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Undergraduate Courses 2017

Financial Mathematics - BSc (Hons)

Canterbury

Overview

The Financial Mathematics programme provides a thorough grounding in the mathematical concepts, tools and skills needed to understand financial decision making. It offers the opportunity to study financial theory and applications built on rigorous foundations within a friendly and highly successful department.

Students gain access to knowledge and capabilities that are valued by financial sector employers, corporations, and postgraduate academic programmes. In combination with specialized finance and economics topics, the programme incorporates core mathematical principles, probability and inference and a range of statistical concepts and techniques. In addition, students have a chance to develop communication and personal skills.

The degree consists of compulsory modules, especially in the first two years, and some optional modules to suit the student’s interests and goals.  There is also the possibility of spending a year on work placement in industry.

Independent rankings

In the National Student Survey 2015, 93% of Mathematics students were satisfied with the overall quality of their course.

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.  Most programmes will require you to study a combination of compulsory and optional modules. You may also have the option to take ‘wild’ modules from other programmes offered by the University in order that you may customise your programme and explore other subject areas of interest to you or that may further enhance your employability.

Stage 1

Possible modules may include:

MA306 - Statistics (15 credits)

This module will introduce the student to the basic concepts of statistics. The material will be related to real data at every stage and MINITAB will be used to provide statistical computing facilities for all the material studied. Data description and data summary will be studied, followed by an introduction to the main methods of inference. Most material will be based on the Normal, t, and F distributions, but some simple non-parametric procedures will also be covered. The following is a brief summary of the topics to be covered in the module: graphical representation of data; numerical summaries of data; sampling distributions; point estimation; interval estimation; hypothesis tests; association between variables; introduction to nonparametric procedures.

Credits: 15 credits (7.5 ECTS credits).

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MA309 - Business Economics (15 credits)

The aim of this module is to introduce students to the core economic principles and how these could be used in a business environment to help decision making and behaviour. The coverage is aimed at being sufficient to enable students to gain exemptions from the Actuarial professional examinations, whilst also giving a coherent coverage of the material suitable for other degree programmes, where understanding economic concepts and principles is beneficial. The syllabus includes: the working of competitive markets, consumer demand and behaviour, product selection, marketing and advertising strategies, costs of production, production function, revenue and profit, profit maximisation under perfect competition and monopoly, imperfect competition, business strategy, the objectives of strategic management, firms' growth strategy, pricing strategies, government intervention, international trade, balance of payment and exchange rates, the role of money and interest rates in the economy, the level of business activity, unemployment, inflation and macroeconomic policy.



Marks on this module can count towards exemption from the professional examination CT7 of the Institute and Faculty of Actuaries. Please see http://www.kent.ac.uk/casri/Accreditation/index.html for further details.

Credits: 15 credits (7.5 ECTS credits).

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MA345 - Introduction to Finance (15 credits)

Time value of money: Basic concepts, Compounding to determine future values, Inflation,

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

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

Terminology in finance: Securities markets, primary market, secondary securities markets, the role of the various financial markets.

Credits: 15 credits (7.5 ECTS credits).

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MA347 - Linear Mathematics (15 credits)

This module serves as an introduction to algebraic methods and linear algebra methods. These are central in modern mathematics, having found applications in many other sciences and also in our everyday life.



Topics covered will include:

Basic set theory: introduction to sets, operations on sets (union, intersection, Cartesian product, complement), basic counting (inclusion-exclusion for 2 sets).

Functions and Relations: injective, surjective, bijective functions. Permutations, sign of a permutation. The Pigeonhole Principle. Cardinality of sets. Binomial coefficients, Binomial Theorem. Equivalence relations and partitions.

Systems of linear equations and Gaussian elimination: operations on systems of equations, echelon form, rank, consistency, homogeneous and non-homogeneous systems.

Matrices: operations, invertible matrices, trace, transpose.

Determinants: definition, properties and criterion for a matrix to be invertible.

Vector spaces: linearly independent and spanning sets, bases, dimension, subspaces.

Linear Transformations: Definition. Matrix of a Linear Transformation. Change of Basis.

Diagonalisation: Eigenvalues and Eigenvectors, invariant spaces, sufficient conditions.

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

Orthonormal systems: the Gram-Schmidt process.

Credits: 15 credits (7.5 ECTS credits).

