Mathematics - BSc (Hons)
with a Foundation Year

This is an archived course for 2021 entry
2023 courses

Mathematics provides the theoretical framework for physical science, statistics and data analysis, and computer science. New discoveries in mathematics affect not only science, but also our general understanding of the world we live in.

Overview

Our Foundation Year programme provides an opportunity for you to develop your mathematics skills and start learning some university-level material, fully preparing you for university study before you progress onto your chosen mathematics programme.

You will benefit from the in-house expertise of our internationally-renowned mathematicians and statisticians to ensure you are fully prepared for your future career.

We will encourage you to fulfil your potential whilst studying in our friendly and dynamic school based in the multi-award-winning Sibson Building.

This programme has been designed for those who have achieved grades or are predicted grades lower than our standard entry requirements.

Our degree programme

To help bridge the gap between school and university, you’ll cover material from the A Level Mathematics and Further Mathematics syllabuses, along with advanced topics taken from university-level studies preparing you for university. Alongside mathematics, you can choose optional modules covering topics from computing to history.

On completion of the Foundation Year, you have the option to continue to one of the following BSc programmes: Mathematics - BSc (Hons), Mathematics and Statistics - BSc (Hons), Mathematics and Accounting and Finance - BA (Hons), Financial Mathematics - BSc (Hons).

In Stage 1 you’ll continue to receive support through small group tutorials, where you can practice the new mathematics you’ll be learning, ask questions and work with other students to find solutions. You’ll study a mixture of pure and applied mathematics, and statistics, providing you with a solid foundation for your later studies.

In Stage 2, you study some core modules which build upon the material learnt at Stage 1. Thereafter you can start to tailor your degree to your interests through our range of optional modules, continuing to explore the areas you enjoy into Stage 3.

This degree can also be taken as a five-year programme with a Year in Industry between your second and final years.

Study resources

You have access to a range of professional mathematical and statistical software such as:

  • Maple
  • MATLAB
  • Minitab.

Our staff use these packages in their teaching and research.

Extra activities

The School of Mathematics and Actuarial Science Student Society is run by students. It aims to improve the student experience for its members, socially and academically. In previous years the Society has organised:

  • talks and workshops
  • extra revision sessions
  • socials and networking events.
  • seminars and workshops employability events.

The School also puts on regular events that you are welcome to attend. In the past, these have included:

  • seminars and workshops
  • employability events.

Featured video

Maths student chatting in a lecture theatre

Accreditation

This degree meets the educational requirements of the Chartered Mathematician designation, awarded by the Institute of Mathematics and its Applications (IMA), when it is followed by subsequent training and experience in employment to obtain equivalent competencies to those specified by the Quality Assurance Agency (QAA) for taught Master’s degrees.

The School is very welcoming and there is lots of support available if you need it. It's a good environment to learn in.

Clarissa Baramki - Mathematics BSc

Entry requirements

Please also see our general entry requirements.

  • medal-empty

    A level

    CCD including a C in Mathematics. Use of Maths A level is not accepted as a required subject.

  • medal-empty Access to HE Diploma

    The University will not necessarily make conditional offers to all Access candidates but will continue to assess them on an individual basis. 

    If we make you an offer, you will need to obtain/pass the overall Access to Higher Education Diploma and may also be required to obtain a proportion of the total level 3 credits and/or credits in particular subjects at merit grade or above.

  • medal-empty BTEC Nationals

    The University will consider applicants holding BTEC National Diploma and Extended National Diploma Qualifications (QCF; NQF; OCR) on a case-by-case basis. Please contact us for further advice on your individual circumstances.

  • medal-empty International Baccalaureate

    34 points overall or 13 points HL including HL Maths or HL Mathematics: Analysis and Approaches at 4 or SL Maths or SL Mathematics: Analysis and Approaches at 6

  • medal-empty International Foundation Programme

    N/A

International students should visit our International Student website for further specific information. International fee-paying students who require a Student visa cannot study part-time due to visa restrictions.

English Language Requirements

Please see our English language entry requirements web page.

If you need to improve your English language standard as a condition of your offer, you can attend one of our pre-sessional courses in English for Academic Purposes before starting your degree programme. You attend these courses before starting your degree programme.

Course structure

Duration: 4 years full-time (5 years with a year in industry)

Modules

The following modules are indicative of those offered on this programme. This listing is based on the current curriculum and may change year to year in response to new curriculum developments and innovation.  

On most programmes, you study a combination of compulsory and optional modules. You may also be able to take ‘elective’ modules from other programmes so you can customise your programme and explore other subjects that interest you.

Foundation year

If your qualifications are not sufficient, for whatever reason, for direct entry onto a degree programme, you can apply for this programme. It covers the mathematical skills you need to enter Stage 1 of the degree. 

Compulsory modules currently include

Through this module, students will develop the transferable linguistic and academic skills necessary to successfully complete other modules on their programme and acquire the specific language skills that they will require when entering SMSAS and SPS Stage 1 programmes. The programme of study focuses on writing and speaking skills, enhancing academic language through classroom, homework and assessed activities. Writing skills will be used to write a technical report, interpret data and describe processes. Spoken skills will be used in presentations and seminars.

Find out more about FOUN0047

This module introduces fundamental methods needed for the study of mathematical subjects at degree level.

Trigonometry: introduction to the trigonometric functions, inverse trigonometric functions, radians, properties of sine and cosine functions, trigonometric identities, solving trigonometric equations

Geometry: circles and ellipses, triangles, SOHCAHTOA, sine and cosine rule, opposite and alternate angle theorems

Hyperbolic functions: introduction to hyperbolic functions and inverse hyperbolic functions including definitions, domains and ranges and graphs.

Complex numbers: introduction to the system of complex numbers and its geometrical interpretation.

Find out more about MAST0016

Statistical techniques are a fundamental tool in being able to measure, analyse and communicate information about sets of data. Using illustrative data sets we show how statistics can be indispensable in applied sciences and other quantitative areas. This module covers the basic methods used in probability and statistics using Excel for larger data sets. A more detailed indication of the module content follows.

