BSc Mathematics with a Foundation Year

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Mathematics is one of the most fundamental and important academic disciplines. So we believe it’s crucial that higher mathematics education is available to anyone who wants to deepen their understanding of it – whether you’re a mature student looking for a career change, you want to get deeper into a lifelong passion, or you’ve left education without the A-levels you need to go straight into a degree.

During your Foundation Year you will focus on the essential concepts, techniques and knowledge you’ll need to progress onto studying mathematics at a higher level – including basic algebra, notation and calculus. On successfully completing the foundation year, you’ll be able to join our full BSc Mathematics degree.

Overview

Our Foundation Year course has been designed to give you access to a degree in Mathematics, without having to meet our traditional entry requirements. Whether you’re looking for a career change or don’t have the standard A-levels needed to go straight into a BSc, your application will be assessed on a case-by-case basis.

Your Foundation Year will focus on the essential concepts, techniques and knowledge you’ll need to study mathematics at a higher level. Complete it successfully and you’ll be accepted onto our full BSc Mathematics degree.

We combine academic rigour with a supportive community, and our enthusiastic and knowledgeable staff will guide through this fascinating subject. We pride ourselves on the personal attention our students receive, keeping seminar groups small and ensuring the relationships between staff and students are really strong. What’s more, we’re experts in a number of cutting-edge topics, in fact, over 87% of our mathematical sciences research outputs were judged as internationally excellent or world-leading (REF 2014).

At UEA you’ll benefit from internationally recognised, research-led teaching and a high academic staff to student ratio, ensuring you graduate with a deep understanding of mathematics, and great career prospects.

Course Structure

Half of the modules you’ll study in your Foundation Year will focus entirely on mathematics. We’ll introduce you to fundamental theorems, standard notation, and core themes like algebra and calculus. The compulsory modules will be supplemented by optional modules in other related sciences, such as Physics, Computing or Chemistry, so you’ll gain an insight into other disciplines that utilise mathematical techniques, too.

Complete your Foundation Year successfully and you’ll be eligible to move onto our three-year BSc Mathematics. The degree programme will build on the mathematical knowledge you will have developed in your Foundation Year, before introducing you to more advanced concepts that will be developed throughout the course. You will have the opportunity to specialise in years three and four, with a variety of modules that will enable you to tailor your degree programme around your particular interests.

For the years of study beyond the Foundation Year, please see the course page specific to the degree programme.

Teaching and Learning

You will be taught by leading mathematicians in their fields. As well as teaching, our academics are actively involved in research collaborations with colleagues throughout the world, examples from which will be used to illustrate lectures and workshops. New material will usually be delivered through lectures, which are complemented by online notes and workshops, where you’ll focus on working through examples, either individually or in small groups, under the guidance of lecturers and mathematical teaching assistants.

Individual Study

To succeed at university-level mathematics, you need to spend at least as much time on individual study as you spend in classes and workshops. Working through your lecture notes and trying the exercises set will be vital to really understanding the mathematics.

We offer a wide range of feedback to our students. Each lecturer has at least two office hours available each week, giving you the chance to discuss the material in more detail or to get face-to-face feedback on exercises you’ve attempted.

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

Assessment

We employ a variety of assessment methods; the method we use is determined by the module in question. They range from 100% coursework to 100% examination, with most Mathematics modules combining 80% examination and 20% coursework.

The coursework component will be made up of problems set from an example sheet, which will be handed in, marked and returned, together with the solutions. For some modules there are also programming assignments and/or class tests.

Optional Study abroad or Placement Year

Depending on your academic results, you may be able to transfer onto our MMath Master of Mathematics, BSc Mathematics (with Education), Masters of Mathematics with a Year Abroad or our BSc Mathematics with a Year in Industry, at the end of year one of the degree course.

After the course

Once you successfully finish your Foundation Year you will go straight onto one of the main degree programmes within the School of Mathematics.

Study with us and you’ll graduate with a deep understanding of mathematics – and with great career prospects.

You could choose to enter one of the professions traditionally associated with mathematics, such as accountancy, banking and finance, statistics and data analysis, and secondary or higher education. Or you could follow other graduates into roles in which logical thought and problem solving are important. These include information technology, engineering, logistics and distribution, central or local government, as well as other business areas. Many of our graduates also choose to continue their studies by going on to a higher degree.

Career destinations

Examples of careers that you could enter include:

  • Secondary school teacher
  • Cyber security consultant
  • Mathematical modeller in industry
  • Accountant
  • Data Scientist
  • Actuary

Course related costs

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

Course Modules 2018/9

Students must study the following modules for 60 credits:

Name Code Credits

ADVANCED MATHEMATICS

This module extends material beyond Basic Mathematics I and Basic Mathematics II, and takes the most useful topics from the equivalent of the Further Maths A-level syllabus: - Simple common sets. - Notions of mathematical rigour and proof by induction. - Ideas of function such as f(x)=(ax+b)/(cx+d) for curve sketching, including identifying asymptotes. - Trigonometric functions and corresponding identities, including graph sketching aided by the derivative as the slope of a curve. - The hyperbolic functions sinhx, coshx and tanhx. - The Maclaurin Series Expansions. - Matrices and determinants (2x2 and 3x3) and their link with vector-cross-product. Examples of matrix-transformations of the plane and of space. - Separable variable first-order differential equations for modelling the motion of objects (once Integration has been covered in Basic Mathematics II). E.g. a car decelerating within a specified breaking distance; a body falling with air-resistance. All this has proved to set up students well for what follows in the degree course.

