THIRD AND FOURTH YEAR SYLLABUSES

301 MATHEMATICAL METHODS (M)

AIMS:

To introduce the student to some frequently used mathematical methods.

DESCRIPTION:

The course covers three main areas - the use of transform methods in the solution of linear differential equations, the solution of linear algebraic systems of equations and the use of complex variable theory and conformal mappings in the solution of boundary-value problems.

SYLLABUS:

Laplace transforms: operator rules, solution of ordinary differential equations, Heaviside function, Dirac delta function, convolution theorem, inversion theorem. Fourier transforms: inversion and convolution; application to solution of partial differential equations. [10]

Linear algebra: rank and nullity of a linear transformation, solution of general systems of linear equations, block matrices. Euclidean and unitary spaces, quadratic and Hermitian forms and rank and signature, positive definiteness. [10]

Functions of a complex variable: complex functions and their representation. Riemann surfaces. Branches, branch points. Analytic functions. Conformal transformations. Dirichlet-Neumann boundary-value problems. Uniform convergence, analytic continuation. [10]

SKILLS AND KNOWLEDGE ACQUIRED:

To be able to analyse and solve linear ordinary and partial differential equations and algebraic systems of equations using a variety of analytical techniques.

READING LIST:

1. "Schaum's outline of theory and problems of advanced mathematics for engineers and scientists", M. Spiegel, (McGraw Hill, 1980)  [Library Cat.: 510.2462 SPI]
2. "Schaum's outline of theory and problems of linear algebra", S. Lipschutz, (McGraw Hill, 1991)  [Library Cat.: 512.5 LIP]
3. "Schaum's outline of theory and problems of complex variables: with an introduction to conformal mapping and its appreciation", M. Spiegel, (McGraw Hill, 1974)  [Library Cat.: 515.9 SPI].

PREREQUISITE:

None

302 DIFFERENTIAL EQUATIONS (M)

AIMS:

To introduce and develop the classical theory of linear ordinary and partial differential equations.

DESCRIPTION:

This course is concerned with fundamental aspects of linear ordinary differential equations and partial differential equations.

SYLLABUS:

Ordinary differential equations: Linear differential equations: existence and uniqueness, Wronskian, fundamental solution set; influence function and initial value problems; boundary value problems, Green's function, eigenvalue problems, Sturm-Liouville systems, eigenfunction expansions. Linear systems: review of matrix solution of constant coefficient equations; systems with periodic coefficients, Floquet theory. [18]

Partial differential equations:

First order equations and systems: Cauchy problem. Linear second order equations in two independent variables: classification, reduction to canonical form; hyperbolic equations, characteristics. Separation of variables and eigenfunction expansions for nonhomogeneous problems. [12]

SKILLS AND KNOWLEDGE ACQUIRED:

To be able to solve and analyse initial and boundary value problems.

READING LIST:

1. "Elementary differential equations and boundary value problems", W.E. Boyce and R.C. DiPrima, (Wiley)  [Library Cat.: 515.35 BOY]
2. "Introduction to differential equations with boundary value problems", W.R. Derrick and S.I. Grossman, (West, 1987)  [Library Cat.: 515.35 DER]
3. "Fundamentals of Differential Equations", R.K. Nagle and E.B. Saff, (Addison-Wesley)  [Library Cat.: 515.35 NAG]
4. "Partial differential equations", P. Duchateau and D.W. Zachmann, (Schaum/McGraw-Hill)  [Library Cat.: 515.353 DUC]
5. "Linear algebra done right", S. Axler, (Springer)  [Library Cat.: 512.5 AXL].

PREREQUISITE:

None

303 DYNAMICAL SYSTEMS (M)

AIMS:

To extend the ideas of qualitative methods of analysis of systems of ordinary differential equations studied at part II and to introduce the notions of bifurcation and chaos.

DESCRIPTION:

The course revises some of the standard phase portrait methods encountered in the Dynamical Systems course at part II and extends these ideas, discussing in some detail centres, via the use of Liapunov functions, limit cycles and global phase portraits. The ideas of bifurcation and chaos are introduced via discrete systems.

SYLLABUS:

Nonlinear second order systems:

Revision of linearization and classification of hyperbolic fixed points. Liapunov functions, centres; global phase portraits; limit cycles and Poincar -Bendixon theorem. Parameter dependent system and Hopf bifurcation. [12]

Hamiltonian systems with first integrals: classification of fixed points, construction of global phase portraits. [7]

Linear systems:

Canonical forms and evolution operators for nth order systems. [5]

First order discrete systems:

Review of linear difference equations. The quadratic map, periodic orbits, bifurcation and chaos. [6]

SKILLS AND KNOWLEDGE ACQUIRED:

To be able to find and identify the critical solutions of a system and use this information to construct its local and global phase portraits.

READING LIST:

1. "Ordinary differential equations", D.K. Arrowsmith and C.M. Place, (Chapman and Hall, 1982)  [Library Cat.: 515.352 ARR]
2. "Nonlinear systems", P. Drazin, (Cambridge)  [Library Cat.: 515.355 DRA].

PREREQUISITE:

203

304 FLUID DYNAMICS (M)

AIMS:

The main aims are to introduce the established mathematical model for the motion of a fluid and to discuss some important solutions.

DESCRIPTION:

The field of fluid dynamics is a large and varied one, encompassing for example such diverse topics as blood flow in the body, weather prediction, space flight and environmental issues such as the dispersion of pollutants. The equations of motion are derived and various exact solutions are obtained using mathematical methods based mainly on vector calculus and complex variable theory. As an example, the flow around an aerofoil is determined, explaining how lift is generated. Effects of friction are also discussed and in the motion of common fluids such as air and water these may be confined to a narrow 'boundary layer' near the surface of a moving body.

SYLLABUS:

Basic concepts: velocity field, streamlines and particle paths, pressure, density. [3]

Equation of continuity, equations of motion for inviscid flow. Boundary conditions. [4]

Steady irrotational, incompressible flow, velocity potential, vorticity, circulation. [3]

Two-dimensional motion, stream function, complex potential for two-dimensional irrotational, incompressible flow. Uniform stream, source, sink, vortex, dipole. Method of images. Circle theorem. Flow past a cylinder. [6]

Flow past a flat plate and aerofoil using conformal mapping, Blasius' theorem. [4]

Introduction to viscous flow, Navier-Stokes equations, simple solutions. [5]

Dynamical similarity, Reynolds number, boundary-layer theory. [5]

SKILLS AND KNOWLEDGE ACQUIRED:

An appreciation of how to formulate and solve mathematical problems governing fluid flows.

READING LIST:

1. "Elementary fluid dynamics", D.J. Acheson, (Clarendon, 1990)   [Library Cat.: 532.05 ACH]
2. "An introduction to fluid dynamics", G.K Batchelor, (CUP, 1967)   [Library Cat.: 532.05 BAT]
3. "Physical fluid dynamics", D.J. Tritton (Oxford: Clarendon, 1988)   [Library Cat.: 532.05 TRI].

PREREQUISITE:

None

305 MATHEMATICAL BIOLOGY AND ECOLOGY (M)

AIMS AND DESCRIPTION:

During this course students will learn how mathematics can help understand important phenomena from Biology and Ecology such as how to stop the spread of infectious diseases, how the human body is being shaped up during development, modelling the growth of animal and plant populations and the management of food resources. Simple examples drawn from real life problems will illustrate how mathematics can help us to understand the patterns of life in Nature.

 

This course presents a selection of well-developed and actual models from diverse areas of Biology and Ecology. Comments on the solutions and revisions to the models will be important aspects.

SYLLABUS:

The course is designed around some essential topics such as:

SKILLS AND KNOWLEDGE ACQUIRED:

Mathematical modelling at its best. To appreciate the usefulness of the mathematical tools and techniques learned during the previous terms. To learn and appreciate the crucial importance of Mathematics in helping understand the dynamics of Life forms on Earth and improving our life style in commitment to preserving ecological interactions between the natural species.

READING LIST:

1. "Mathematical Biology", Jim Murray, (Springer-Verlag, new 3rd edition to appear in 2002)  [Library Cat.:   510.24574 MUR]
2. "Mathematical models in Biology", Leah-Edelstein Keshet (Random House/Birkhauser Mathematics Series, 1988)  [Library Cat.:   ]
3. "Mathematics in Medicine and the Life Sciences", Hoppensteadt, F.C. and Peskin, C.S. (Springer-Verlay, 1992)  [Library Cat.:   ].

PREREQUISITE:

None

306 MATHEMATICAL MODELS AND MODELLING (M)

AIMS:

To help the student to overcome the difficult transition from basic assumptions made on a real problem to the setting up of a model in mathematical terms.

DESCRIPTION:

This course covers the presentation of a selection of well-developed models from diverse areas of Mathematics. Comments on the solutions and revisions to the models will be important aspects. The models presented will vary from year to year, each topic being given a weighting of about five lectures.