Sampling from populations. Data handling and analysis using Excel. Graphical representation for the interpretation of univariate and bivariate data; outliers. Sample summary statistics: mean, variance, standard deviation, median, quartiles, inter-quartile range, correlation. Probability: combinatorics, conditional probability, Bayes' Theorem. Random variables: discrete, continuous; expectation, variance, standard deviation. Discrete and continuous distributions: Binomial, discrete uniform, Normal, uniform. Sampling distributions for the mean and proportion. Hypothesis testing: one sample, mean of Normal with known variance and proportion, 1- and 2-tail. Confidence intervals: one sample, mean of Normal with known variance and population proportion.

Find out more about MAST0025

Functions: Functions, inverse functions and composite functions. Domain and range.

Elementary functions including the exponential function, the logarithm and natural logarithm functions and ax for positive real numbers a. Basic introduction to limits and continuity of a function, without epsilon-delta proofs.

The derivative: The derivative as the gradient of the tangent to the graph; interpretation of the derivative as a rate of change. The formal definition of the derivative and the calculation of simple examples from first principles. Elementary properties of the derivative, including the product rule, quotient rule and the chain rule; differentiation of inverse functions; calculating derivatives of familiar functions, including trigonometric, exponential and logarithmic functions. Applications of the derivative, including optimisation, gradients, tangents and normal. Parametric and implicit differentiation of simple functions. Additional material may include L'Hopital’s Rule and Taylor series.

Graphs: Curve sketching including maxima, minima, stationary points, points of inflection, vertical and horizontal asymptotes and simple transformations on graphs of functions. Additional material may include parametric curves and use of Maple to plot functions.

Find out more about MAST3001

Vectors: Vectors in two and three dimensions. Magnitude and direction. Algebraic operations involving vectors and their geometrical interpretations including the scalar product between two vectors. Use vectors to solve simple problems in pure mathematics and applications.

Kinematics: Fundamental and derived quantities and units in the S.I. system. Position, displacement, distance travelled, velocity, speed, acceleration. Constant acceleration for motion in one and two dimensions. Motion under gravity in a vertical plane. Projectiles. Use of calculus for motion in a straight line.

Forces and Newton's Laws: Newton’s laws of motion applied to simple models of single and coupled bodies.

Find out more about MAST3002

This module introduces the ideas of integration and numerical methods.

a) Integration: Integration as a limit of a sum and graphical principles of integration, derivatives, anti-derivatives and the Fundamental Theorem of Calculus (without proof), definite and indefinite integrals, integration of simple functions.

b) Methods of integration: integration by parts, integration by change of variables and by substitution, integration by partial fractions.

c) Solving first order differential equations: separable and linear first order differential equations. Construction of differential equations in context, applications of differential equations and interpretation of solutions of differential equations.

d) Maple: differentiation and integration, curve sketching, polygon plots, summations.

Additional material may include root finding using iterative methods, parametric integration, surfaces and volumes of revolution.

Find out more about MAST3003

Students will be introduced to key mathematical skills, necessary in studying for a mathematics degree: use of the University Library and other sources to support their learning, presenting mathematical arguments in a variety of formats, learn about the mathematical background and career progression of staff in the School and beyond, etc.

Students will also study various techniques of proof (by deduction, by exhaustion, by contradiction, etc.). These techniques will be illustrated through examples chosen from various areas of mathematics (and, in particular, co-requisite modules).

Find out more about MAST3004

Optional modules may include

Algebra: simplifying expressions and rearranging formulae, indices, surds, algebraic fractions, quadratic equations and the discriminant, completing the square and turning points of quadratics, simultaneous equations, inequalities, manipulating and factorising polynomials, polynomial long division, binomial expansions, exponentials and logarithms, equations involving exponentials, partial fractions.

Functions and graphs: sketching and recognising the graphs of elementary functions (powers of x, exponential, etc.) and the modulus function, the link between algebra and geometry, roots, points of intersection of curves, simple graph transformations.

Find out more about MAST0017

This module introduces the students to the basics of Maple and two topics in the mathematical sciences. The precise topics will vary in any particular year. Potential topics include (for example): history and/or people active in the mathematical sciences, algorithms, engaging the public in the mathematical sciences, mathematical games.

Maple: the Maple environment, basic commands, basic calculus, curve sketching.

There is no specific mathematical syllabus for the topics part of the module.

Find out more about MAST0018

Stage 1

Compulsory modules currently include

This module serves as an introduction to algebraic methods which are central in modern mathematics and that have found applications in many other sciences, but also in our everyday life. In this course students will also gain an appreciation of the concept of proof in mathematics.

Find out more about MAST4001

This module introduces mathematical modelling and Newtonian mechanics. Tutorials and Maple worksheets will be used to support taught material.

The modelling cycle: General description with examples; Newton's law of cooling; population growth (Malthusian and logistic models); simple reaction kinetics (unimolecular and bimolecular reactions); dimensional consistency

Motion of a body: frames of reference; a particle's position vector and its time derivatives (velocity and acceleration) in Cartesian coordinates; mass, momentum and centre of mass; Newton's laws of motion; linear springs; gravitational acceleration and the pendulum; projectile motion

Orbital motion: Newton's law of gravitation; position, velocity and acceleration in plane polar coordinates; planetary motion and Kepler's laws.

Find out more about MAST4002

This module considers the abstract theory of linear spaces together with applications to matrix algebra and other areas of Mathematics (and its applications). Since linear spaces are of fundamental importance in almost every area of mathematics, the ideas and techniques discussed in this module lie at the heart of mathematics. Topics covered will include vector spaces, linear transformations, eigenvalues and eigenvectors, diagonalisation, orthogonality and applications.

Find out more about MAST4004

This module introduces widely-used mathematical methods for functions of a single variable. The emphasis is on the practical use of these methods; key theorems are stated but not proved at this stage.