MTHB3003B

20

BASIC MATHEMATICS I

Taught by lectures and seminars to bring students from Maths GCSE towards A-level standard, this module covers several algebraic topics including functions, polynomials and quadratic equations. Trigonometry is approached both geometrically up to Sine and Cosine Rule and as a collection of waves and other functions. The main new topic is Differential Calculus including the Product and Chain Rules. We will also introduce Integral Calculus and apply it to areas.

MTHB3001A

20

BASIC MATHEMATICS II

Following MTHB3001A (Basic Mathematics I), this module brings students up to the standard needed to begin year one of a range of degree courses. The first half covers Integral Calculus including Integration by Parts and Substitution. Trigonometric identities, polynomial expressions, partial fractions and exponential functions are explored, all with the object of integrating a wider range of functions. The second half of the module is split into two: Complex Numbers and Vectors. We will meet and use the imaginary number i (the square root of negative one), represent it on a diagram, solve equations using it and link it to trigonometry and exponential functions. Strange but true: imaginary numbers are useful in the real world. The last section is practical rather than abstract too; we will be looking at three dimensional position and movement and solving geometric problems through vector techniques.

MTHB3002B

20

Students will select 60 credits from the following modules:

Name Code Credits

FOUNDATIONS OF COMPUTING 1

In taking this module you will learn about a wide range of topics that are fundamental to computing science. You will study areas such as history of computing, web site design, the binary system, logic circuits, and algorithms. In the practical work for the module you will use a range of tools and techniques appropriate to the topic being studied.

CMP-3002A

20

FOUNDATIONS OF COMPUTING 2

This module follows on from Foundations of Computing 1. You will learn about a further range of topics that are fundamental to computing science. You will study areas such as database design, accessing databases via dynamic websites, an introduction to machine code, machine learning and an introduction to higher level languages.

CMP-3006B

20

FURTHER CHEMISTRY

A course in chemistry intended to take you to the level required to begin a relevant degree in the Faculty of Science. The module will help you to develop an understanding of: reactions of functional groups in organic chemistry; basic thermodynamics; spectroscopic techniques; transition metal chemistry and practical laboratory skills.

CHE-3003B

20

FURTHER PHYSICS

This course follows on from Introductory Physics and continues to introduce you to the fundamental principles of physics and uses them to explain a variety of physical phenomena. You will study gravitational, electric and magnetic fields, radioactivity and energy levels. There is some coursework based around the discharge of capacitors. The module finishes with you studying some aspects of thermal physics, conservation of momentum and simple harmonic motion.

PHY-3010B

20

INTRODUCTORY CHEMISTRY

A module designed for you if you are on a Science Faculty degree with a Foundation Year or Medicine with a Foundation Year. You will receive an introduction to the structure and electronic configuration of the atom. You will learn how to predict the nature of bonding given the position of elements in the periodic table and therefore. You will be introduced to the chemistry of key groups of elements. You will become familiar with key measures such as the mole and the determination of concentrations. The module includes laboratory work. No prior knowledge of chemistry is assumed.

CHE-3004A

20

INTRODUCTORY PHYSICS

This is a first module in physics if you are a student who is taking a Faculty of Science degree with a foundation year. In this 20 credit module you will begin your physics journey with units, accuracy and measurement. You will then progress through the topics of waves, light and sound, forces and dynamics, energy, materials and finish by studying aspects of electricity. The module has a piece of coursework which is based around PV cell technology.

PHY-3011A

20

INTRODUCTORY PROGRAMMING

This module will introduce you to computer programming. The module comprises of an introduction to programming and involves learning a programming language relevant to today's world.

CMP-3005A

20

Students must study the following modules for 120 credits:

Name Code Credits

CALCULUS AND MULTIVARIABLE CALCULUS

(a) Complex numbers. (b) Vectors. (c) Differentiation; power series. (d) Integration: applications, curve sketching, area, arc-length. (e) First and second-order, constant-coefficient ordinary differential equations. Reduction of order. Numerical solutions using MAPLE. Partial derivatives, chain rule. (f) Line integrals. Multiple integrals, including change of co-ordinates by Jacobians. Green's Theorem in the plane. (g) Vector calculus: divergence, gradient, curl of vector field. The Laplacian. Scalar potential and path-independence of line integral. (h) Surface integrals, Divergence Theorem and Stokes' Theorem. Operators in orthogonal curvilinear coordinates. (i) Introduction to Matlab.

MTHA4005Y

40

LINEAR ALGEBRA

In the first semester we develop the algebra of matrices: Matrix operations, linear equations, determinants, eigenvalues and eigenvectors, diagonalisation and geometric aspects. This is followed in the second semester by vectors space theory: Subspaces, basis and dimension, linear maps, rank-nullity theorem, change of basis and the characteristic polynomial.

MTHA4002Y

20

MATHEMATICAL PROBLEM SOLVING, MECHANICS AND MODELLING

This module comprises two parts: andquot;Mathematical Problem Solvingandquot; and andquot;Mechanics and Modellingandquot;. Being able to tackle unfamiliar problems using existing knowledge is an essential part of mathematics and a key transferable skill. Equally important is being able to express mathematical ideas in written and verbal form. In the first part of this module you will acquire these skills through collaborative group work on a number of example problems covering different areas of mathematics. The module will promote accurate reading, writing, and thinking about mathematics, and will also improve your confidence and ability to tackle unfamiliar problems. Newtonian mechanics provides a basic description of how particles and rigid bodies move in response to applied forces. In the second part of the module you will study Newton's laws of motion and how they can be applied to particle dynamics, vibrations, motion in polar coordinates, and conservation laws.

