Mathematics

MMath MASTER OF MATHEMATICS (WITH A YEAR ABROAD)

Key details 

MMATH MASTER OF MATHEMATICS (WITH A YEAR ABROAD)

Start Year
2021
Attendance
Full Time
Award
Degree of Master of Mathematics
UCAS course code
G10A
Entry Requirements
AAB
Duration (years)
4

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.

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Assessment for Year 2

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.

Admissions Live Chat   
Register interest   
Open Days   
Admissions Live Chat   
Register interest   
Open Days   

Assessment for Year 4

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.

Admissions Live Chat   
Register interest   
Open Days   

NOTE: 2021 Course Profile below as a backup save (dated 23 Feb)

 

Year 1

Compulsory Modules (120 Credits)

Code MTHA4001A   (20 Credits)

The module 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.

Code MTHA4001B  (10 Credits)

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.

Code MTHA4003B  (20 Credits)

In the Real Analysis thread, this module extends the material studied in the first semester module “Linear algebra, sequences and series” (MTHA4003A) We learn about limits of functions and continuity before moving on to study precise definitions of differentiation and integration. This then leads to the Fundamental Theorem of Calculus. We are introduced to Group Theory via the study of symmetry and Group Axioms.  The basic concepts are subgroups, Lagrange’s theorem, factor groups, group actions and the Isomorphism Theorem.

Code MTHA4003A  (20 Credits) 

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. 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. Another topic underlying all mathematics is Real Analysis. We will explore the mathematical notion of a limit and see the precise definition of the limit of a sequence of real numbers and learn how to prove that a sequence converges to a limit. After studying limits of infinite sequences, we move on to series, which capture the notion of an infinite sum.

Code MTHA4007Y  (20 Credits)

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.

Code MTHA4008Y  (30 Credits)

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.

 

Year 2

Compulsory Modules (80 Credits)

Code MTHA5002A  (20 Credits)

In this module, building on knowledge from Calculus, you will develop skills in a variety of mathematical techniques for solving differential equations, and how they can be applied to model a range of applications. As a particular focus, you will consider how we can describe mathematically how a fluid behaves. Techniques for solving differential equations will consider both Ordinary Differential Equations, including series solutions and the method of Frobenius, and Partial Differential Equations, where the method of separation of variables will be introduced. Fourier series (representations of functions as infinite series in Sin and Cos) are also considered. You will also discover the fundamentals of Vector Calculus, how differentiation can be applied to vector fields such as fluid velocity. You will encounter a variety of important Partial Differential Equations from applied mathematics, including deriving the heat equation and the wave equation. The knowledge of vector calculus will also be applied to formulating the differential equations that govern fluid flows, and solving problems such as the flow out of a reservoir.

Code MTHA5003A  (20 Credits)

One thread of this module covers the standard basic theory of the complex plane. The areas covered include continuity, power series and how they represent functions for both real and complex variables, differentiation, holomorphic functions, Cauchy-Riemann equations. The second thread follows on from the Linear Algebra studied in Year One. We introduce the concept of a vector space over a field. Throughout the module we will see examples of different vector spaces which will illustrate the results presented. We will learn about vector subspaces. We will see the definition of a basis of a vector space, why this construction is useful and how we can then talk about the dimension of the space. We will then look at linear transformations between pairs of vector spaces, which will lead to the definitions of the kernel and the image of a linear transformation and hence to the rank-nullity theorem. We will see how by fixing bases, a linear transformation can be encoded in matrix form and how changing the bases changes that matrix, which will lead on to the study of eigenvectors and the diagonalization of matrices.

Code  MTHA5002B  (20 Credits)

A range of methods applicable to solving physical problems are studied, including the Method of Characteristics for solving Partial Differential Equations and Fourier Transforms. This is followed by an introduction to Dynamical Systems – understanding the behaviour of nonlinear differential equations. In the other part of this module, solving equations of fluid flow are considered using both numeric and analytic methods.

Code MTHA5003B  (20 Credits)

Study of complex integration will include consideration of the topology of the complex plane along with proof of the Cauchy and Laurent theorems along with applications including residue calculus. The other area of mathematics studied in this module is Ring Theory. After 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 Range  (20-40 Credits) 

Code CMP-5034A  (20 Credits)

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.

Code MTHF5031Y  (20 Credits)

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 Cayley-Hamilton theorem and the Jordan normal form of a matrix.