Basic notation for sets and number systems including complex numbers (a+ib representation only). Standard functions: trig functions, polynomials, rational functions, exponentials and logarithms.

Single variable calculus: Differentiation, including product and chain rules; Fundamental Theorem of Calculus (statement only), elementary integrals, change of variables, integration by parts, differentiation of integrals with variable limits.

Curve sketching: graphs of elementary functions, maxima, minima and points of inflection, asymptotes.

Algebra of matrices and vectors; addition, multiplication, transposes, inner-products.

Row reduced echelon form, solving linear systems (homogeneous and inhomogeneous).

Inverse of a matrix.

Find out more about MAST4006

This module introduces widely-used mathematical methods for vectors and functions of two or more variables. The emphasis is on the practical use of these methods; key theorems are stated but not proved at this stage. Tutorials and Maple worksheets will be used to support taught material.

Vectors: Cartesian coordinates; vector algebra; scalar, vector and triple products (and geometric interpretation); straight lines and planes expressed as vector equations; parametrized curves; differentiation of vector-valued functions of a scalar variable; tangent vectors; vector fields (with everyday examples)

Partial differentiation: Functions of two variables; partial differentiation (including the chain rule and change of variables); maxima, minima and saddle points; Lagrange multipliers

Integration in two dimensions: Double integrals in Cartesian coordinates; plane polar coordinates; change of variables for double integrals; line integrals; Green's theorem (statement – justification on rectangular domains only).

Find out more about MAST4007

Introduction to Probability. Concepts of events and sample space. Set theoretic description of probability, axioms of probability, interpretations of probability (objective and subjective probability).

Theory for unstructured sample spaces. Addition law for mutually exclusive events. Conditional probability. Independence. Law of total probability. Bayes' theorem. Permutations and combinations. Inclusion-Exclusion formula.

Discrete random variables. Concept of random variable (r.v.) and their distribution. Discrete r.v.: Probability function (p.f.). (Cumulative) distribution function (c.d.f.). Mean and variance of a discrete r.v. Examples: Binomial, Poisson, Geometric.

Continuous random variables. Probability density function; mean and variance; exponential, uniform and normal distributions; normal approximations: standardisation of the normal and use of tables. Transformation of a single r.v.

Joint distributions. Discrete r.v.'s; independent random variables; expectation and its application.

Generating functions. Idea of generating functions. Probability generating functions (pgfs) and moment generating functions (mgfs). Finding moments from pgfs and mgfs. Sums of independent random variables.

Laws of Large Numbers. Weak law of large numbers. Central Limit Theorem.

Find out more about MAST4009

Real Numbers: Rational and real numbers, absolute value and metric structure on the real numbers, induction, infimum and supremum.

Limits of Sequences: Sequences, definition of convergence, epsilon terminology, uniqueness, algebra of limits, comparison principles, standard limits, subsequences and non-existence of limits, convergence to infinity.

Completeness Properties: Cantor's Intersection Theorem, limit points, Bolzano-Weierstrass theorem, Cauchy sequences.

Continuity of Functions: Functions and basic definitions, limits of functions, continuity and epsilon terminology, sequential continuity, Intermediate Value Theorem.

Differentiation: Definition of the derivative, product rule, quotient rule and chain rule, derivatives and local properties, Mean Value Theorem, L'Hospital's Rule.

Taylor Approximation: Taylor's Theorem, remainder term, Taylor series, standard examples, limits using Taylor series.

Find out more about MAST4010

Introduction to R and investigating data sets. Basic use of R (Input and manipulation of data). Graphical representations of data. Numerical summaries of data.

Sampling and sampling distributions. ?² distribution. t-distribution. F-distribution. Definition of sampling distribution. Standard error. Sampling distribution of sample mean (for arbitrary distributions) and sample variance (for normal distribution) .

Point estimation. Principles. Unbiased estimators. Bias, Likelihood estimation for samples of discrete r.v.s

Interval estimation. Concept. One-sided/two-sided confidence intervals. Examples for population mean, population variance (with normal data) and proportion.

Hypothesis testing. Concept. Type I and II errors, size, p-values and power function. One-sample test, two sample test and paired sample test. Examples for population mean and population variance for normal data. Testing hypotheses for a proportion with large n. Link between hypothesis test and confidence interval. Goodness-of-fit testing.

Association between variables. Product moment and rank correlation coefficients. Two-way contingency tables. ?² test of independence.

Find out more about MAST4011

Stage 2

Compulsory modules currently include

The concept of symmetry is one of the most fruitful ideas through which mankind has tried to understand order and beauty in nature and art. This module first develops the concept of symmetry in geometry. It subsequently discusses links with the fundamental notion of a group in algebra. Outline syllabus includes: Groups from geometry; Permutations; Basic group theory; Action of groups and applications to (i) isometries of regular polyhedra; (ii) counting colouring problems; Matrix groups.

Find out more about MAST5003

In this module we will study linear partial differential equations, we will explore their properties and discuss the physical interpretation of certain equations and their solutions. We will learn how to solve first order equations using the method of characteristics and second order equations using the method of separation of variables.

Introduction to linear PDEs: Review of partial differentiation; first-order linear PDEs, the heat equation, Laplace's equation and the wave equation, with simple models that lead to these equations; the superposition principle; initial and boundary conditions

Separation of variables and series solutions: The method of separation of variables; simple separable solutions of the heat equation and Laplace’s equation; Fourier series; orthogonality of the Fourier basis; examples and interpretation of solutions

Solution by characteristics: the method of characteristics for first-order linear PDEs; examples and interpretation of solutions; characteristics of the wave equation; d’Alembert’s solution, with examples; domains of influence and dependence; causality.

Find out more about MAST5005

This module builds on the Stage 1 Real Analysis 1 module. We will extend our knowledge of functions of one real variable, look at series, and study functions of several real variables and their derivatives.

The outline syllabus includes: Continuity and uniform continuity of functions of one variable, series and power series, the Riemann integral, limits and continuity for functions of several variables, differentiation of functions of several variables, extrema, the Inverse and Implicit Function Theorems.

