BSc Mathematics with a Foundation Year


Attendance
Full Time
Award
Degree of Bachelor of Science



UCAS Course Code
G10F
A-Level typical
CCC (2019/0 entry) See All Requirements
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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 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), 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: Recent graduates have gone on to become: 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 2019/0

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. Students should have a strong understanding of GCSE Mathematics.

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 module 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

In this 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

Introductory Programming introduces a number of programming concepts to students at the start of their programming careers, using a modern programming language common to many digital industries. We structure learning through lectures, delivering core materials, and tutor supported exercises to reinforce learning, and to prepare students for programming in their following studies.

CMP-3005A

20

Students must study the following modules for 120 credits:

Name Code Credits

ALGEBRA 1

Algebra plays a key role in pure mathematics and its applications. We will provide you with a thorough introduction and develop this theory from first principles. In the first semester, we consider linear algebra and in the second semester, we move on to group theory. In the first semester, we develop the theory of matrices, mainly (though not exclusively) over the real numbers. The material covers matrix operations, linear equations, determinants, eigenvalues and eigenvectors, diagonalization and geometric aspects. We conclude with the definition of abstract vector spaces. At the heart of group theory in Semester 2 is the study of symmetry and the axiomatic development of the theory. The basic concepts are subgroups, Lagrange's theorem, factor groups, group actions and the Isomorphism Theorem.

MTHA4006Y

20

CALCULUS AND MULTIVARIABLE CALCULUS

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

MTHA4008Y

30

COMPUTATION AND MODELLING

Computation and modelling are essential skills for the modern mathematician. While many applied problems are amenable to analytic methods, many require some numerical computation to complete the solution. The synthesis of these two approaches can provide deep insight into highly complex mathematical ideas. This module will introduce you to the art of mathematical modelling, and train you in the computer programming skills needed to perform numerical computations. A particular focus is classical mechanics, which describes the motion of solid bodies. Central to this is Newton's second law of motion, which states that a mass will accelerate at a rate proportional to the force imposed upon it. This leads to an ordinary differential equation to be solved for the velocity and position of the mass. In the simplest cases the solution can be constructed using analytical methods, but in more complex situations, for example motion under resistance, numerical methods may be required. Iterative methods for solving nonlinear algebraic equations are fundamental and will also be studied. Further examples drawn from pure mathematics and statistics demonstrate the power of modern computational techniques.

MTHA4007Y

20

MATHEMATICAL SKILLS

The module provides you with a thorough introduction to some systems of numbers commonly found in Mathematics: natural numbers, integers, rational numbers, modular arithmetic. It also introduces you to common set theoretic notation and terminology and a precise language in which to talk about functions. There is emphasis on precise definitions of concepts and careful proofs of results. Styles of mathematical proofs you will discuss include: proof by induction, direct proofs, proof by contradiction, contrapositive statements, equivalent statements and the role of examples and counterexamples. In addition, this unit will also provide you with an introduction to producing mathematical documents using Latex, and an introduction to solving mathematical problems computationally using both Symbolic Algebra packages and Excel.

MTHA4001A

20

PROBABILITY

MTHA4001B

10

REAL ANALYSIS

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

Students must study the following modules for 80 credits:

Name Code Credits

ALGEBRA

We 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 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

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

This module introduces some of the fundamental physical concepts and mathematical theory need to analyse the motion of a fluid, with the focus predominantly on inviscid, incompressible motions. Methods for visualising flow fields are examined, including the use of particle paths and streamlines. The dynamical theory of fluid flow is studied 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 are discussed. The reduction to Laplace's equation for irrotational flow is 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.

MTHA5002Y

20

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

Name Code Credits

INTRODUCTION TO QUANTUM MECHANICS AND SPECIAL RELATIVITY

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

MTHF5030Y

20

MATHEMATICAL STATISTICS

It introduces the essential concepts of mathematical statistics deriving the necessary distribution theory as required. In consequence in addition to ideas of sampling and central limit theorem, it will cover estimation methods and hypothesis-testing. Some Bayesian ideas will be also introduced.

CMP-5034A

20

TOPOLOGY AND COMPUTABILITY

This module provides an introduction to two self-contained topics which have not been seen before. Topology: This is an introduction to point-set topology, which studies spaces up to continuous deformations and thereby generalises analysis, using only basic set theory. We will begin by defining a topological space, and will then investigate notions like open and closed sets, limit points and closure, bases of a topology, continuous maps, homeomorphisms, and subspace and product topologies. Computability: This is an introduction to the theoretical foundation of computability theory. The main question we will focus on is "which functions can in principle (i.e., given unlimited resources of space and time) be computed?". The main object of study will be certain devices known as unlimited register machines (URM's). We will adopt the point of view that a function is computable, if and only if, I is computable by a URM. We will identify large families of computable functions and will prove that certain naturally occurring functions are not computable.

MTHF5029Y

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 you gained in 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.

EDUB5012A

20

ELECTROMAGNETISM, OPTICS, RELATIVITY AND QUANTUM MECHANICS

You will be introduced to important topics in physics, with particular, but not exclusive, relevance to chemical and molecular physics. You will cover areas including optics, electrostatics and magnetism and special relativity.