SYLLABUS:

The course is designed around topics as they occur in the literature, such as

Overhead Electrification Wires Population Dynamics Conservation of Fishing Stocks Epidemiology Contra-flow Kidney Machines Aggregation of Slime Mould Amoebae Planetary Orbits Physiological Flow Problems Biochemical Kinetics Projectile Motion Motor Insurance Road Traffic Situations Radiative Equilibrium in the Atmosphere Optimal Forest Harvesting Structure of Residential Districts The Severn Bore [30]

SKILLS AND KNOWLEDGE ACQUIRED:

To appreciate some of the difficulties and successes of mathematical modelling.

READING LIST:

1. "Mathematical modelling", J.G. Andrews and R.R. McLone, (Butterworths, 1976)  [Library Cat.: 511.8 AND]
2. "Thinking with models", T.L. Saaty and J.M. Alexander, (Pergamon, 1981)   [Library Cat.: 511.8 SAA].

PREREQUISITE:

None

307 NUMERICAL ANALYSIS (M)

AIMS:

To introduce numerical methods for the solution of partial differential equations.

DESCRIPTION:

This course is a continuation of the Computational Mathematics and Numerical Mathematics covered in the first and second years although these courses are not prerequisites.

SYLLABUS:

Numerical solution of partial differential equations: classification of second order equations, finite difference approximation to partial derivatives. Finite difference methods for parabolic equations: explicit and implicit methods, local truncation error, consistency, convergence, stability. Newton's method for nonlinear parabolic equations. Finite difference methods for hyperbolic equations, including method of characteristics. Finite difference methods for elliptic equations: 5- and 9-point schemes. Introduction to the finite element method for Poisson's equation. [30]

SKILLS AND KNOWLEDGE ACQUIRED:

To be able to solve partial differential equations numerically.

READING LIST:

1. "Numerical solution of partial differential equations: with exercises and worked solutions", G.D. Smith, (Oxford UP, 1965)  [Library Cat.: 515.353 SMI]
2. "Numerical solutions of partial differential equations by the finite element method", C. Johnson (Cambridge UP, 1987)  [Library Cat.: 515.353 JOH]
3. "Numerical methods for partial differential equations", W.F. Ames, (Academic Press, 1992)   [Library Cat.: 515.353 AME].

PREREQUISITE:

None

308 QUANTUM MECHANICS (M)

AIMS:

To introduce the student to the mathematical theory of the behaviour of very small particles on atomic and subatomic scale.

DESCRIPTION:

Virtually all the achievements of modern physical sciences are based directly or indirectly on quantum mechanics. The behaviour of complex systems such as transistors, silicon chips, components in modern computers, lasers and even biological systems is governed ultimately by a universal differential equation, the Schrodinger equation. In the first part of the course the form of the Schrodinger equation is postulated and general interpretation of its solutions is given. In the second part simple, mainly one-dimensional, solutions of the Schrodinger equation are obtained and their properties are discussed. Finally, the most general formulation of quantum theory in which physical states of a system are pictured as vectors in an infinite-dimensional vector space is outlined.

Quantum mechanics is a self-contained course and the basic techniques involved are the manipulation of differential operators (such as D, D2) and the solution of differential equations.

SYLLABUS:

Wave-particle duality; the postulates of quantum mechanics; statistical interpretation of the wave function; observables as Hermitian operators; eigenfunctions and eigenvalues; expectation value of observables; prediction of measurements; position, momentum, energy and angular momentum operators; commutation relations; the Dirac formalism; the Schrodinger equation; compatible observables; the uncertainty principle.

One-dimensional problems; the infinitely deep potential well; the finite square-well potential; scattering by a potential barrier; probability current density; equation of continuity; reflection and transmission coefficients; the linear harmonic oscillator; the hydrogen atom.

Approximation methods: bound-state perturbation theory; the Rayleigh-Ritz variational method. [30]

SKILLS AND KNOWLEDGE ACQUIRED:

To appreciate the concepts of quantum mechanics and its place in modern physics.

READING LIST:

1. "Quantum mechanics", F. Mandl, (Wiley)   [Library Cat.: 530.12 MAN]
2. "Basic quantum mechanics", J.M. Cassels, (McMillan)   [Library Cat.: 530.12 CAS]
3. "Quantum physics", S. Gasiorowicz, (Wiley, 1974)   [Library Cat.: 530.12 GAS].

PREREQUISITE:

None

309 SYMMETRIES IN PHYSICS (M)

AIMS:

Symmetry is a universal phenomenon appearing in areas as distinct as science, arts and architecture. In this course, the student learns basic mathematical tools for the description of symmetry.

DESCRIPTION:

Basic concepts of group theory are introduced and applied to the study of patterns and molecules.

SYLLABUS:

  • The description of symmetry via group theory.
  • Basic concepts in group theory.
  • Applications to the study of patterns and tilings.
  • Applications in crystallography. [30]

SKILLS AND KNOWLEDGE ACQUIRED:

The student gets acquainted with mathematical tools for the description of symmetry and their applications. These skills are fundamental in many areas of modern mathematics and physics.

READING LIST:

1. J.W. Leech and D.J. Newman: “How to use groups”, Science Paperback, 1969,>  [Library Cat.: 512.2 LEE]
2. A.P. Cracknell: “Applied Group Theory”, Pergamon Press, 1968,   [Library Cat.: 512.22 CRA]
3. F.A. Cotton: ”Chemical Applications of Group Theory”, Wiley-Interscience, 1971,  [Library Cat.: 512.22 COT]
4. M. Senechal: “Quasicrystals and Geometry”, Cambridge University Press, 1996

PREREQUISITE:

None

310 CLASSICAL AND BAYESIAN INFERENCE (S)

AIMS:

To provide a sound footing in basic Bayesian inference and Bayesian decision theory.

DESCRIPTION:

Bayesian prior-posterior analysis with applications. An introduction to Bayesian predictive analysis. The formulation and application of the Bayesian decision theoretic framework.

SYLLABUS:

Prior distributions. Bayesian methods, exchangeability, conjugate prior distributions. Hierarchical modelling. Markov Chain Monte Carlo. Loss functions and scoring rules, decision rules, Bayes loss and risk. Decision trees. [30]

SKILLS AND KNOWLEDGE ACQUIRED:

An appreciation of Bayesian analysis.

READING LIST:

1. "Making Decisions", D.V. Lindley, (Wiley)  [Library Cat.: 519.4 LIN]
2. "Introduction to Probability and Statistics from a Bayesian Viewpoint", D.V. Lindley, (CUP)   [Library Cat.: 519 LIN]
3. "Optimal Statistical Decisions", M.DeGroot, (McGraw-Hill)    [Library Cat.: 519.54 DEG].

PREREQUISITE:

211

312 DATA ANALYSIS II (S)

AIMS:

The aims are to present modern statistical modelling techniques to cope with continuous and discrete response variables in the presence of covariates.

DESCRIPTION:

The emphasis of the course is placed on non-normal response variables, following on from the first course in Data Analysis (210).  Practical aspects of the course will be conducted using the S-Plus software package.

SYLLABUS:

Structured data sets.  Experimental and non-experimental studies and their interpretation.  Statistical analysis of data from prospective and retrospective studies: binomial distribution and logistic regression: multinomial models.   Modelling association between categorical variables: analysis of multidimensional contingency tables, graphical and hierarchical log-linear models.  Generalised Linear Models (GLM) and exponential families of distributions.  Fitting of GLM: analysis of deviance and diagnostics.  Modelling with over-dispersion.  Classification models. [30]

READING LIST:

1. "Graphical Models", S. Lauritzen, (Oxford University Press, 1996)    [Library Cat.: 511.5 LAU]
2. "Generalised Linear Models", P. McCullagh and J.A. Nelder, (Chapman & Hall, 1989)   [Library Cat.: 519.5 MCC]
3. "Statistical Models in S", J.M. Chambers and T.J. Hastie, (Chapman & Hall, 1992)   [Library Cat.: 519.502854 CHA]
4. "Modern Applied Statistics with S-Plus", W.N. Venables and B.D. Ripley, (Springer-Verlag, NY, 1994)   [Library Cat.: 005.369 S-PLUS VEN]
5. "Graphical Models in Applied Multivariate Statistics", J. Whittaker, (Wiley, 1990)   [Library Cat.: 519.535 WHI].

PREREQUISITE:

210

313 ECONOMETRICS (S)

AIMS:

To provide a basic introduction to the meaning of econometrics and to how it uses quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, and relates them by appropriate methods of inference.

DESCRIPTION:

Econometrics may be considered as the integration of economics, mathematics and statistics for the purpose of providing numerical values for the parameters of economic relationships (for example, elasticities, propensities, marginal values) and verifying economic theories. It is a special type of economic analysis in which the general economic theory, formulated in mathematical terms, is combined with empirical measurement of economic phenomena. Starting from the relationships of economic theory, we express them in mathematical terms (ie we build a model) so that they can be measured.