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MA348 - Mathematical Methods 1 (15 credits)

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

Credits: 15 credits (7.5 ECTS credits).

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MA349 - Mathematical Methods 2 (15 credits)

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)

Credits: 15 credits (7.5 ECTS credits).

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MA351 - Probability (15 credits)

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.

Credits: 15 credits (7.5 ECTS credits).

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MA352 - Real Analysis 1 (15 credits)

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.

Credits: 15 credits (7.5 ECTS credits).

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Stage 2

Possible modules may include:

MA517 - Corporate Finance for Financial Mathematics (15 credits)

This module introduces and explores a range of topics relating to corporate finance which are fundamental to understanding why and how companies raise money to start a business or expand an existing one. The module covers the different ways that the money can be raised, for example from a bank or through a stocks and shares market, and the interest rate or investment return that an investor will expect to receive from a company in order to provide the money required. This is a very practical module to the extent that it will help students develop business awareness in the field of company finance. Reference will often be made to actual happenings in the financial markets in support of the material covered.

Credits: 15 credits (7.5 ECTS credits).

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MA519 - Economics 2 (15 credits)

This module examines recent developments and methodologies in economics and the links between the theory and practical application. Micro- and macroeconomic models of economic behaviour are developed and analysed.  The syllabus includes: consumer demand, firms and supply; uncertainty and assets; macroeconomic measures; developments in growth theory; borrowing, lending and the inter-temporal budget constraint, consumption and investment theory, fiscal and monetary policy.

Credits: 15 credits (7.5 ECTS credits).

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MA535 - Portfolio Theory and Asset Pricing Models (15 credits)

An investor needs an assortment of tools in their toolkit to weigh up risk and return in alternative investment opportunities. This module introduces various measures of investment risk and optimal investment strategies using modern portfolio theory. Pricing of assets using the classical capital asset pricing model and arbitrage pricing theory are discussed. The theory of Brownian motion is used to analyse the behaviour of the lognormal model of asset prices, which is then compared with the auto-regressive Wilkie model of economic variables and asset prices. Principles of utility theory, behavioural finance and efficient market hypothesis provide the context from an investor's perspective. Outline syllabus includes: Measures of investment risk, Mean-Variance Portfolio Theory, Capital Asset Pricing Model, Arbitrage Pricing Theory, Brownian Motion, Lognormal Model, Wilkie Model, Utility Theory and Stochastic Dominance, Efficient Market Hypothesis and Behavioural Finance.



Marks on this module can count towards exemption from the professional examination CT8 of the Institute and Faculty of Actuaries. Please see http://www.kent.ac.uk/casri/Accreditation/index.html for further details.

Credits: 15 credits (7.5 ECTS credits).

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MA552 - Analysis (15 credits)

This module will consider many concepts you know from Calculus and put them on a more rigorous basis. The concept of a limit is basic to Calculus and, unless this concept is defined precisely, uncertainties and paradoxes will creep into the subject. Based on the foundation of the real number system, this module develops the theory of convergence of sequences and series and the study of continuity and differentiability of functions. The notion of Riemann integration is also explored. The syllabus includes the following: Sequences and their convergence. The convergence of bounded increasing sequences. Series and their convergence: the comparison test, the ratio test, absolute and conditional convergence, the alternating series test. Continuous functions: the boundedness theorem, the Intermediate Value Theorem. Differentiable functions: The Mean Value Theorem with applications, power series, Taylor expansions. Construction and properties of the Riemann integral.

Credits: 15 credits (7.5 ECTS credits).

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MA553 - Linear Algebra (15 credits)

Systems of linear equations appear in numerous applications of mathematics. Studying solution sets to such systems leads to the abstract notions of a vector space and a linear transformation. Matrices can be used to represent linear transformations and to do concrete calculations. This module is about the properties of vector spaces, linear transformations and matrices. The syllabus includes: vector spaces, linearly independent and spanning sets, bases, dimension, subspaces, linear transformations, the matrix of a linear transformation, similar matrices, the determinant, diagonalisation, bilinear forms, norms, and the Gram-Schmidt process.

Credits: 15 credits (7.5 ECTS credits).

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MA629 - Probability and Inference (15 credits)

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 MA321. 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, known as the method of maximum likelihood, is introduced, which is then 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; Generating functions; Transformations of random variables; Sampling distributions; Point and interval estimation; Properties of estimators; Maximum likelihood; Hypothesis testing; Neyman-Pearson lemma; Maximum likelihood ratio test.