MTHA4004Y

20

REAL ANALYSIS

You will explore the mathematical notion of a limit and see the precise definition of the limit of a sequence of real numbers and learn how to prove that a sequence converges to a limit. After studying limits of infinite sequences, we move on to series, which capture the notion of an infinite sum. We then learn about limits of functions and continuity. Finally, we will learn precise definitions of differentiation and integration and see the Fundamental Theorem of Calculus.

MTHA4003Y

20

SETS, NUMBERS AND PROBABILITY

You will explore basic set-theoretic notation, functions, proof by induction, arithmetic, rationals and irrationals, the Euclidean algorithm and the styles of proof. Elementary set theory, modular arithmetic, equivalence relations and countability are also covered during this module. You will study probability as a measurement of uncertainty, statistical experiments and Bayes' theorem as well as discrete and continuous distributions. Expectation. Applications of probability: Markov chains, reliability theory.

MTHA4001Y

20

Students must study the following modules for 80 credits:

Name Code Credits

ALGEBRA

This module will introduce groups and rings. Together with vector spaces these are the most important structures in modern algebra. At the heart of group theory in Semester I is the study of symmetry and the axiomatic development of the theory. Groups appear in many parts of mathematics. The basic concepts are subgroups, Lagrange's theorem, factor groups, group actions and the First Isomorphism Theorem. In Semester II we introduce rings, using the Integers as a model and we will develop the theory with many examples related to familiar concepts such as substitution and factorisation. Important examples of commutative rings are fields, domains, polynomial rings and their quotients.

MTHA5003Y

20

ANALYSIS

You will study the standard basic theory of the complex plane. In the first semester, you will study within the areas of continuity, power series and how they represent functions for both real and complex variables, differentiation, holomorphic functions, Cauchy-Riemann equations, Moebius transformations. In the second semester, you will study within the areas of topology of the complex plane, complex integration, Cauchy and Laurent theorems, residue calculus.

MTHA5001Y

20

DIFFERENTIAL EQUATIONS AND APPLIED METHODS

You'll gain a solid understanding in the following areas: Ordinary Differential Equations: solution by reduction of order; variation of parameters for inhomogeneous problems; series solution and the method of Frobenius. Legendre's and Bessel's equations: Legendre polynomials, Bessel functions and their recurrence relations; Fourier series; Partial differential equations (PDEs): heat equation, wave equation, Laplace's equation; solution by separation of variables. Method of characteristics for hyperbolic equations; the characteristic equations; Fourier transform and its use in solving linear PDEs; Dynamical Systems: equilibrium points and their stability; the phase plane; theory and applications.

MTHA5004Y

20

FLUID DYNAMICS - THEORY AND COMPUTATION

This module introduces some of the fundamental physical concepts and mathematical theory needed to analyse the motion of a fluid, with the focus predominantly on inviscid, incompressible motions. You will examine methods for visualising flow fields, including the use of particle paths and streamlines. You will study the dynamical theory of fluid flow taking Newton's laws of motion as its point of departure, and the fundamental set of equations comprising conservation of mass and Euler's equations will be discussed. The reduction to Laplace's equation for irrotational flow will be demonstrated, and Bernoulli's equation is derived as a first integral of the equation of motion. Having established the basic theory, the way is set for a broader discussion of flow dynamics including everyday practical examples.

MTHA5002Y

20

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

Name Code Credits

COMBINATORICS AND FURTHER LINEAR ALGEBRA

Combinatorics is one of the most applicable and accessible part of mathematics, yet it is also full of challenging problems. We shall cover many basic combinatorial concepts including counting arguments (enumerative combinatorics) and Ramsey theory. Linear Algebra underpins much of modern mathematics and is the key to many applications. We will introduce bilinear forms and symmetric operators on vector spaces leading to the diagonalization of linear maps and the spectral theorem. This theorem is key to many applications in statistics and physics. Other topics covered will include polynomials of linear maps, the Cayley-Hamilton theorem and the Jordan normal form of a matrix.

MTHF5031Y

20

MATHEMATICAL MODELLING

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

MTHF5032Y

20

MATHEMATICAL STATISTICS

Learn the essential concepts of mathematical statistics, deriving the necessary distribution theory as required. Additionally, you'll explore ideas of sampling and central limit theorem, covering estimation methods and hypothesis-testing, with the introduction of some Bayesian ideas.

CMP-5034A

20

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

Name Code Credits

APPLIED GEOPHYSICS

What lies beneath our feet? This module addresses this question by exploring how wavefields and potential fields are used in geophysics to image the subsurface on scales of metres to kilometres. You'll study the basic theory, data acquisition and interpretation methods of seismic, electrical, gravity and magnetic surveys. A wide range of applications are covered, including archaeological geophysics, energy resources and geohazards. Highly valued by employers, this module features guest lecturers from industry who explain the latest 'state-of-the-art' applications and give you unique insight into real world situations. Students doing this module are normally expected to have a good mathematical ability, notably in calculus and algebra.

