# BSc Mathematics with a Year in Industry

- UCAS Course Code
- G10N
- A-Level typical
- AAB/(ABBC) (2016/7 entry) See All Requirements

## About this course

Studying with us means that you will 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.

You’ll also experience a whole year on placement in a relevant industry, giving you the chance to learn from experience and stand out in the job market.

Your lectures are complemented by small-group teaching that provides you with quality contact time with our world class lecturers – we were ranked 7th in the UK for the quality of our research outputs (REF 2014).

You’ll also experience a whole year on placement in a relevant industry, giving you the chance to learn from experience and stand out in the job market.

Your lectures are complemented by small-group teaching that provides you with quality contact time with our world class lecturers – we were ranked 7th in the UK for the quality of our research outputs (REF 2014).

## Course Profile

### Overview

Mathematics is a profound subject that has proven incredibly useful in just about every field of human endeavour. It is used in everything from science, exploration and industry to government, business and forecasting, providing a rational, objective means for the foundation of knowledge.

At UEA, we combine academic rigour with a supportive community so that our enthusiastic and knowledgeable staff can guide students through this fascinating subject.

The BSc Mathematics is our most popular maths programme, and taking the Year in Industry option allows to you spend an entire academic year putting your theoretical research into practice.

### Rated highly for research and teaching

Our lecturers are active researchers who conduct world-leading work in both pure and applied mathematics, which is incorporated into their teaching.

We’re experts in a number of cutting-edge topics and the quality of our research output is ranked 7th in the UK (REF 2014).

### The course

This BSc allows you to develop your interests in mathematics and statistics, while spending a year building experience in a professional setting. The course is designed to give you the flexibility to study pure maths, applied maths and statistics, while also developing an awareness of context through modules that explore the history of mathematics or the theory of teaching mathematics.

We pride ourselves on the personal attention our students receive. In the first year, weekly tutorials in groups of 6-7 students allow you to really get to know the lecturer who will act as your academic advisor throughout your degree. Just as importantly, it lets your advisor really get to know you. You’ll also have the chance to undertake an individual mathematical project in a field of your choice; this involves working closely with one of the lecturers to produce a poster or oral presentation in addition to a written report.

### Course structure

The first year of this four year degree programme builds on your existing A-level mathematical knowledge and introduces you to more advanced concepts that will be developed through the course. You will have the opportunity to specialise in years two and four, with a variety of modules available so that you can tailor your degree programme around your particular interests, while your third year is spent on placement. Assessment is by a mixture of coursework and examinations and you have the opportunity to work on an individual project during your second or final year.

**Year 1**

The first year develops calculus and other topics you might have seen at A-level such as mechanics and probability. Modules on linear algebra and analysis introduce important new ideas which will be used in the following years. A module on problem solving skills encourages you to develop ways of tackling unfamiliar problems and provides an opportunity for group working.

**Year 2**

The second year combines compulsory and optional modules. The compulsory modules introduce you to exciting applications of mathematics such as fluid flow and aerodynamics, alongside developing your understanding of the theoretical underpinning of modern mathematics.

In addition to optional modules such as statistics, which is available every year, we offer four specialist topics each year. These topics are updated annually: recent topics offered include quantum mechanics, mathematical modelling, cryptography and topology. You are also able to take a module in a mathematics-related subject such as business, computing or accounting, which will be lectured by another School in the University.

**Year 3 (Year in Industry)**

The third year of study will be spent on an industrial placement consisting of nine to fourteen months of full-time employment. You’ll need to source and secure your placement, but UEA will provide plenty of help as well as established links with employers. During this period you will pay a reduced tuition fee and likely receive a wage (this is at the discretion of the employer). Throughout the work placement you will keep in close contact with an assigned mentor at UEA, who will also visit you at least once during the year, and you will be supported by an industrial supervisor for the duration.

**Year 4**

In the final year of your degree programme there are no compulsory modules. There is wide choice of modules covering topics in pure mathematics, applied mathematics and statistics as well as modules on the history of mathematics and the theory of teaching mathematics. As in year two, you are able to study a mathematics-related subject lectured by another School in the University.

### Assessment

A variety of assessment methods are used in different modules, ranging from 100% coursework to 100% examination. Most mathematics modules are assessed 80% by examination and 20% by coursework. The coursework component is made up of problems set from an example sheet, to be handed in, marked and returned together with solutions. For some modules there are also programming assignments and/or class tests.

### Course Modules

Students must study the following modules for 120 credits:

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

CALCULUS AND MULTIVARIABLE CALCULUS This module is incompatible with MTHB4006Y and ENV-4002Y. (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:

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

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 |

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

In this option range 20 credits may be selected from modules not listed below, with the approval of the course director.

