Mathematics, Operational Research, Statistics and Economics (MORSE) (Industry) BSc Hons - 2021 Entry

Course Structure

Lancaster University offers a range of programmes, some of which follow a structured study programme, and others which offer the chance for you to devise a more flexible programme to complement your main specialism. We divide academic study into two sections - Part 1 (Year 1) and Part 2 (Year 2, 3 and sometimes 4). For most programmes Part 1 requires you to study 120 credits spread over at least three modules which, depending upon your programme, will be drawn from one, two or three different academic subjects. A higher degree of specialisation then develops in subsequent years. For more information about our teaching methods at Lancaster please visit our Teaching and Learning section.

The following courses do not offer modules outside of the subject area due to the structured nature of the programmes: Architecture, Law, Physics, Engineering, Medicine, Sports and Exercise Science, Biochemistry, Biology, Biomedicine and Biomedical Science.

Information contained on the website with respect to modules is correct at the time of publication, and the University will make every reasonable effort to offer modules as advertised. In some cases changes may be necessary and may result in some combinations being unavailable, for example as a result of student feedback, timetabling, Professional Statutory and Regulatory Bodies' (PSRB) requirements, staff changes and new research.

Year 1

Core

• Calculus

  Students are provided with an understanding of functions, limits, and series, and knowledge of the basic techniques of differentiation and integration. Examples of functions and their graphs are presented, as are techniques for building new functions from old. Then the notion of a limit is considered along with the main tools of calculus and Taylor Series. Students will also learn how to add, multiply and divide polynomials, and will learn about rational functions and their partial fractions.

  The exponential function is defined by means of a power series which is subsequently extended to the complex exponential function of an imaginary variable, so that students understand the connection between analysis, trigonometry and geometry. The trigonometric and hyperbolic functions are introduced in parallel with analogous power series so that students understand the role of functional identities. Such functional identities are later used to simplify integrals and to parametrise geometrical curves.

• Further Calculus

  This course extends ideas of MATH101 from functions of a single real variable to functions of two real variables. The notions of differentiation and integration are extended from functions defined on a line to functions defined on the plane. Partial derivatives help us to understand surfaces, while repeated integrals enable us to calculate volumes.

  In mathematical models, it is common to use functions of several variables. For example, the speed of an airliner can depend upon the air pressure and temperature, and the direction of the wind. To study functions of several variables, we introduce rates of change with respect to several quantities. We learn how to find maxima and minima. Applications include the method of least squares. Finally, we investigate various methods for solving differential equations of one variable.

• Linear Algebra

  Introducing the theory of matrices together with some basic applications, students will learn essential techniques such as arithmetic rules, row operations and computation of determinants by expansion about a row or a column.

  The second part of the module covers a notable range of applications of matrices, such as solving systems of simultaneous linear equations, linear transformations, characteristic eigenvectors and eigenvalues.

  The student will learn how to express a linear transformation of the real Euclidean space using a matrix, from which they will be able to determine whether it is singular or not and obtain its characteristic equation and eigenspaces.

• Preparation for Placement

  During this Preparation for Placement module, you will learn about the skills and expertise employers expect you to evidence; how to produce excellent CVs and cover letters; how to make an impact on application forms, what to expect at interviews and assessment centres. You will get to hear from final year students about their placement experience and a chance for you to learn about the placement opportunities on offer meeting graduate employers.

• Principles of Economics A

  Providing a thorough introduction to the discipline of Economics, this module is divided into two parts. The first part covers microeconomic analysis, including the theory of demand, costs and pricing under various forms of industrial organisation, and welfare economics. Many applications of theoretical models are examined. The second part focuses on macroeconomic analysis, including national income analysis, monetary theory, business cycles, inflation, unemployment, and the great macroeconomic debates.

• Probability

  Probability theory is the study of chance phenomena, the concepts of which are fundamental to the study of statistics. This module will introduce students to some simple combinatorics, set theory and the axioms of probability.