ENV-5004B

20

DYNAMICS AND VIBRATION

You will build on the introductory material from first year engineering mechanics. An appreciation of why dynamics and vibration are important for engineering designers leads to consideration of Single-degree-of-freedom (SDOF) systems, Equation of motion, free vibration analysis, energy methods, natural frequency, undamped and damped systems and loading. Fourier series expansion and modal analysis are applied to vibration concepts: eigenfrequency, resonance, beats, critical, under-critical and overcritical damping, and transfer function. Introduction to multi-degree of freedom (MDOF) systems. Applications to beams and cantilevers. MathCAD will be used to support learning.

ENG-5004B

20

EDUCATIONAL PSYCHOLOGY

This module will provide you with an introduction to key areas of psychology with a focus on learning and teaching in education. By the end of the module you should be able to: - Discuss the role of perception, attention and memory in learning; - Compare and contrast key theories related to learning, intelligence, language, thinking and reasoning; - Critically reflect on key theories related to learning,intelligence, language, thinking and reasoning in the practical context; - Discuss the influence of key intrapersonal, interpersonal and situational factors on pupils learning and engagement in educational settings. Assessment: Coursework 100%

EDUB5012A

20

ELECTROMAGNETISM, OPTICS, RELATIVITY AND QUANTUM MECHANICS

This module gives an introduction to important topics in physics, with particular, but not exclusive, relevance to chemical and molecular physics. Areas covered include optics, electrostatics and magnetism, aspect of chemical physics, basic quantum mechanics and special relativity. The module will involve both lectures and workshops, where you will develop analytical thinking and problem solving skills. The module may be taken by any science students who wish to study physics beyond A Level.

PHY-4001Y

20

INTRODUCTION TO BUSINESS (2)

How are businesses organised and managed? This module helps non-Norwich Business School students explore the dynamic and ever-changing world of business and provides insights into the managerial role. You'll explore the business environment, key environmental drivers and the basic functions of organisations. There will be a review of how organisations are managed in response to various environmental drivers. You will consider some of the current issues faced by every organisation, such as business sustainability, corporate responsibility and internationalisation. This module is designed to provide an overview of the corporate world for non-business specialists, so no previous knowledge of business or business management is required for this module. General business concepts are introduced in lectures and applied in a practical manner during seminars. By the end of this module, you will be able to understand and apply key business concepts and employ a number of analytical tools to help explore the business environment, industry structure and business management. You will be assessed through a range of assignments, for example an individual piece of coursework, group work and an exam. Therefore, the module reinforces fundamental study skills development through a combination of academic writing, presentational skills, teamwork and the practical application of theory. Core business theory is introduced in lectures and applied practically with the use of examples in seminars. By the end of this module you will be able to understand and apply key business concepts and a range of analytical tools to explore the business environment. Introduction to Business facilitates study skills development that is essential across all 3 years of the undergraduate degree by developing academic writing, presentation, team working and communication skills effectively.

NBS-4008Y

20

INTRODUCTION TO FINANCIAL AND MANAGEMENT ACCOUNTING (2)

It is vital that everyone working in business has an understanding of accounting data in order that financial information can be used to add value to the organisation. You'll be provided with a foundation in the theory and practice of accounting and an introduction to the role, context and language of financial reporting and management accounting. The module assumes no previous study of accounting. You'll begin with building a set of accounts from scratch so that you will be able to analyse and provide insight form the major financial statements. You'll also look at management decision making tools such as costing, budgeting and financial decision making. You will be required to actively participate in your learning both in lectures and seminars. The module employs a learn by doing approach.

NBS-4010Y

20

INTRODUCTORY MACROECONOMICS

This module will introduce you to the economic way of reasoning, exploring how to apply this to a variety of real world macroeconomic issues. You'll begin your journey by learning how to measure macroeconomic aggregates, such as GDP, GDP growth, unemployment and inflation. Establishing the foundations to conduct rigorous Macroeconomics analysis, you'll learn how to identify and characterise equilibrium on the goods market and on the money market. You'll examine policy-making, exploring and evaluating features and applications of fiscal and monetary policy, and grow an appreciation of the methods of economic analysis, such as mathematical modelling, diagrammatic representation, and narrative. Discussion of theoretical frameworks will be enriched by real world applications and supported by an interactive teaching approach.

ECO-4006Y

20

INTRODUCTORY MICROECONOMICS

Forming a foundation for subsequent economic modules, this module will introduce you to the fundamental principles, concepts and tools of microeconomics and show you how to apply these to a variety of real world economic issues. There is some mathematical content - you will be required to interpret linear equations, solve simple linear simultaneous equations and use differentiation. The module is primarily concerned with: 1) the ways individuals and households behave in the economy 2) the analysis of firms producing goods and services 3) how goods and services are traded or otherwise distributed - often but not exclusively through markets 4) the role of government as provider and/or regulator.

ECO-4005Y

20

METEOROLOGY I

The weather affects everyone and influences decisions that are made on a daily basis around the world. From whether to hang your washing out on a sunny afternoon, to which route a commercial aircraft takes as it travels across the ocean, weather plays a vital role. With that in mind, what actually causes the weather we experience? In this module you'll learn the fundamentals of the science of meteorology. You'll concentrate on the physical process that allow moisture and radiation to transfer through the atmosphere and how they ultimately influence our weather. The module contains both descriptive and mathematical treatments of radiation balance, thermodynamics, dynamics, boundary layers, weather systems and the water cycle. The module is assessed through a combination of one piece of coursework and an exam, and is designed in a way that allows those with either mathematical or descriptive abilities to do well, although a reasonable mathematical competence is essential, including basic understanding of differentiation and integration.