We then use specific methods, called econometric methods, in order to obtain numerical estimates of the coefficients of the economic relationship. Econometric methods are statistical methods specifically adapted to the peculiarities of economic phenomena. The most important characteristic of economic relationships is that they contain a random element which is ignored by economic theory and mathematical economics which postulate exact relationships between the various economic magnitudes. Econometrics has developed methods for dealing with the random component of economic relations. Testing, predicting and forecasting for future policy decisions are the major ingredients of econometrics.

SYLLABUS:

The general linear model: Assumptions, Least Squares Estimators, significance tests and confidence intervals, linear restrictions, predictions, testing for structural changes, multicollinearity problem.

Generalised Least-Squares: violation of the assumptions, consequences for OLS, properties of the estimators, efficiency.

Autocorrelation: The nature and causes of autocorrelation, the consequences for OLS, representation of autocorrelation, testing for autocorrelation, Theil's Blus procedure.

Heteroscedasticity: The causes of Heteroscedasticity, the consequences of OLS, representation of Heteroscedasticity, corrective procedure after testing.

Stochastic Regressors, Models: Stochastic Regressors, Instrumental Variables, errors in variables.

Introduction to distributed lagged models: Dynamic models. [30]

SKILLS AND KNOWLEDGE ACQUIRED:

Some aspects of basic econometrics.

READING LIST:

1. "Theory of Econometrics", A. Koutsoyiannis, (Macmillan)    [Library Cat.: 330.018 KOU]
2. "Learning and practicing Econometrics", E. Griffiths, R. Hill and G.G. Judge, (Wiley)   [Library Cat.: 330.015195 GRI]
3. "Introducing Econometrics", S. Brown, (West Publishing Company)    [Library Cat.: 330.015195 BRO].

PREREQUISITE:

210

314 OPERATIONAL RESEARCH (S)

AIMS:

The course aims to introduce the theoretical basis for decision theory, and then to develop a number of techniques for making optimal decisions in deterministic situations..

DESCRIPTION:

Deterministic situations are typified by problems in which the consequences of actions are known with certainty and need to be ranked or ordered to determine an optimal decision.  Practical applications are in mixing and blending problems, resource allocation problems, and production planning where there is no uncertainty in, for example, demand or supply.

SYLLABUS:

Introduction to decision theory. Criteria for decision making: coherence of decision criteria; orderings and indifference; utility.
How to structure decision problems.
Deterministic decisions as optimization problems. The theory will be illustrated by resource allocation problems, location and assignment problems, stock control, mechanical design problems. There will be an emphasis on problem formulation and solution.
The techniques developed include: Classical non-linear optimization; convexity and duality; linear programming; game theory; dynamic programming. [30]

READING LIST:

"Basic Optimisation Methods", B.D. Bunday, (Edward Arnold)    [Library Cat.: 551.66 BUN]
"Basic Linear Programming", B.D. Bunday, (Edward Arnold)   [Library Cat.: 519.72 BUN].

PREREQUISITE:

211

315 CONTINUOUS STOCHASTIC MODELLING (S)

AIMS:

To provide a thorough grounding in the theory and practice of linear Time Series analysis; to introduce Brownian motion and related stochastic processes; to teach a part of the material required for exemption in Institute/Faculty of Actuaries subject 103.

DESCRIPTION:

At the end of the course students should be able to (i) formulate a suitable time series model for a sequence of data observed at equal time intervals; (ii) conduct a computer-moderated analysis of the data in the light of the model; (iii) apply and analyse a continuous-time model.

SYLLABUS:

Time Series. Introduction; data structure, objectives. Background probability and stochastic processes. Stationarity. I(0) and I(1).
Time domain: seasonality, differencing, Box-Jenkins methodology, ARMA, ARIMA, SARIMA models. Parameter estimation and forecasting.
Frequency domain; spectral density and introduction to spectral analysis.
Cointegrated and multivariate time series.
Continuous-time processes. Martingale property. Brownian motion: derivation, elementary properties, applications. Exponential Brownian motion. Ornstein-Uhlenbeck process. Diffusions, stochastic differential equations, It˘ calculus. LÚvy processes and stable laws. [30]

READING LIST:

1. "Time Series Analysis", James D. Hamilton, (Princeton University Press, 1994)   [Library Cat.: 519.55 HAM]
2. "Core Reading for Subject 103", (Institute and Faculty of Actuaries, 1999)    [Library Cat.: ]
3. "The Analysis of Time Series: an Introduction", C. Chatfield, (4th edition, Chapman and Hall, 1989)   [Library Cat.: 519.232 CHA]
4. "Stochastic Processes, S.M. Ross, (Wiley, 1996)   [Library Cat.: 519.2 ROS]
5. "Probability and Random Processes, G.R. Grimmett and D. Stirzacker, (2nd edition, Clarendon, 1992)   [Library Cat.: 519.2 GRI].

PREREQUISITE:

211

316 RELIABILITY MODELLING (S)

AIMS:

To provide a thorough grounding in measures and concepts of reliability; to instruct in methods for expressing system reliability in terms of system component reliabilities; to contrast methods appropriate to repairable and non-repairable systems.

At the end of the course students should be able to (i) identify suitable failure models and analyse the structure of a system, (ii) use test data and component reliabilities to estimate and put bounds on system reliability, (iii) quantify the behaviour of a renewable system over time, and evaluate the influence of different system maintenance strategies.

DESCRIPTION:

Reliability is the science of predicting, estimating, or optimising the life distribution of components of systems. Issues of safety, product liability and warranties are all strongly dependent on reliability. Statistical theory is used in the design and analysis of life tests and in the collection and analysis of data from the field. Reliability data are usually measurements of some variable to do with failure, such as time or load at failure, and possibly additional measurements on a group of units. Many systems may be broken down into components. The reliability of a system may be characterised by the individual component reliabilities, and the contributions which individual components make to the reliability of the system. Reliability is measured either in terms of probability of failure or in terms of the loss, i.e. the consequence of failure.

SYLLABUS:

Basic concepts, reliability and hazard functions; common lifetime models, exponential, Weibull, normal, lognormal, gamma distributions; order statistics and extreme value distributions, non-parametric estimation of reliability and hazard functions; censoring and Kaplan-Meier estimation; inference for the exponential distribution; repairable systems and trend testing; renewal theory; tie and cut set analysis; state space methods; availability; maintenance strategies; ystem reliability from subsystem data; delta method for variance approximation. [30]

READING LIST:

1. "Practical Methods for Reliability Data Analysis", J.I. Ansell and M.J. Philips, (OUP, 1994)   [Library Cat.: 620.00452 ANS]
2. "Reliability: Probabilistic Models and Statistical Methods", L.M. Leemis, (Prentice-Hall, 1995)   [Library Cat.: 20.00452 LEE].

PREREQUISITE:

210

317 INVESTMENT (S)

AIMS:

To ensure students have an understanding of theoretical investment principles relating to
the analysis of individual investments, asset allocation and investment risk.

To provide background in investment markets and fundamental mathematics of
invesment analysis, where it is not taught in other courses.

To ensure that students understand the practical problems faced by investing institutions and
the theoretical and practical tools used to solve those problems.

To ensure that students are able to communicate their knowledge of investment effectively.

DESCRIPTION:

On completing this course a student will be able to

Have a general knowledge of the existing investment markets.
Have knowledge of the range of instruments traded in each investment market.
Understand the practical problems faced by institutional investors and the theoretical and practical tools used to solve those problems.
Be able prospectively to use the instruments and techniques for the control of risk.

SYLLABUS:

Introduction to financial markets: role of the market, types of instruments and institutional investors.

Equity markets: share issues, summary measures for ordinary shares, share analysis, market indices, portfolio performance measurement.

Bond and interest rate derivatives:

  • Interest rates and bonds: basic definitions;
  • Typologies of bond contracts;
  • Duration and convexity, hedging via duration;
  • Interest rate derivatives
  • Term structure of interest rates

Derivatives:

  • Typologies of derivatives instruments: basic definitions and features
  • Forward: main features, price and value of a forward contract, the case of a dividend-paying asset, forward for exchange rates;
  • Futures: futures versus forward, equivalence of futures and forward prices, hedging using futures, the basis risk;
  • Options: factors affecting option prices, upper and lower bounds for option prices, the put-call parity, trading strategies;
  • Real options and corporate decisions.
  • VaR, credit risk and credit derivatives. [30]

READING LIST:

1. "Options, Futures and other Derivatives", JC Hull, (4th edition, Prentice Hall International Editions, 2000)   [Library Cat.: 332.63228 HUL]
2. "Introduction to Stock Exchange Investment", J Rutterford, (Macmillan Press, 1993)   [Library Cat.:  332.642 RUT]

PREREQUISITE:

237

318 EXTREME VALUES IN FINANCE AND INSURANCE (S)

AIMS:

To provide an understanding of how, and when, it is appropriate to apply extreme value techniques to real problems in finance and insurance. To provide a thorough grounding in the concepts of univariate extreme value statistics.

