Mathematics

Mathematics and Statistics with a Year in Industry - BSc (Hons)

UCAS code GG1K

2019

Mathematics is important to the modern world. All quantitative science, including both physical and social sciences, is based on it. It provides the theoretical framework for physical science, statistics and data analysis as well as computer science. Our programme reflects this diversity and the excitement generated by new discoveries within mathematics.

Overview

The School of Mathematics, Statistics and Actuarial Science provides a supportive learning environment with high contact hours per module. Our academic staff are available to advise and support you throughout your studies, helping you to take responsibility for your own learning.

Graduates of this programme may be eligible to receive Graduate Statistician status from the Royal Statistical Society. This is the first step to becoming a Chartered Statistician.

Our degree programme

This programme, studied over four years, is for students who want to specialise in statistics, perhaps with a view to a career as a statistician. It shares a common core of Mathematics at Stage 1, and then moves on to cover abstract, analytical and computational techniques that give you the opportunity to specialise in areas such as non-linear differential equations, computational algebra and geometry, financial mathematics, forecasting, design and analysis of experiments, inference and stochastic processes.

Student view

Kezia shares her experiences studying BSc Mathematics and Statistics with a Year in Industry at Kent.



Year in industry

You spend a year working in industry between Stages 2 and 3. We can offer help and advice in finding a placement. This greatly enhances your CV and gives you the opportunity to apply your academic skills in a practical context. It also gives you an idea of your career options. Recent placements have included IBM, management consultancies, government departments, insurance companies and banks.

This degree is also available as a three-year course without a year in industry. For more details, see Mathematics and Statistics. 

Foundation year

If your grades do not qualify you for direct entry to this programme, you may be able to take a four-year degree with a foundation year. For more details see Mathematics including a Foundation Year.

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 of Mathematics, Statistics and Actuarial Science also puts on regular events that you are welcome to attend. In the past, these have included:

  • seminars and workshops
  • employability events.

Independent rankings

Of Mathematics and Statistics students who graduated from Kent in 2016, over 96% were in work or further study within six months (DLHE).

Teaching Excellence Framework

Based on the evidence available, the TEF Panel judged that the University of Kent delivers consistently outstanding teaching, learning and outcomes for its students. It is of the highest quality found in the UK.

Please see the University of Kent's Statement of Findings for more information.

TEF Gold logo

Course structure

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 ‘wild’ modules from other programmes so you can customise your programme and explore other subjects that interest you.

Stage 1

Modules may include Credits

Increasingly data are collected to inform future decisions, varying from which websites people access on a regular basis to how patients respond to new drugs, to how the stock market responds to global events, or to how animals move around their local habitat. Therefore, most professionals will need to extract useful information from data and to manage and present data in their working lives.  This module explores some of the basic concepts of statistics, from data summarisation to the main methods of statistical inference. The techniques that are discussed can be used in their own right for simple statistical analyses, but serve as an important foundation for later, more advanced, modules. The statistical computing package R is used throughout the module for data analysis. The syllabus includes: an introduction to R and investigating data sets, sampling and sampling distributions, point and interval estimation, hypothesis testing, association between variables.

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15

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

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15

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.

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15

This module is a sequel to Algebraic Methods. It 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:

1 Vector Spaces: definition, examples, linearly independent and spanning sets, bases, dimension, subspaces.

2 Linear transformations: definition, examples, matrix of a linear transformation, change of basis, similar matrices.

3 Determinant of a linear transformation.

4 Eigenvalues/eigenvectors and diagonalisation: characteristic polynomial, invariant subspaces and upper triangular forms. Cayley-Hamilton Theorem.

5 Bilinear forms: inner products, norms, Cauchy-Schwarz inequality.

6 Orthonormal systems, the Gram-Schmidt process.

7 Symmetric Matrices. Every real symmetric matrix is diagonalisable.

8 Quadratic forms: Sylvester's Law of Inertia; signature of a quadratic form; application to conics (and quadrics if time permits).

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15

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. Tutorials and Maple worksheets will be used to support taught material.

Complex numbers: Complex arithmetic, the complex conjugate, the Argand diagram, de Moivre's Theorem, modulus-argument form; elementary functions

Polynomials: Fundamental Theorem of Algebra (statement only), roots, factorization, rational functions, partial fractions

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

Scalar ordinary differential equations (ODEs): definition; methods for first-order ODEs; principle of superposition for linear ODEs; particular integrals; second-order linear ODEs with constant coefficients; initial-value problems

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

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15

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)

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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.