Credits: 15 credits (7.5 ECTS credits).

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MA632 - Regression Models (15 credits)

Regression is a fundamental technique of statistical modelling, in which we aim to model a response variable using one or more explanatory variables. For example, we might want to model the yield of a chemical process in terms of the temperature and pressure of the process. The need for statistical modelling arises because even when temperature and pressure are fixed, there will typically be variation in the resulting yield, so the model must include a random component. In this module we study the broad class of linear regression models, which are widely used in practice. We learn how to formulate such models and fit them to data, how to make predictions with associated measures of uncertainty, and how to select appropriate explanatory variables. Both theory and practical aspects are covered, including the use of computer software for regression. Outline of the syllabus: simple linear regression; the method of least squares; sums of squares; the ANOVA table; residuals and diagnostics; matrix formulation of the general linear model; prediction; variable selection; one-way analysis of variance; practical regression analysis using software; logistic regression.

Credits: 15 credits (7.5 ECTS credits).

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Year in industry

All single honours Mathematics degrees (except Mathematics with Secondary Education) offer the option of spending a year working in industry between Stages 2 and 3. We can offer help and advice in finding a placement.


Stage 3

Possible modules may include:

MA636 - Stochastic Processes (15 credits)

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.

Credits: 15 credits (7.5 ECTS credits).

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MA639 - Time Series Modelling and Simulation (15 credits)

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.

Credits: 15 credits (7.5 ECTS credits).

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MA537 - Mathematics of Financial Derivatives (15 credits)

This module introduces the main features of basic financial derivative contracts and develops pricing techniques. Principle of no-arbitrage, or absence of risk-free arbitrage opportunities, is applied to determine prices of derivative contracts, within the framework of binomial tree and geometric Brownian motion models. The interplay between pricing and hedging strategies, along with risk management principles, are emphasized to explain the mechanisms behind derivative instruments. Models of interest rate and credit risk are also discussed in this context. Outline syllabus includes: An introduction to derivatives, binomial tree model, Black-Scholes option pricing formula, Greeks and derivative risk management, interest rate models, credit risk models.



Marks on this module can count towards exemption from the professional examination CT8 of the Institute and Faculty of Actuaries. Please see http://www.kent.ac.uk/casri/Accreditation/index.html for further details.

Credits: 15 credits (7.5 ECTS credits).

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MA549 - Discrete Mathematics (15 credits)

Recently some quite novel applications have been found for "Discrete Mathematics", as opposed to the “Continuous Mathematics” based on the Differential and Integral Calculus. Thus methods for the encoding of information in order to safeguard against eavesdropping or distortion by noise, for example in online banking and digital television, have involved using some basic results from abstract algebra. This module will provide a self-contained introduction to this general area and will cover most of the following topics: (a) Modular arithmetic, polynomials and finite fields: Applications to orthogonal Latin squares, cryptography, “coin-tossing over a telephone”, linear feedback shift registers and m-sequences. (b) Error correcting codes: Binary block, linear and cyclic codes including repetition, parity-check, Hamming, simplex, Reed-Muller, BCH, Golay codes; channel capacity; Maximum likelihood, nearest neighbour, syndrome and algebraic decoding.

Credits: 15 credits (7.5 ECTS credits).

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CB600 - Games and Networks (15 credits)

The module is divided into three main topics, namely Combinatorial Optimisation, Dynamic Programming and Game Theory. A more detailed listing of content is given below.



Combinatorial Optimisation:

The Shortest Path Problem

The Minimal Spanning Tree Problem

Flows in Networks

Scheduling Theory

Computational Complexity





Theory of Games:

Matrix Games – Pure Strategies

Matrix Games – Mixed Strategies

Bimatrix Games

N-person Games

Multi-criteria Decision Theory

Credits: 15 credits (7.5 ECTS credits).

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MA771 - Applied Stochastic Modelling and Data Analysis (15 credits)

This applied statistics module focusses on problems that occur in the fields of ecology, biology, genetics and psychology. Motivated by real examples, you will learn how to define and fit stochastic models to the data. In more complex situations this will mean using optimisation routines in MATLAB to obtain maximum likelihood estimates for the parameters. You will also learn how construct, fit and evaluate such stochastic models. Outline Syllabus includes: Function optimisation. Basic likelihood tools. Fundamental features of modelling.  Model selection. The EM algorithm. Simulation techniques. Generalised linear models.