Upon successful course completion, the students should be familiar with the advantages and disadvantages of applying univarite extreme value statistics to a range of problems.   They should be able to apply the basic methods and obtain estimates of risk and uncertainty when confronted with suitable finance and insurance data.  They should also be able to pre-process a data set into a form suitable for extreme value analyses.  

DESCRIPTION:

Extreme value theory (EVT) provides a framework for performing a seemingly impossible task: to predict the probability of events that are more extreme than any that have happened before.  Although EVT has been around for over 60 years, methods for its application in complex real-life problems have only recently been developed.  For example, EVT is currently used by actuaries to calculate, and insure against, the probability of rare but financially devastating events.  The governmental coastal flood defence division employs statisticians to use EVT to calculate the required height of sea-walls to prevent flooding.  EVT is also used to tell engineers how strong to build bridges or oil rigs and to model excessively high pollution levels.  In more light-hearted settings, EVT is currently being used to answer questions like: what is the ultimate time in which the mile can be run by a human being?; is there an upper limit to how long humans can live?; what is the distribution of the highest score in the football matches next weekend?

The course is divided broadly into three sections.  The first is the development of the theory and ideas behind univariate EVT.  The second is the application of these ideas to real life problems, and the final part of the course will be a non-mathematical overview of more sophisticated extreme value ideas such as multivariate extreme value applications.  The emphasis throughout is on applications of EVT and on illustrating techniques of statistical inference within the extreme value framework.

SYLLABUS:

The motivation of extreme values in finance and insurance problems.  The Extremal Types Theorem, the generalised extreme value distribution (GEV), likelihood and estimation for the GEV, its uses and limitations.  An overview of alternative extreme value characterisations: the distribution of extreme r order statistics and the generalised Pareto distribution, the point process characterisation.  Application of EVT to real problems: an overview of temporal dependence and non-stationarity.   Issues involved in extreme value modelling of financial, insurance and other data.  Sophisticated use of R (free Splus clone), and the extreme values package. [30]

READING LIST:

As Extreme Value Statistics is a relatively new subject, there is, as yet, no printed text suitable for undergraduate study in this course.  Printed course notes, and specialist software, which are to be published by Arnold Publishers in 2001 as "A course in Extreme Value Statistics" will be provided, and a copy is available for pre-course reading: please see Mark Dixon.  A more advanced introduction is available from the Lancaster University Statistics web site: Extreme Value Theory and Applications, by Stuart Coles.

PREREQUISITE:

None

319 FINANCIAL ECONOMICS II (S)

AIMS:

To give students an understanding of stochastic asset models and to introduce them to methods used to value derivative securities.

DESCRIPTION:

Students should be able to demonstrate an understanding of stochastic models used to simulate the behaviour of securities and the techniques used to value derivative securities.

On completing this course a student will be able to

  1. Have knowledge of the range of derivatives products existing in the market.
  2. Understand the use of tools from stochastic calculus theory to model and price financial securities.
  3. Understand and be able to use numerical techniques to simulate the behaviour of more complex securities.

SYLLABUS:

  • Valuation of derivative securities
    • Definition of derivative security, classes of derivatives
    • Upper and lower bounds for option prices
    • The put-call parity
    • Market modelling assumptions and the no-arbitrage principle
  • Option theory
    • Upper and lower bounds for option prices
    • The put-call parity
    • Option valuation: the discrete time case: the binomial model (Cox-Ross-Rubinstein)
    • Option valuation: the continuous time case: the Black-Scholes model and its extensions
    • Black and Scholes analysis: the Greeks
  • American options
    • Upper and lower bounds for option prices and the price of the American call
    • The problem of the American put in the discrete: the Snell Envelope pricing procedure
  • Futures
    • Main contract features
    • Futures prices and martingales
    • Futures options: the Black model
  • Term structure of interest rates and interest rate derivatives
    • Equilibrium models
    • No-arbitrage models
    • Pricing options on bonds: the forward measure
  • Introduction to exotic options
    • Path-dependent options: Asian options, Lookback options and Barrier options
    • Correlation options
  • Numerical schemes for option pricing  [30]

READING LIST:

1. "Risk-Neutral Valuation - Pricing and Hedging of Financial Derivatives", NH Bingham and R Kiesel (Springer, 1998)   [Library Cat.:  332.015118 BIN]
2. "Financial Theory and Corporate Policy", TE Copeland and JF Weston (Addison-Wesley, 1988)   [Library Cat.:  658.15 COP]
3. "Options, Futures and Other Derivatives", JC Hull (Prentice Hall International Editions, 1997) [Library Cat.:   332.63228 HUL]
4. "An Introduction to the Mathematics of Financial Derivatives", SN Neftci (Academic Press, 1996) [Library Cat.:  332.632 NEF]
5. "Exotic Options - A guide to second generation options", PG Zhang (World Scientific, 1998) [Library Cat.:  332.645 ZHA]

PREREQUISITES:

211, 236 and 237

320 STATISTICS AND PROBABILISTIC MODELLING IN INSURANCE (S)

AIMS:

This module will explain the fundamental statistical techniques used in the analysis of short-term insurance contracts.

DESCRIPTION:

Students should be able to identify and apply the most suitable statistical methods to simple insurance problems.

SYLLABUS:

Generating functions; independence and convolution; conditional expectation and compound distributions; Bayesian statistics; decision theory; probability and moments of loss distributions; simple reinsurance; constructing risk models; aggregate claims distributions; ruin theory; credibility theory & experience rating; run-off triangles; no-claims discount systems.  [30]

READING LIST:

1. "Official Core Reading - Subject 106", (Institute and Faculty of Actuaries, 1999)   [Library Cat.:  ]
2. "Introductory Statistics with Applications in General Insurance", Hossack, Pollard & Zehnwirth (2nd edition, CUP, 1999)   [Library Cat.:    519.5024 HOS]
3. "Loss Models from Data to Decisions", SA Klugman, HH Panjer and GE Willmot (Wiley International Science, 1998) [Library Cat.:    368.01 KLU]

PREREQUISITE:

210

330 COMPUTER SYSTEMS ARCHITECTURE(C)

AIMS:

To explore implementations and techniques which are used to make modern computers better in terms of speed, capacity, reliability and convenience of support for applications.

DESCRIPTION:

The course considers base technologies, performance, I/O systems, parallelism and reliability.

SYLLABUS:

Base technologies: silicon, magnetic media, fibre optics; performance, cost, reliability.

Register transfer level: components: store, register file, ALU; data path, controller, microcode, synchronous and asynchronous buses, direct and memory mapped I/O.

Performance: memory and CPU: slave stores, cache and virtual storage, pipelining, register windows, RISC vs. CISC.

I/O: bandwidth and latency of disc systems, communications and controller; SCSI and Ethernet.

Parallelism: multiprocessor (shared store) and multicomputer (distributed store) and their communications network (bandwidth and latency); shared variable/message passing; granularity/coupling; cache consistency.

Reliability: fault tolerance, resilience, MTBF, MTTR; redundancy: software (checkpoints) and hardware (hot standby/TMR). [30]

SKILLS AND KNOWLEDGE ACQUIRED:

To have an appreciation of modern computer systems.

READING LIST:

1. "Computer Architecture, Design and Performance", B.Wilkinson, (Prentice Hall)   [Library Cat.: 004.22 WIL]
2. "Computer Architecture and Design", A.J.van de Goor, (Addison Wesley)    [Library Cat.: 004.16 GOO]
3. "Computer Organization and Architecture", W.Stallings, (Macmillan)    [Library Cat.: 004.22 STA].

PREREQUISITE:

221

331 PARALLEL AND CONCURRENT PROGRAMMING (C)

AIMS:

To provide the student with the practical knowledge of the techniques used to implement parallel and concurrent systems.

DESCRIPTION:

The course considers the reasons for, and the nature of, parallel and concurrent programming with the latter being described in terms of the three concepts, shared variables and memory, message passing and tuple spaces.

SYLLABUS:

Reason for parallel and concurrent programming: distinction between, benefits, problems. The course discusses the three main paradigms: shared variables and memory, message passing, tuple spaces. Synchronisation: semaphores, monitors, rendezvous. Deadlocks: identification, avoidance. [30]

SKILLS AND KNOWLEDGE ACQUIRED; To have an appreciation of the problems involved in constructing a concurrent system and to have the basic ideas necessary to understand and develop such a system.

READING LIST:

"Concurrent Programming", A. Burns and G. Davies, (Addison-Wesley)    [Library Cat.: 005.1 BUR].