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Topics covered will include:

Real Numbers: Rational and real numbers, absolute value and metric structure on the real numbers, induction, countability and uncountability, 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, O and o notation, limits using Taylor series.

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15

Stage 2

Modules may include Credits

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.

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15

This module is a pre-requisite for many of the other statistics modules at Stages 2, 3 and 4, but it can equally well be studied as a module in its own right, extending the ideas of probability and statistics met at Stage 1 and providing practice with the mathematical skills learned in MA348 and MA349. It starts by revising the idea of a probability distribution for one or more random variables and looks at different methods to derive the distribution of a function of random variables. These techniques are then used to prove some of the results underpinning the hypothesis test and confidence interval calculations met at Stage 1, such as for the t-test or the F-test. With these tools to hand, the module moves on to look at how to fit models (probability distributions) to sets of data. A standard technique, the method of maximum likelihood, is used to fit the model to the data to obtain point estimates of the model parameters and to construct hypothesis tests and confidence intervals for these parameters. Outline Syllabus includes: Joint, marginal and conditional distributions of discrete and continuous random variables; Transformations of random variables; Sampling distributions; Point and interval estimation; Properties of estimators; Maximum likelihood; Hypothesis testing; Neyman-Pearson lemma; Maximum likelihood ratio test.

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15

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, we study how suitable models can be constructed, how to fit them to data and how suitable conclusions can be drawn. Both theoretical and practical aspects are covered, including the use of R.

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15

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.

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15

This module builds on the Stage 1 Real Analysis 1 module. You will extend your knowledge of functions of one real variable, look at series, and study functions of several real variables and their derivatives. Outline syllabus includes: Continuity and uniform continuity of functions of one variable; Sequences of functions; Series; The Riemann integral; Functions of several variables; Differentiation of functions of several variables; Extrema; Inverse function and Implicit function theorems.

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15

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.

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15

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.

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15

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.

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15

This module covers aspects of Statistics which are particularly relevant to insurance. Some topics (such as risk theory and credibility theory) have been developed specifically for actuarial use. Other areas (such as Bayesian Statistics) have been developed in other contexts but now find applications in actuarial fields. Stochastic processes of events such as accidents, together with the financial flow of their payouts underpin much of the work. Since the earliest games of chance, the probability of ruin has been a topic of interest. Outline Syllabus includes: Decision Theory; Bayesian Statistics; Loss Distributions; Reinsurance; Credibility Theory; Empirical Bayes Credibility theory; Risk Models; Ruin Theory; Generalised Linear Models; Run-off Triangles.

Marks on this module can count towards exemption from the professional examination CT6 of the Institute and Faculty of Actuaries. Please see http://www.kent.ac.uk/casri/Accreditation/index.html for further details.

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15

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.

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15

Year in industry

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

Modules may include Credits

Students spend a year (minimum 900 hours) doing paid work in an organisation outside the University, usually in an industrial or commercial environment, applying and enhancing the skills and techniques they have developed and studied in the earlier stages of their degree programme.

The work they do is entirely under the direction of their industrial supervisor, but support is provided by the SMSAS Placement Officer or a member of the academic team. This support includes ensuring that the work they are being expected to do is such that they can meet the learning outcomes of the module.

Participation in this module is dependent on students obtaining an appropriate placement, for which support and guidance is provided through the School in the year leading up to the placement. It is also dependent on students progressing from Stage 2 of their studies.

Students who do not obtain a placement will be required to transfer to the appropriate programme without a Year in Industry.

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Students spend a year (minimum 900 hours) doing paid work in an organisation outside the University, usually in an industrial or commercial environment, applying and enhancing the skills and techniques they have developed and studied in the earlier stages of their degree programme. Employer evaluation, personal and professional reviews and on-line blogs are assessed under MAST5801 (Industrial Placement Experience) which is a co-requisite of this module. The assessment of this module draws on the experience gained in MAST5801 and is assessed through a Placement Report and Presentation.

The placement work they do is entirely under the direction of their industrial supervisor, but support is provided by the SMSAS Placement Officer or a member of the academic team. This support includes ensuring that the work they are being expected to do is such that they can meet the learning outcomes of this module.