Credits: 15 credits (7.5 ECTS credits).

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MA781 - Practical Multivariate Analysis (15 credits)

This module considers statistical analysis when we observe multiple characteristics on an experimental unit. For example, a sample of students' marks on several exams or the genders, ages and blood pressures of a group of patients. We are particularly interested in understanding the relationships between the characteristics and differences between experimental units. Outline syllabus includes: measure of dependence, principal component analysis, factor analysis, canonical correlation analysis, hypothesis testing, discriminant analysis, clustering, scaling.

Credits: 15 credits (7.5 ECTS credits).

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MA574 - Polynomials in Several Variables (15 credits)

Systems of polynomial equations arise naturally in many applications of mathematics. This module focuses on methods for solving such systems and understanding the solutions sets. The key abstract concept is an ideal in a commutative ring and the fundamental computational concept is Buchberger's algorithm for computing a Groebner basis for an ideal in a polynomial ring. The syllabus includes: multivariate polynomials, Hilbert's Basis Theorem, monomial orders, division algorithms, Groebner bases, Hilbert's Nullstellensatz, elimination theory, linear equations over systems of polynomials, and syzygies.

Credits: 15 credits (7.5 ECTS credits).

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MA587 - Numerical Solution of Differential Equations (15 credits)

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.

Credits: 15 credits (7.5 ECTS credits).

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MA598 - Project on Financial Mathematics (15 credits)

Financial Mathematicians employ a wide range of skills when collaborating on work-related projects. This module is designed to give students the opportunity to experience what it is like to work on such a project, and to develop the team-working, communication, time management and problem-solving skills that are vital in the workplace. Students are arranged into small teams, with each team working together under the guidance of a supervisor to produce a single written report, worth 50% of the total module mark. In addition, each student will submit project-related coursework, and coursework related to the Key Skills workshops attended in the Autumn Term. Each of these coursework elements will contribute a further 25% to the total module mark. The syllabus is determined by the topics offered by supervisors. A range of topics will be available, with many replicating the 'real-world' work that Financial Mathematicians undertake in their professional lives.

Credits: 15 credits (7.5 ECTS credits).

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MA600 - Dissertation (30 credits)

This module provides an opportunity to explore and research a topic in mathematics or statistics that is of interest to the student. Under the guidance of a supervisor, the student will engage in self-directed study to produce a dissertation. Students work largely independently to research a mathematical or statistical topic in depth and will be expected to incorporate high level material. For this reason, this module is best suited to students with a Stage 2 average exceeding 60%. Some topics may also have pre-requisite modules. Acceptance onto a topic is at the supervisor's and convenor's discretion. Outline syllabus: This is determined by the topic of the dissertation. Indicative mathematics titles include the following: Topological Solitons; Symmetries and finite groups; Acoustics; Totally non-negative matrices; Minkowski's question mark function; Mathematics of the gyroscope; Young tableaux; Lie algebras; Non-Euclidean geometry; Averaging methods in nonlinear ODE; Zeta functions; Linear operators and spectral theory; Group theory of Rubik's cube. Indicative statistics titles include the following: Generalised linear models in ecology; Stochastic frontier analysis using WinBUGs; Hyperbolic geometry and shape analysis; Topics in sample surveys; Computational and probabilistic genome analysis; Mastering Monopoly with Markov chains; Sighting frequencies of tortoises; Logistic regression analysis; Objective Bayesian analysis; Capital asset pricing model and risk analysis of investment.

Credits: 30 credits (15 ECTS credits).

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MA772 - Analysis of Variance (15 credits)

Analysis of variance is a fundamentally important method for the statistical analysis of data. It is used widely in biological, medical, psychological, sociological and industrial research when we wish to compare more than two treatments at once. In analysing experimental data, the appropriate form of analysis of variance is determined by the design of the experiment, and we shall therefore discuss some aspects of experimental design in this module. Lectures are supplemented by computing classes which explore the analysis of variance facilities of the statistical package R. Syllabus: One-way ANOVA (fixed effects model); alternative models; least squares estimation; expectations of mean squares; distributional results; ANOVA table; follow-up analysis; multiple comparisons; least significant difference; confidence intervals; contrasts; orthogonal polynomials; checking assumptions; residual plots; Bartlett's test; transformations; one-way ANOVA (random effects model); types of experiment; experimental and observational units; treatment structure; randomisation; replication; blocking; the size of an experiment; two-way ANOVA; the randomised complete block design; two-way layout with interaction; the general linear model; matrix formulation; models of full rank; constraints; motivations for using least squares; properties of estimators; model partitions; extra sum of squares principle; orthogonality; multiple regression; polynomial regression; comparison of regression lines; analysis of covariance; balanced incomplete block designs; Latin square designs; Youden rectangles; factorial experiments; main effects and interactions.

