# MMath Master of Mathematics (with a Year Abroad)

- UCAS Course Code
- G10A
- A-Level typical
- A*AB (2016/7 entry) See All Requirements

## About this course

Studying with us means that you’ll benefit from internationally recognised, research-led 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 prestigious four-year programme offers advanced study and the opportunity to broaden your experience at a University in another country. Your lectures are complemented by small-group teaching that provides you with quality contact time with our world class lecturers, and you’ll spend a full year at a partner institution in North America or Australasia.

We were ranked 7th in the UK for the quality of our research outputs (REF 2014).

This prestigious four-year programme offers advanced study and the opportunity to broaden your experience at a University in another country. Your lectures are complemented by small-group teaching that provides you with quality contact time with our world class lecturers, and you’ll spend a full year at a partner institution in North America or Australasia.

We were ranked 7th in the UK for the quality of our research outputs (REF 2014).

## Course Profile

### Overview

This prestigious four-year Master of Mathematics programme allows you to develop your interests in pure and applied mathematics, with greater depth of study than a three-year programme.

This programme allows you to spend your third year abroad, studying maths modules with one of our exchange partners. Going to a university in another country is a fantastic opportunity to experience other cultures and lifestyles, as well as to study within departments where different aspects of mathematics are taught.

One of the advantages of studying with us is that our course is extremely flexible, enabling you to specialise in either pure or applied mathematics, or pursue a balanced combination of these topics. Apart from engaging in the study of essential mathematical theory and technique, you will also have the opportunity to carry out a significant research-led, individually supervised project in the final year, allowing you to experience the challenge of independent study and the thrill of discovery. Furthermore, this helps you to develop certain skills, including report-writing and oral-presentation skills that are essential for many future career paths.

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 in the wide range of career paths open to mathematicians.

### Course Structure

This four-year course follows a similar structure to the Masters of Mathematics, but with the third year spent abroad with one of our university exchange partners. The first year of study comprises core compulsory modules to establish your knowledge on essential topics. You will have the chance to select from optional modules in the second and final years in order to allow you to direct your own studies. In the final year you also undertake an independent research project on a subject of your choice, with a project supervisor to help guide you.

**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**

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. Topics covered in optional courses include cryptography, quantum theory, mathematical modelling and topology. You will also have the opportunity to study an individual research project, which is excellent preparation for the final year and allows you to widen your mathematical expertise.

**Year 3 (Year Abroad)**

After developing a broad mathematical knowledge during your first two years, you will spend your third year studying at one of our university exchange partners in another country. We have particularly strong links with institutions in North America and Australia – in recent years students have spent their year abroad in Sydney, Melbourne, Adelaide, Canberra, San Diego, Illinois and Colorado – but other locations are available. We take into account your field of interest and placement preferences, and do our best to place you at the university of your choice. See the “Year Abroad” tab for more details.

**Year 4**

You will undertake a substantial individual project during your final year, working closely under the 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 “The Mobius function of Finite Groups” to “The Aerodynamics of Golf Balls” (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 Master’s-level modules that explore topics such as lie algebra, fluid structure interaction and statistical mechanics. 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, except in years 3 and 4 where most are 100% examinations. The coursework component is made up of problems set from an example sheet, to be handed in, marked and returned together with detailed feedback and solutions. For some modules there are also programming or written project assignments.

### Study Abroad

Students studying the Master of Mathematics with a Year Abroad programme will spend their entire third year in a partner institution in destinations like North America, Australia and Hong Kong.

Experiencing a Year Abroad as part of your degree programme is a once-in-a-lifetime opportunity; as well as providing you with the chance to experience a different culture and language, studying abroad exposes you to exciting branches of mathematics from a different perspective. The first two years of the programme are spent at UEA, while the third year is spent with one of our exchange partners overseas. Students return to UEA for the fourth and final year. Employers really value students who have opted for a Year Abroad as part of their studies, recognising valued qualities such as adaptability, flexibility and independence.

Students on an exchange programme will only have to pay 15% of their annual tuition fee to UEA during their year abroad and we will pay the overseas university’s costs.

