

Teaching and Learning

Individual Study

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Assessment for Year 3

Structure

By year three there are no compulsory modules. Instead you’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 you’ll use this year to focus on these topics, laying the foundations for a successful final-year research project.

Teaching and Learning

Individual Study

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Assessment for Year 4

Structure

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 “The Mobius function of Finite Groups” to “The Aerodynamics of Golf Balls” (a topic suggested by the student). In order to be assessed, you’ll submit a written report on the project, and you’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 Master’s-level modules that explore topics such as Lie Algebras, fluid-structure 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

Individual Study

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Assessment for Year 1

Compulsory Modules

MATHEMATICAL SKILLS

Code MTHA4001A

Credits 20

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.

PROBABILITY

Code MTHA4001B

Credits 10

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 decision-making. 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 computer-lab sessions of (2 hours each) where you will apply probability theory to specific everyday life case studies. The only pre-requisites 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 A-level you will rediscover its contents now taught using a proper and more elegant mathematical formalism.

REAL ANALYSIS

Code MTHA4003Y

Credits 20

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.

ALGEBRA 1

Code MTHA4006Y

Credits 20

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.

COMPUTATION AND MODELLING

Code MTHA4007Y

Credits 20

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.

CALCULUS AND MULTIVARIABLE CALCULUS

Code MTHA4008Y

Credits 30

In this module you will study: (a) Complex numbers. (b) Vectors. (c) Differentiation; power series. (d) Integration: applications, curve sketching, area, arc-length. (e) First and second-order, constant-coefficient ordinary differential equations. Reduction of order. Numerical solutions using MAPLE. Partial derivatives, chain rule. (f) Line integrals. Multiple integrals, including change of coordinates by Jacobians. Green's Theorem in the plane.

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Important Information

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. Where this activity leads to significant (but not minor) changes to programmes and their constituent modules, the University will endeavour to consult with 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. 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 inform students.

Assessment for Year 2

Compulsory Modules

DIFFERENTIAL EQUATIONS AND APPLIED METHODS

Code MTHA5004Y

Credits 20

(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.

COMPLEX ANALYSIS

Code MTHA5006Y

Credits 20

This module covers the standard basic theory of the complex plane. The areas covered in the first semester, (a), and the second semester, (b), are roughly the following: (a) Continuity, power series and how they represent functions for both real and complex variables, differentiation, holomorphic functions, Cauchy-Riemann equations. (b) Topology of the complex plane, complex integration, Cauchy and Laurent theorems, residue calculus.

INVISCID FLUID FLOW

Code MTHA5007Y

Credits 20

This module will introduce the student to fundamental principles and ideas in the study of fluid dynamics, including flow kinematics and dynamics.

ALGEBRA II

Code MTHA5008Y

Credits 20

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, rank-nullity 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.

Optional A Modules

(20-40 credits)

MATHEMATICAL STATISTICS

Code CMP-5034A

Credits 20

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 hypothesis-testing.

INTRODUCTION TO QUANTUM MECHANICS AND SPECIAL RELATIVITY

Code MTHF5030Y

Credits 20

This module introduces you to quantum mechanics and special relativity. In quantum mechanics focus will be on: 1. Studying systems involving very short length scales – eg structure of atoms. 2. Understanding why the ideas of classical mechanics fail to describe physical effects when sub-atomic particles are involved. 3. Deriving and solving the Schrodinger equation. 4. Understanding the probabilistic interpretation of the Schrodinger equation. 5. Understanding how this equation implies that certain physical quantities such as energy do not vary continuously, but can only take on discrete values. The energy levels are said to be quantized. For special relativity, the general concept of space and time drastically changes for an observer moving at speeds close to the speed of light: for example time undergoes a dilation and space a contraction. These counterintuitive phenomena are however direct consequences of physical laws. The module will also explain the basis of Special Relativity using simple mathematics and physical intuition. Important well-known topics like inertial and non-inertial frames, the Lorentz transformations, the concept of simultaneity, time dilation and Lorentz contraction, mass and energy relation will be explained. The module will end with the implications of special relativity and quantum mechanics on a relativistic theory of quantum mechanics.