Credits: 15 credits (7.5 ECTS credits).

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MA584 - Computational Mathematics (15 credits)

The aim of the module is to provide an introduction to the methods, tools and ideas of numerical computation. In applications mathematics frequently generates specific instances of standard problems for which there are no easily obtainable analytic solutions. Examples might be the task of determining the value of a particular integral, or of finding the roots of a certain non- linear equation. Methods are presented for solving such problems on a modern computer. Besides a description of the basic numerical procedure, each method is analysed in terms of when it best works, how it compares with alternative approaches, and the way it may be implemented on a computer. Numerical computations are almost invariably contaminated by errors, and an important concern throughout the module is to understand the source, propagation and magnitude of these errors.The syllabus will cover: Introduction to numerics; solutions of equations in one variable; interpolation and polynomial approximation; numerical differentiation; numerical integration; direct methods for solving linear systems; iterative techniques for solving linear systems.

Credits: 15 credits (7.5 ECTS credits).

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CB668 - Linear Programming and its Application (15 credits)

The broad areas will be as defined as shown below:



Modelling LP applications (management, finance, business, marketing)

The use of graphical method for small problems and the development Simplex Method (optimality and feasibility criteria) including the two-phase method.

The use of a computer software such as Excel to solve LP instances and discussion of results (through a couple of Labs).

Degeneracy issues in LP (brief)

Duality theory (dual problems, duality theorem, and complementary slackness conditions), and application of duality to other problems (brief)

Dual Simplex Method

Sensitivity analysis and brief pot-optimality analysis

Extension of LP to Integer Programming or Ratio Programming (DEA)

Credits: 15 credits (7.5 ECTS credits).

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MA564 - Functions of Several Variables (15 credits)

Functions of several variables occur in many important applications. In this module we introduce the derivative for functions of several variables and derive an important consequence, namely the chain rule. We use this to calculate maxima and minima and Taylor series for functions of several variables. We also discuss the important problem of finding maxima and minima of functions subject to a constraint using the method of Lagrange multipliers. Furthermore, we define different ways to integrate functions of several variables such as arclength integrals, line integrals, surface integrals and volume integrals. Outline Syllabus includes: Continuity and Differentiation; tangent plane; swapping order of partial derivatives; implicit function theorem; inverse function theorem; paths independence of line integrals; use of polar, cylindrical and spherical polar coordinates; integral theorems such as Green's theorem.

Credits: 15 credits (7.5 ECTS credits).

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MA565 - Groups and Rings (15 credits)

Groups are sets with a single binary operation. They arise as symmetry groups in contexts from puzzles like Rubik's cube to chemistry, where they help list molecules with a given number of atoms involved. In contrast, rings have two binary operations, generalising the arithmetic of integer numbers. This part of algebra has many applications in electronic communication, in particular in coding theory and cryptography. Outline Syllabus includes: permutations and cycle decomposition, subgroups, cosets, Lagrange's theorem, normal subgroups, symmetry groups, group actions, homomorphisms of groups and rings, ideals, factorization in rings, polynomial rings, domains, fields, quotient fields, finite fields.

Credits: 15 credits (7.5 ECTS credits).

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Teaching & 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:

  • instil in students the technical appreciation, skills and knowledge required by graduates in financial mathematics
  • develop students’ abilities for rigorous reasoning and precise expression, and formulate and solve problems relevant to financial mathematics
  • encourage an appreciation of recent developments in financial mathematics, and the links between theory and practical application
  • encourage a logical, mathematical approach to solving problems
  • develop 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 opportunities to study advanced topics in financial mathematics, engage in research, and develop communication and personal skills
  • instil awareness of the application of technical concepts in the workplace (for students undertaking a year in industry).