We are constantly reviewing our exchange agreements with our overseas partners and as such the destination Universities are subject to change, however, potential destinations include:

**North America and Canada**

- University of California
- University of Colorado
- University of British Columbia
- University of Victoria
- University of Illinois at Urbana-Champaign

**Australia**

### Course Modules

Students must study the following modules for 120 credits:

Name | Code | Credits |
---|---|---|

CALCULUS AND MULTIVARIABLE CALCULUS IN TAKING THIS MODULE YOU CANNOT TAKE ENV-4015Y OR TAKE MTHB4006Y (a) Complex numbers. (b) Differentiation and integration. Taylor and MacLaurin series. Applications: curve sketching, areas, arc length. (c) First order, second order constant coefficient ordinary differential equations. Reduction of order. Numerical solutions using MAPLE. Partial derivatives, chain rule. (d) Vectors. (e) Line integrals. Multiple integrals, including change of co-ordinates by Jacobians. Green's theorem in the plane. (f) Euler type and general linear ODEs. (g) Divergence, gradient and curl of a vector field. Scalar potential and path independence of line integral. Divergence and Stokes' theorems. (h) Introduction to Matlab | MTHA4005Y | 40 |

LINEAR ALGEBRA Linear equations and matrices (including geometric aspects); Determinants. Eigenvalues and eigenvectors, Diagonalization. Vector spaces and linear transformations. | MTHA4002Y | 20 |

MATHEMATICAL PROBLEM SOLVING, MECHANICS AND MODELLING The first part of the module is about how to approach mathematical problems (both pure and applied) and write mathematics. It aims to promote accurate writing, reading and thinking about mathematics, and to improve students' confidence and abilities to tackle unfamiliar problems. The second part of the module is about Mechanics. It includes discussion of Newton's laws of motion, particle dynamics, orbits, and conservation laws. This module is reserved for students registered in the School of Mathematics or registered on the Natural Sciences programme. | MTHA4004Y | 20 |

REAL ANALYSIS Sequences and series, tests for convergence. Limits, continuity, differentiation, Riemann integration, Fundamental Theorem. | MTHA4003Y | 20 |

SETS, NUMBERS AND PROBABILITY Basic set-theoretic notation, functions. Proof by induction, arithmetic, rationals and irrationals, the Euclidean algorithm. Styles of proof. Elementary set theory. Modular arithmetic, equivalence relations. Countability. Probability as a measurement of uncertainty, statistical experiments and Bayes' theorem. Discrete and continuous distributions. Expectation. Applications of probability: Markov chains, reliability theory. | MTHA4001Y | 20 |

Students must study the following modules for 80 credits:

Name | Code | Credits |
---|---|---|

ALGEBRA (a) Group theory: basic concepts and examples. Cosets, Lagrange's theorem. Normal subgroups and quotient groups. First isomorphism theorem. Quotient spaces in linear algebra. (b) Rings, elementary properties and examples of commutative rings. Ideals, quotient rings. Polynomial rings and construction of finite fields. Unique Factorization in rings. Applications in linear algebra. | MTHA5003Y | 20 |

ANALYSIS 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, Moebius transformations. (b) Topology of the complex plane, complex integration, Cauchy and Laurent theorems, residue calculus. | MTHA5001Y | 20 |

DIFFERENTIAL EQUATIONS AND APPLIED METHODS (a) Ordinary Differential Equations: solution by reduction of order; variation of parameters for inhomogeneous problems; series solution and the method of Frobenius. Legendre's and Bessel's equations: Legendre polynomials, Bessel functions and their recurrence relations; Fourier series; Partial differential equations (PDEs): heat equation, wave equation, Laplace's equation; solution by separation of variables. (b) Method of characteristics for hyperbolic equations; the characteristic equations; Fourier transform and its use in solving linear PDEs; (c) Dynamical Systems: equilibrium points and their stability; the phase plane; theory and applications. | MTHA5004Y | 20 |

FLUID DYNAMICS - THEORY AND COMPUTATION (a) Hydrostatics, compressibility. Kinematics: velocity, particle path, streamlines. Continuity, incompressibility, streamtubes. Dynamics: Material derivative, Euler's equations, vorticity and irrotational flows. Velocity potential and streamfunction. Bernoulli's equation for unsteady flow. Circulation: Kelvin's Theorem, Helmholtz's theorems. Basic water waves. (b) Computational methods for fluid dynamics; Euler's method and Runge-Kutta methods and their use for computing particle paths and streamlines in a variety of two-dimensional and three-dimensional flows; numerical computation and flow visualisation using Matlab; convergence, consistency and stability of numerical integration methods for ODEs. (c) Theory of Irrotational and Incompressible Flows: velocity potential, Laplace's Equation, sources and vortices, complex potential. Force on a body and the Blasius theorem. Method of images and conformal mappings. | MTHA5002Y | 20 |