PREREQUISITE:

220

332 DATA STRUCTURES AND ALGORITHMS (C)

AIMS:

To give: a language-independent appreciation of well-known data structures and algorithms; an understanding of data structures as abstractions which may be implemented and used in a variety of ways dependent on language constraints, clarity of expression, and efficiency; an introduction to computational complexity and analysis of algorithms; an introduction to abstract data types.

DESCRIPTION:

The course covers the idea of data structures and their application in developing algorithms for a set of well-known basic problems.

SYLLABUS:

Review of basic data structures and their alternative implementations: lists, arrays, tables, stacks, queues, trees, graphs. Algorithms, including sorting and searching and relationship to data structures studies, relationship of recursion to mathematical induction, comparison of iterative and recursive algorithms. Asymptotic analysis (big 0 notation) and time versus space trade-offs. Problem-solving strategies (eg. greedy, divide and conquer, backtracking) with correctness and complexity. Abstract data types: encapsulation techniques as methods for separation of application and module or class specification from implementation; support for ADTs in various programming languages, relationship to algebraic formal specifications and object-oriented programming. [30]

SKILLS AND KNOWLEDGE ACQUIRED:

The ability to construct efficient algorithms and implement them using appropriate data types.

READING LIST:

1. "Introduction to Functional Programming", R. Bird and P. Wadler, (Prentice Hall)   [Library Cat.: 001.642 BIR].

PREREQUISITE:

220

333 DECLARATIVE (LOGIC) PROGRAMMING (C)

AIMS:

To introduce logic programming as a declarative programming technique based on the model of first order predicate logic.

DESCRIPTION:

Logic programs are studied using two abstract, machine independent concepts: truth and logical deduction. Logic programming languages are associated with a concrete execution mechanism and programs in such languages are shown to be instructions for non von Neumann computers. Prolog is introduced as the exemplar logic programming language, but other computational models within the logic programming paradigm will be discussed. The module will be illustrated by the study of applications of logic programming, for example some of: game-playing programs, theorem-provers, image processing, medical diagnostics, logic and grammars, natural language processing, meta- interpreters. The associated laboratories and workshops will provide students with opportunities to explore in practice some of the issues introduced in the lectures.

SYLLABUS:

Horn Clause Programs: Horn clauses, Horn clause programs and goals.

SLD-Resolution: Logical variables, Most General Unifiers and the unification algorithm, SLD- Resolution as a mechanizable proof method, soundness and completeness of SLD-Resolution, the closed- world assumption, search strategies and selection rules, the procedural interpretation, pruning the search tree with the `cut', program testing.

Negation in Logic Programming: SLDNF-extending SLD with finite failure.

Logic Programming Paradigms: Prolog including I/0 and database update, constraint logic programming, concurrent logic programming.

Logic Programming Techniques: generate and test, programming with recursive data structures and incomplete data structures, search techniques, meta-level programming, partial evaluation. [30]

SKILLS AND KNOWLEDGE ACQUIRED:

To be able to program small applications in Prolog, to be able to read Prolog code, and to transfer these skills to other logic programming paradigms.

READING LIST:

1. "The Art of Prolog", L. Sterling and E. Shapiro, (MIT)    [Library Cat.: 005.133 Prolog STE]
2. "Prolog Programming for Artificial Intelligence", I. Bratko, (Addison-Wesley)    [Library Cat.: 006.302855133 Prolog BRA].

PREREQUISITE:

None

334 NETWORKS AND COMMUNICATIONS (C)

AIMS:

To explain the basic principles of data communications, computer networks and their operating protocols. On completion of the course students should have a sound knowledge of data networks and their design, and an understanding of the criteria involved in the selection and implementation of such systems.

SYLLABUS:

Brief history of communications from early speech, through written and printed formats up to modern high speed electronic transfers. Data communications: transmission media, transmission techniques (AM, FM, PM); broadband and baseband communications; standard formats. Digital versus analogue representation. Serial and parallel formats: asynchronous versus synchronous transmission. Data compression. Reliability and security: error detecting and correcting coding.  Data encryption for privacy and authentication. Viruses. Networks: local area and wide area.

Topologies: star, bus, ring, tree; examples in current service. Data switching: circuit, message and packet switching; routing; flow control. Standard in communicaiton and data networks. The ISO OSI seven layer reference model; Transmission Control/Internet Protocol (TCP/IP); Integraed Digital Services Network (ISDN), Mobile communications. Applications examples: Technical Office and Factory environments; Telecomms network; email; Internet and World Wide Web. [30]

PREREQUISITE:

221

335 LANGUAGE PROCESSORS (C)

AIMS:

To appreciate that most computer programs interpret or translate structured input in a variety of forms, including graphics input, text processing macro, shell and other command input, database queries, other computer programs, etc.

To understand the use of simple formal languages to define input language syntax, and understand alternative techniques for translation and interpretation using appropriate tools. To understand programming language implementation through translation to machine code and have examined example code generation algorithms.

To understand the relationship between programming language semantics and both compiled code generation, and run-time environment requirements for compiled and interpreted programs.

SYLLABUS:

Language Processing: Translation from concrete to abstract syntax (eg for programming languages) and interpretation (eg of command or graphics or text processing input languages) recursive descent parsers and state machines as recognisers, context free and regular grammars, YACC and LEX as tools.

Machine Code Generation: Algorithms for programming languages with expressions, control flow and procedure call for stack and general register machines, linking, loading and relocation.

Run-time Environments: Stacks for procedure call and return, heaps for dynamic storage allocation for compiled and interpreted languages, garbage collection. [30]

PREREQUISITE:

220

337 COMPUTATIONAL GRAPHICS (C)

AIMS:

The aim of this course is twofold. Firstly to introduce students to a range of issues and techniques in three-dimensional graphics for realistic scene representation, and then secondly to investigate techniques that have been developed for computer vision to enable robots to see. For each of the main areas considered, some typical methods are analysed in detail. Students' understanding of theory will be enhanced by coursework involving the implementation of some major algorithms applied to practical problems. On completion of the course students should be equipped to: understand design and processing issues in 3D graphics and computer vision; implement a wide range of applications; understand how to extend their knowledge to more advanced aspects.

SYLLABUS:

Stereoscopic viewing: Hardware and software;

Virtual reality: The building of, and interaction with virtual environments;

Animation: Applications in films and advertising, morphing;

Multimedia: Techniques for combining text, sound, images and video in a single application. Applications in education, business and entertainment.

Data compression. Generation of interactive video.

Basic image processing operations: Choice of digitisation parameters; histogram flattening, smoothing, normalisation, thinning; edge detection, region identification, structural characteristics.

Computational architectures for image processing: Serial processing, SIMD; processing structure at the cell level.

Pattern recognition: Patterns, vectors, classes and features; statistical pattern recognition, decision rules, clustering techniques; memory network classifiers. [30]

READING LIST:

1. Selected articles to be taken from 'Hitchh-Hikers' Guide to Graphics', distributed freely for educational use by the Advisory group on Computer Graphics.
2. "Computer Graphics", Hearn, D. and Baker, M.P. (2nd edit, Prentice Hall, 1994)    [Library Cat.: 001.6443 HEA].
3. "Digital Image Processing", Gonzalez, R.C. and Woods, R.E. (Addison Wesley, 1993) [Library Cat.:  621.367 GON].
4. "Introduction to Computer Graphics", Foley, van Dam, Feiner, Hughes and Phillips (Addison Wesley, 1994) [Library Cat.: 006.6 FOL].

PREREQUISITE:

222

338 PRINCIPLES OF HUMAN COMPUTER INTERACTION (C)

AIMS:

The purpose of this course is to give a general introduction to the field of HCI. The major aim is to lead students away from an uncritically accepting attitude to interfaces and interaction, through a purely intuitive appreciation of good and bad interface design, to understanding the principles of interaction so that they are able to analyse what is wrong with an interface, and specify how interaction could be improved. Students should understand a broad range of basic concepts and issues in HCI, and be able to apply HCI principles, guidelines and techniques to the analysis and design of a variety of computer systems.

SYLLABUS:

Introduction: Motivation and overview of HCI. Place of HCI in systems development. Need for interface design. Theories and approaches to HCI.

The Human and the Interface: Appreciation of the significance of human cognitive abilities in informing interface design. User psychology, including perception, memory and attention. Problem solving and mental models.

The Computer and the Interaction: Appreciation of the nature and potential of various interaction tools and techniques. Devices and interaction styles.

Usability: An overview of guidelines and principles. Identification of inadequate HCI design, with respect to guidelines and principles.

Evaluation Techniques: Goals and types of evaluation, both formative and summative. Heuristic evaluation and cognitive walkthroughs.

Experimental and empirical methods.

User Modelling: Introduction to approaches to modelling the user's view of a task. GOMS analysis.

Task Analysis: Formalisms for task analysis and device models.

Hierarchical Task Analysis. Integration with Systems Analysis. Dialogue Notation and Design: Transformation of task models to dialogue models. Dialogue model notations. Construction and validation of dialogue models. Integration of presentation with dialogue design.