  Students will become aware of the different probability models used to characterise the outcomes of experiments that involve a chance or random component. The module covers ideas associated with the axioms of probability, conditional probability, independence, discrete random variables and their distributions, expectation and probability models.

• Statistics

  To enable students to achieve a solid understanding of the broad role that statistical thinking plays in addressing scientific problems, the module begins with a brief overview of statistics in science and society. It then moves on to the selection of appropriate probability models to describe systematic and random variations of discrete and continuous real data sets. Students will learn to implement statistical techniques and to draw clear and informative conclusions.

  The module will be supported by the statistical software package ‘R’, which forms the basis of weekly lab sessions. Students will develop a strategic understanding of statistics and the use of associated software, which will underpin the skills needed for all subsequent statistical modules of the degree.

• Tools and Techniques for Business Analytics

  Business Analytics utilises skills from a number of disciplines. Management Science (also known as Operational Research) is used in all major organisations in industry, commerce, finance and government. Its application might involve well-defined problems, like reducing the cost of a complex goods distribution network, or more nebulous problems, such as improving the care of patients in hospital. Implementation can also involve specialised software or bespoke programmes.

  The techniques of Management Science, based on mathematics, statistics, analytics and computing, can be extremely powerful in helping to solve these organisational problems and are widely used in practice. This module explains the business situations in which such techniques apply and shows how to use the techniques and interpret the results to make better business decisions. Techniques are introduced through a mix of lectures, computer workshops and tutorials at which tutors can give extra help. The techniques introduced include decision analysis, simulation, queueing analysis, computer algorithms and linear programming. To support development, students are introduced to probability and probability distributions and gain familiarity with useful computer tools such as Excel and Python programming.

  In this module, students work on two challenging case studies based on real problems. These provide the opportunity to apply the concepts and techniques of problem solving, making recommendations and reporting results. There is a stress on practical examples of using the techniques. The module lays for foundation for learning more advance techniques later in their degrees and emphasises not only how to apply techniques, but also when (and when not) to apply them.

Year 2

Core

• Business Modelling and Simulation

  This module covers the skills needed to improve business process by modelling and simulation.

  Computer simulation methods are among the most commonly used approaches within operational research and management science. This module teaches you the skills required to apply simulation successfully to help improve the running of a business, and it shows how companies can find good solutions by predicting the effects of changes before implementing them.

  Modern simulation packages are a valuable aid in building a simulation model, and this module uses the Witness simulation package, which is widely used commercially. However, without the proper approach, the results of a simulation project can be incorrect or misleading. This module looks at each task required in a simulation project. It emphasises the practical application of simulation, with a good understanding of how a simulation model works being an essential part of this.

• Linear Algebra II

  Students will be provided with the foundational results and language of linear algebra, which they will be able to build upon in the second half of Year Two, and the more specialised Year Three modules. This module will give students the opportunity to study vector spaces, together with their structure-preserving maps and their relationship to matrices.

  They will consider the effect of changing bases on the matrix representing one of these maps, and will examine how to choose bases so that this matrix is as simple as possible. Part of their study will also involve looking at the concepts of length and angle with regard to vector spaces.

• Macroeconomic Analysis

  Business activities are affected by national economic policies through their influence on inflation, interest rates, exchange rates and aggregate demand. This module examines the main channels of influence from the international business perspective as well as studying macroeconomics, with particular emphasis on the international financial sector and the effects of monetary and fiscal policy. It seeks to explain the implications of macroeconomic policy changes for the international business environment.

  The objective is therefore to develop your understanding of the workings of macroeconomic policy and familiarise you with interpreting macroeconomic and monetary data, and you are encouraged to use your knowledge of macroeconomic theory to gain a better understanding of current macroeconomic events and issues.

• Microeconomic Analysis

  Various topics of interest to prospective managers are covered within this module, including production and demand, competition and strategic behaviour, advertising and distribution, capital budgeting and inventories, the foreign exchange market, the economics of the multinational enterprise and the politics of corporate economics. The module provides knowledge of aspects of microeconomics relevant to general management, and also emphasises techniques and tools of analysis alongside relevant theory.

