BSc Mathematics with a Foundation Year

Key details

BSC MATHEMATICS WITH A FOUNDATION YEAR

Start Year

2020

Attendance

Full Time

Award

Degree of Bachelor of Science

UCAS course code

G10F

Entry Requirements

CCC

Duration (years)

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 programme.

Our expert academics are enthusiastic and knowledgeable. All of our lecturers are active internationally-recognised researchers who conduct world-leading work and incorporate it into their teaching. Over 87% of our mathematical sciences research outputs were judged internationally excellent or world-leading (REF 2014).

About

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, vectors trigonometry, and calculus. You will also take optional introductory modules in computing, chemistry and/or physics. On successfully completing the Foundation Year you can join our full BSc Mathematics degree.

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Course Reference Number: 666010

Important Information

Whilst the University will make every effort to offer the courses listed, changes may sometimes be made arising from the regular review of course programmes. Where this activity leads to significant (but not minor) changes to programmes, there will normally be prior consultation of students and others. Changes may for example consist of variations to the content and method of delivery of programmes, courses and other services, to discontinue programmes, courses and other services and to merge or combine programmes or courses. The University will endeavour to keep such changes to a minimum, and will inform students.

After the Course

Once you successfully complete your Foundation Year you will go straight on to the remaining years of the programme. Or you can change to one of the other degree programmes in the School of Mathematics.

Study with us and you’ll graduate with a deep understanding of mathematics – and great career prospects. The experience of previous students suggests that completing a substantial dissertation project is viewed very positively by potential employers.

There are many professions that are traditionally associated with mathematics, such as accountancy, banking and finance, statistics and data analysis, and secondary or higher education. However, there are many others 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. The School of Mathematics works together with the University’s Careers Service to offer support to students at every stage of their course, from finding paid or voluntary work opportunities and choosing a career, through to applying for graduate jobs.

Career destinations

Examples of careers that you could enter include:

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

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Course Reference Number: 666010

Assessment for Year 1

We employ a variety of assessment methods; the method we use is determined by the module in question. They range from 100% coursework to 100% examination, with most Mathematics modules combining 60-80% examination and 20-40% coursework.

The coursework component is usually 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.

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 and chemistry, so you’ll gain an insight into other disciplines that use mathematical techniques too.

Complete your Foundation Year successfully and you’ll be eligible to move onto our three-year BSc Mathematics course. 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 3 and 4, 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 BSc Mathematics degree programme.

Teaching and Learning

Live workshop sessions will focus on applying the lectured material to problems. Optional modules on offer during your foundation year will involve small group laboratory classes or IT Labs.

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 fully 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 verbal and written feedback you receive will help with your coursework.

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Assessment for Year 2

Structure

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

Teaching and Learning

New material will usually be delivered through lectures. This year they will be online – either given and recorded live by the lecturer or pre-recorded in small bite-size chunks. In either case you will be able to re-watch the lectures in your own time to fully absorb the material. Lectures are complemented by online notes and quizzes. Live workshop sessions will focus on applying the lectured material to problems. Optional modules on offer during your foundation year will involve small group laboratory classes or IT Labs.

Individual Study

Prior to undertaking formal coursework (which will contribute to your module mark), you’ll submit answers to questions based on similar material. The verbal and written feedback you receive will help with your coursework.

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Assessment for Year 3

Structure

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

Teaching and Learning

Individual Study

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Assessment for Year 4

Structure

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

Teaching and Learning

Live workshop sessions will focus on applying the lectured material to problems. Optional modules on offer during your foundation year will involve small group laboratory classes or IT Labs.

Individual Study

Prior to undertaking formal coursework (which will contribute to your module mark), you’ll submit answers to questions based on similar material The verbal and written feedback you receive will help with your coursework.

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Assessment for Year 1

Compulsory Modules

BASIC MATHEMATICS I

Code MTHB3001A

Credits 20

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.

BASIC MATHEMATICS II

Code MTHB3002B

Credits 20

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.

ADVANCED MATHEMATICS

Code MTHB3003B

Credits 20

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.

Optional A Modules

(60 credits)

FURTHER CHEMISTRY

Code CHE-3003B

Credits 20

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.