ENV-5008A

20

PROGRAMMING FOR NON-SPECIALISTS

The purpose of this module is to give you a solid grounding in the essential features of programming using the Java programming language. The module is designed to meet the needs of the student who has not previously studied programming.

CMP-5020B

20

UNDERSTANDING THE DYNAMIC PLANET

Understanding of natural systems is underpinned by physical laws and processes. You will explore the energy, mechanics, and physical properties of Earth materials and their relevance to environmental science using examples from across the Earth's differing systems. The formation, subsequent evolution and current state of our planet are considered through its structure and behaviour - from the planetary interior to the dynamic surface and into the atmosphere. You will study Plate Tectonics to explain Earth's physiographic features - such as mountain belts and volcanoes - and how the processes of erosion and deposition modify them. The distribution of land masses is tied to global patterns of rock, ice and soil distribution and to atmospheric and ocean circulation. You will also explore geological time - the 4.6 billion year record of changing conditions on the planet - and how geological maps can be used to understand Earth history. This course provides you with an introduction to geological materials - rocks, minerals and sediments - and to geological resources and natural hazards.

ENV-4005A

20

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

Name Code Credits

ADVANCED STATISTICS

This module covers two topics in statistical theory: Linear and Generalised Linear models and also includes Stochastic processes. The first two topics consider both the theory and practice of statistical model fitting and students will be expected to analyse real data using R. Stochastic processes including the random walk, Markov chains, Poisson processes, and birth and death processes.

CMP-6004A

20

DIFFERENTIAL GEOMETRY

This module gives an introduction to ideas of differential geometry. Key examples will be curves and surfaces embedded in 3-dimensional Euclidean space. We will start with curves and will study the curvature and torsion, building up to the fundamental theorem of curve theory. From here we move on to more advanced topics including surfaces.

MTHE6030A

20

DYNAMICAL OCEANOGRAPHY

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

MTHE6007B

20

ELECTRICITY AND MAGNETISM

The behaviour of electric and magnetic fields is fundamental to many features of life we take for granted yet the underlying equations are surprisingly compact and elegant. We will begin with a historical overview of electrodynamics to see where the governing equations (Maxwell's) come from. We will then use these equations as axioms and apply them to a variety of situations including electro- and magneto-statics problems and then time-dependent problems (eg electromagnetic waves). We shall also consider how the equations change in an electromagnetic media and look at some simple examples.

MTHE6010A

20

FINANCIAL MATHEMATICS

The Mathematical Modelling of Finance is a relatively new area of application of mathematics yet it is expanding rapidly and has great importance for world financial markets. The module is concerned with the valuation of financial instruments known as derivatives. You will be introduced to options, futures and the no-arbitrage principle. Mathematical models for various types of options are also discussed. We consider 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.

MTHE6026B

20

FLUID STRUCTURE INTERACTION

Think of a fish swimming in river or a long container ship vibrating in sea waves. This may give you a clue about fluid-structure interaction (FSI), where a "structure" (fish or ship) moves interacting with a "fluid" (water and/or air). The flow of the fluid is changed by the moving structure which in turn is affected by the fluid loads. The fluid loads depend on the structure motions, and the structure motions depend on the fluid loads. A fluid and a structure cannot be considered separately in the problems you will study in this module. Their motions are coupled. The problems of fluid-structure interaction become even more complex if the structure is deformable. You will study interesting and practical FSI problems from ship hydrodynamics and offshore/coastal engineering, including wave interaction with coastal structures, underwater motions of rigid bodies, water impact onto elastic surfaces and others. The problems will be formulated and methods of their analysis will be presented. The module covers mathematical models of liquid motion and motions of rigid and elastic bodies, coupled problems of FSI and methods to find solutions to such problems. The mathematical techniques include method of separating variables, methods of analytic function theory, and methods of asymptotic analysis.

MTHE6013B

20

REPRESENTATION THEORY

This module gives an introduction the area of representation theory. It introduces you to algebras, representations, modules and related concepts. Important theorems of the module are the Jordan-Hoelder and Artin-Wedderburn Theorems.

MTHD6016B

20

SEMIGROUP THEORY

This module introduces you to Semigroup Theory. Semigroups are algebraic objects which generalize groups. They are of interests because they arise naturally in many parts of mathematics, for example, whenever we are composing functions, multiplying matrices, or considering homomorphisms between objects, there are semigroups underlying our mathematics. You will study a class of algebraic objects called semigroups. A semigroup is an algebraic structure consisting of a set together with an associative binary operation. For example, every group is a semigroup, but the converse is far from being true. Semigroups are ubiquitous in pure mathematics: whenever we are composing functions, multiplying matrices, or considering homomorphisms between objects, there are semigroups underlying our mathematics. Finite semigroups are also of importance in the theory of finite automata (an area of theoretical computer science). You will cover the fundamentals of semigroup theory, with the focus on using Green's relations to study their underlying structure. Topics covered will include: definition of semigroups and monoids with examples, idempotents, maximal subgroups, ideals and Rees quotients, Green's relations and regular semigroups, 0-simple semigroups, principal factors, Rees matrix semigroups and the Rees theorem.