Design Tools: Principles and purposes of prototyping tools especially Hypercard and Visual Basic. UI components. HCI artefacts: hypertext, hypermedia and multimedia.   [30]

PREREQUISITE:

None

339 SYMBOLIC ARTIFICIAL INTELLIGENCE (C)

AIMS:

This module is an introduction to the discipline of Symbolic Artificial Intelligence (AI) and its application in building useful Knowledge Based Systems (KBSs) for practical problems. The module aims to provide students with a knowledge and grasp of the basic concepts in Symbolic AI and KBS sufficient for further independent study, and to give students an understanding and appreciation for what applications a KBS would be appropriate for. It also aims to allow students to gain experience with a tool for constructing KBSs, and to outline basic methodologies for the principled design, construction, and validation of knowledge-based systems. Finally, it aims to introduce the students to a selection of common AI/KBS techniques with illustrative applications. 

DESCRIPTION:

On completion of this module, students should be able to:

A) describe and discuss the main concepts behind Symbolic AI research, its applications and methodology.

B) describe, apply and implement each stage of the KBS development process.

C) describe and apply a number of common knowledge representation methods (i.e. logic, production rules, decision trees, frames, and semantic nets).

D) describe and apply a range of AI architectures (i.e. production systems, CBR, blackboard systems), and show awareness of their applications.

E) describe and apply principles, techniques and applications of AI search, planning and learning.

SYLLABUS:

READING LIST:

"The Essence of Artificial Intelligence" A. Cawsey, (Prentice Hall, 1997) [Library Cat:  006.3 CAW]

PREREQUISITE:

None

340 CORPORATE RISK MANAGEMENT (F)

AIMS:

To analyse the risks facing industrial and commercial enterprises and develop a framework for managing these risks.

DESCRIPTION:

Particular emphasis will be placed on those risks that are insurable and the role that insurance plays in their management. The management of exchange rate, interest rate and financial market risks will be covered in the course. The role that insurance brokers and investment banks play in the risk management process will also be investigated.

SYLLABUS:

The principles of risk management. The evolution of the practice of risk management. Identification and measurement of insurable/hedgeable risks. Models for determining optimal risk retention. Designing insurance and hedging programmes. The role of futures, options, swaps and other financial instruments in risk management. Captives and the use of corporate vehicles. The role of insurance broker and investment banks in risk management. [30]

SKILLS AND KNOWLEDGE ACQUIRED:

An ability to identify and control financial risk, using the insurance markets and other financial instruments.

PREREQUISITE:

None

341 FINANCIAL MARKETS (F)

This is a double module.

AIMS:

To introduce the student to the theory and practice of investing in the stock exchange and other money markets.

DESCRIPTION:

The course introduces the student to the jargon and techniques of investment markets. It deals with the analysis and construction of models for investing in stocks, bonds, derivatives, etc. and emphasises concepts such as portfolio strategies, performance measures and regulation.

SYLLABUS:

Overview of the fixed interest market. Measurement of yields and returns: Yield to maturity/redemption yield, flat yield, reinvestment. Determination of bond prices: Coupon paying bods, Zero coupon bond, Accrued Interest. Volatility, duration and convexity: Estimating bond price changes with respect to changes in yields. Use of spot yields: non-parallel shifts in the yield curve. Term structure of interest rates: Spot yields, implied forward rates. Expectations Hypothesis, Liquidity Preference, Market Segmentation. Bond portfolio strategies: Immunisation, cash flow matching, indexing. Stock market returns: fundamental value: Types of security transaction, transaction costs etc. Efficient markets hypothesis: Stock market: Anomalies in the stock market: empirics and noise traders. Predictability in stock returns. Measuring time varying risk premia: Poterba-Summers model and developments, simple ARCH and GARCH model. Performance measures and portfolio strategies: Index funds, the CAPM and Sharpe, Jensen and Traynor indices, technical analysis. Regulation of financial institutions: Concepts of asymmetric information, adverse selection, moral hazard and principal/agent problems. Capital adequacy arrangements for UK banks, Basle arrangements, risk adjusted capital-asset ratios. Regulation in the US: Deposit Insurance. The Treasury Plan.

Derivative markets: an overview. Hedging with futures: basics. Hedging with futures: bond and stock index futures. Speculation and arbitrage with futures. Option pricing theory. Hedging with options. Portfolio insurance. Speculation and arbitrage with options. Interest rate swaps. Issues in derivative markets. [60]

SKILLS AND KNOWLEDGE ACQUIRED:

Expertise in the theory and practice of operating in the stock exchange and other investment markets.

READING LIST:

1. "Introduction to Stock Exchange Investment", J. Rutterford, (Macmillan)   [Library Cat.: 332.642 RUT]
2. "Modern Portfolio Theory and Investment Analysis", E.J. Elton and M.J. Gruber, (Wiley)   [Library Cat.: 332.6 ELT]
3. "Portfolio and Investment Selection: Theory & Practice", H. Levy and M. Sarnat, (Pentice Hall)   [Library Cat.: 332.6 LEV].

PREREQUISITE:

None

342 INTERNATIONAL FINANCE (F)

This is a double module.

AIMS:

To introduce the student to the ways and means of operating in global financial markets.

DESCRIPTION:

The course is in two parts. The first part deals with basic concepts such as the balance of payments, the budget, foreign trade, capital mobility, inflation and exchange rate systems. The second part discusses the following: (i) Empirical results on the behaviour and determination of exchange rates. (ii) Prices, purchasing power and monetary models. (iii) Empirical evidence on interest rate parity, market efficiency and controls on international capital movements.

SYLLABUS:

Basic relations: Balance of payments accounts: National income accounts: Balance of payments, credit creation by the banking system, and the budget. The Keynesian system and the foreign trade multipliers. Relative prices and the balance of payments. Money, prices, and the adjustment mechanism. Capital mobility and stabilization policies. Inflation and the exchange rate system. Fixed versus flexible exchange rates and optimum currency areas. International monetary regimes: The Bretton Woods system; The European Monetary System.

Brief overview of the various approaches to the balance of payments; stylized empirical results about exchange rate behaviour. Prices in the open economy: Purchasing power parity. Exchange rate determination: Flexible prices and the monetary model. Sticky prices and the Dornbusch model. Portfolio balance and the current account. Empirical evidence. Interest rate parity, transaction costs and the modern theory of forward rate; market efficiency and rational expectations. Controls and international capital movements. [60]

SKILLS AND KNOWLEDGE ACQUIRED:

A detailed understanding of concepts such as national income accounts, the balance of payments, exchange rate systems, interest rate parity etc.

READING LIST:

1. "Open Economy Macroeconomics", R.Dornbusch, (Basic Books)    [Library Cat.: 339 DOR]
2. "The Balance of Payments", J.E.Meade, (OUP)   [Library Cat.: 382.17 MEA]
3. "Exchange Rates and International Finance", L.S.Copeland, (Addison-Wesley)    [Library Cat.: 332.456 COP].

PREREQUISITE:

None

343 EQUITY INVESTMENT MANAGEMENT AND FIXED INCOME SECURITIES (F)

This is a double module.

Equity Investment Management:

AIMS:

The course aims to provide a good understanding of different types of equity investment management styles. The emphasis will be placed on the active and passive investment management, equity indexing, market-neutral and equitisation strategies, understanding equity risk premium and sources of abnormal returns in equities. The aim of the course is to provide a good background for equity investment management overall. The course is highly participative and it will be based on practical cases and uptodate research papers related to the main issues in equity investment management.

SYLLABUS:

READING LIST:

The following material along with the financial papers will provide a general guideline to the topics covered in the course.

1. "Handbook of Equity Style Management", Fabozzi, F.J. et al, (2nd edition, Frank J. Fabozzi Associates)    [Library Cat.: 332.6 COG]
2. "Equity Investment Management", Lofthouse, S., (John Wiley and Sons)   [Library Cat.: 332.6 LOF]
3. "Active Asset Allocation", Arnott, R.D. and Fabozzi, F.J., (Probus Publishing Co.)    [Library Cat.: 332.6 ARN]
4. "Equity Style Management: Evaluating and Selecting Investment Styles", Klein R.A. and Lederman, J., (Irwin Professional Publishing)  [Library Cat.: 332.67 KLE]
5. "Current Topics in Investment Management", Fabozzi, F.J. and Fabozzi T.D., (Harper & Row)  [Library Cat.: 332.6 FAB]

Fixed Income Securities:

AIMS:

The course is intended to provide a broad and comprehensive review of the techniques and strategies that emanate from the fundamental representation of the trade-off between bond risk and bond return: the yield curve. It is actually designed to cover both the academic and practitioners views on the fundamentals and the complexities of the fixed income market. The course addresses both the general and specific aspects of yield curve analysis in a practical and understandable manner. The empirical illustrations along with the use of spreadsheets form the basis for more complex applications of this subject matter, which are discussed throughout the course. Specifically the course offers a) a thorough grounding of the fixed income securities market and the way they operate, b) the necessary theoretical knowledge and statistical tools to measure and analyse volatility in the fixed income market, and c) a comprehensive analysis of the practical techniques. The course is highly participative and there will be highly practical cases in measuring and managing the risks of bond portfolios.