Find out more about MAST5013

Optional modules may include

Constructing suitable models for data is a key part of statistics. For example, we might want to model the yield of a chemical process in terms of the temperature and pressure of the process. Even if the temperature and pressure are fixed, there will be variation in the yield which motivates the use of a statistical model which includes a random component. In this module, students study linear regression models (including estimation from data and drawing of conclusions), the use of likelihood to estimate models and its application in simple stochastic models. Both theoretical and practical aspects are covered, including the use of R.

Find out more about MAST5001

The main aim of this module is to give an introduction to the basics of differential geometry, keeping in mind the recent applications in mathematical physics and the analysis of pattern recognition. Outline syllabus includes: Curves and parameterization; Curvature of curves; Surfaces in Euclidean space; The first fundamental form; Curvature of surfaces; Geodesics.

Find out more about MAST5002

This module will present a new perspective on Newton's familiar laws of motion. First we introduce variational calculus with applications such as finding the paths of shortest distance. This will lead us to the principle of least action from which we can derive Newton's law for conservative forces. We will also learn how symmetries lead to constants of motion. We then derive Hamilton's equations and discuss their underlying structures. The formalisms we introduce in this module form the basis for all of fundamental modern physics, from electromagnetism and general relativity, to the standard model of particle physics and string theory.

Indicative syllabus:

Review of Newton mechanics: Newton's law; harmonic and anharmonic oscillators (closed and unbound orbits, turning points); Kepler problem: energy and angular momentum conservation

Lagrangian Mechanics: Introdution to variational calculus with simple applications (shortest path - geodesic, soap film, brachistochrone problem); principle of least action: Euler-Lagrange equations (Newtonian mechanics with conservative forces); constraints and generalised coordinates (particle on a hoop, double pendulum, normal modes); Noether's theorem (energy and angular momentum conservation)

Hamiltonian Dynamics: Hamilton's equations; Legendre transform; Hamiltonian phase space (harmonic oscillator, anharmonic oscillators and the mathematical pendulum); Liouville's theorem; Poisson brackets.

Find out more about MAST5004

Probability: Joint distributions of two or more discrete or continuous random variables. Marginal and conditional distributions. Independence. Properties of expectation, variance, covariance and correlation. Poisson process and its application. Sums of random variables with a random number of terms.

Transformations of random variables: Various methods for obtaining the distribution of a function of a random variable —method of distribution functions, method of transformations, method of generating functions. Method of transformations for several variables. Convolutions. Approximate method for transformations.

Sampling distributions: Sampling distributions related to the Normal distribution — distribution of sample mean and sample variance; independence of sample mean and variance; the t distribution in one- and two-sample problems.

Statistical inference: Basic ideas of inference — point and interval estimation, hypothesis testing.

Point estimation: Methods of comparing estimators — bias, variance, mean square error, consistency, efficiency. Method of moments estimation. The likelihood and log-likelihood functions. Maximum likelihood estimation.

Hypothesis testing: Basic ideas of hypothesis testing — null and alternative hypotheses; simple and composite hypotheses; one and two-sided alternatives; critical regions; types of error; size and power. Neyman-Pearson lemma. Simple null hypothesis versus composite alternative. Power functions. Locally and uniformly most powerful tests.

Composite null hypotheses. The maximum likelihood ratio test.

Interval estimation: Confidence limits and intervals. Intervals related to sampling from the Normal distribution. The method of pivotal functions. Confidence intervals based on the large sample distribution of the maximum likelihood estimator – Fisher information, Cramer-Rao lower bound. Relationship with hypothesis tests. Likelihood-based intervals.

Find out more about MAST5007

This module is an introduction to the methods, tools and ideas of numerical computation. In mathematics, one often encounters standard problems for which there are no easily obtainable explicit solutions, given by a closed formula. Examples might be the task of determining the value of a particular integral, finding the roots of a certain non-linear equation or approximating the solution of a given differential equation. Different methods are presented for solving such problems on a modern computer, together with their applicability and error analysis. A significant part of the module is devoted to programming these methods and running them in MATLAB.

Introduction: Importance of numerical methods; short description of flops, round-off error, conditioning

Solution of linear and non-linear equations: bisection, Newton-Raphson, fixed point iteration

Interpolation and polynomial approximation: Taylor polynomials, Lagrange interpolation, divided differences, splines

Numerical integration: Newton-Cotes rules, Gaussian rules

Numerical differentiation: finite differences

Introduction to initial value problems for ODEs: Euler methods, trapezoidal method, Runge-Kutta methods.

Find out more about MAST5009

This module introduces the basic ideas to solve certain ordinary differential equations, like first order scalar equations, second order linear equations and systems of linear equations. It mainly considers their qualitative and analytical aspects. Outline syllabus includes: First-order scalar ODEs; Second-order scalar linear ODEs; Existence and Uniqueness of Solutions; Autonomous systems of two linear first-order ODEs.

Find out more about MAST5012

Can we square a circle? Can we trisect an angle? These two questions were studied by the Ancient Greeks and were only solved in the 19th century using algebraic structures such as rings, fields and polynomials. In this module, we introduce these ideas and concepts and show how they generalise well-known objects such as integers, rational numbers, prime numbers, etc. The theory is then applied to solve problems in Geometry and Number Theory. This part of algebra has many applications in electronic communication, in particular in coding theory and cryptography.

Find out more about MAST5014

The security of our phone calls, bank transfers, etc. all rely on one area of Mathematics: Number Theory. This module is an elementary introduction to this wide area and focuses on solving Diophantine equations. In particular, we discuss (without proof) Fermat's Last Theorem, arguably one of the most spectacular mathematical achievements of the twentieth century. Outline syllabus includes: Modular Arithmetic; Prime Numbers; Introduction to Cryptography; Quadratic Residues; Diophantine Equations.