Students will select 20 - 40 credits from the following modules:

If you wish to select all four MTH topics (A: Combinatorics, B: Quantum Mechanics, C: Boolean Algebras, Measures, Probabilities and D: Mathematical Modelling) then you must select MTHF5028Y (40 credits). If you wish to select one MTH topic in Autumn (A: Combinatorics, or B: Quantum Mechanics) and one in the Spring (C: Boolean Algebras, Measures, Probabilities or D: Mathematical Modelling) then you should select MTHF5027Y (20 credits).

Name | Code | Credits |
---|---|---|

BOOLEAN ALGEBRAS, MEASURES, PROBABILITIES AND MATHEMATICAL MODELLING This module is an optional Spring module. It covers two topics: C: Boolean algebras, measures and probabilities, and D: Mathematical Modelling. Topic C: Boolean algebras, measures and probabilities This topic will consider the notion of a measure and discuss its connection with integration. We shall discuss Riemann integration versus Jordan measure and Lebesgue integral versus Lebesgue integration. This will lead us to the idea of Boolean algebras, and in particular measure algebras. Probabilities are just a special kind of measures, so we shall also discuss them. Clearly, integration plays a central role in mathematics and physics. One encounters integrals in the notions of area or volume, when solving a differential equation, in the fundamental theorem of calculus, in Stokes' theorem, or in classical and quantum mechanics. The first year analysis module includes an introduction to the Riemann integral, which is satisfactory for many applications. However, it has certain disadvantages, in that some very basic functions are not Riemann integrable, that the pointwise limit of a sequence of Riemann integrable functions need not be Riemann integrable, etc. We introduce Lebesgue integration, which does not suffer from these drawbacks and agrees with the Riemann integral whenever the latter is defined. Topic D: Mathematical Modelling: Mathematical modelling is concerned with how to convert real problems, 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. | MTHF5026B | 20 |

COMBINATORICS AND QUANTUM MECHANICS This module is an optional Autumn module. It covers two topics: A: Combinatorics and B: Quantum Mechanics. Topic A: Combinatorics: The topic is about Counting Things. We will cover: binomial coefficients, the inclusion-exclusion principle, compositions, the pigeonhole principle and Ramsey Theory. Topic B: Quantum mechanics: The motion of very small systems such as atoms does not satisfy the equations of classical mechanics. For example an electron orbiting a nucleus can only have certain discrete energy levels. In quantum mechanics the motion of a particle is described by a wave function which describes the probability of the particle having a certain energy. Topics addressed in this module include: Wave Functions, Schrodinger's Equation, Uncertainty Principle, Wave Scattering, Harmonic Oscillators. In classical mechanics, a physical system is described in terms of particles moving with a particular linear momentum. Other phenomena such as the transmission of light are described in terms of the propagation of electromagnetic waves. In the 20th century it became clear that some physical observations can not be explained in such terms - for example the formation of fringe patterns due to the scattering of light through two slits. The concept of a photon having both particle and wave-like properties is at the heart of Quantum Mechanics. In this unit the emphasis is on detailed mathematical study of simplified model systems rather than broad descriptions of quantum phenomena. The main mathematical topics from Year One mathematics modules that this module builds on are differential equations and vector calculus (definitions of grad etc). | MTHF5025A | 20 |

MATHEMATICAL STATISTICS It 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. Some Bayesian ideas will be also introduced. | CMP-5034A | 20 |

MATHEMATICS PROJECT NOT COMPATIBLE WITH MTHA6005Y. This module is reserved for second-year students registered in the School of Mathematics only. It is a second year project on a mathematical topic supervised by a member of staff within the School. Assessment will be by written project and poster presentation. | MTHA5005Y | 20 |