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

The aim of this module is to introduce students to the economic way of reasoning, and to apply these to a variety of real world macroeconomic issues. Students will begin their journey by learning how to measure macroeconomic aggregates, such as GDP, GDP growth, unemployment and inflation. The module will establish the foundations to conduct rigorous Macroeconomics analysis, as students will learn how to identify and characterise equilibrium on the goods market and on the money market. The module will also introduce students to policy-making, exploring and evaluating features and applications of fiscal and monetary policy. Students will grow an appreciation of the methods of economic analysis, such as mathematical modelling, diagrammatic representation, and narrative. The discussion of theoretical frameworks will be enriched by real world applications, and it will be supported by an interactive teaching approach.

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 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

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

MATHEMATICAL TECHNIQUES

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

MTHD6032B

20

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

CRYPTOGRAPHY

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

MTHD6025B

20

DYNAMICAL METEOROLOGY

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

MTHD6018A

20

FLUID DYNAMICS

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

MTHD6020A

20

FUNCTIONAL ANALYSIS

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

MTHD6033B

20

GALOIS THEORY

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

MTHE6004B

20

GRAPH THEORY

A graph is a set of 'vertices' - usually finite - which may or may not be linked by 'edges'. Graphs are very basic structures and therefore play an important role in many parts of mathematics, computing and science more generally. In this module, you will develop the basic notions of connectivity and matchings. You'll explore the connection between graphs and topology via the planarity of graphs. We aim to prove a famous theorem due to Kuratowski which provides the exact conditions for a graph to be planar. You will also be able to study an additional topic on graph colourings. One of the best known theorems in graph theory is the Four-Colour-Theorem. While this result is not within our reach, we shall aim to prove the Five-Colour-Theorem.

MTHD6005A

20

MATHEMATICAL BIOLOGY

Mathematics finds wide-ranging applications in biological systems: including population dynamics, epidemics and the spread of diseases, enzyme kinetics, some diffusion models in biology including Turing instabilities and pattern formation, and various aspects of physiological fluid dynamics.

MTHD6021B

20

MATHEMATICAL LOGIC

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

MTHD6015A

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

Our aim is to show how environmental problems may be solved from the initial problem, to mathematical formulation and numerical solution. Problems will be described conceptually, then defined mathematically, then solved numerically via computer programming. The module consists of lectures on numerical methods and computing practicals; the practicals being designed to illustrate the solution of problems using the methods covered in lectures. We will guide 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.

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.

ENV-6025B

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.

EDUB5012A

20

INTRODUCTION TO QUANTUM MECHANICS AND SPECIAL RELATIVITY

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

MTHF5030Y

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

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

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 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

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

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

TOPOLOGY AND COMPUTABILITY

This module provides an introduction to two self-contained topics which have not been seen before. Topology: This is an introduction to point-set topology, which studies spaces up to continuous deformations and thereby generalises analysis, using only basic set theory. We will begin by defining a topological space, and will then investigate notions like open and closed sets, limit points and closure, bases of a topology, continuous maps, homeomorphisms, and subspace and product topologies. Computability: This is an introduction to the theoretical foundation of computability theory. The main question we will focus on is "which functions can in principle (i.e., given unlimited resources of space and time) be computed?". The main object of study will be certain devices known as unlimited register machines (URM's). We will adopt the point of view that a function is computable, if and only if, I is computable by a URM. We will identify large families of computable functions and will prove that certain naturally occurring functions are not computable.

MTHF5029Y

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

  • 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

Entry Requirements

  • A Level CCC - for further details on how we review your application please see below.
  • International Baccalaureate 28 points
  • Scottish Highers BBCCC
  • Scottish Advanced Highers DDD
  • Irish Leaving Certificate 6 subjects at H4
  • Access Course Pass the Access to HE Diploma with 45 credits at Level 3
  • BTEC MMM
  • European Baccalaureate 60% overall

Entry Requirement

We welcome applications from students with non-traditional academic backgrounds.  If you have been out of study for the last three years and you do not have the entry grades for our three year degree, we will consider your educational and employment history, along with your personal statement and reference to gain a holistic view of your suitability for the course. You will still need to meet our GCSE English Language and Mathematics requirements.

If you are currently studying your level 3 qualifications, we may be able to give you a reduced grade offer based on these circumstances:

• You live in an area with low progression to higher education (we use Polar 3, quintile 1 & 2 data)
• You have been in care or you are a young/full time carer
• You are studying at a school which our outreach team are working closely with

 

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

Occasionally we may you to an interview to further explore your application and suitability for the course.

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 in your UCAS personal statement.

Special Entry Requirements

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

A-Level General Studies and Critical Thinking are not accepted.

IB applicants - 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.

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.

GCSE Offer

GCSE English Language grade 4/C and GCSE Mathematics grade 4/C are required for all applicants.

Course Open To

UK and EU students 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

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

Tel: +44 (0)1603 591515

Email: admissions@uea.ac.uk

    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