MTHE6011A

20

SET THEORY

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

MTHE6003B

20

WAVES

You will gain an introduction to the theory of waves. You will study aspects of linear and nonlinear waves using analytical techniques and Hyperbolic Waves and Water Waves will also be covered. It requires some knowledge of hydrodynamics and multi-variable calculus. The unit is suitable for those with an interest in Applied Mathematics.

MTHE6031A

20

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

Name Code Credits

HISTORY OF MATHEMATICS

You will trace the development of mathematics from prehistory to the high cultures of ancient Egypt, Mesopotamia, and the Indus Valley civilisation, through Islamic mathematics, and on to mathematical modernity, through a selection of topics. You will explore the rise of calculus and algebra from the time of Greek and Indian mathematicians, up to the era of Newton and Leibniz. We also discuss other topics, such as mathematical logic: ideas of propositions, axiomatisation and quantifiers. Our style is to explore mathematical practice and conceptual developments, in different historical and geographical settings.

MTHA6002A

20

MATHEMATICS PROJECT

This module is reserved for third year students who have completed an appropriate number of mathematics modules at levels 4 and 5. It is a project on a mathematical topic supervised by a member of staff within the school, or in a closely related school. The focus of the project is on independent study; you will have the opportunity to undertake research in an area which is interesting to you. You will write an in-depth report on your chosen project, in the mathematical typesetting language LaTeX. There will also be a short oral presentation.

MTHA6005Y

20

MODELLING ENVIRONMENTAL PROCESSES

The aim of the module is to show how environmental problems may be solved from the initial problem, to mathematical formulation and numerical solution. Problems will be described conceptually, then defined mathematically, then solved numerically via computer programming. The module consists of lectures on numerical methods and computing practicals; the practicals being designed to illustrate the solution of problems using the methods covered in lectures. The module will guide students through the solution of a model of an environmental process of their own choosing. The skills developed in this module are highly valued by prospective employers.

ENV-6004A

20

THE LEARNING AND TEACHING OF MATHEMATICS

This module will introduce you to the study of the teaching and learning of mathematics with a particular focus on secondary and post compulsory level. You'll also explore theories of learning and teaching of mathematical concepts typically included in the secondary and post compulsory curriculum, and study mathematics knowledge for teaching. If you're interested in mathematics teaching as a career or interested in mathematics education as a research discipline, then this module will equip you with the necessary knowledge and skills.

EDUB6014A

20

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

Students who have selected EDUB6014A from Option Range B cannot select EDUB6006A

Name Code Credits

APPLIED GEOPHYSICS

What lies beneath our feet? This module addresses this question by exploring how wavefields and potential fields are used in geophysics to image the subsurface on scales of metres to kilometres. You'll study the basic theory, data acquisition and interpretation methods of seismic, electrical, gravity and magnetic surveys. A wide range of applications are covered, including archaeological geophysics, energy resources and geohazards. Highly valued by employers, this module features guest lecturers from industry who explain the latest 'state-of-the-art' applications and give you unique insight into real world situations. Students doing this module are normally expected to have a good mathematical ability, notably in calculus and algebra.

ENV-5004B

20

CHILDREN, TEACHERS AND MATHEMATICS

This module will introduce you to key issues in mathematics education, particularly those that relate to the years of compulsory schooling. Specifically in this module we: Introduce the mathematics curriculum and pupils' perception of, and difficulties with, key mathematical concepts; Discuss public and popular culture perceptions of mathematics, mathematical ability and mathematicians as well as address ways in which these perceptions can be modified; Outline and discuss specific pedagogical actions (focused on challenge and motivation) that can be taken as early as possible during children's schooling and can provide a solid basis for pupils' understanding and appreciation of mathematics. By the end of the module you will be able to: Gain understanding of key curricular, pedagogical and social issues that relate to the teaching and learning of mathematics, a crucial subject area in the curriculum; Reflect on pedagogical action that aims to address those issues, particularly in the years of compulsory schooling; Be informed and able to consider the potential of pursuing a career in education, either as a teacher, educational professional or researcher in education with particular specialisation in the teaching and learning of mathematics. Assessment: Written Assignment 40% 3000 words Mini Project 60% 4500 words

EDUB6006A

20

CLIMATE SYSTEMS

What sets the mean global temperature of the world? Why are some parts of the world arid whilst others at the same latitudes are humid? This module aims to provide you with an understanding of the processes that determine why the Earth's climate (defined, for example, by temperature and moisture distribution) looks like it does, what the major circulation patterns and climate zones are and how they arise. You will study why the climate changes in time over different timescales, and how we use this knowledge to understand the climate systems of other planets. This module is aimed at you if you wish to further your knowledge of climate, or want a base for any future study of climate change, such as the Meteorology/Oceanography or Climate Change degrees.

ENV-6025B

20

COMBINATORICS AND FURTHER LINEAR ALGEBRA

Combinatorics is one of the most applicable and accessible part of mathematics, yet it is also full of challenging problems. We shall cover many basic combinatorial concepts including counting arguments (enumerative combinatorics) and Ramsey theory. Linear Algebra underpins much of modern mathematics and is the key to many applications. We will introduce bilinear forms and symmetric operators on vector spaces leading to the diagonalization of linear maps and the spectral theorem. This theorem is key to many applications in statistics and physics. Other topics covered will include polynomials of linear maps, the Cayley-Hamilton theorem and the Jordan normal form of a matrix.