SELECTED TOPICS IN MATHEMATICS This module is an optional Year long module. It covers two topics, one in Autumn Semester (chosen between A: Combinatorics and B: Quantum mechanics), one in Spring semester (chosen between C: Boolean algebras, measures and probabilities, and D:Mathematical Modelling). Topic A: Combinatorics: The topic is about Counting Things. We will cover: binomial coefficients, the inclusion-exclusion principle, compositions, the pigeonhole principle and Ramsey Theory. Topic B: Quantum mechanics: The motion of very small systems such as atoms does not satisfy the equations of classical mechanics. For example an electron orbiting a nucleus can only have certain discrete energy levels. In quantum mechanics the motion of a particle is described by a wave function which describes the probability of the particle having a certain energy. Topics addressed in this module include: Wave Functions, Schrodinger's Equation, Uncertainty Principle, Wave Scattering, Harmonic Oscillators. In classical mechanics, a physical system is described in terms of particles moving with a particular linear momentum. Other phenomena such as the transmission of light are described in terms of the propagation of electromagnetic waves. In the 20th century it became clear that some physical observations can not be explained in such terms - for example the formation of fringe patterns due to the scattering of light through two slits. The concept of a photon having both particle and wave-like properties is at the heart of Quantum Mechanics. In this unit the emphasis is on detailed mathematical study of simplified model systems rather than broad descriptions of quantum phenomena. The main mathematical topics from Year One mathematics modules that this module builds on are differential equations and vector calculus (definitions of grad etc). Topic C: Boolean algebras, measures and probabilities This topic will consider the notion of a measure and discuss its connection with integration. We shall discuss Riemann integration versus Jordan measure and Lebesgue integral versus Lebesgue integration. This will lead us to the idea of Boolean algebras, and in particular measure algebras. Probabilities are just a special kind of measures, so we shall also discuss them. Clearly, integration plays a central role in mathematics and physics. One encounters integrals in the notions of area or volume, when solving a differential equation, in the fundamental theorem of calculus, in Stokes' theorem, or in classical and quantum mechanics. The first year analysis module includes an introduction to the Riemann integral, which is satisfactory for many applications. However, it has certain disadvantages, in that some very basic functions are not Riemann integrable, that the pointwise limit of a sequence of Riemann integrable functions need not be Riemann integrable, etc. We introduce Lebesgue integration, which does not suffer from these drawbacks and agrees with the Riemann integral whenever the latter is defined. Topic D: Mathematical Modelling: Mathematical modelling is concerned with how to convert real problems, 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. | MTHF5027Y | 20 |

TOPICS IN MATHEMATICS This module is an optional Year long module. It covers four topics, two in Autumn Semester (A: Combinatorics and B: Quantum mechanics), two in Spring semester (C: Boolean algebras, measures and probabilities, and D: Mathematical Modelling). Topic A: Combinatorics: The topic is about Counting Things. We will cover: binomial coefficients, the inclusion-exclusion principle, compositions, the pigeonhole principle and Ramsey Theory. Topic B: Quantum mechanics: The motion of very small systems such as atoms does not satisfy the equations of classical mechanics. For example an electron orbiting a nucleus can only have certain discrete energy levels. In quantum mechanics the motion of a particle is described by a wave function which describes the probability of the particle having a certain energy. Topics addressed in this module include: Wave Functions, Schrodinger's Equation, Uncertainty Principle, Wave Scattering, Harmonic Oscillators. In classical mechanics, a physical system is described in terms of particles moving with a particular linear momentum. Other phenomena such as the transmission of light are described in terms of the propagation of electromagnetic waves. In the 20th century it became clear that some physical observations can not be explained in such terms - for example the formation of fringe patterns due to the scattering of light through two slits. The concept of a photon having both particle and wave-like properties is at the heart of Quantum Mechanics. In this unit the emphasis is on detailed mathematical study of simplified model systems rather than broad descriptions of quantum phenomena. The main mathematical topics from Year One mathematics modules that this module builds on are differential equations and vector calculus (definitions of grad etc). Topic C: Boolean algebras, measures and probabilities This topic will consider the notion of a measure and discuss its connection with integration. We shall discuss Riemann integration versus Jordan measure and Lebesgue integral versus Lebesgue integration. This will lead us to the idea of Boolean algebras, and in particular measure algebras. Probabilities are just a special kind of measures, so we shall also discuss them. Clearly, integration plays a central role in mathematics and physics. One encounters integrals in the notions of area or volume, when solving a differential equation, in the fundamental theorem of calculus, in Stokes' theorem, or in classical and quantum mechanics. The first year analysis module includes an introduction to the Riemann integral, which is satisfactory for many applications. However, it has certain disadvantages, in that some very basic functions are not Riemann integrable, that the pointwise limit of a sequence of Riemann integrable functions need not be Riemann integrable, etc. We introduce Lebesgue integration, which does not suffer from these drawbacks and agrees with the Riemann integral whenever the latter is defined. Topic D: Mathematical Modelling: Mathematical modelling is concerned with how to convert real problems, 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. | MTHF5028Y | 40 |

Students will select 0 - 20 credits from the following modules:

Non-listed modules may be taken with the permission of the school.