  The module is designed to as an introduction to aspects of the firm and its environment which are of particular relevance to management. The topics selected aim to bridge the gap between the traditional approach to managerial economics and the more modern study of the organisation.

• Optimisation

  This module describes a variety of optimisation algorithms and how business problems can be modelled using these techniques.

  Optimisation is one of the primary techniques associated with management science/operational research. Linear programming models are used routinely in many industries, including petroleum refining and the food industry. Integer linear programming models are increasingly being used in practice for complex scheduling problems such as those that arise in the airline industry where such models have saved large amounts of money. Skills in formulating and solving applied optimisation problems are valuable for anybody interested in a career in operational research or business modelling and consultancy.

  This module is designed to enable you to apply optimisation techniques to business problems.

  Four main topics are covered:

  • Linear programming

  • Specially-structured linear programs

  • Integer and mixed-integer programming

  • Heuristics for large-scale problems

• Probability II

  Probability provides the theoretical basis for statistics and is of interest in its own right.

  Basic concepts from the first year probability module will be revisited and extended to these to encompass continuous random variables, with students investigating several important continuous probability distributions. Commonly used distributions are introduced and key properties proved, and examples from a variety of applications will be used to illustrate theoretical ideas.

  Students will then focus on transformations of random variables and groups of two or more random variables, leading to two theoretical results about the behaviour of averages of large numbers of random variables which have important practical consequences in statistics.

• Statistics II

  Statistics is the science of understanding patterns of population behaviour from data. In the module, this topic will be approached by specifying a statistical model for the data. Statistical models usually include a number of unknown parameters, which need to be estimated.

  The focus will be on likelihood-based parameter estimation to demonstrate how statistical models can be used to draw conclusions from observations and experimental data, and linear regression techniques within the statistical modelling framework will also be considered.

  Students will come to recognise the role, and limitations, of the linear model for understanding, exploring and making inferences concerning the relationships between variables and making predictions.

• Work Based Learning

  This module, is scheduled for one week in the Lent Term of Year 2 and is the first in a series of compulsory modules designed for students undertaking a placement in Year 3.

  This first module takes the form of a number of lectures, workshops and seminars and combines academic work with work-based learning and careers knowledge of placement opportunities in preparation for the placement year.

Optional

• Applied Economics

  This module helps you to explore the connections between economic theory and econometric and statistical methods as applied to issues of global significance.

  The areas it covers include:

  • the economics of food security

  • the economics of crime, including cybercrime and the effects of deterrents and policing on crime

  • the transatlantic financial crisis: its causes, consequences and the future of macroeconomics poverty and inequality

• Computational Mathematics

  Students will gain a solid understanding of computation and computer programming within the context of maths and statistics. This module expands on five key areas:

  • Programming and R
  • Numerical solutions of equations
  • Numerical differentiation and integration
  • Monte Carlo methods
  • Numerical solutions to ODEs

  Under these headings, students will study a range of complex mathematical concepts, such as: data structures, fixed-point iteration, higher dimensions, first and second derivatives, non-parametric bootstraps, and modified Euler methods.

  Throughout the module, students will gain an understanding of general programming and algorithms. They will develop a good level of IT skills and familiarity with computer tools that support mathematical computation.

  Over the course of this module, students will have the opportunity to put their knowledge and skills into practice. Workshops, based in dedicated computing labs, allow them to gain relatable, practical experience of computational mathematics.

• Economic Policy

  This module focuses on the role of governments within the economy, looking at the extent to which they can intervene in markets and in other areas such as climate change. It builds your skills in evaluating the effectiveness of economic policies, and provides insights into the difficulties of decision-making in collective-choice environments.

• Game Theory

  Over the course of this module, you will enhance your knowledge and understanding of how to specify economic problems in the confines of a game-theoretic model and to solve those problems using appropriate mathematical techniques. The module aims to build your capacity for logical and structured problem analysis.