INTRODUCTORY CHEMISTRY

Code CHE-3004A

Credits 20

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. 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.

FOUNDATIONS OF COMPUTING 1

Code CMP-3002A

Credits 20

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.

INTRODUCTORY PROGRAMMING

Code CMP-3005A

Credits 20

Introductory Programming introduces a number of programming concepts at the start of your programming career, 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.

FOUNDATIONS OF COMPUTING 2

Code CMP-3006B

Credits 20

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.

FURTHER PHYSICS

Code PHY-3010B

Credits 20

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.

INTRODUCTORY PHYSICS

Code PHY-3011A

Credits 20

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 aspects of thermal physics. The module has a piece of coursework which is based around PV cell technology.

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Important Information

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. Where this activity leads to significant (but not minor) changes to programmes and their constituent modules, the University will endeavour to consult with 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. 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 inform students.

Assessment for Year 2

Compulsory Modules

REAL ANALYSIS

Code MTHA4003Y

Credits 20

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.

CALCULUS AND MULTIVARIABLE CALCULUS

Code MTHA4008Y

Credits 30

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

MATHEMATICAL SKILLS

Code MTHA4001A

Credits 20

The unit 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.

ALGEBRA 1

Code MTHA4006Y

Credits 20

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.

COMPUTATION AND MODELLING

Code MTHA4007Y

Credits 20

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.

PROBABILITY

Code MTHA4001B

Credits 10

Probability is the study of the chance of events occurring. It has important applications to understand the likelihood of multiple events happening together and therefore to rational decision-making. This module will give you an introduction to the modern theory of probability developed from the seminal works of the Russian mathematician A.N. Kolmogorov in 1930s. Kolmogorov’s axiomatic theory describes the outcomes (events) of a random experiment as mathematical sets. Using set theory language you will be introduced to the concept of random variables, and consider different examples of discrete random variables (like binomial, geometric and Poisson random variables) and continuous random variables (like the normal random variable). In the last part of the module you will explore two applications of probability: reliability theory and Markov chains. Aside of the standard lectures and workshop sessions, there will be two computer-lab sessions of (2 hours each) where you will apply probability theory to specific everyday life case studies. The only pre-requisites for this module are a basic knowledge of set theory and of calculus that you would have acquired during the Autumn semester. If you have done probability or statistic at A-level you will rediscover its contents now taught using a proper and more elegant mathematical formalism.

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Important Information

Assessment for Year 3

Compulsory Modules

DIFFERENTIAL EQUATIONS AND APPLIED METHODS

Code MTHA5004Y

Credits 20

(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.

COMPLEX ANALYSIS

Code MTHA5006Y

Credits 20

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. (b) Topology of the complex plane, complex integration, Cauchy and Laurent theorems, residue calculus.

INVISCID FLUID FLOW

Code MTHA5007Y

Credits 20

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. Vector calculus will cover divergence, gradient, curl of vector field, the Laplacian, scalar potential and path-independence of line integral, surface integrals, divergence theorem and Stokes' theorem. Computational fluid dynamics will also be studied.

ALGEBRA II

Code MTHA5008Y

Credits 20

The module offers an introduction to vector space theory in the first semester followed by ring theory in the second semester. For vector spaces you will learn about subspaces, basis and dimension, linear maps, rank-nullity theorem, change of basis and the characteristic polynomial. This is followed by an introduction to rings using integers as a model. We develop the theory with many examples related to familiar concepts such as substitution and factorisation. Important examples of commutative rings include fields, domains, polynomial rings and their quotients.

Optional A Modules

(20-40 credits)

MATHEMATICAL STATISTICS

Code CMP-5034A

Credits 20

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

COMBINATORICS AND FURTHER LINEAR ALGEBRA

Code MTHF5031Y

Credits 20

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.

MATHEMATICAL MODELLING

Code MTHF5032Y

Credits 20

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

Optional B Modules

(0-20 credits)

PROGRAMMING FOR NON-SPECIALISTS

Code CMP-5020B

Credits 20

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

TIME SERIES

Code CMP-5042B

Credits 10

Students taking this module will gain an understanding of the nature and processes used to analyse time-series data, to understand what trends might exist within a set of data and the complexities of being able to use this information to make predictions or forecasts.