Find out more about MAST5660

Year in industry

The year in industry included in this programme provides you with the opportunity to gain valuable work experience and greatly enhances your cv. We can help you to find a placement and support you while you are there.

Stage 3

Optional modules may include

This module will present a new perspective on Newton's familiar laws of motion. First we introduce variational calculus with applications such as finding the paths of shortest distance. This will lead us to the principle of least action from which we can derive Newton's law for conservative forces. We will also learn how symmetries lead to constants of motion. We then derive Hamilton's equations and discuss their underlying structures. The formalisms we introduce in this module form the basis for all of fundamental modern physics, from electromagnetism and general relativity, to the standard model of particle physics and string theory.

Indicative syllabus:

Review of Newton mechanics: Newton's law; harmonic and anharmonic oscillators (closed and unbound orbits, turning points); Kepler problem: energy and angular momentum conservation

Lagrangian Mechanics: Introdution to variational calculus with simple applications (shortest path - geodesic, soap film, brachistochrone problem); principle of least action: Euler-Lagrange equations (Newtonian mechanics with conservative forces); constraints and generalised coordinates (particle on a hoop, double pendulum, normal modes); Noether's theorem (energy and angular momentum conservation)

Hamiltonian Dynamics: Hamilton's equations; Legendre transform; Hamiltonian phase space (harmonic oscillator, anharmonic oscillators and the mathematical pendulum); Liouville's theorem; Poisson brackets.

Find out more about MAST5004

The origins of Bayesian inference lie in Bayes' Theorem for density functions; the likelihood function and the prior distribution combine to provide a posterior distribution which reflects beliefs about an unknown parameter based on the data and prior beliefs. Statistical inference is determined solely by the posterior distribution. So, for example, an estimate of the parameter could be the mean value of the posterior distribution. This module will provide a full description of Bayesian analysis and cover popular models, such as the normal distribution. Initially, the flavour will be one of describing the Bayesian counterparts to well known classical procedures such as hypothesis testing and confidence intervals. Outline Syllabus includes: Bayes Theorem for density functions; Exchangeability; Choice of priors; Conjugate models; Predictive distribution; Bayes estimates; Sampling density functions; Gibbs samplers; OpenBUGS; Bayesian hierarchical models; Applications of hierarchical models; Bayesian model choice.

Find out more about MAST5380

This module is an introduction to point-set topology, a topic that is relevant to many other areas of mathematics. In it, we will be looking at the concept of topological spaces and related constructions. In an Euclidean space, an "open set" is defined as a (possibly infinite) union of open "epsilon-balls". A topological space generalises the notion of "open set" axiomatically, leading to some interesting and sometimes surprising geometric consequences. For example, we will encounter spaces where every sequence of points converges to every point in the space, see why for topologists a doughnut is the same as a coffee cup, and have a look at famous objects such as the Moebius strip or the Klein bottle. 

Find out more about MAST5670

This module provides an introduction to the study of orthogonal polynomials and special functions. They are essentially useful mathematical functions with remarkable properties and applications in mathematical physics and other branches of mathematics. Closely related to many branches of analysis, orthogonal polynomials and special functions are related to important problems in approximation theory of functions, the theory of differential, difference and integral equations, whilst having important applications to recent problems in quantum mechanics, mathematical statistics, combinatorics and number theory. The emphasis will be on developing an understanding of the structural, analytical and geometrical properties of orthogonal polynomials and special functions. The module will utilise physical, combinatorial and number theory problems to illustrate the theory and give an insight into a plank of applications, whilst including some recent developments in this field. The development will bring aspects of mathematics as well as computation through the use of MAPLE. The topics covered will include: The hypergeometric functions, the parabolic cylinder functions, the confluent hypergeometric functions (Kummer and Whittaker) explored from their series expansions, analytical and geometrical properties, functional and differential equations; sequences of orthogonal polynomials and their weight functions; study of the classical polynomials and their applications as well as other hypergeometric type polynomials.

Find out more about MAST5680

This module provides a rigorous foundation for the solution of systems of polynomial equations in many variables. In the 1890s, David Hilbert proved four ground-breaking theorems that prepared the way for Emmy Nöther's famous foundational work in the 1920s on ring theory and ideals in abstract algebra. This module will echo that historical progress, developing Hilbert's theorems and the essential canon of ring theory in the context of polynomial rings. It will take a modern perspective on the subject, using the Gröbner bases developed in the 1960s together with ideas of computer algebra pioneered in the 1980s. The syllabus will include

• Multivariate polynomials, monomial orders, division algorithm, Gröbner bases;

• Hilbert's Nullstellensatz and its meaning and consequences for solving polynomials in several variables;

• Elimination theory and applications;

• Linear equations over systems of polynomials, syzygies.

Find out more about MAST5740

Most differential equations which arise from physical systems cannot be solved explicitly in closed form, and thus numerical solutions are an invaluable way to obtain information about the underlying physical system. The first half of the module is concerned with ordinary differential equations. Several different numerical methods are introduced and error growth is studied. Both initial value and boundary value problems are investigated. The second half of the module deals with the numerical solution of partial differential equations. The syllabus includes: initial value problems for ordinary differential equations; Taylor methods; Runge-Kutta methods; multistep methods; error bounds and stability; boundary value problems for ordinary differential equations; finite difference schemes; difference schemes for partial differential equations; iterative methods; stability analysis.

Find out more about MAST5870

Combinatorics is a field in mathematics that studies discrete, usually finite, structures, such as graphs. It not only plays an important role in numerous parts of mathematics, but also has real world applications. In particular, it underpins a variety of computational processes used in digital technologies and the design of computing hardware.

Among other things, this module provides an introduction to graph theory. Graphs are discrete objects consisting of vertices that are connected by edges. We will discuss a variety of concepts and results in graph theory, and some fundamental graph algorithms. Topics may include, but are not restricted to: trees, shortest paths problems, walks on graphs, graph colourings and embeddings, flows and matchings, and matrices and graphs.