• Introduction to Operations Management

  Operations management is the core managerial discipline in all kinds of operation – from private-sector manufacturing through to public-sector services. It is about the human capacity to organise all the operations that underpin the modern world: transportation, the generation of energy, retailing, the production of goods, the provision of medical and educational services, and so on.

  The module will introduce students to key concepts and themes of Operations Management such as operations strategy and performance objectives, operations design (e.g. layout, facility location and capacity), inventory planning and control, project management, quality management and supply chain management. These topics will be approached using a combination of qualitative and simple quantitative methods.

  By the end of the course students should be able to:

  • identify different kinds of operations and predict their characteristics
  • apply basic planning and analysis techniques to particular cases
  • understand operations problems and identify improvement strategies
• IT in Organisations: Introduction to ERPs

  Enterprise resource planning systems (ERPs) and integration solutions are essential to every modern enterprise, and this module gives you hands-on experience of SAP, a widely used enterprise technology. The module develops your understanding of how information technologies can help companies to achieve their strategic objectives, and introduces you to techniques and tools that can be used to evaluate the performance of business processes, diagnosing where problems lie and how processes can be improved.

  After introductory sessions which look at the pervasive use of IT by business and at quantitative and qualitative business process analysis, you then work in small teams to compete in running a virtual dairy company, using SAP GUI as your ERP technology.

• Managing Business Information Systems

  This module provides an introduction to the use and impact of information, communication and integrated technology systems on business and organisations. It focusses not on technical specifications, but rather on managerial and business implications of using these systems.

  The following issues will be addressed:

  • Data, Information and Decision-making
  • Business Uses and Benefits of IS
  • IT Selection
  • Obtaining Information Systems
  • Strategy and Information Systems

  The course provides the business foundation for other more specialised or technical topics in Information Systems.

• Spreadsheet Modelling for Management

  Many organisational recruiters have identified a number of skills and knowledge they want to see from a prospective employee. Top in the priorities are spreadsheet modelling, problem structuring, statistics, and project management.

  Students will be introduced to Microsoft Excel 2016 and the basics of dynamic model building, including skills such as data handling, filtering and analysis, using functions, charting, plus advanced techniques such as optimisation, simulation, and the use of Visual Basic for Applications (VBA) to automate models and construct decision support models.

  The course will make extensive use of case-studies and workshop-orientated learning tasks.

Year 3

Core

• Work Based Learning

  This module aims to bridge the gap between the workplace and study and to provide a closer link between activities undertaken on the placement and the academic programme. While on placement students submit a negotiated learning agreement followed by monthly reflective learning logs.

Year 4

Core

• Likelihood Inference

  Statistical inference is the theory of the extraction of information about the unknown parameters of an underlying probability distribution from observed data. Consequently, statistical inference underpins all practical statistical applications.

  This module reinforces the likelihood approach taken in second year Statistics for single parameter statistical models, and extends this to problems where the probability for the data depends on more than one unknown parameter.

  Students will also consider the issue of model choice: in situations where there are multiple models under consideration for the same data, how do we make a justified choice of which model is the 'best'?

  The approach taken in this course is just one approach to statistical inference: a contrasting approach is covered in the Bayesian Inference module.

• Work Based Learning

  On return from placement for the final year of the degree, students engage in group presentations. They present their work-based learning experience in small groups and critically reflect on, and draw out, relationships between theory and practice. Students also complete a portfolio of professional practice, to show the links between theory and practice, and an extended essay which takes the form of a critical reflection on work-based learning experiences.

Optional

• Advanced Spreadsheet Modelling

  Many organisational recruiters have identified particular skills and knowledge they want to see from a prospective employee. Top in the priorities are spreadsheet modelling, problem structuring, statistics, and project management. This highly practical module equips you with an advanced set of spreadsheet modelling skills, including advanced functions and programming using Visual Basic for Applications (VBA) that can be used to produce a wide range of effective decision-support models.

  You will learn general concepts about spreadsheet modelling using VBA and a wide range of modelling skills which are highly relevant to management. These include structured programming, program documentation, program verification, user interface design, and general investigative modelling – including applications involving optimisation, forecasting and simulation.