Code MTHF5032Y - (20 Credits)

Mathematical modelling is concerned with how to convert real problems, such as those arising in industry or other sciences, into mathematical equations, and then solving them and using the results to better understand, or make predictions about, the original problem. This topic will look at techniques of mathematical modelling, examining how mathematics can be applied to a variety of real problems and give insight in various areas. The topics will include approximation and non-dimensionalising, and discussion of how a mathematical model is created. We will then apply this theory to a variety of models such as traffic flow as well as examples of problems arising in industry. We will consider population modelling, chaos, and aerodynamics.

Optional B Range  (0-20 Credits)

Code ECO-4006Y  (20 Credits)

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. 

Code  EDUB5012A  (20 Credits)

This module will provide you with an introduction to key areas of psychology with a focus on learning and teaching in education.

Code CMP-5020B (20 Credits)

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.

Code PHY-4003A (20 Credits)

In this module, you will learn about the methods used to model the physics of the Earth and Universe. You will explore the energy, mechanics, and physical processes underpinning Earth's systems. This includes the study of its formation, subsequent evolution and current state through the understanding of its structure and behaviour - from our planet's interior to the dynamic surface and into the atmosphere. In the second part of this module, you will study aspects of astrophysics including the history of astrophysics, radiation, matter, gravitation, astrophysical measurements, spectroscopy, stars and some aspects of cosmology. You will learn to predict differences between idealised physics and real life situations. You will also improve your skills in problem solving, written communication, information retrieval, poster design, information technology, numeracy and calculations, time management and organisation.

Code CMP-5042B (10 Credits)

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

Code CMP-5043B (10 Credits)

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.

Code NBS-4108B (20 Credits)

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. 

Code ENV-5043A - (20 Credits)

The weather affects everyone and influences decisions that are made continuously around the world. From designing and siting a wind farm to assessing flood risk and public safety, weather plays a vital role. Have you ever wondered what actually causes the weather we experience, for example why large storms are so frequent across north western Europe, especially in Winter? In this module you will learn the fundamentals of the science of meteorology. We will concentrate on the physical processes that underpin the radiation balance, thermodynamics, wind-flow, atmospheric stability, weather systems and the water cycle. We will link these to renewable energy and the weather we experience throughout the Semester. Assessment will be based entirely on a set of practical reports that you will submit, helping you to spread your work evenly through the semester. You will learn how Weather is a rich fusion of descriptive and numerical elements and you will be able to draw effectively on your own skill strengths while practising and developing others, guided by Weatherquest’s Meteorologists.

 

Year 3

Compulsory Module (120 Credits)

Code MTHX6014Y (120 Credits)

A year studying abroad.

 

Year 4

Compulsory Module (40 Credits)

Code MTHA7029Y (40 Credits)

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

Optional Range A (80 Credits)

Code MTHE70003B (20 Credits)

Zermelo-Fraenkel set theory. The Axiom of Choice and equivalents. Cardinality, countability, and uncountability. Trees, Combinatorial set theory. Advanced topic: Constructibility. 

Code MTHE7007B (20 Credits)

The ocean is an important component of the Earth's climate system. This module covers mathematically modelling of the large-scale ocean circulation and oceanic wave motion. This module builds upon the techniques in fluid dynamics and differential equations that you developed in previous years of study. It then uses these techniques to explain some interesting phenomena in the ocean that are relevant to the real world. We begin by examining the effects of rotation on fluid flows. This naturally leads to the important concept of geostrophy, which enables ocean currents to be inferred from measurements of the sea surface height or from vertical profiles of seawater density. Geostrophy also plays a key role in the development of a model for the global scale circulation of abyssal ocean. The role of the wind in driving the ocean will be examined. This enables us to model the large-scale circulation of the ocean including the development of oceanic gyres and strong western boundary currents, such as the Gulf Stream. The module concludes by examining the role of waves, both at the sea surface and internal to the ocean. The differences between wave motion at mid-latitudes and the Equator are examined, as is the roll of the Equator as a wave-guide. The equatorial waves that you will study are intimately linked with the El Niño phenomenon that affects the climate throughout the globe. The advanced topic is a study of barotropic and baroclinic instability.

Code MTHE7026B (20 Credits)

The Mathematical Modelling of Finance is a relatively new area of application of mathematics yet it is expanding rapidly and has great importance for world financial markets. The module is concerned with the valuation of financial instruments known as derivatives. Introduction to options, futures and the no-arbitrage principle. Mathematical models for various types of options are discussed. We consider also Brownian motion, stochastic processes, stochastic calculus and Ito's lemma. The Black-Scholes 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.

Code MTHE7030A (20 Credits)

This module will give an introduction to ideas of differential geometry. Key examples will be curves and surfaces embedded in 3-dimensional Euclidean space. We will start with curves and will study the curvature and torsion, building up to the fundamental theorem of curve theory. From here we move on to tangent spaces and the first and second fundamental forms, Gaussian curvature, and further topics, including the advanced topics for 4th year students.  