LINEAR REGRESSION USING R

Code CMP-5043B

Credits 10

This is a module designed to give you the opportunity to apply linear regression techniques using R. The aim is to provide an introduction to R and then provide the specifics in linear regression.

INTRODUCTORY MACROECONOMICS

Code ECO-4006Y

Credits 20

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.

EDUCATIONAL PSYCHOLOGY

Code EDUB5012A

Credits 20

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.

INTRODUCTION TO FINANCIAL AND MANAGEMENT ACCOUNTING

Code NBS-4108B

Credits 20

This module provides a foundation in the theory and practice of accounting and an introduction to the role, context and language of financial reporting and management accounting. The module assumes no previous study of accounting. It is be taken to provide a foundation to underpin subsequent specialist studies in accounting.

ELECTROMAGNETISM, OPTICS, RELATIVITY AND QUANTUM MECHANICS

Code PHY-4001Y

Credits 20

This module gives an introduction to important topics in physics, with particular, but not exclusive, relevance to chemical and molecular physics. Areas covered include optics, electrostatics and magnetism and special relativity. The module may be taken by any science students who wish to study physics beyond A Level.

GEOPHYSICS AND ASTROPHYSICS

Code PHY-4003A

Credits 20

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

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Important Information

Assessment for Year 4

Compulsory Modules

Optional A Modules

(60-120 credits)

ADVANCED STATISTICS

Code CMP-6004A

Credits 20

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.

SET THEORY

Code MTHE6003B

Credits 20

This module is concerned with foundational issues in mathematics and provides the appropriate mathematical framework for discussing ‘sizes of infinity’. On the one hand we shall cover concepts such as ordinals, cardinals, and the Zermelo-Fraenkel axioms with the Axiom of Choice. On the other, we shall see how these ideas come up in other areas of mathematics, such as graph theory and topology. Familiarity with and a taste for mathematical proofs will be assumed. Therefore, second year Analysis is a desired prerequisite.

DYNAMICAL OCEANOGRAPHY

Code MTHE6007B

Credits 20

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

FINANCIAL MATHEMATICS

Code MTHE6026B

Credits 20

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

DIFFERENTIAL GEOMETRY

Code MTHE6030A

Credits 20

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

WAVES

Code MTHE6031B

Credits 20

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

QUANTUM MECHANICS

Code MTHE6032A

Credits 20

This module covers the laws of physics described by quantum mechanics that govern the behaviour of microscopic particles. The module will focus on non-relativitic quantum mechanics that is described by the Schrodinger equation. Time-dependent and time-independent solutions will be presented in different contexts including an application to the hydrogen atom. Approximation schemes will also be discussed, with particular emphasis on variational principles, WKB approximation.

GROUPS AND ALGEBRA

Code MTHE6033A

Credits 20

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

PARTIAL DIFFERENTIAL EQUATIONS

Code MTHE6034A

Credits 20

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

NUMBER THEORY

Code MTHE6035B

Credits 20

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

ADVANCED TOPICS IN PHYSICS

Code PHY-6002Y

Credits 20

On this module you will study a selection of advanced topics in classical physics that provide powerful tools in many applications as well as provide a deep theoretical background for further advanced studies in both classical and quantum physics. The topics include analytical mechanics, electromagnetic field theory and special relativity. Within this module you will also complete a computational assignment, developing necessary skills applicable for computations in many areas of physics

Optional B Modules

(0-60 credits)

THE LEARNING AND TEACHING OF MATHEMATICS

Code EDUB6014A

Credits 20

The aim of the module is to introduce you to the study of the teaching and learning of mathematics with particular focus to secondary and post compulsory level. In this module, you will explore theories of learning and teaching of mathematical concepts typically included in the secondary and post compulsory curriculum. Also, you will learn about knowledge related to mathematical teaching. If you are 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.

MODELLING ENVIRONMENTAL PROCESSES

Code ENV-6004A

Credits 20

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 you through the solution of a model of an environmental process of your own choosing. The skills developed in this module are highly valued by prospective employers.