Find out more about MAST5950

Linear PDEs. Dispersion relations. Review of d'Alembert’s solutions of the wave equation. Review of Fourier transforms for solving linear diffusion equations.

Quasi-linear first-order PDEs. Total differential equations. Integral curves and integrability conditions. The method of characteristics.

Shock waves. Discontinuous solutions. Breaking time. Rankine-Hugoniot jump condition. Shock waves. Rarefaction waves. Applications of shock waves, including traffic flow.

General first-order nonlinear PDEs. Charpit's method, Monge Cone, the complete integral.

Nonlinear PDEs. Burgers' equation; the Cole-Hopf transformation and exact solutions. Travelling wave and scaling solutions of nonlinear PDEs. Applications of travelling wave and scaling solutions to reaction-diffusion equations. Exact solutions of nonlinear PDEs. Applications of nonlinear waves, including to ocean waves (e.g. rogue waves, tsunamis).

Find out more about MAST6002

This is a practical module to develop the skills required by a professional statistician (report writing, consultancy, presentation, wider appreciation of assumptions underlying methods, selection and application of analysis method, researching methods).

Software: R, SPSS and Excel (where appropriate/possible). Report writing in Word. PowerPoint for presentations.

• Presentation of data

• Report writing and presentation skills

• Hypothesis testing: formulating questions, converting to hypotheses, parametric and non-parametric methods and their assumptions, selection of appropriate method,

application and reporting. Use of resources to explore and apply additional tests. Parametric and non-parametric tests include, but are not limited to, t-tests, likelihood

ratio tests, score tests, Wald test, chi-squared tests, Mann Whitney U-test, Wilcoxon signed rank test, McNemar's test.

• Linear and Generalised Linear Models: simple linear and multiple regression, ANOVA and ANCOVA, understanding the limitations of linear regression, generalised linear

models, selecting the appropriate distribution for the data set, understanding the difference between fixed and random effects, fitting models with random effects, model

selection.

• Consultancy skills: group work exercise(s)

Find out more about MAST6012

Revision of complex numbers, the complex plane, de Moivre's and Euler's theorems, roots of unity, triangle inequality

Sequences and limits: Convergence of a sequence in the complex plane. Absolute convergence of complex series. Criteria for convergence. Power series, radius of convergence

Complex functions: Domains, continuity, complex differentiation. Differentiation of power series. Complex exponential and logarithm, trigonometric, hyperbolic functions. Cauchy-Riemann equations

Complex Integration: Jordan curves, winding numbers. Cauchy's Theorem. Analytic functions. Liouville's Theorem, Maximum Modulus Theorem

Singularities of functions: poles, classification of singularities. Residues. Laurent expansions. Applications of Cauchy's theorem. The residue theorem. Evaluation of real integrals.

Possible additional topics may include Rouche’s Theorem, other proofs of the Fundamental Theorem of Algebra, conformal mappings, Mobius mappings, elementary Riemann surfaces, and harmonic functions.

Find out more about MAST6017

In this module we study the fundamental concepts and results in game theory. We start by analysing combinatorial games, and discuss game trees, winning strategies, and the classification of positions in so called impartial combinatorial games. We then move on to discuss two-player zero-sum games and introduce security levels, pure and mixed strategies, and prove the famous von Neumann Minimax Theorem. We will see how to solve zero-sum two player games using domination and discuss a general method based on linear programming. Subsequently we analyse arbitrary sum two-player games and discuss utility, best responses, Nash equilibria, and the Nash Equilibrium Theorem. The final part of the module is devoted to multi-player games and cooperation; we analyse coalitions, the core of the game, and the Shapley value.

Find out more about MAST6018

Metric spaces: Examples of metrics and norms, topology in metric spaces, sequences and convergence, uniform convergence, continuous maps, compactness, completeness and completions, contraction mapping theorem and applications.

Normed spaces: Examples, including function spaces, Banach spaces and completeness, finite and infinite dimensional normed spaces, continuity of linear operators and spaces of bounded linear operators, compactness in normed spaces, Arzela-Ascoli theorem, Weierstrass approximation theorem.

Find out more about MAST6024

Sampling: Simple random sampling. Sampling for proportions and percentages. Estimation of sample size. Stratified sampling. Systematic sampling. Ratio and regression estimates. Cluster sampling. Multi-stage sampling and design effect. Questionnaire design. Response bias and non-response.

General principles of experimental design: blocking, randomization, replication. One-way ANOVA. Two-way ANOVA. Orthogonal and non-orthogonal designs. Factorial designs: confounding, fractional replication. Analysis of covariance.

Design of clinical trials: blinding, placebos, eligibility, ethics, data monitoring and interim analysis. Good clinical practice, the statistical analysis plan, the protocol. Equivalence and noninferiority. Sample size. Phase I, II, III and IV trials. Parallel group trials. Multicentre trials.

Find out more about MAST6028

Multivariate normal distribution, Inference from multivariate normal samples, principal component analysis, mixture models, factor analysis, clustering methods, discrimination and classification, graphical models, the use of appropriate software.

Find out more about MAST6029

This module provides an overview of analytical careers in finance and explores the mathematical techniques used by actuaries, accountants and financial analysts. Students will learn about different types of financials assets, such as shares, bonds and derivatives and how to work out how much they are worth. They will also look at different types of debt and learn how mortgages and other loans are calculated. Developing these themes, the module will explain how to use maths to make financial decisions, such as how much an investor should pay for a financial asset or how a company can decide which projects to invest in or how much money to borrow. Risk management is a vital part of most mathematical careers in finance so the module will also cover different mathematical techniques for measuring and mitigating financial risk. Extension topics may include complex derivatives, economic theories of finance and the dangers of misusing mathematics. The module provides an opportunity to apply complex mathematical techniques to important real-world questions and is excellent preparation for those considering a financial career.

Introduction to financial mathematics: Key uses of mathematics in finance; key practitioners of financial mathematics.

Financial valuation and cash flow analysis: Discounting, Interest rates and time requirements, Future and Present value. Project Evaluation.