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 IN INDUSTRY MODULE NOT AVAILABLE UNTIL 2018/19. Mathematics students on placement will receive 2 site visits (or more if circumstances dictate). They will be expected to submit to MTH Industrial Coordinator a 500 word (approx) report on their working experience every 2 months. There will be a final report (a combination of progress reports previously discussed and some self-reflection on the placement. Students not engaging in this activity will be transferred to BSc Maths. Support in finding work placements will be provided by the MTH School and SCI Faculty, the MTH Industrial Coordinator and UEA Careers and Employability, which offers CV and application writing, interview preparation and practice. The MTH School will provide Alumni Careers evening (attendance compulsory), with those on programme invited to dinner with alumni. | MTHX5030Y | 120 |

Students will select 60 - 120 credits from the following modules:

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

ADVANCED STATISTICS This module covers three topics in statistical theory. For this year they are Regression and Linear Model, Generalised Models and Non-parametric Methods. The first two topics consider both the theory and practice of statistical model fitting and students will be expected to analyse real data. The third topic is chosen to be a contrasting one. Non-parametric methods are a vital part of the statisticians armoury and cheap computing makes such techniques very powerful. We look at the traditional permutation based methods as well as the empirical distribution function. | CMP-6004A | 20 |

DYNAMICAL OCEANOGRAPHY This level 6 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. | MTHE6007B | 20 |

FINANCIAL MATHEMATICS The Mathematical Modelling of Finance is a relatively new area of application of mathematics yet it is expanding rapidly and has great importance for world financial markets. The module is concerned with the valuation of financial instruments known as derivatives. Introduction to options, futures and the 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. | MTHE6026A | 20 |

GALOIS THEORY Introduction: This module is an introduction to Galois Theory, which beautifully brings together the notions of a group and of a field. In particular, the ideas developed will be applied to looking at the question of solving polynomial equations. Overview: 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. | MTHE6004A | 20 |

INTRODUCTION TO NUMERICAL ANALYSIS 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. | MTHE6012B | 20 |

LINEAR ALGEBRA AND APPLICATIONS 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. | MTHA6003A | 20 |

QUIVERS AND REPRESENTATIONS 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. | MTHD6026B | 20 |

SEMIGROUP THEORY 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. | MTHE6011A | 20 |

SET THEORY Introduction: This unit is concerned with foundational issues in mathematics and provides the appropriate mathematical framework for discussing 'sizes of infinity'. On the one hand we shall cover concepts such as ordinals, cardinals, and the Zermelo-Fraenkel axioms with the Axiom of Choice. On the other, we shall see how these ideas come up in other areas of mathematics, such as graph theory and topology. Familiarity with and a taste for mathematical proofs will be assumed. Therefore, second year Analysis is a desired prerequisite. Overview: Set theory plays a dual role in mathematics. It provides a manageable foundation to mathematics and it is itself a sophisticated area of mathematics. The foundational role of set theory consists in providing a reasonable set of assumptions (axioms) which enable us to construct most mathematical objects, and from which most mathematics can be derived by proving theorems based on these axioms. We will discuss this system of axioms, known as ZFC (Zermelo-Fraenkel Axioms with the Axiom of Choice), and will demonstrate how it can be used to build the foundations of mathematics. We will discuss some background foundational issues, including Godel's Incompleteness Theorems and the notion of consistency (these issues will be discussed without proofs), and will discuss some alternatives to ZFC. We will give a complete development of the general theory of ordinals and, along with it, we will introduce the methods of transfinite induction and recursion. Armed with these tools, we shall see how set theory provides the right framework for studying infinite sets. Examples of such sets are the set of all natural numbers, the set of all rationals, and the set of all real numbers. It turns out that there is a very natural way to assign a notion of size to such sets, providing us with more information than just 'infinite'. According to this notion (cardinality), the first two of the above sets have the same size, which is strictly smaller than that of the third. We will construct concrete examples of infinite objects in mathematics, such as infinite graphs, almost disjoint families, topological spaces, and groups, and will study some of their properties. Finally, if we have time we will briefly discuss the limitations of ZFC as well as criteria for extending ZFC in a sensible way. . | MTHE6003B | 20 |

THEORY OF WATER WAVES 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 | MTHE6014A | 20 |

Students will select 0 - 60 credits from the following modules:

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

HISTORY OF MATHEMATICS We trace the development of Arithmetic and Algebra from the high cultures of the Egyptian Middle Kingdom and Mesopotamia (1600BC) through Islamic mathematics and early algebra and on to the beginnings of mathematical modernity in the work of Galois in the 1830's. We present the rise of the Calculus from the first work of Archimedes and Apollonius around 200BC onwards, to trace ideas on differentiation and integration through to the time of Newton and Leibniz in the early 18th century. We explore mathematical logic, the ideas of propositions, logical methods in the axiomatisation of mathematics, and the idea of quantifiers. Of special interest is interplay between the development of logic and the development of mathematics, including theoretical computing. We discuss the Hilbert programme, first order logic, and the completeness and incompleteness theorems of Goedel, undecidability and independence. Our style will be to explore mathematical practice and conceptual developments in different historical contexts. | MTHA6002B | 20 |

MATHEMATICS PROJECT Not compatible with MTHA5005Y. This module is reserved for third year students who have completed an appropriate number of mathematics modules at levels 4 and 5. It is a project on a mathematical topic supervised by a member of staff within the school, or in a closely related school. Assessment will be by written project and oral presentation. | MTHA6005Y | 20 |