MTHF5031Y

20

EDUCATIONAL PSYCHOLOGY

This module will provide you with an introduction to key areas of psychology with a focus on learning and teaching in education. By the end of the module you should be able to: - Discuss the role of perception, attention and memory in learning; - Compare and contrast key theories related to learning, intelligence, language, thinking and reasoning; - Critically reflect on key theories related to learning,intelligence, language, thinking and reasoning in the practical context; - Discuss the influence of key intrapersonal, interpersonal and situational factors on pupils learning and engagement in educational settings. Assessment: Coursework 100%

EDUB5012A

20

FINANCIAL ACCOUNTING

What are the rules that dictate how company accounts should be prepared and why do those rules exist? This is the essence of this module. Whilst company directors may wish to present the financial condition of a business in the best possible light, rules have been developed to protect investors and users of the accounts from being misled. You'll develop knowledge and skills in understanding and applying accounting standards when preparing financial statements. You'll also prepare and analyse statements of both individual businesses and groups of companies. Large UK companies report using International Financial Reporting Standards and these are the standards that you'll use. You'll begin by preparing basic financial statements and progress, preparing accounts of increasing complexity by looking at topics including goodwill, leases, cashflow statements, foreign currency transactions, financial instruments and group accounts. You'll also deepen your analytical skills through ratio analysis. You'll learn through a mixture of lectures, seminars and self-study, and be assessed by coursework (20%) and final examination (80%). On successful completion of this module, you'll have acquired significant technical skills in both the preparation and analysis of financial statements. This will give you a strong basis from which to build should you wish to study advanced financial accounting or are planning on a career in business or accounting.

NBS-5002Y

20

KNOWLEDGE SCIENCE AND PROOF FOR SECOND YEARS

Epistemology examines what knowledge is. Science is concerned with the acquisition of secure knowledge, and philosophy of science considers what counts as science, what objects the scientist knows about, and what methods can be used to attain such knowledge; logic uses formal tools to investigate different forms of reasoning deployed to acquire knowledge. You will be given an opportunity to explore a selection of these areas of philosophy, through teaching informed by recent and ongoing research: which ones will be explored on this occasion will be selected in the light of the lecturers' current research interests and their general appeal.

PPLP5175B

20

MANAGEMENT ACCOUNTING

This module aims to develop students' understanding of the theory and practice of management accounting. It develops underpinning competencies in management accounting and builds on topics introduced in the first year. It extends comprehension of the role and system of management accounting for performance measurement, planning, decision making and control across a range of organisations. Additionally, it introduces recent developments in management accounting practice, particularly those which underpin its growing strategic role.

NBS-5007Y

20

MATHEMATICAL MODELLING

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

MTHF5032Y

20

MATHEMATICAL STATISTICS

Learn the essential concepts of mathematical statistics, deriving the necessary distribution theory as required. Additionally, you'll explore ideas of sampling and central limit theorem, covering estimation methods and hypothesis-testing, with the introduction of some Bayesian ideas.

CMP-5034A

20

METEOROLOGY I

The weather affects everyone and influences decisions that are made on a daily basis around the world. From whether to hang your washing out on a sunny afternoon, to which route a commercial aircraft takes as it travels across the ocean, weather plays a vital role. With that in mind, what actually causes the weather we experience? In this module you'll learn the fundamentals of the science of meteorology. You'll concentrate on the physical process that allow moisture and radiation to transfer through the atmosphere and how they ultimately influence our weather. The module contains both descriptive and mathematical treatments of radiation balance, thermodynamics, dynamics, boundary layers, weather systems and the water cycle. The module is assessed through a combination of one piece of coursework and an exam, and is designed in a way that allows those with either mathematical or descriptive abilities to do well, although a reasonable mathematical competence is essential, including basic understanding of differentiation and integration.

ENV-5008A

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. Shelf Sea Dynamics 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 field course.

ENV-5016A

20

PROGRAMMING FOR NON-SPECIALISTS

The purpose of this module is to give you a solid grounding in the essential features of programming using the Java programming language. The module is designed to meet the needs of the student who has not previously studied programming.

CMP-5020B

20

SCIENCE COMMUNICATION

You will gain an understanding of how science is disseminated to the public and explore the theories surrounding learning and communication. You will investigate science as a culture and how this culture interfaces with the public. Examining case studies in a variety of different scientific areas, looking at how information is released in scientific literature and how this is subsequently picked up by the public press will provide you with an understanding of the importance of science communication. You will gain an appreciation of how science information can be used to change public perception and how it can sometimes be misinterpreted. You will also learn practical skills by designing, running and evaluating a public outreach event at a school or in a public area. If you wish to take this module, you will be required to write a statement of selection. These statements will be assessed and students will be allocated to the module accordingly.

BIO-6018Y

20

SHELF SEA DYNAMICS AND COASTAL PROCESSES

The shallow shelf seas that surround the continents are the oceans that we most interact with. They contribute a disproportionate amount to global marine primary production and CO2 drawdown into the ocean, and are important economically through commercial fisheries, offshore oil and gas exploration, and renewable energy developments (e.g. offshore wind farms). You will explore the physical processes that occur in shelf seas and coastal waters, their effect on biological, chemical and sedimentary processes, and how they can be harnessed to generate renewable energy. You will develop new skills during this module that will support careers in the offshore oil and gas industry, renewable energy industry, environmental consultancy, government laboratories (e.g. Cefas) and academia. The level of mathematical ability required to take this module is similar to Ocean Circulation and Meteorology I. You should be familiar with radians, rearranging equations and plotting functions.