Code MTHE7031B (20 Credits)

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 multi-variable calculus. The module is suitable for those with an interest in Applied Mathematics.

Code MTHE7032A (20 Credits)

This module covers the laws of physics described by quantum mechanics that govern the behaviour of microscopic particles. The module will focus on non-relativitic quantum mechanics that is described by the Schrodinger equation. Time-dependent and time-independent solutions will be presented in different contexts including an application to the hydrogen atom. Approximation schemes will also be discussed, with particular emphasis on variational principles, WKB approximation. Extensions of this content to describe quantum fluids such as ultra-cold Bose gases and superfluids in terms of the Gross-Pitaevskii equation will also be presented.

Code MTHE7033A (20 Credits)

This module is about further topics in algebra. It builds on the knowledge obtained on groups, rings and vector spaces in the first two years. Groups can be studied directly, or via objects called algebras (which have the structures of both rings and vector spaces). On the other hand, algebras can also be studied in their own right. Some of these concepts will be explored in this module.

Code MTHE7034A (20 Credits)

Partial Differential Equations (PDEs) are ubiquitous in applied mathematics. They arise in many models of physical systems where there is coupling between the variation in space and time, or more than one spatial dimension. Examples include fluid flows, electromagnetism, population dynamics, and the spread of infectious diseases. It is therefore important to understand the theory of PDEs, as well as different analytic and numerical methods for solving them. This module will provide you with an understanding of the different types of PDE, including linear, non-linear, elliptic, parabolic and hyperbolic; and how these features affect the required boundary conditions and solution techniques. We will study different methods of analytical solution (such as greens functions, boundary-integral methods, similarity solutions, and characteristics); as well as appropriate numerical methods (with topics such as implicit versus explicit schemes, convergence and stability). Examples and applications will be taken from a variety of fields.

Code MTHE7035B - (20 Credits)

Number Theory is the study of arithmetical properties of the integers: properties of, and patterns in, prime numbers, integer solutions of equations with integer coefficients, etc. Gauss called Number Theory the queen of mathematics and, following on from work of Fermat and Euler, is responsible for the emergence of Number Theory as a central subject in modern mathematics. Since then, Number Theory has developed in many directions, including Algebraic, Analytic and Probabilistic Number Theory, Diophantine Geometry and has found surprising applications in modern life (notably in Cryptography). In this module, building on first year material on prime factorization and basic congruences, and second year material on groups, rings and fields, you will study various aspects of Number Theory, including certain diophantine equations, polynomial congruences and the famous theorem of Quadratic Reciprocity. The Advanced Topics will be on applications of Number Theory in Cryptography.

 

 

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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. Science A Levels to include a pass in the practical element

BTEC

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

Scottish highers

AAAAA alongside Scottish Advanced Highers Mathematics at grade B.

Scottish highers advanced

BBC including grade B in Mathematics

Irish leaving certificate

4 subjects at H2 including Mathematics, 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: 

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.

 

Course Reference Number: 1545405

Fees and Funding

Undergraduate University Fees and Financial Support

Tuition Fees

Information on tuition fees can be found here:

UK students

EU Students 

Overseas Students

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.

Course related costs

You are eligible for reduced fees during the year abroad. Further details are available on our Tuition Fee website. 

There will be extra costs related to items such as your travel and accommodation during your year abroad, which will vary depending on location.

Please see Additional Course Fees for details of other course-related costs.

Course Reference Number: 1545405

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 full-time Undergraduate courses at universities and colleges in the United Kingdom. It is made up of different sections that you need to complete. Your application does not have to be completed all at once. The application allows you to leave a section partially completed so you can return to it later and add to or edit any information you have entered. Once your application is complete, it is sent to UCAS so that they can process it and send it to your chosen universities and colleges.

The Institution code for the University of East Anglia is E14.

FURTHER INFORMATION

Please complete our Online Enquiry Form to request a prospectus and to be kept up to date with news and events at the University. 

 

Course Reference Number: 1545405
Key details
Attendance
Full Time
Award
Degree of Master of Mathematics
UCAS course code
G10A
Entry Requirements
AAB
Duration (years)
4
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. On our Year Abroad programme you’ll have the opportunity to spend a year broadening your mathematical knowledge and experiencing a different lifestyle and culture by studyingat one of our partner universities across North America and Australasia. You’ll then return to UEA to undertake a substantial final year research project. At UEA you’ll benefit from internationally recognised, research-led teaching and a high academic staff to student ratio, so you’ll graduate with a deep understanding of mathematics – and fantastic career prospects.
Schools
Mathematics
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