TOPOLOGY AND GRAPH THEORY

Code MTHF5033Y

Credits 20

Topology and Graph Theory

Optional B Modules

(0-20 credits)

PROGRAMMING FOR NON-SPECIALISTS

Code CMP-5020B

Credits 20

You will be introduced to a number of programming concepts at the start of your programming career, using a modern programming language common to many digital industries, with specific focus on applications within STEM fields. We structure learning through lectures, delivering core materials, and tutor supported exercises to reinforce learning, and to prepare you for programming in your following studies.

TIME SERIES

Code CMP-5042B

Credits 10

This module considers both the theory and practice of statistical modelling of time series. Students will be expected to analyse real data using R.

LINEAR REGRESSION USING R

Code CMP-5043B

Credits 10

This is a module designed to give you the opportunity to apply linear regression techniques using R. While no advanced knowledge of probability and statistics is required, we expect you to have some background in probability and statistics before taking this module. The aim is to provide an introduction to R and then provide the specifics in linear regression.

INTRODUCTORY MACROECONOMICS

Code ECO-4006Y

Credits 20

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 characterize equilibrium on the goods market and on the money market. The module will also introduce students to policy-making, 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.

EDUCATIONAL PSYCHOLOGY

Code EDUB5012A

Credits 20

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.

INTRODUCTION TO FINANCIAL AND MANAGEMENT ACCOUNTING

Code NBS-4108B

Credits 20

This module provides a foundation in the theory and practice of accounting and an introduction to the role, context and language of financial reporting and management accounting. The module assumes no previous study of accounting. It is be taken to provide a foundation to underpin subsequent specialist studies in accounting.

ELECTROMAGNETISM, OPTICS, RELATIVITY AND QUANTUM MECHANICS

Code PHY-4001Y

Credits 20

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.

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Important Information

Assessment for Year 3

Compulsory Modules

Optional A Modules

(60-100 credits)

ADVANCED STATISTICS

Code CMP-6004A

Credits 20

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.

MATHEMATICAL LOGIC

Code MTHD6015A

Credits 20

Mathematical logic analyses symbolically the way in which we reason formally, particularly about mathematical structures. The ideas have applications to other parts of Mathematics, as well as being important in theoretical computer science and philosophy. We give a thorough treatment of predicate and propositional logic and an introduction to model theory.

DYNAMICAL METEOROLOGY

Code MTHD6018B

Credits 20

Dynamical meteorology is a core subject on which weather forecasting and the study of climate and climate change are based. This module applies fluid dynamics to the study of the circulation of the Earth's atmosphere. The fluid dynamical equations and some basic thermodynamics for the atmosphere are introduced. These are then applied to topics such as geostrophic flow, thermal wind and the jet streams, boundary layers, gravity waves, the Hadley circulation, vorticity and potential vorticity, Rossby waves, and equatorial waves. Emphasis will be placed on fluid dynamical concepts as well as on finding analytical solutions to the equations of motion.

FLUID DYNAMICS

Code MTHD6020A

Credits 20

Fluid dynamics has wide ranging applications across nature, engineering, and biology. From understanding the behaviour of ocean waves and weather, designing efficient aircraft and ships, to capturing blood flow, the ability the understand and predict how fluids (liquids and gasses) behave is of fundamental importance. This Module considers mathematical models of fluids, particularly including viscosity (or stickiness) of a fluid. Illustrated by practical examples throughout, we develop the governing differential Navier-Stokes equations, and then consider their solution either finding exact solutions, or using analytical techniques to obtain solutions in certain limits (for example low viscosity or high viscosity).