Characteristics and valuation of different financial securities: Debt capital, bonds and stocks, valuation of bonds and stocks.

Loans and interest rates: term structure of interest rates, spot and forward rates, types of loan, APR, loan schedules.

Capital structure and the cost of capital: Gearing, WACC, understanding betas.

Additional topics that may be covered: arbitrage and forward contracts, efficient markets hypothesis, pricing and valuing forward contracts, option pricing and the Black Scholes model, credit derivatives and systemic risks, limitations of mathematical modelling.

Find out more about MAST6091

Introduction: Principles and examples of stochastic modelling, types of stochastic process, Markov property and Markov processes, short-term and long-run properties. Applications in various research areas.

Random walks: The simple random walk. Walk with two absorbing barriers. First–step decomposition technique. Probabilities of absorption. Duration of walk. Application of results to other simple random walks. General random walks. Applications.

Discrete time Markov chains: n–step transition probabilities. Chapman-Kolmogorov equations. Classification of states. Equilibrium and stationary distribution. Mean recurrence times. Simple estimation of transition probabilities. Time inhomogeneous chains. Elementary renewal theory. Simulations. Applications.

Continuous time Markov chains: Transition probability functions. Generator matrix. Kolmogorov forward and backward equations. Poisson process. Birth and death processes. Time inhomogeneous chains. Renewal processes. Applications.

Queues and branching processes: Properties of queues - arrivals, service time, length of the queue, waiting times, busy periods. The single-server queue and its stationary behaviour. Queues with several servers. Branching processes. Applications.

In addition, level 7 students will study more complex queuing systems and continuous-time branching processes.

This module will cover a number of syllabus items set out in Subject CS2 published by the Institute and Faculty of Actuaries. This is a dynamic syllabus, changing regularly to reflect current practice.

Find out more about MAST6360

Stationary Time Series: Stationarity, autocovariance and autocorrelation functions, partial autocorrelation functions, ARMA processes.

ARIMA Model Building and Testing: estimation, Box-Jenkins, criteria for choosing between models, diagnostic tests for residuals of a time series after estimation.

Forecasting: Holt-Winters, Box-Jenkins, prediction bounds.

Testing for Trends and Unit Roots: Dickey-Fuller, ADF, structural change, trend-stationarity vs difference stationarity.

Seasonality and Volatility: ARCH, GARCH, ML estimation.

Multiequation Time Series Models: transfer function models, vector autoregressive moving average (VARM(p,q)) models, impulse responses.

Spectral Analysis: spectral distribution and density functions, linear filters, estimation in the frequency domain, periodogram.

Simulation: generation of pseudo-random numbers, random variate generation by the inverse transform, acceptance rejection. Normal random variate generation: design issues and sensitivity analysis.

This module will cover a number of syllabus items set out in Subject CS2 published by the Institute and Faculty of Actuaries. This is a dynamic syllabus, changing regularly to reflect current practice.

Find out more about MAST6390

There is no specific mathematical syllabus for this module; students will chose a topic in mathematics, statistics or financial mathematics from a published list on which to base their coursework assessments (different topics for levels 6 and 7). The coursework is supported by a series of workshops covering various forms of written and oral communication. These may include critically evaluating the following: a research article in mathematics, statistics or finance; a survey or magazine article aimed at a scientifically-literate but non-specialist audience; a mathematical biography; a poster presentation of a mathematical topic; a curriculum vitae; an oral presentation with slides or board; a video or podcast on a mathematical topic. Guidance will be given on typesetting mathematics using LaTeX.

Find out more about MAST6703

There is no specific mathematical syllabus for this module. Students will study a topic in mathematics or statistics, either individually or within a small group, and produce an individual or group project on the topic as well as individual coursework assignments. Projects will be chosen from published lists of individual and of group projects. The coursework and project-work are supported by a series of workshops covering various forms of written and oral communication and by supervision from an academic member of staff.

The workshops may include critically evaluating the following: a research article in mathematics or statistics; a survey or magazine article aimed at a scientifically-literate but non-specialist audience; a mathematical biography; a poster presentation of a mathematical topic; a curriculum vitae; an oral presentation with slides or board; a video or podcast on a mathematical topic. Guidance will be given on typesetting mathematics using LaTeX.

Find out more about MAST6704

Statistics methods contribute significantly to areas such as biology, ecology, sociology and economics. The real data collected does not always follow standard statistical models. This module looks at modern statistical models and methods that can be utilised for such data, making use of R programs to execute these methods.

Indicative module content: Motivating examples; model fitting through maximum likelihood for specific examples; function optimization methods; profile likelihood; score tests; Wald tests; confidence interval construction; latent variable models; EM algorithm; mixture models; simulation methods; importance sampling; kernel density estimation; Monte Carlo inference; bootstrap; permutation tests; R programs.

Find out more about MAST7710

Fees

The 2021/22 annual tuition fees for this programme are:

  • Home full-time £9,250
  • EU full-time £12,600
  • International full-time £16,800

For details of when and how to pay fees and charges, please see our Student Finance Guide.

For students continuing on this programme, fees will increase year on year by no more than RPI + 3% in each academic year of study except where regulated.* 

Your fee status

The University will assess your fee status as part of the application process. If you are uncertain about your fee status you may wish to seek advice from UKCISA before applying.

Fees for Year in Industry

Fees for Home undergraduates are £1,385.

Fees for Year Abroad

Fees for Home undergraduates are £1,385.

Students studying abroad for less than one academic year will pay full fees according to their fee status. 

Additional costs

General additional costs

Find out more about accommodation and living costs, plus general additional costs that you may pay when studying at Kent.

Funding

We have a range of subject-specific awards and scholarships for academic, sporting and musical achievement.

Search scholarships

University funding

Kent offers generous financial support schemes to assist eligible undergraduate students during their studies. See our funding page for more details. 

Government funding

You may be eligible for government finance to help pay for the costs of studying. See the Government's student finance website.