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. The basic theory, data acquisition and interpretation methods of seismic, electrical, gravity and magnetic surveys are studied. A wide range of applications is covered including archaeological geophysics, energy resources and geohazards. This module is highly valued by employers in industry; guest industrial lecturers will cover the current 'state-of-the-art' applications in real world situations. Students doing this module are normally expected to have a good mathematical ability, notably in calculus and algebra before taking this module (ENV-4002Y Mathematics for Scientists A or equivalent). | ENV-5004B | 20 |

APPLIED STATISTICS A ACTUARIAL SCIENCE AND BUSINESS STATISTICS STUDENTS SHOULD TAKE CMP-5019B, APPLIED STATISTICS B, DUE TO THE DIFFERENT REQUIREMENTS OF THEIR COURSE. This is a module designed to give students the opportunity to apply statistical methods in realistic situations. While no advanced knowledge of probability and statistics is required, we expect students to have some background in probability and statistics before taking this module. The aim is to introduce students to R statistical language and to cover Regression, Analysis of Variance and Survival analysis. Other topics from a list including: Extremes and quartiles, Bootstrap methods and their application, Sample surveys, Simulations, Subjective statistics, Forecasting and Clustering methods, may be offered to cover the interests of those in the class. | CMP-5017B | 20 |

INTRODUCTION TO BUSINESS (2) Introduction to Business is organised in thematic units across semesters 1 and 2, aiming to provide a platform for understanding the world of management and the managerial role. The module explores the business environment, key environmental drivers and functions of organisations, providing an up-to-date view of current issues faced from every contemporary enterprise such as business sustainability, corporate responsibility and internationalisation. There is consideration of how organisations are managed in response to environmental drivers. To address this aspect, this module introduces key theoretical principles in lectures and seminars are designed to facilitate fundamental study skills development, teamwork and practical application of theory. By the end of this module, students will be able to understand and apply key concepts and analytical tools in exploring the business environment and industry structure respectively. This module is for NON-NBS students only. | NBS-4008Y | 20 |

INTRODUCTION TO FINANCIAL AND MANAGEMENT ACCOUNTING 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 may be taken as a standalone course for those students following a more general management pathway or to provide a foundation to underpin subsequent specialist studies in accounting. This module is for NBS students only. | NBS-4001Y | 20 |

INTRODUCTORY MACROECONOMICS This is a compulsory module for all ECO students and it is a prerequisite for later economic modules. The aim of the module is to introduce you to the fundamental principles, concepts and tools of macroeconomics and to apply these to a variety of real world macroeconomic issues. There is some mathematical content - you will be required to interpret linear equations and solve simple linear simultaneous equations. The module will introduce students to core macroeconomic indicators such as income, inflation, unemployment and the stance of the balance of payments. Thus, focussing predominantly on the short-run, the module will consider: (1) models for equilibrium in the goods market and the money market, (2) applications of such models to discuss the role of fiscal and monetary policy, (3) the trade-off between inflation and unemployment, and (4) the role of expectations in macroeconomic analysis. | ECO-4006Y | 20 |

INTRODUCTORY MICROECONOMICS This is a compulsory module for all ECO students and it is a prerequisite for later economic modules. The aim of the module is to introduce you to the fundamental principles, concepts and tools of microeconomics. The aim of the module is apply these to a variety of real world economic issues. There is some mathematical content - you will be required to interpret linear equations and solve simple linear simultaneous equations. 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; and (4) the role of government as provider and/or regulator. | ECO-4005Y | 20 |