Participation in the placement year, and hence in this module, is dependent on students obtaining an appropriate placement, for which support and guidance is provided through the School in the year leading up to the placement. It is also dependent on students progressing satisfactorily from Stage 2 of their studies.

Students who do not obtain a placement or who fail module MAST5801 (Industrial Placement Experience) will be required to transfer to the appropriate programme without a Year in Industry and any marks obtained on this module will not contribute to their final degree classification.

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Stage 3

Modules may include Credits

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)

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15

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.

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15

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.

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15

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.

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15

Each year three topics will be offered and will reflect recent advances in statistical modelling and statistical methodology. Example topics are:

a) Statistical Ecology: Understanding demographic parameters and how they are used to model population dynamics. Estimating abundance and the effect of heterogeneity. Models for estimating survival probabilities. Multi-site and multi-state models. Classical model-selection. Complex models. Case studies.

b) Survival analysis: Survival data, types of censoring. Failure times and hazard functions; Accelerated failure time model. Parametric models, exponential, piecewise exponential, Weibull. Nonparametric estimates: the Kaplan-Meier estimator, and asymptotic confidence regions. Parametric inference. Survival data with covariates. Proportional hazards. Cox's model and inference. Computer software: R and WinBUGS.

c) Regression models with many variables: Examples of high-dimensional problems; Penalized maximum likelihood; Ridge regression; non-negative garrote; Lasso and adaptive Lasso estimation; LARS algorithm; Oracle property; Elastic Net; Group lasso.

d) Modern nonparametric statistics: Bias-variance trade-off, Kernel density estimation, Kernel smoothing, Locally linear and locally quadratic estimation, basis function methods.

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15

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.

In addition, for level 7 students: advanced EM algorithm methods, advanced simulation methods, writing R programs for advanced methods and applications.

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15

A stochastic process is a process developing in time according to probability rules, for example, models for reserves in insurance companies, queue formation, the behaviour of a population of bacteria, and the persistence (or otherwise) of an unusual surname through successive generations.The syllabus will include coverage of a wide variety of stochastic processes and their applications: Markov chains; processes in continuous-time such as the Poisson process, the birth and death process and queues.

Marks on this module can count towards exemption from the professional examination CT4 of the Institute and Faculty of Actuaries. Please see http://www.kent.ac.uk/casri/Accreditation/index.html for further details.

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15

A time series is a collection of observations made sequentially in time. Examples occur in a variety of fields, ranging from economics to engineering, and methods of analysing time series constitute an important area of statistics. This module focuses initially on various time series models, including some recent developments, and provides modern statistical tools for their analysis. The second part of the module covers extensively simulation methods. These methods are becoming increasingly important tools as simulation models can be easily designed and run on modern PCs. Various practical examples are considered to help students tackle the analysis of real data.The syllabus includes: Difference equations, Stationary Time Series: ARMA process. Nonstationary Processes: ARIMA Model Building and Testing: Estimation, Box Jenkins, Criteria for choosing between models, Diagnostic tests.Forecasting: 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: Spectral Analysis. Generation of pseudo – random numbers, simulation methods: inverse transform and acceptance-rejection, design issues and sensitivity analysis.

Marks on this module can count towards exemption from the professional examination CT6 of the Institute and Faculty of Actuaries. Please see http://www.kent.ac.uk/casri/Accreditation/index.html for further details.

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15

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.

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15

Discrete mathematics has found new applications in the encoding of information. Online banking requires the encoding of information to protect it from eavesdroppers. Digital television signals are subject to distortion by noise, so information must be encoded in a way that allows for the correction of this noise contamination. Different methods are used to encode information in these scenarios, but they are each based on results in abstract algebra. This module will provide a self-contained introduction to this general area of mathematics.

Syllabus: Modular arithmetic, polynomials and finite fields. Applications to

• orthogonal Latin squares,

• cryptography, including introduction to classical ciphers and public key ciphers such as RSA,

• "coin-tossing over a telephone",

• linear feedback shift registers and m-sequences,

• cyclic codes including Hamming,

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15

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. 

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15

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.

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15

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.

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15

The aim of this module is to equip students with the skills needed to communicate mathematics effectively to the world. This module is supported by a series of workshops covering various forms of written and oral communication. Each student will choose a topic in mathematics, statistics or financial mathematics from a published list on which to base their three coursework assessments which include a scientific writing assessment and an oral presentation.

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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.