MODELLING ENVIRONMENTAL PROCESSES The aim of the module is to show how environmental problems may be solved from the initial problem, to mathematical formulation and numerical solution. Problems will be described conceptually, then defined mathematically, then solved numerically via computer programming. The module consists of lectures on numerical methods and computing practicals (using Matlab); the practicals being designed to illustrate the solution of problems using the methods covered in lectures. The module will guide students through the solution of a model of an environmental process of their own choosing. The problem will be discussed and placed into context through a project proposal, instead of an essay, and then solved and written up in a project report. The skills developed in this module are highly valued by prospective employers of students wishing to carry on into further studies or in professional employment. TEACHING AND LEARNING The aim of this course is to show how environmental problems may be solved from the initial problem, to mathematical formulation and numerical solution. There is a focus on examples within meteorology, oceanography and also the solid earth. The course consists of lectures on numerical methods, taught computing practicals and an independent project. The taught practicals illustrate the solution of a broad range of environmental problems using the methods covered in lectures. The module will guide students through an individual project which will develop a simple numerical model of an environmental process of their own choosing. The problem will be discussed and placed into context through a proposal, and then solved and written up in a project report. The first 8 weeks of the module are taught lectures and practicals, while the last 4 weeks is devoted to completing the independent project. The computing practicals are run in Matlab and a brief review of programming in Matlab is included in the module. Previous programming experience in any language will be extremely useful. The skills developed in this unit are highly valued by prospective employers of students wishing to carry on into further studies or in professional employment. COURSE CONTENT: Lectures, computing practicals and an independent project CAREER PROSPECTS: Numerical modelling and computer programming are commonly requested skills for science graduates, especially those looking towards further study or to stay in science. | ENV-6004A | 20 |

THE LEARNING AND TEACHING OF MATHEMATICS The aim of the module is to introduce students to the study of the teaching and learning of mathematics with particular focus to secondary and post compulsory level; to explore theories of learning and teaching of mathematical concepts typically included in the secondary and post compulsory curriculum and to explore mathematics knowledge for teaching. This module is recommended for anyone interested in Mathematics teaching as a career or, indeed, for anyone interested in mathematics education as a research discipline. | EDUB6014A | 20 |

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

In this option range 20 credits may be selected from modules not listed below, with the approval of the course director. If you have selected EDUB6014A above, you may not select EDUB6006A. 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 |
---|---|---|

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 |

ASTROPHYSICS This 20 credit module gives an overview of astrophysics through lectures and workshops. Assessment will involve some coursework and a coursetest. The module assumes previous study of either A level physics or an equivalent course. Topics covered will include some history of astrophysics, radiation, matter, gravitation, astrophysical measurements, spectroscopy, stars and some aspects of cosmology. Some of these topics will be taken to a more advanced level. The more advanced topics will include workshop examples and course test questions at level 5 standard. | NAT-5001A | 20 |

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 |

CHILDREN, TEACHERS AND MATHEMATICS Learning Outcomes: This module aims to introduce students 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 childrens' 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 persuing a career in education, either as a teacher, educational professional or researcher in education with particular specialisation in the teaching and learning of mathematics. Assessment: Written Assignment 40% 3000 words Mini Project 60% 4500 words | EDUB6006A | 20 |

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 |

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 |

METEOROLOGY II This module will build upon material introduced in ENV-5008A (Meteorology I) covering topics such as synoptic meteorology, micro-scale processes, the General Circulation and weather forecasting. Practical sessions, some computer based, will provide opportunities for individual- and group-based work in which problem sheets, simulations and case study exercises are tackled, coupled with experiential sessions in forecasting and broadcast meteorology. 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. Lectures 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. A non-compulsory programme of complementary monthly evening seminars is also available through the Royal Meteorological Society's East Anglian Centre, based at UEA, including talks by employers. | ENV-5009B | 20 |

OCEAN CIRCULATION This module gives you an understanding of the physical processes occurring in the basin-scale ocean environment. We will introduce and discuss large scale global ocean circulation, including gyres, boundary currents and the overturning circulation. Major themes include the interaction between ocean and atmosphere, and the forces which drive ocean circulation. You should be familiar with partial differentiation, integration, handling equations and using calculators. ENV-5017B is a natural follow-on module and builds on some of the concepts introduced here. We strongly recommend that you also gain oceanographic fieldwork experience by taking the 20-credit biennial Marine Sciences fieldcourse. | ENV-5016A | 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 |

SCIENCE COMMUNICATION This module brings an understanding of how science is disseminated to the public. Students on the module will be made aware of the theories surrounding learning and communication. They will investigate science as a culture and how this culture interfaces with the public. Students will examine case studies in a variety of different scientific areas. They will look at how information is released in scientific literature and how this is subsequently picked up by the public press. They will gain an appreciation of how science information can be used to change public perception and how it can sometimes be misinterpreted. Students will also learn practical skills by designing, running and evaluating a public outreach event at a school or in a public area. Students who wish to take this module will be required to write a statement of selection. These statements will be assessed and students will be allocated to the module accordingly. | BIO-6018Y | 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 |

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 |

#### 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

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