• Bayesian Inference

  Bayesian statistics provides a mechanism for making decisions in the presence of uncertainty. Using Bayes’ theorem, knowledge or rational beliefs are updated as fresh observations are collected. The purpose of the data collection exercise is expressed through a utility function, which is specific to the client or user. It defines what is to be gained or lost through taking particular actions in the current environment. Actions are continually made or not made depending on the expectation of this utility function at any point in time.

  Bayesians admit probability as the sole measure of uncertainty. Thus Bayesian reasoning is based on a firm axiomatic system. In addition, since most people have an intuitive notion about probability, Bayesian analysis is readily communicated.

• Business Forecasting

  This module introduces you to various current techniques for forecasting future customer demand, including a range of predictive models that develop your knowledge of the best ways of forecasting in problem situations.

  The aim is to ensure that you have the skills needed to develop a validated quantitative set of forecasts using both extrapolative and causal forecasting methods, and that you can apply a simple forecasting method to support demand and revenue management.

  You will also learn to identify and exploit opportunities for revenue optimisation in different business contexts. You review the main methodologies used in each of these areas, discuss legal issues associated with different pricing strategies, and survey current practices in different industries. Most of the topics covered are either directly or indirectly related to pricing issues faced by firms operating in environments where they enjoy some degree of market power.

• Data Mining for Direct Marketing and Finance

  At the heart of many real-world industrial and scientific problems are increasingly large data sets that need to be analysed efficiently in order to gain novel and useful insights. The field of as data mining (also known as intelligent data analysis) brings together real large-scale datasets and algorithms from statistics, machine learning and computational intelligence that can work efficiently with real-world datasets.

  he course provides an introduction to the fundamental methods and approaches from the interrelated areas of data mining, statistical/ machine learning, and intelligent data analysis. The course covers the entire data analysis process, starting from the formulation of a project objective, developing an understanding of the available data and other resources, up to the point of statistical modelling and performance assessment. The focus of the course is classification. The course content covers:

  -Exploratory data analysis including visualisation and simple feature selection methods

  -Classification methods like: Logistic Regression, Decision trees (Random forests), k-Nearest Neighbours, and Naive Bayes

  -Performance assessment and model selection

  The course uses the R programming language and more specifically the RStudio integrated programming environment.

• Developing Business Information Systems

  In this module we look at how to study business operations, analyse the situation and develop appropriate information systems designs. The same techniques can be of value whether you develop them further and become an information systems professional or use them in general management or consultancy. There is an emphasis on practical application and extensive use of class exercises.

  The techniques taught in this module are widely employed by analysts in the fields of information systems and general business consultancy, and the ability to analyse information requirements and design efficient and effective information systems to meet those requirements is increasingly recognised and valued by employers as an important management skill.

• Development Economics

  This module develops your understanding of advanced material in the field of economic growth as well as the problems of economic development. There is particular reference to the application of theoretical material to the development experience and policy-making in developing and emerging economies.

• E-Business Management and Technology

  Digital or 'e' business is today’s leading form of doing business. Not only the Internet giants like Google and Facebook are e-businesses, but also any 'going concern' needs to understand how to ‘enhance the digital’ if it is to survive and thrive in today’s fast-moving world. To this end, the module presents a variety of frameworks that help the student formulate a comprehensive understanding of e-business in theory and practice. By creating their own Internet venture, students are introduced to the process of ideation and testing their business model assumptions, which are valuable tools in an area that is evolving quickly and faces a lot of uncertainties. The module features guest lectures from speakers from industry and a number of case studies.

• Generalised Linear Models

  The concept of generalised linear models (GLMs), which have a range of applications in the biomedical, natural and social sciences, and can be used to relate a response variable to one or more explanatory variables, will be explored. The response variable may be classified as quantitative (continuous or discrete, i.e. countable) or categorical (two categories, i.e. binary, or more than categories, i.e. ordinal or nominal).