METEOROLOGY I This module is designed to give a general introduction to meteorology, concentrating on the physical processed in the atmosphere and how these influence our weather. The module contains both descriptive and mathematical treatments of Radiation Balance, Cloud Physics, Thermodynamics and Dynamics and the assessment is designed to allow those with either mathematical or descriptive abilities to do well; however a reasonable mathematical competence is essential. TEACHING AND LEARNING Practical session will provide opportunities for individual and group-based work in which problem sheets and data analysis exercises are tackled. Lectures will provide the forum for introduction of theoretical material and also for following up and summarising the key points emanating from previous practical sessions. Lecturers will also ensure that attention is drawn, as appropriate, to links between theory and 'current weather', often in the form of references to online information resources. The course Blackboard site will provide opportunities for students to assess their own progress through informal formative assessment material. # The Structure of the Atmosphere # Short and long wave radiation in the atmosphere # Thermal equilibrium of the Earth atmosphere system # Laws of thermodynamics applied to the atmosphere # Atmospheric Stability # Atmospheric Dynamics # Atmospheric momentum balance # Meteorological surface observations and plotting codes # Cloud physics CAREER PROSPECTS Students regularly go on to careers in the Met Office, in meteorological consultancy and in a number of other research organisations in the UK and abroad, either directly or after taking a higher degree. Meteorology interfaces with many other disciplines n the environmental sciences (eg oceanography, hydrology, energy and epidemiology) and impacts upon most sectors of the economy. While graduates regularly move directly into weather forecasting and analysis jobs, a career in meteorological research would often first require a higher degree. This module is designed to give a general introduction to meteorology, concentrating on the physical processes in the atmosphere and how these influence our weather. The module contains both descriptive and mathematical treatments of Radiation Balance, Cloud Physics, Thermodynamics and Dynamics and the assessment is designed to allow those with either mathematical or descriptive abilities to do well; however a reasonable mathematical competence is essential, including a basic understanding of differentiation and integration. | ENV-5008A | 20 |

PROGRAMMING FOR NON-SPECIALISTS The purpose of this module is to give the student a solid grounding in the essential features programming using the Java programming language. The module is designed to meet the needs of the student who has not previously studied programming. | CMP-5020B | 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). This module explores 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. Career development: New skills developed during this module will support careers in the offshore oil and gas industry, renewable energy industry, environmental consultancy, government laboratories (e.g. Cefas) and academia. Mathematical background: 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. | ENV-5017B | 20 |

TOPICS IN PHYSICS 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. | CHE-4801Y | 20 |

UNDERSTANDING THE DYNAMIC PLANET Understanding of natural systems is underpinned by physical laws and processes. This module explores energy, mechanics, 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. Plate Tectonics is studied 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. We also explore geological time#the 4.6 billion year record of changing conditions on the planet and introduce geological materials, resources and hazards. | ENV-4005A | 20 |

Students must study the following modules for 120 credits:

Name | Code | Credits |
---|---|---|

YEAR ABROAD A year studying abroad. | MTHX6014Y | 120 |

Students will select 40 credits from the following modules:

Please note that CMP-6004A Advanced Statistics or equivalent is a prerequisite for CMP-7017Y.

Name | Code | Credits |
---|---|---|

MATHEMATICS DISSERTATION Reserved for courses G102, G103 and G106. 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 MTH-MA9Y. However, in this case it consists of a supervised dissertation on a topic in the general area of probability or statistics. It may involve some computation, this will depend on the topic chosen. | CMP-7017Y | 40 |

Students will select 20 credits from the following modules:

Name | Code | Credits |
---|---|---|

MODEL THEORY Model Theory is a branch of mathematical logic which studies the connection between mathematical structures and their formal descriptions, or theories. It has deep and surprising applications in many branches of mathematics including number theory, algebra, and analytic geometry. One of the central questions which this course will address is when a theory has exactly one model. In most cases a theory is ambiguous in that it has many different models, but this apparent defect is in fact a rich source of ideas in Model Theory. | MTHD7013B | 20 |

SLOW VISCOUS FLOW The Reynolds number gives the ratio of inertial to viscous effects in a fluid flow. When the Reynolds number is small, inertial effects are negligible and the Du/Dt term in the Navier-Stokes equations may be neglected. This simplifies the Navier-Stokes equations, making them linear and instantaneous. These simplifications make solving low Reynolds number flow problems much easier than high Reynolds number flows. This module will consider the circumstances under which the Reynolds number will be small, examine the basic properties of low-Reynolds-number flows, present a number of solution techniques, and show how they can be applied to simple problems. | MTHD7011B | 20 |

Students will select 60 credits from the following modules:

Name | Code | Credits |
---|---|---|

DYNAMICAL OCEANOGRAPHY WITH ADVANCED TOPICS This level 7 module covers modelling the large scale ocean circulation and structure, internal waves and coastal flows. The mathematical modelling of the oceans in this module provides a demonstration of how the techniques developed in second year modules on fluid dynamics and differential equations can be used to explain some interesting phenomena in the real physical world. The module begins with a discussion of the effects of rotation in fluid flows. The dynamics of large scale ocean circulation is discussed including the development of ocean gyres and strong western boundary currents. The thermal structure associated with these flows is examined. These large scale currents are responsible for the variation in climate between land on the eastern and western side of major ocean basins. The dynamics of equatorial waves are examined. Such waves are intimately linked with the El Nino phenomena which affects the climate throughout the globe. The advanced topic is Baroclinic instability. | MTHD7007B | 20 |

FINANCIAL MATHEMATICS WITH ADVANCED TOPICS The Mathematical Modelling of Finance is a relatively new area of application of mathematics yet it is expanding rapidly and has great importance for world financial markets. The module is concerned with the valuation of financial instruments known as derivatives. Introduction to options, futures and the 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. The advanced topic will be stochastic interest rate models. | MTHE7013A | 20 |

GALOIS THEORY WITH ADVANCED TOPICS Polynomials and irreducibility: field extensions: algebraic, transcendental, normal, separable, splitting fields: field automorphisms, Galois group, Fundamental Theorem of Galois Theory: applications to constructability and roots of polynomial equations. Advanced topic: the inverse Galois problem | MTHE7004A | 20 |

INTRODUCTION TO NUMERICAL ANALYSIS WITH ADVANCED TOPICS This is an introductory course in numerical analysis which will cover approximating a function and it's derivative numerically. Further topics will include the numerical solution to boundary and initial value problems, numerical integration and nonlinear equations. Advanced topics will include an introduction to the numerical solution to hyperbolic partial differential equations. | MTHE7012B | 20 |

LINEAR ALGEBRA AND APPLICATIONS WITH ADVANCED TOPICS This course is about a central subject in mathematics. It aims to develop the theory (Part A) and computational implementations of Linear Algebra (Part B). Topics include A1: Review of basis, linear map, matrix of linear map, change of basis; A2: Bilinear forms, adjoint of a map, self-adjoint maps, diagonalization, spectral theorem; A3: Polynomials of linear maps, characteristic and minimal polynomial, triangularization, Cayley-Hamilton theorem, normal forms; B1: Orthogonality: Representation through projections in computational approximations; B2: Matrix norms and condition number. Computational matrix inversion; B3: Basic finite element methods for ODEs and the Fast Fourier Transform. | MTHA7030A | 20 |

QUIVERS AND REPRESENTATIONS WITH ADVANCED TOPICS This module is about representation of associative algebras over fields. Algebras, and their representations, will be studied using quivers, which are dots with arrows between them. The emphasis will be on noncommutative, finite-dimensional algebras. A key topic will be understanding extensions of modules. | MTHD7031B | 20 |

SEMIGROUP THEORY WITH ADVANCED TOPICS Introduction: This module is an introduction 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. Overview: This course is concerned with the study of 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). This course 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, 0-simple semigroups, principal factors, Rees matrix semigroups and the Rees theorem. | MTHE7011A | 20 |

SET THEORY WITH ADVANCED TOPICS Zermelo-Fraenkel set theory. The Axiom of Choice and equivalents. Cardinality, countability, and uncountability. Trees, Combinatorial set theory. Advanced topic: Infinite Ramsey theory. | MTHE7003B | 20 |

THEORY OF WATER WAVES WITH ADVANCED TOPICS This course provides an introduction to the theory of water waves. It requires some knowledge of hydrodynamics and multivariable calculus. The unit is suitable for those with an interest in Applied Mathematics. Overview: Free surface problems occur in many aspects of science and everyday life. Examples of free surface problems are waves on a beach, bubbles rising in a glass of champagne and a liquid jet flowing from a tap. In these examples the free surface is the surface of the sea, the interface between the gas and the champagne and the boundary of the falling jet. We will study aspects of linear and nonlinear water waves using analytical techniques. | MTHE7002A | 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 (five-yearly) review of course programmes. Where this activity leads to significant (but not minor) changes to programmes and their constituent modules, there will normally be prior consultation of students and others. It is also possible that the University may not be able to offer a module for reasons outside of its control, such as the illness of a member of staff or sabbatical leave. Where this is the case, the University will endeavour to inform students.## Essential Information

### Entry Requirements

### Fees and Funding

**Undergraduate University Fees and Financial Support: Home and EU Students**

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### How to Apply

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