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• 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.

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15

Combinatorial games, game trees, strategy, classification of positions. Two-player zero-sum games, security levels, pure and mixed strategies, von Neumann's minimax theorem. Solving zero-sum two player games using linear programming. Arbitrary sum games, utility, and matrix games. Nash equilibrium, Nash equilibrium theorem, applications, and cooperation. Multi-player games, coalitions, and the Shapley value.

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15

Linear PDEs. Dispersion relations. Review of d'Alembert's solutions of the wave equation.

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).

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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.

Programme aims

The programme aims to:

  • equip students with the technical appreciation, skills and knowledge appropriate to a degree in mathematics and statistics
  • 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 statistics and of the links between theory and practical applications
  • 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, and statistics engage in research at some level, and develop communication and personal skills
  • provide successful students with eligibility for certain exemptions from examinations of the Royal Statistical Society
  • enable those students who are taking a year in industry to gain awareness of the application of technical concepts in the workplace.

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 and statistics
  • 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 and statistics
  • the calculation and manipulation of the material 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 and statistical 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 and statistical 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 and statistical processes
  • the presentation of mathematical and statistical 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 word-processing, 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.

Careers

This year in industry option gives you a real advantage in the graduate job market. Through your studies, you also acquire many transferable skills, including the ability to deal with challenging ideas, to think critically, to write well and to present your ideas clearly, all of which are considered essential by graduate employers.

Recent graduates have gone into careers in medical statistics, the pharmaceutical industry, the aerospace industry, software development, teaching, actuarial work, Civil Service statistics, chartered accountancy, the oil industry and postgraduate research.

Professional recognition

Graduates of this course can apply for Graduate Statistician Status awarded by the Royal Statistical Society. This is the first step to becoming a Chartered Statistician.

Entry requirements

Home/EU students

The University will consider applications from students offering a wide range of qualifications. Typical requirements are listed below. Students offering alternative qualifications should contact us for further advice. 

It is not possible to offer places to all students who meet this typical offer/minimum requirement.

New GCSE grades

If you’ve taken exams under the new GCSE grading system, please see our conversion table to convert your GCSE grades.

Qualification Typical offer/minimum requirement
A level

AAB including A in Mathematics (not Use of Mathematics). Either General Studies or Critical Thinking (but not both) can be accepted against the requirements.

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.

BTEC Level 3 Extended Diploma (formerly BTEC National Diploma)

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.

International Baccalaureate

34 points overall or 17 points at HL with Mathematics 6 at HL

International students

The University welcomes applications from international students. Our international recruitment team can guide you on entry requirements. See our International Student website for further information about entry requirements for your country.

If you need to increase your level of qualification ready for undergraduate study, we offer a number of International Foundation Programmes.

Meet our staff in your country

For more advice about applying to Kent, you can meet our staff at a range of international events.

English Language Requirements

Please see our English language entry requirements web page.

Please note that if you are required to meet an English language condition, we offer a number of 'pre-sessional' courses in English for Academic Purposes. You attend these courses before starting your degree programme. 

General entry requirements

Please also see our general entry requirements.

Fees

The 2019/20 tuition fees have not yet been set. As a guide only, the 2018/19 annual tuition fees for this programme are:

UK/EU Overseas
Full-time £9250 £15200

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

For 2018/19 entrants, the standard year in industry fee for home, EU and international students is £1,385

Fees for Year Abroad

UK, EU and international students on an approved year abroad for the full 2018/19 academic year pay £1,385 for that year. 

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

General additional costs

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

Funding

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. 

For 2018/19 entry, the scholarship will be awarded to any applicant who achieves a minimum of AAA over three A levels, or the equivalent qualifications (including BTEC and IB) as specified on our scholarships pages

The scholarship is also extended to those who achieve AAB at A level (or specified equivalents) where one of the subjects is either Mathematics or a Modern Foreign Language. Please review the eligibility criteria.

The Key Information Set (KIS) data is compiled by UNISTATS and draws from a variety of sources which includes the National Student Survey and the Higher Education Statistical Agency. The data for assessment and contact hours is compiled from the most populous modules (to the total of 120 credits for an academic session) for this particular degree programme. 

Depending on module selection, there may be some variation between the KIS data and an individual's experience. For further information on how the KIS data is compiled please see the UNISTATS website.

If you have any queries about a particular programme, please contact information@kent.ac.uk.