  Students will come to understand the effect of censoring in the statistical analyses and will use appropriate statistical techniques for lifetime data. They will also become familiar with the programme R, which they will have the opportunity to use in weekly workshops.

• Health Economics

  This applied module is designed as an introduction to the economics of health and health care, and helps to develop your awareness of the main policy issues in this field. It provides a comprehensive set of economic tools for critically appraising fundamental issues in the economics of health while offering a broad overview of the UK National Health Service and other health care systems around the world. The emphasis is on the use and interpretation of microeconomic models and the latest empirical evidence.

• Industrial Organisation

  This module focuses on firm behaviour and competition, using theoretical (especially game theoretic) and empirical models. It also explores the relationship between industry structure and firm conduct, together with aspects of firm behaviour such as advertising, R&D and mergers.

• Innovative Developments in Operations Management

  There have been a number of innovative developments in Operations Management that have sought to organise resources in a significantly new manner in order to make a big step change in performance. This module discusses these key innovative developments in detail, including those that have led to extensive modernisation both in the manufacturing and service sectors.

  There will be an emphasis on the importance of successful innovation in the current competitive environment, and the key role of Operations Management in sustaining a competitive advantage and bringing about service improvements.

• International Business

  This module develops your understanding of advanced material in the field of international business. There is particular emphasis on analysing the strategic economic and financial behaviour of multinational firms in the global economy. The module also considers the role and effects of government intervention on firms and multinational firms and how they adapt.

• International Trade

  This module develops your understanding of concepts and theories of international trade and factor flows, with particular reference to the way in which such material can inform policy-making.

  You will gain knowledge and understanding of international trade theory, and learn to apply this theory to the analysis of present-day policy issues in international economics.

• Labour Economics

  Focusing on the microeconomics of labour and personnel, this module covers topics such as the economics of migration, wage determination, job search and labour market discrimination.

  There is a particular emphasis on principal agent problems in human resources and the design of incentives within firms.

  Economics theory is used to analyse the operation of labour markers and assess the empirical evidence. Areas covered include:

  • the firm's demand for labour
  • labour supply at an individual and aggregate level
  • causes of wage rigidity
  • the economic impact of trade unions
  • inflation and unemployment
• Machine Learning

  Using the classical problem of data classification as a running example, this module covers mathematical representation and visualisation of multivariate data; dimensionality reduction; linear discriminant analysis; and Support Vector Machines. While studying these theoretical aspects, students will also gain experience of applying them using R.

  An appreciation for multivariate statistical analysis will be developed during the module, as will an ability to represent and visualise high-dimensional data. Students will also gain the ability to evaluate larger statistical models, apply statistical computer packages to analyse large data sets, and extract and evaluate meaning from data.

• Mathematics for Stochastic Finance

  This module formally introduces students to the discipline of financial mathematics, providing them with an understanding of some of the maths that is used in the financial and business sectors.

  Students will begin to encounter financial terminology and will study both European and American option pricing. The module will cover these in relation to discrete and continuous financial models, which include binomial, finite market and Black-Scholes models.

  Students will also explore mathematical topics, some of which may be familiar, specifically in relation to finance. These include:

  • Conditional expectation
  • Filtrations
  • Martingales
  • Stopping times
  • Brownian motion
  • Black-Scholes formula

  Throughout the module, students will learn key financial maths skills, such as constructing binomial tree models; determining associated risk-neutral probability; performing calculations with the Black-Scholes formula; and proving various steps in the derivation of the Black-Scholes formula. They will also be able to describe basic concepts of investment strategy analysis, and perform price calculations for stocks with and without dividend payments.

  In addition, to these subject specific skills and knowledge, students will gain an appreciation for how mathematics can be used to model the real-world; improve their written and oral communication skills; and develop their critical thinking.

• Medical Statistics: study design and data analysis

  The aim is to introduce students to the study designs and statistical methods commonly used in health investigations, such as measuring disease, causality and confounding.