HISTORY OF MATHEMATICS

Code MTHA6002A

Credits 20

We will trace the development of mathematics from prehistory to the high cultures of ancient Egypt, Mesopotamia, and other civilisations, through Islamic mathematics, and on to mathematical modernity, through a selection of topics. We trace the rise of calculus and algebra, from the time of Ancient Greek and Indian mathematicians, up to the era of Newton and Leibniz. Other topics are also discussed. We will explore mathematical practice and conceptual developments in different historical and geographical settings.

MATHEMATICS PROJECT

Code MTHA6005Y

Credits 20

This module is reserved for 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.

Optional C Modules

(0-20 credits)

SCIENCE COMMUNICATION

Code BIO-6018Y

Credits 20

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.

PROGRAMMING FOR NON-SPECIALISTS

Code CMP-5020B

Credits 20

MATHEMATICAL STATISTICS

Code CMP-5034A

Credits 20

EDUCATIONAL PSYCHOLOGY

Code EDUB5012A

Credits 20

CHILDREN, TEACHERS AND MATHEMATICS

Code EDUB6006A

Credits 20

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.

EXPLORING THE EARTH'S SUBSURFACE

Code ENV-5004B

Credits 20

In this module you will learn about the processes that shape the Earth's shallow subsurface, and how to detect and map subsurface structures and resources. Physical properties of solid materials and subsurface fluids will be explored, including how fluid movement affects these properties. Methods to image the subsurface will be introduced using real datasets, collected by the class where possible. We will apply the theory to real-life problems including risk mitigation, engineering and resource exploration. This module will include fieldwork on campus where possible, specialist computer software, and some light mathematical analysis (trigonometry, rearranging linear equations, logarithms).

WEATHER APPLICATIONS

Code ENV-5009B

Credits 20

WEATHER

Code ENV-5043A

Credits 20

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

CLIMATE SYSTEMS

Code ENV-6025B

Credits 20

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.

COMBINATORICS AND FURTHER LINEAR ALGEBRA

Code MTHF5031Y

Credits 20

MATHEMATICAL MODELLING

Code MTHF5032Y

Credits 20

KNOWLEDGE SCIENCE AND PROOF FOR SECOND YEARS

Code PPLP5175B

Credits 20

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.

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Important Information

Entry Requirements

A Levels

CCC. All Science A-Levels must include a pass in the practical element.

BTEC

MMM.

Scottish highers

BBCCC.

Scottish highers advanced

DDD

Irish leaving certificate

6 subjects at H4.

Access course

Pass the Access to HE Diploma with 45 credits at Level 3.

European Baccalaureate

60% overall

International Baccalaureate

28 points.

GCSE offer

You are required to have Mathematics and English Language at a minimum of Grade C or Grade 4 or above at GCSE.

Additional entry requirements

General Studies and Critical Thinking A Levels are not accepted.

Alternative Qualifications

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

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 4, quintile 1 & 2 data)
You will be 21 years of age or over at the start of the course
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

Applications from students whose first language is not English are welcome. We require evidence of proficiency in English (including writing, speaking, listening and reading):

IELTS: 6.5 overall (minimum 5.5 in all components)

We also accept a number of other English language tests. Please click here to see our full list.

Interviews

Most applicants will not be called for an interview and a decision will be made via UCAS Track. However, for some applicants an interview will be requested. Where an interview is required the Admissions Service will contact you directly to arrange a time.

Gap year

We welcome applications from students who have already taken or intend to take a gap year. We believe that a year between school and university can be of substantial benefit. You are advised to indicate your reason for wishing to defer entry on your UCAS application.

Intakes

This course is open to UK applicants only. The annual intake for this course is in September each year.

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Course Reference Number: 666010

Mathematics

BSc MATHEMATICS WITH A FOUNDATION YEAR

Key details

Year of Entry:

Attendance

Full Time

Award

Degree of Bachelor of Science

UCAS course code

G10F

Entry Requirements

CCC

Duration (years)

Important Information

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 or to get deeper into a lifelong passion, or someone leaving education without the A levels you needs 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, vectors trigonometry, and calculus. You will also take optional introductory modules in computing, chemistry and/or physics.

Admissions Live Chat

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.

JUST ASK >

Taster Days

Come to one of our taster events and experience university life for yourself.

LEARN MORE >

UEA Award

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

LEARN MORE >

BSc MATHEMATICS WITH A FOUNDATION YEAR