MATHEMATICAL BIOLOGY

Code MTHD6021A

Credits 20

Mathematical Biology is a rapidly developing and hugely exciting field with many areas the focus of dedicated research. In this module you will discover how to use the mathematics you have learned to date to understand a wide range of interesting biological problems. In many cases, important biological insights can be gained from quite simple mathematical models. Examples include the diffusion-limited growth of solid tumours, and the reasons why animal coats patterns are so widely varied - for example, why does the tiger have stripes and the leopard have spots? Mathematics has made fundamental contributions in these and many other areas which we will explore during the module. Further examples may include the propagation of wave-fronts in migrating animal populations, blood flow in arteries and veins and the onset of arterial disease, cochlear mechanics in the ear, and tear film dynamics on the human eye. No prior knowledge of biology is required to be able to take this module.

CRYPTOGRAPHY

Code MTHD6025B

Credits 20

Cryptography is the science of coding and decoding messages so as to keep these messages secure, and has been used throughout history. In the past, encryption was mainly used by a small number of individuals in positions of authority. Nowadays the universal presence of the internet and e-commerce means that we all have transactions that we want to keep secret. The speed of modern home computers means that an encrypted message that would have been perfectly secure (that is, would have taken an inordinately long time to break) a few decades ago can now be broken in seconds. But as decryption methods have advanced, the methods of encryption have also become more sophisticated. Modern cryptosystems depend on mathematics, in particular Number Theory and Algebra. The most famous example of a public key cryptosystem, RSA, relies on the fact that it is 'hard' to factor a large number into a product of primes. In this course, we will look at the mathematics underpinning both classical and modern methods of cryptography and consider how these methods can be applied. This course will compare material on symmetric key cryptography and public key cryptography. Examples of both will be given, along with discussion of their strengths and weaknesses, with the emphasis being on the mathematics. We will look at how prime numbers can be used in cryptography, with material on primality testing and factorisation. We will also define and study elliptic curves in order to investigate the relatively new field of elliptic curve cryptography.

ADVANCED MATHEMATICAL TECHNIQUES

Code MTHD6032B

Credits 20

We provide techniques for a wide range of applications, while stressing the importance of rigor in developing such techniques. The Calculus of Variations includes techniques for maximising integrals subject to constraints. A typical problem is the curve described by a heavy chain hanging under the effect of gravity. We develop techniques for algebraic and differential equations. This includes asymptotic analysis, which provides approximate solutions when exact solutions can not be found and when numerical solutions are difficult. Integral transforms are useful for solving problems including integro-differential equations. This unit will include illustration of concepts using numerical investigation with MAPLE and/or MATLAB.

FUNCTIONAL ANALYSIS

Code MTHD6033B

Credits 20

This course will cover normed spaces; completeness; functionals; Hahn-Banach theorem; duality; and operators. Time permitting, we shall discuss Lebesgue measure; measurable functions; integrability; completeness of L-p spaces; Hilbert space; compact, Hilbert-Schmidt and trace class operators; as well as the spectral theorem.

ALGEBRAIC TOPOLOGY

Code MTHD6034A

Credits 20

GALOIS THEORY

Code MTHE6004B

Credits 20

A prerequisite of this module is that you have studied the Algebra module. Galois theory is one of the most spectacular mathematical theories. It gives a beautiful connection between the theory of polynomial equations and group theory. In fact, many fundamental notions of group theory originated in the work of Galois. For example, why are some groups called solvable ? Because they correspond to the equations which can be solved (by some formula based on the coefficients and involving algebraic operations and extracting roots of various degrees). Galois theory explains why we can solve quadratic, cubic and quartic equations, but no similar formulae exist for equations of degree greater than 4. In modern exposition, Galois theory deals with field extensions , and the central topic is the Galois correspondence between extensions and groups.

Optional B Modules

(20-60 credits)

THE LEARNING AND TEACHING OF MATHEMATICS

Code EDUB6014A

Credits 20

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.

MODELLING ENVIRONMENTAL PROCESSES

Code ENV-6004A

Credits 20

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.

HISTORY OF MATHEMATICS

Code MTHA6002A

Credits 20

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.

MATHEMATICS PROJECT

Code MTHA6005Y

Credits 20

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 in-depth report on your topic, using the mathematical typesetting system LaTeX. You will also give a short oral presentation on your topic.