  Students will develop a firm understanding of the key analytical methods and procedures used in studies of disease aetiology, appreciate the effect of censoring in the statistical analyses, and use appropriate statistical techniques for time to event data.

  They will look at both observational and experimental designs and consider various health outcomes, studying a number of published articles to gain an understanding of the problems they are investigating as well as the mathematical and statistical concepts underpinning inference.

• Monetary Macroeconomics

  This module examines the essential characteristics of a money economy, and the topics covered include:

  • Non-neutral money

  • Interest rate determination

  • Monetary and labour market disequilibria

  • The national debt and monetary disequilibrium (fiscal monetarism)

  • Monetary and international payments disequilibria

  • Rational expectations (RE) solutions and applications to stabilisation policy

  • Market efficiency and the application of RE to bubbles and to exchange rates

  • The central bank and inflation bias

• Project Management: Negotiation and Decision Support

  Central to this module is the Crossbay Contracting Game, a management game designed by the module convenor and his colleagues at HCS Ltd.

  Three (health service) organisations are involved in a contract negotiation, and you will be part of the management team of one of these organisations. The contract concerns funding requirements for core activities over the coming financial year.

  The main aim is to reach an agreement that is satisfactory to all three parties – but you must of course ensure that your own organisation is likely to come out of it well. Much of your time will be spent analysing the emerging situation and negotiating with the other parties.

  Alongside this 'management' task there is also a modelling task. Teams are provided with a decision support system they can use to analyse the emerging situation and help them decide which strategies are cost-effective for their organisation.

• Public Economics

  This module is concerned with understanding the role of government in the economy. Among the topics covered are the characteristics of public goods, basic characteristics of a tax system under both classical and political economy approaches, and the effects of globalisation and its effects on modern tax systems. The module also explores how economic models can be used to understand current affairs.

• Sports Economics

  This module looks at how theoretical and empirical methods can be applied to the growing field of sports economics.

  It helps you to understand the particular characteristics of labour and product markets in professional sports, and what implications these have for economic analysis. You will also learn more about how theoretical and empirical work in the economics of sport can be used to inform policy issues, including competitive structures in sports leagues, free agency and player mobility, and the financing of professional sport. You will also gain insights into how betting markets function and why people gamble on sports.

• Stochastic Processes

  Important examples of stochastic processes, and how these processes can be analysed, will be the focus of this module.

  As an introduction to stochastic processes, students will look at the random walk process. Historically this is an important process, and was initially motivated as a model for how the wealth of a gambler varies over time (initial analyses focused on whether there are betting strategies for a gambler that would ensure they won).

  The focus will then be on the most important class of stochastic processes, Markov processes (of which the random walk is a simple example). Students will discover how to analyse Markov processes, and how they are used to model queues and populations.

• Structuring Complex Problems

  Issues and problems in the complex world of management do not necessarily arise in a well-structured form. People often do not know what they want or what is possible. They may also disagree about what they are trying to achieve and the means for arriving at their goals. Much thinking needs to be done in order to define an appropriate framework within which a useful analysis or project can be carried out.

  Various approaches have been developed in recent years to assist in this task, often referred to as problem-structuring methods (PSMs). These very practically oriented methodologies typically involve the management team to help facilitate the structuring of complex situations. They place emphasis on dialogue to think through strategic problems, identify the salient issues, formulate goals and negotiate action plans. This module introduces you to several PSMs and some of the process skills needed to use them.

• Time series analysis

  Modern statistics is characterised by computer-intensive methods for data analysis and development of new theory for their justification. In this module students will become familiar with topics from classical statistics as well as some from emerging areas.

  Time series data will be explored through a wide variety of sequences of observations arising in environmental, economic, engineering and scientific contexts. Time series and volatility modelling will also be studied, and the techniques for the analysis of such data will be discussed, with emphasis on financial application.

  Another area the module will focus on is some of the techniques developed for the analysis of multivariates, such as principal components analysis and cluster analysis.

  Lastly,students will spend time looking at Change-Point Methods, which include traditional as well as some recently developed techniques for the detection of change in trend and variance.