Scholarships

General scholarships

Scholarships are available for excellence in academic performance, sport and music and are awarded on merit. For further information on the range of awards available and to make an application see our scholarships website.

The Kent Scholarship for Academic Excellence

At Kent we recognise, encourage and reward excellence. We have created the Kent Scholarship for Academic Excellence. 

The scholarship will be awarded to any applicant who achieves a minimum of A*AA over three A levels, or the equivalent qualifications (including BTEC and IB) as specified on our scholarships pages.

Teaching and assessment

Teaching amounts to approximately 16 hours of lectures and classes per week. Modules that involve programming or working with computer software packages usually include practical sessions.

The majority of Stage 1 modules are assessed by end-of-year examinations. Many Stage 2 and 3 modules include coursework which normally counts for 20% of the final assessment. Both Stage 2 and 3 marks count towards your final degree result.

Contact hours

For a student studying full time, each academic year of the programme will comprise 1200 learning hours which include both direct contact hours and private study hours.  The precise breakdown of hours will be subject dependent and will vary according to modules.  Please refer to the individual module details under Course Structure.

Methods of assessment will vary according to subject specialism and individual modules.  Please refer to the individual module details under Course Structure.

Programme aims

The programme aims to:

  • equip students with the technical appreciation, skills and knowledge appropriate to a degree in Mathematics
  • develop students’ facilities of rigorous reasoning and precise expression
  • develop students’ abilities to formulate and solve mathematical problems
  • encourage an appreciation of recent developments in mathematics and of the links between the theory of mathematics and its practical application
  • provide students with a logical, mathematical approach to solving problems
  • provide students with an enhanced capacity for independent thought and work
  • ensure students are competent in the use of information technology and are familiar with computers and the relevant software
  • provide students with opportunities to study advanced topics in mathematics, engage in research at some level, and develop communication and personal skills.

Learning outcomes

Knowledge and understanding

You gain knowledge and understanding of:

  • the core principles of calculus, algebra, mathematical methods, discrete mathematics, analysis and linear algebra
  • statistics in the areas of probability and inference
  • information technology as relevant to mathematicians
  • methods and techniques of mathematics
  • the role of logical mathematical argument and deductive reasoning.

Intellectual skills

You develop your intellectual skills in the following areas:

  • the ability to demonstrate a reasonable understanding of mathematics
  • the calculation and manipulation of the material written within the programme
  • the ability to apply a range of concepts and principles in various contexts
  • the ability to use logical argument
  • the ability to solve mathematical problems by various methods
  • the relevant computer skills
  • the ability to work independently.

Subject-specific skills

You gain subject-specific skills in the following areas:

  • the ability to demonstrate knowledge of key mathematical concepts and topics, both explicitly and by applying them to the solution of problems
  • the ability to comprehend problems, abstract the essentials of problems and formulate them mathematically and in symbolic form so as to facilitate their analysis and solution
  • the use of computational and more general IT facilities as an aid to mathematical processes
  • the presentation of mathematical arguments and conclusions with clarity and accuracy.

Transferable skills

You gain transferable skills in the following areas:

  • problem-solving skills, relating to qualitative and quantitative information
  • communication skills
  • numeracy and computational skills
  • information-retrieval skills, in relation to primary and secondary information sources, including through online computer searches
  • information technology skills such as wordprocessing, spreadsheet use and internet communication
  • time-management and organisational skills, as shown by the ability to plan and implement effective modes of working
  • study skills needed for continuing professional development.

Independent rankings

Mathematics at Kent scored 91% overall in The Complete University Guide 2021.

For graduate prospects, Mathematics at Kent was ranked 3rd in The Complete University Guide 2021, and scored over 89% in The Times Good University Guide 2020 and 87% in The Guardian University Guide 2020.

Over 95% of Mathematics and Statistics graduates who responded to the most recent national survey of graduate destinations were in work or further study within six months (DLHE, 2017).

Careers

Graduate destinations

Recent graduates have gone on to work in:

  • medical statistics
  • the pharmaceutical industry
  • the aerospace industry
  • software development
  • teaching
  • actuarial work
  • civil service statistics
  • chartered accountancy
  • the oil industry.

Help finding a job

The University has a friendly Careers and Employability Service, which can give you advice on how to:

  • apply for jobs
  • write a good CV
  • perform well in interviews.

Career-enhancing skills

You graduate with an excellent grounding in the fundamental concepts and principles of mathematics. Many career paths can benefit from the numerical and analytical skills you develop during your studies.

To help you appeal to employers, you also learn key transferable skills that are essential for all graduates. These include the ability to:

  • think critically
  • communicate your ideas and opinions
  • manage your time effectively
  • work independently or as part of a team.

You can also gain extra skills by signing up for one of our Kent Extra activities, such as learning a language or volunteering.

Professional recognition

This degree will meet the educational requirements of the Chartered Mathematician designation, awarded by the Institute of Mathematics and its Applications (IMA),

when it is followed by subsequent training and experience in employment to obtain equivalent competencies to those specified by the Quality Assurance Agency (QAA) for taught Master’s degrees.

Apply for Mathematics with a Foundation Year - BSc (Hons)

This course page is for the 2021/22 academic year. Please visit the current online prospectus for a list of undergraduate courses we offer.

Contact us

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United Kingdom/EU enquiries

Enquire online for full-time study

T: +44 (0)1227 816410

E: smsasugadmissions@kent.ac.uk


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International student enquiries

Enquire online

T: +44 (0)1227 823254
E: internationalstudent@kent.ac.uk

Discover Uni information

Discover Uni is designed to support prospective students in deciding whether, where and what to study. The site replaces Unistats from September 2019.

Discover Uni is jointly owned by the Office for Students, the Department for the Economy Northern Ireland, the Higher Education Funding Council for Wales and the Scottish Funding Council.

It includes:

  • Information and guidance about higher education
  • Information about courses
  • Information about providers

Find out more about the Unistats dataset on the Higher Education Statistics Agency website.