SYLLABUS:

READING LIST:

The following material along with the financial papers will provide a general guideline to the topics covered in the course.

1. "Yield curve analysis", Douglas, L.G., NYIF    [Library Cat.: 332.6323 DOU]
2. "Fixed income mathematics", Fabozzi, F.J., (Irwin)   [Library Cat.: 332.6320151 FAB]
3. "Bond markets, analysis and strategies", Fabozzi, F.J., (Prentice-Hall)    [Library Cat.: 332.6323 FAB]
4. "Bond portfolio management", Fabozzi, F.J., (FJF Associates)  [Library Cat.: ]
5. "CMO portfolio management", Fabozzi, F.J., (FJF Associates)  [Library Cat.: ]
6. "Measuring and controlling interest rate risk", Fabozzi, F.J., (FJF Associates)  [Library Cat.: ]
7. "Valuation of fixed income securities and derivatives", Fabozzi, F.J., (FJF Associates)  [Library Cat.: ]
8. "CMO: structure and analysis", Fabozzi, F.J., Ramsey, C. and Ramirez, F.R., (FJF Associates)  [Library Cat.: ]
9. "The handbook of fixed income securities", Fabozzi, F.J. and Fabozzi, T.D., (Irwin) [Library Cat.: ]
10. "Advanced fixed income portfolio management", Fabozzi, F.J., (Probus) [Library Cat.: ]
11. "Money market and bond calculations", Stigum, M. and Robinson, F.L., (Irwin) [Library Cat.: 332.632 STI]
12. "Fixed income arbitrage", Wong, M.A., (Wiley) [Library Cat.: 332.632 WON]
13. "Trading and investing in bond options", (Wiley) [Library Cat.: 332.6323 WON]

PREREQUISITE:

None

344 CORPORATE FINANCE (F)

This is a double module.

AIMS:

Students will gain an understanding of the key decision areas confronting the financial director, learn how companies interact with capital markets to maximise their value to their shareholders, apply key concepts in real case studies and practical exercises.

DESCRIPTION:

The course deals with the relationship between companies and financial markets. The capital structure of a company and the role played by its financial director. The creation of value for shareholders and the restructuring of companies in the wake of takeovers and bankruptcy.

SYLLABUS:

Corporates and capital markets. Analysis of capital expenditure. Risk assessment. The cost of capital. Company valuation. Going public. The performance of IPOs. Rights issues. Creating value for shareholders. An alternative perspective. Capital structure and the cost of capital: the theory of capital structure. Capital structure and taxes. The capital structure in practice: introduction of the costs of financial distress; other influences on capital structure; is there an optimal capital structure? Dividend Policy: dividends and retained earnings; the effect of dividend policy on share values; the influence of dividends on shareholder wealth. Dividend Policy in practice: how do companies decide on dividend payments; impact of taxation on dividend policy; other influences on dividend policy. The pre-bid period: methods of amalgamation; valuation methods. The bid process. The post-bid period: post merger performance; managerial options in failed takeovers; who gains in takeovers? Corporate bankruptcy: nature of bankruptcy; prediction of bankruptcy; creditor priorities; costs of bankruptcy; choice between liquidation and reorganisation. Corporate restructuring: reasons for restructuring; different types of restructuring; market reaction to corporate restructuring. [60]

SKILLS AND KNOWLEDGE ACQUIRED:

An ability to analyse the financial interactions that take place between companies, their shareholders and the capital markets.

READING LIST:

1. "Modern Corporate Finance", A. Shapiro, (Collier Macmillan)  [Library Cat.: 658.15 SHA]
2. "Principles of Corporate Finance", R. Brealey and S. Myers, (McGraw-Hill)   [Library Cat.: 658.15 BRE]
3. "Cases in Corporate Finance", E. Dimson and P. Marsh, (Wiley)  [Library Cat.: 658.15 DIM].

PREREQUISITE:

None

345 FINANCE AND FINANCIAL REPORTING (F)

This is a double module.

AIMS:

The aim of the finance section of this course is to provide the student with a basic understanding of the methods and types of instrument used by companies to raise finance. The aim of the accounting section of the course is to enable students to interpret the published financial statements of companies and financial institutions.

DESCRIPTION:

Students should be able to demonstrate a knowledge of the structure of joint stock companies, the methods used by them to raise capital, and the markets and institutions which enable them to do so. Students should also be able to demonstrate a knowledge of the main features of financial statements, the principles which apply to their construction, and simple techniques used to interpret them.

SYLLABUS:

Finance - 50% of teaching time: the joint stock company and other business entities;   capital structure of a limited company; personal and corporate taxation; capital markets and financial instruments; financial institutions; cost of capital and project evaluation.

Accounting - 50% of teaching time: legal requirements which apply to financial reporting; fundamental accounting concepts and financial statements; construction of simple financial statements; financial statements of insurance companies and pension funds: interpretation of accounts by calculation of simple ratios; limitations to interpretation of accounts.

READING LIST:

1. "Investment", A. Adams, (Graham and Trotman, 1991)  [Library Cat.: 332.6 ADA]
2. "Interpreting Company Reports and Accounts", G. Holmes and A. Sugden, (Woodhead-Faulkener, 1994)  [Library Cat.: 658.1512 HOL].

PREREQUISITE:

234

346 DERIVATIVES, TRADING AND HEDGING AND FINANCIAL ENGINEERING (F)

This is a double module.

Derivatives, Trading and Hedging:

AIMS:

To develop an understanding of the key derivative securities and their application in risk management situations.

SYLLABUS:

READING LIST:

1. "Options, futures and other derivative securities", Hull, John, (Prentice-Hall)  [Library Cat.: 332.63228 HUL]
2. "Government bond futures", LIFFE, (LIFFE)  [Library Cat.: 332.6329 LIF].

Financial Engineering:

AIMS:

To build on existing knowledge (the derivatives trading and hedging course) to enhance understanding of the key derivative securities and their application in risk management situations.

SYLLABUS:

READING LIST:

1. "Options, futures and other derivative securities", Hull, John, (Prentice-Hall)  [Library Cat.: 332.63228 HUL]
2. "Government bond futures", LIFFE, (LIFFE)  [Library Cat.: 332.6329 LIF].

PREREQUISITE:

None

347 FINANCIAL AND INVESTMENT MATHEMATICS II (F)

AIMS AND DESCRIPTION:

To provide a grounding in financial mathematics and its applications by building on Financial and Investment Mathematics I (module 234).

SYLLABUS:

SKILLS AND KNOWLEDGE ACQUIRED:

To introduce and enable students to use additional the mathematical techniques which are necessary for the analysis of investments.

To enable students to apply relevant concepts from probability and statistics to investment analysis.

READING LIST:

1. "An Introduction to the Mathematics of Finance", McCutcheon & Scott (Heinemann, 1987) [Library Cat.:  368.37 MCC]

2. "Investment Mathematics and Statistics", Adams, Bloomfield, Booth & England (Kluwer, 1993) [Library Cat.:  322.60151 ADA]

PREREQUISITE:

234

350 BUSINESS ECONOMICS (E)

AIMS:

To provide a rigorous understanding of the economics of industry and the rationale, as well as different mechanisms, for government intervention.

DESCRIPTION:

The dominant tradition in industrial economics in the post-war period is strongly rooted in the empirical structure-conduct-performance paradigm. While close attention will be paid to aspects of this tradition that retain their importance and relevance, the course also aims to acquaint the student with recent developments in the theory of the firm and industrial organisation. The aim here would be to draw upon insights pertinent to business policy as, for example, the greater understanding now emerging in the internal organisation of the firm and relationships with customers and suppliers. Not only are theoretical and policy-related aspects of industrial economics rapidly changing, but the technology, organisation and market conditions under which firms compete have been undergoing substantive changes in the last decade. These devlopments in manufacturing industry and their implications for R&D, vertical integration, diversification, cross-border collaborative alliances, mergers and acquisitions and competition policy are examined throughout the course.

SYLLABUS:

Introduction and overview: world industry and business in the 1990's: the global restructuring of industry during the period 1970's-1990's. The transformation of the competitive environment facing international business. New technologies, the new manufacturing and business strategy. Science, technology and industrial strategies of nations in the 1990's. New technologies, new manufacturing conditions and business strategies: the restructuring of industry, globalisation of markets, organisational changes through Just-in-Time, micro-electronics based automation technologies and sources of competitive advantage. Economic theory and business economics: the market structure, business conduct and market performance paradigm in industrial economics; recent developments in the theory of the firm and industrial organisation. The firm: Neo-classical, new managerial, behavioural and contractual theories of the firm. Ownership, control and performance of the joint stock company - the need for an `alternative' theory? Costs and supply conditions: economies of scale and the size of plant and the firm. Oligopoly: pricing, product differentiation, advertising. Barriers to entry. Industrial structure and profitability. Diversification and vertical integration. Research and development and technical change. Public policy issues. [30]

SKILLS AND KNOWLEDGE ACQUIRED:

A detailed understanding of the changing face of industrial economics and the role of government intervention.