Learning outcomes

Knowledge and understanding

You gain knowledge and understanding of:

  • core mathematical skills in the principles of calculus, algebra, mathematical methods, descrete mathematics, analysis and linear algebra
  • statistical aspects of probability and inference
  • information technology skills relevant to mathematicians
  • methods and techniques appropriate to financial mathematics
  • logical mathematical argument and deductive reasoning.

Intellectual skills

You gain the following intellectual abilities:

  • demonstrate a reasonable understanding of knowledge in financial mathematics
  • skills of calculation and manipulation of the material written within the programme
  • apply concepts and principles in various contexts, relevant to financial mathematics
  • a capacity for logical argument
  • problem solving by various methods
  • computer skills
  • the capacity to work with relatively little guidance.

Subject-specific skills

You gain subject-specific skills in the following:

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

Transferable skills

You gain transferable skills in the following:

  • problem-solving, in relation to qualitative and quantitative information
  • effective communication
  • numeracy and computational abilities
  • information retrieval in relation to primary and secondary information sources, including online computer searches
  • computer skills, such as word-processing and spreadsheet use, internet communication
  • time-management and organisational skills: the ability to plan and implement efficient and effective modes of working
  • continuing professional development.

Careers

Those students who choose to take the year in industry option find the practical experience they gain gives them 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 from the School 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.

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 the Admissions Office for further advice. It is not possible to offer places to all students who meet this typical offer/minimum requirement.

Qualification Typical offer/minimum requirement
A level

AAB including A in Mathematics (not Use of Mathematics). Only one General Studies and Critical Thinking can be accepted against the requirements.

Access to HE Diploma

The University of Kent will not necessarily make conditional offers to all access candidates but will continue to assess them on an individual basis. If an offer is made candidates will be required 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 via the enquiries tab for further advice on your individual circumstances.

International Baccalaureate

34 points overall or 16 at HL with Mathematics 6 at HL

International students

The University receives applications from over 140 different nationalities and consequently will consider applications from prospective students offering a wide range of international qualifications. Our International Development Office will be happy to advise prospective students on entry requirements. See our International Student website for further information about our country-specific requirements.

Please note that if you need to increase your level of qualification ready for undergraduate study, the School of Mathematics, Statistics and Actuarial Science offers a foundation year.

Qualification Typical offer/minimum requirement
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 through Kent International Pathways.

General entry requirements

Please also see our general entry requirements.

Funding

Kent offers generous financial support schemes to assist eligible undergraduate students during their studies. Our funding opportunities for 2017 entry have not been finalised. However, details of our proposed funding opportunities for 2016 entry can be found on our funding page.  

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. Details of the scholarship for 2017 entry have not yet been finalised. However, for 2016 entry, the scholarship will be awarded to any applicant who achieves a minimum of AAA over three A levels, or the equivalent qualifications as specified on our scholarships pages. Please review the eligibility criteria on that page. 

Enquire or order a prospectus

Resources

Read our student profiles

Contacts

Related schools

Enquiries

T: +44 (0)1227 827272

Fees

The 2017/18 tuition fees for this programme are:

UK/EU Overseas
Full-time £9250 £13810

As a guide only, UK/EU/International students on an approved year abroad for the full 2017/18 academic year pay an annual fee of £1,350 to Kent for that year. Students studying abroad for less than one academic year will pay full fees according to their fee status. Please note that for 2017/18 entrants the University will increase the standard year in industry fee for home/EU/international students to £1,350.

The Government has announced changes to allow undergraduate tuition fees to rise in line with inflation from 2017/18.

The University of Kent intends to increase its regulated full-time tuition fees for all Home and EU undergraduates starting in September 2017 from £9,000 to £9,250. This is subject to us satisfying the Government's Teaching Excellence Framework and the access regulator's requirements. The equivalent part-time fees for these courses will also rise by 2.8%.

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.* If you are uncertain about your fee status please contact information@kent.ac.uk

Key Information Sets


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.

The University of Kent makes every effort to ensure that the information contained in its publicity materials is fair and accurate and to provide educational services as described. However, the courses, services and other matters may be subject to change. Full details of our terms and conditions can be found at: www.kent.ac.uk/termsandconditions.

*Where fees are regulated (such as by the Department of Business Innovation and Skills or Research Council UK) they will be increased up to the allowable level.

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The University of Kent, Canterbury, Kent, CT2 7NZ, T: +44 (0)1227 764000