Optional C Modules

(0-20 credits)

SCIENCE COMMUNICATION

Code BIO-6018Y

Credits 20

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.

PROGRAMMING FOR NON-SPECIALISTS

Code CMP-5020B

Credits 20

MATHEMATICAL STATISTICS

Code CMP-5034A

Credits 20

EDUCATIONAL PSYCHOLOGY

Code EDUB5012A

Credits 20

CHILDREN, TEACHERS AND MATHEMATICS

Code EDUB6006A

Credits 20

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.

APPLIED GEOPHYSICS

Code ENV-5004B

Credits 20

In this module you will learn about the processes that shape the Earth's shallow subsurface, and how to detect and map subsurface structures and resources. Physical properties of solid materials and subsurface fluids will be explored, including how fluid movement affects these properties. Methods to image the subsurface will be introduced using real datasets, collected by the class where possible. We will apply the theory to real-life problems including risk mitigation, engineering and resource exploration. This module will include fieldwork on campus where possible, specialist computer software, and some light mathematical analysis (trigonometry, rearranging linear equations, logarithms).

METEOROLOGY I

Code ENV-5008A

Credits 20

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.

WEATHER APPLICATIONS

Code ENV-5009B

Credits 20

This module will build upon material covered in Meteorology I, by covering topics such as synoptic meteorology, weather hazards, micro-meteorology, further thermodynamics and weather forecasting. The module includes a major summative coursework assignment based on data collected on a UEA meteorology fieldcourse in a previous year.

CLIMATE SYSTEMS

Code ENV-6025B

Credits 20

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.

INTRODUCTION TO QUANTUM MECHANICS AND SPECIAL RELATIVITY

Code MTHF5030Y

Credits 20

TOPOLOGY AND GRAPH THEORY

Code MTHF5033Y

Credits 20

Topology and Graph Theory

KNOWLEDGE SCIENCE AND PROOF FOR SECOND YEARS

Code PPLP5175B

Credits 20

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.

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Important Information

Assessment for Year 4

Compulsory Modules

MATHEMATICS DISSERTATION

Code MTHA7029Y

Credits 40

You will complete a fourth year dissertation on a mathematical topic. This is a compulsory part of the Master of Mathematics degree.

Optional A Modules

(80 credits)

MATHEMATICAL LOGIC WITH ADVANCED TOPICS

Code MTHD7015A

Credits 20

Mathematical Logic analyses symbolically the way in which we reason formally, particularly about mathematical structures. The ideas have applications to other parts of Mathematics, as well as being important in theoretical computer science and philosophy. We give a thorough treatment of predicate and propositional logic and an introduction to model theory.

FLUID DYNAMICS WITH ADVANCED TOPICS

Code MTHD7020A

Credits 20

Fluid dynamics has wide ranging applications across nature, engineering, and biology. From understanding the behaviour of ocean waves and weather, designing efficient aircraft and ships, to capturing blood flow, the ability to understand and predict how fluids (liquids and gasses) behave is of fundamental importance. You will consider mathematical models of fluids, particularly including viscosity (or stickiness) of a fluid. Illustrated by practical examples throughout, you will develop the governing differential Navier-Stokes equations, and then consider their solution either finding exact solutions, or using analytical techniques to obtain solutions in certain limits (for example low viscosity or high viscosity).

MATHEMATICAL BIOLOGY WITH ADVANCED TOPICS

Code MTHD7021A

Credits 20

Mathematical Biology is a rapidly developing and hugely exciting field with many areas the focus of dedicated research. In this module, you will discover how to use the mathematics you have learned to date to understand a wide range of interesting biological problems. In many cases, important biological insights can be gained from quite simple mathematical models. Examples include the diffusion-limited growth of solid tumours, and the reasons why animal coats patterns are so widely varied - for example, why does the tiger have stripes and the leopard have spots? Mathematics has made fundamental contributions in these and many other areas which we will explore during the module. Further examples may include the propagation of wave-fronts in migrating animal populations, blood flow in arteries and veins and the onset of arterial disease, cochlear mechanics in the ear, and tear film dynamics on the human eye. No prior knowledge of biology is required to be able to take this module.