ENV-5017B

20

WEATHER APPLICATIONS

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

ENV-5009B

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. In some cases optional modules can have limited places available and so you may be asked to make additional module choices in the event you do not gain a place on your first choice. Where this is the case, the University will endeavour to inform students.

Further Reading

  • Discover Maths Taster Event

    Join us for a day of interactive problem-solving sessions and the opportunity to find out what it is like to really study maths at degree-level. Book now.

    Read it Discover Maths Taster Event
  • Ask a Student

    This is your chance to ask UEA's students about UEA, university life, Norwich and anything else you would like an answer to

    Read it Ask a Student
  • UEA Award

    Develop your skills, build a strong CV and focus your extra-curricular activities while studying with our employer-valued UEA award.

    Read it UEA Award
  • HEAR FROM OUR STUDENTS

    Find out what it’s like to be a part of the School of Mathematics at UEA.

    Read it HEAR FROM OUR STUDENTS

Entry Requirements

  • A Level CCC. All Science A-Levels must include a pass in the practical element.
  • International Baccalaureate 28 points. If no GCSE equivalent is held, offer will include Mathematics and English requirements.
  • Scottish Highers Only accepted in combination with Scottish Advanced Highers.
  • Scottish Advanced Highers DDD. A combination of Advanced Highers and Highers may be acceptable.
  • Irish Leaving Certificate CCCCCC or 6 subjects at H3
  • Access Course Pass the Access to HE Diploma.
  • BTEC MMM. BTEC and A-level combinations are considered - please contact us.
  • European Baccalaureate 60% overall

Entry Requirement

GCSE Requirements:  GCSE English Language grade 4 and GCSE Mathematics grade 4 or GCSE English Language grade C and GCSE Mathematics grade C.

General Studies and Critical Thinking are not accepted.  

Contextual Criteria
We use contextual criteria for entry. Applicants must meet ONE of the following criteria:
•    You have been out of full time education for at least 3 years prior to your application.
or
•    You have not previously studied more than one science (Chemistry, Biology, Physics or Mathematics) at ‘A’ Level or equivalent.
or
•    You have been in Local Authority Care.
or
•    You have previously studied science but your Secondary School had 60% or less students achieving 5+ grade A*-C GCSEs (or equivalent) including English and Maths in the year you achieved your GCSEs.  If you completed your GCSEs in 2016 onwards we will refer to Progress 8 data.   - Data from Department of Education website: www.education.gov.uk/schools/performance/

UEA recognises that some students take a mixture of International Baccalaureate IB or International Baccalaureate Career-related Programme IBCP study rather than the full diploma, taking Higher levels in addition to A levels and/or BTEC qualifications. At UEA we do consider a combination of qualifications for entry, provided a minimum of three qualifications are taken at a higher Level. In addition some degree programmes require specific subjects at a higher level.

Students for whom English is a Foreign language

We welcome applications from students from all academic backgrounds. We require evidence of proficiency in English (including speaking, listening, reading and writing) at the following level:

  • IELTS: 6.5 overall (minimum 6.0 in any component)

We will also accept a number of other English language qualifications. Review our English Language Equivalences here.

INTO University of East Anglia 

If you do not yet meet the English language requirements for this course, INTO UEA offer a variety of English language programmes which are designed to help you develop the English skills necessary for successful undergraduate study:

Interviews

The majority of candidates will not be called for an interview. However, for some students an interview will be requested. These are normally quite informal and generally cover topics such as your current studies, reasons for choosing the course and your personal interests and extra-curricular activities.

Gap Year

We welcome applications from students who have already taken or intend to take a gap year, believing that a year between school and university can be of substantial benefit. You are advised to indicate your reason for wishing to defer entry and may wish to contact the appropriate Admissions Office directly to discuss this further.

Intakes

The School's annual intake is in September of each year.

Alternative Qualifications

We encourage you to apply if you have alternative qualifications equivalent to our stated entry requirements. Please contact us for further information.

 

Course Open To

This course is open to UK and EU applicants only. Foundation courses for international applicants are run by our partners at INTO.

Fees and Funding

Undergraduate University Fees and Financial Support

Tuition Fees

Information on tuition fees can be found here:

UK students

EU Students

Overseas Students

Scholarships and Bursaries

We are committed to ensuring that costs do not act as a barrier to those aspiring to come to a world leading university and have developed a funding package to reward those with excellent qualifications and assist those from lower income backgrounds. 

The University of East Anglia offers a range of Scholarships; please click the link for eligibility, details of how to apply and closing dates.

How to Apply

Applications need to be made via the Universities Colleges and Admissions Services (UCAS), using the UCAS Apply option.

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

The UCAS code name and number for the University of East Anglia is EANGL E14.

Further Information

If you would like to discuss your individual circumstances with the Admissions Office prior to applying please do contact us:

Undergraduate Admissions Office

Tel: +44 (0)1603 591515
Email: admissions@uea.ac.uk

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    Next Steps

    We can’t wait to hear from you. Just pop any questions about this course into the form below and our enquiries team will answer as soon as they can.

    Admissions enquiries:
    admissions@uea.ac.uk or
    telephone +44 (0)1603 591515