READING LIST:

1. "Industrial Economics and Organization - Theory and Evidence", D.A. Hay and D.J. Morris, Oxford University Press)  [Library Cat.: 338.7 HAY]
2. "Industrial Economics", R. Clarke, (Basil Blackwell)  [Library Cat.: 338.5 CLA]
3. "Industrial Market Structure and Economic Performance", F.M. Scherer and D. Ross, (Houghton Mifflin)  [Library Cat.: 338 SCH].

PREREQUISITE:

None

351 MATHEMATICAL ECONOMICS (E)

This is a double module.

AIMS:

To train students in advanced micro- and macroeconomic analysis using formal mathematical techniques.

DESCRIPTION:

The ideas presented in 253 Economic Theory Treated Mathematically are developed and generalised here, and further advanced topics including uncertainty, Nash Programming Solution, optimal growth theory, and principal-agent problems are introduced.

SYLLABUS:

General equilibrium analysis Advanced consumer and producer and producer theory Kuhn-Tucker theory Linear models Techniques from the calculus of variations Game theory Classical and Keynesian macroeconomic models of closed and open economics [60]

SKILLS AND KNOWLEDGE ACQUIRED:

Advanced mathematical skills in micro- and macroeconomic analysis.

READING LIST:

1. "The Structure of Economics: A Mathematical Analysis", E.Silberberg, (McGraw-Hill)  [Library Cat.: 330.0151 SIL]
2. "Microeconomic Analysis", H.R. Varian, (Norton)  [Library Cat.: 338 VAR]
3. "General Equilibrium Theory", R.E. Weintraub, (Macmillan Studies in Economics)  [Library Cat.: 330.018 WEI].

PREREQUISITE:

233

352 LABOUR ECONOMICS (E)

This is a double module.

AIMS:

To present an advanced treatment of the economics of labour markets at both the micro and macro levels.

DESCRIPTION:

The course attempts to show the contributions of micro- and macroeconomic theory to the determination of levels of wages and employment, and of the distribution of income within society. The scope for welfare-improving interventions by trade unions and government is critically examined.

SYLLABUS:

The supply of and demand for labour Human capital and search theoretic modifications of conventional analysis Wage structure The impact of trades unions Strikes Government intervention in the labour market -equal pay -anti-discrimination laws -minimum wages Micro- and macroeconomics of unemployment Wage inflation Incomes policy Theories of income distribution [60]

SKILLS AND KNOWLEDGE ACQUIRED:

An understanding of the mechanisms underlying labour remuneration in theory and practice, and of the scope for trade union and government intervention in labour markets.

READING LIST:

1. "Unemployment", K.Hawkins, (Penguin)   [Library Cat.: 331.137 HAW]
2. "The Inequality of Pay", H.Phelps Brown, (Oxford)   [Library Cat.: 339.2 BRO].

PREREQUISITE:

None

353 INDUSTRIAL ECONOMICS (E)

This is a double module.

AIMS:

To present an in-depth examination of the microeconomic functioning of firms, industries and markets.

DESCRIPTION:

The course is mainly a presentation of the theory of industrial economics, with some attention to empirical aspects. It examines traditional and alternative theories of the firm and market structure, including perfect and monopolistic competition, oligopoly and monopoly. The behaviours - such as the erection of artificial barriers to entry and product differentiation - which emerge under various market structures, as well as their consequences for economic welfare are analysed. Topics such as the diffusion of technology, government regulation of monopoly, and the privatisation versus nationalisation debate, are also examined.

SYLLABUS:

Theory of the firm and its objectives Industrial concentration Market structure and firm content Potential competition and barriers to entry Product differentiation The economics of innovation Welfare and market structure Public ownership and privatisation [60]

SKILLS AND KNOWLEDGE ACQUIRED:

Knowledge and understanding of the theory and empirics of the economic behaviour of firms and industries.

READING LIST:

1. "Industrial Economics", R. Clarke, (Basil Blackwell)   [Library Cat.: 338.5 CLA]
2. "Modern Microeconomics", A. Koutsoyiannis, (Macmillan)   [Library Cat.: 338.KOU]
3. "The Economics of Industries and Firms", M.C. Sawyer, (Croom-Helm)    [Library Cat.: 338 SAW]
4. "Economic Theory of Industry", M. Waterson, (CUP)   [Library Cat.: 338.001 WAT].

PREREQUISITE:

None

300 SPECIAL TOPICS (M)

This is for MMath students only.

AIMS:

To introduce some of the more advanced areas of mathematical methods and analysis.

DESCRIPTION:

The course will include a selection of topics and will introduce the student to methods of study through guided reading.

SYLLABUS:

Topics will be selected from advanced areas of mathematics, such as:

Differentiation of functions f: Rn Rm. Solution of partial differential equations using Green's functions. Series solution of differential equations and special functions. Perturbation methods and asymptotic analysis. Variational methods and optimisation. Tensors. Stochastic calculus. Algebraic structures. Measure theory and integration. Topology. Nonlinear evolution equations. [30]

SKILLS AND KNOWLEDGE ACQUIRED:

An appreciation of some of the more sophisticated areas of mathematical analysis and an ability to learn new mathematics through guided reading.

READING LIST:

The reading list will be selected from relevant texts, such as:

1. "Calculus on manifolds: a modern approach to classical theorems of advanced calculus", M. Spivak, (Benjamin, 1965)   [Library Cat.: 514.7 SPI]
2. "Principles and techniques of applied mathematics", B. Friedman, (Wiley, 1966)   [Library Cat.: 515 FRI]
3. "Fundamentals of differential equation", R.K. Nagle and E.B. Staff, (Addison-Wesley, 1966)   [Library Cat.: 515.35 NAG]
4. "Introduction to perturbation techniques", A.H. Nayfeh, (Wiley, 1981)    [Library Cat.: 515.35 NAY]
5. "Mathematical methods of physics", J. Mathews and R.L. Walker, (Benjamin, 1970)   [Library Cat.: 510.2453 MAT]
6. "Theory and applications of stochastic differential equations", Z. Schuss, (Wiley, 1980)   [Library Cat.: 519.2 SCH]
7. "Nonlinear waves in one-dimensional dispersive systems", P.L. Bhatnagar, (Oxford, 1979)   [Library Cat.: 531.1133 BHA].

PREREQUISITE:

None

400 SPECIAL TOPICS (M)

This is for MMath students only.

AIMS:

To introduce some of the more advanced areas of mathematical methods and analysis.

DESCRIPTION:

The course will include a selection of topics not covered in the corresponding Part 3 module (300) but selected from the same list. The course will make use of further guided reading and will in addition be supported by laboratory work.

SYLLABUS:

Topics will be selected from advanced areas of mathematics, such as:

Differentiation of functions f: Rn Rm. Solution of partial differential equations using Green's functions. Series solution of differential equations and special functions. Perturbation methods and asymptotic analysis. Variational methods and optimisation. Tensors. Stochastic calculus. Algebraic structures. Measure theory and integration. Topology. Nonlinear evolution equations. [30]

SKILLS AND KNOWLEDGE ACQUIRED:

An appreciation of some of the more sophisticated areas of mathematical analysis and an ability to learn new mathematics through guided reading.

READING LIST:

The reading list will be selected from relevant texts, such as:

1. "Calculus on manifolds: a modern approach to classical theorems of advanced calculus", M. Spivak, (Benjamin, 1965)   [Library Cat.: 514.7 SPI]
2. "Principles and techniques of applied mathematics", B. Friedman, (Wiley, 1966)   [Library Cat.: 515 FRI]
3. "Fundamentals of differential equation", R.K. Nagle and E.B. Staff, (Addison-Wesley, 1966)   [Library Cat.: 515.35 NAG]
4. "Introduction to perturbation techniques", A.H. Nayfeh, (Wiley, 1981)    [Library Cat.: 515.35 NAY]
5. "Mathematical methods of physics", J. Mathews and R.L. Walker, (Benjamin, 1970)   [Library Cat.: 510.2453 MAT]
6. "Cartesian Tensors", H. Jeffreys, (CUP)   [Library Cat.: 515.63 JEF]
7. "Theory and applications of stochastic differential equations", Z. Schuss, (Wiley, 1980)   [Library Cat.: 519.2 SCH]
8. "Nonlinear waves in one-dimensional dispersive systems", P.L. Bhatnagar, (Oxford, 1979)   [Library Cat.: 531.1133 BHA].

PREREQUISITE:

None

Last Edited 18/09/02