CRYPTOGRAPHY WITH ADVANCED TOPICS

Code MTHD7025B

Credits 20

Cryptography is the science of coding and decoding messages to keep them secure, and has been used throughout history. While previously only a few people in authority used cryptography, the internet and e-commerce mean that we now all have transactions that we want to keep secret. The speed of modern computers means messages encrypted using techniques from just a few decades ago can now be broken in seconds; thus the methods of encryption have also become more sophisticated. In this module, we will explore some of the mathematics behind cryptography and how to apply it. This includes standard material from elementary number theory, including primality testing and methods of factorization and their application to symmetric key and public key cryptography, including Diffie-Hellman Key exchange, RSA and ElGamal. The last section of the course will be on elliptic curve cryptography. There will be additional material on an advance topic, to be determined.

MATHEMATICAL TECHNIQUES WITH ADVANCED TOPICS

Code MTHD7032B

Credits 20

This unit provides a selection of techniques applicable to mathematical problems in a wide range of applications, while at the time stressing the importance of rigor in developing such techniques. Topics to be studied include calculus of variation, asymptotic analysis, Green’s functions and Integral transforms. There will be in depth study of other aspects of asymptotic theory, including Matched Asymptotic Expansions and the WKB approximation. This unit will include illustration of concepts using numerical investigation with MAPLE and MATLAB.

FUNCTIONAL ANALYSIS WITH ADVANCED TOPICS

Code MTHD7033B

Credits 20

ALGEBRAIC TOPOLOGY WITH ADVANCED TOPICS

Code MTHD7034A

Credits 20

GALOIS THEORY WITH ADVANCED TOPICS

Code MTHE7004B

Credits 20

A prerequisite of this module is that you have studied the Algebra module. Galois theory is one of the most spectacular mathematical theories. It gives a beautiful connection between the theory of polynomial equations and group theory. In fact, many fundamental notions of group theory originated in the work of Galois. For example, why are some groups called solvable ? Because they correspond to the equations that can be solved (by some formula based on the coefficients, involving algebraic operations, and extracting roots of various degrees). Galois theory explains why we can solve quadratic, cubic and quartic equations, but no similar formulae exist for equations of degree greater than 4. In modern exposition, Galois theory deals with field extensions , and the central topic is the Galois correspondence between extensions and groups. The advanced topic concerns the so-called Inverse Galois problem : does every group correspond to some polynomial, and is the answer dependent on the base field?

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Entry Requirements

A Levels

AAB including an A in Mathematics or ABB including A in Mathematics and B in Further Mathematics or ABB with an A in Mathematics and the Extended Project. Scince A Levels to include a pass in the practical element

BTEC

DDD alongside grade A in A level Maths. Excludes BTEC Public Services, BTEC Uniformed Services and BTEC Business Administration

Scottish highers advanced

BBC including grade B in Mathematics

Irish leaving certificate

4 subjects at H2 including Mathematics and 2 subjects at H3

Access course

Pass the Access to HE Diploma with Distinction in 36 credits at Level 3 and Merit in 9 credits at Level 3, including 12 Level 3 Maths credits. Interview required

European Baccalaureate

80% overall including 85% in Mathematics

International Baccalaureate

33 points including HL6 in Mathematics

GCSE offer

You are required to have Mathematics and English Language at a minimum of Grade C or Grade 4 or above at GCSE.

Additional entry requirements

Science A-levels must include a pass in the practical element.

A-Level 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:

BSc Mathematics with a Foundation Year

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 Mathematics and Actuarial Sciences

International Foundation in Physical Sciences and Engineering

Alternative Qualifications

UEA recognises that some students take a mixture of International Baccalaureate IB or International Baccalaureate Career-related 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

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: 6.0 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.

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:

Pre-sessional English at INTO UEA

Academic English at INTO UEA

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

This course is open to UK, EU and International applicants. The annual intake for this course is in September each year.

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Course Reference Number: 1545401

MMath MASTER OF MATHEMATICS