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 Mathematics, Operational Research, Statistics and Economics (MORSE) BSc Hons (GLN0)
Mathematics, Operational Research, Statistics and Economics (MORSE) BSc Hons  2018 Entry
UCAS Code
GLN0
Entry Year
2018
A Level Requirements
AAA
see all requirements
see all requirements
Duration
Full time 3 Year(s)
Course Overview
The MORSE scheme at Lancaster is specifically designed for numerate students wishing to pursue careers in industry, commerce, finance and the public sector. It provides knowledge and key skills in areas that are in great demand and emphasises the application of those ideas in the real world.
The programme equips you with competencies in a variety of quantitative and analytical subjects. Creating strong foundations in mathematics, operations research, statistics and economics in the first year of study, the programme then allows you to tailor your personal programme, whether this is by developing your knowledge in all areas or specialising in those topics that you see as most relevant to your future career. These might be in pure mathematics, statistics, business analytics, economics or management topics. Taught by our worldclass Departments of Mathematics and Statistics, Economics, and Management Science the programme offers a wide range of choice for students, all of which focus on applying mathematical knowledge and theory in a practical context.
Entry Requirements
Grade Requirements
A Level AAA
Subject Requirement A level Mathematics grade A
GCSE Mathematics grade B, English Language grade C
IELTS 6.5 overall with at least 5.5 in each component. For other English language qualifications we accept, please see our English language requirements webpages.
Other Qualifications
International Baccalaureate 36 points overall with 16 points from the best 3 Higher Level subjects including 6 in Mathematics HL
BTEC Considered alongside A level Mathematics grade A
Access to HE Diploma May occasionally be accepted
We welcome applications from students with a range of alternative UK and international qualifications, including combinations of qualification. Further guidance on admission to the University, including other qualifications that we accept, frequently asked questions and information on applying, can be found on our general admissions webpages.
Contact Admissions Team + 44 (0) 1524 592028 or via ugadmissions@lancaster.ac.uk
Course Structure
Many of Lancaster's degree programmes are flexible, offering students the opportunity to cover a wide selection of subject areas to complement their main specialism. You will be able to study a range of modules, some examples of which are listed below.
Year 1

Calculus
This module provides the student with an understanding of functions, limits, and series, and knowledge of the basic techniques of differentiation and integration. We introduce examples of functions and their graphs, and techniques for building new functions from old. We then consider the notion of a limit and introduce the main tools of calculus and Taylor Series. Students will also learn how to add, multiply and divide polynomials, and be introduced to 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 module extends the theory of calculus from functions of a single real variable to functions of two real variables. Students will learn more about the notions of differentiation and integration and how they extend from functions defined on a line to functions defined on the plane. We see how partial derivatives help us to understand surfaces, while repeated integrals enable us to calculate volumes. Students will also investigate complex polynomials and use De Moivre’s theorem to calculate complex roots.
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, temperature and wind direction. 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.

Introduction to Management Science / Operational Research
Management science is used in all major organisations in industry, commerce, finance and government. Its application might involve welldefined problems, such as reducing the cost of a complex goods distribution network, or more nebulous problems, such as improving patient care in hospital. Techniques based on mathematics and statistics can be extremely powerful in helping to solve these organisational problems.
Five such techniques will be introduced:
 forecasting
 linear programming
 decision analysis
 simulation
 stock control
The module emphasises not only how to apply techniques, but also when (and when not) to apply them. There is a stress on practical examples of using the techniques.
You will work on two challenging case studies based on real problems. These provide the opportunity to apply concepts and techniques of problem solving, making recommendations and reporting results. To take this module you must also be taking one of MSCI 101, 100 or MNGT130.

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 equation and eigenvectors and eigenvalues.

Mathematics (Part I subject)
Information for this module is currently unavailable.

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 and 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, and this underpins the skills needed for all subsequent statistical modules of the degree.

Statistics and Computing for Management
This module is designed to give you an introduction to probability and statistics and to make you familiar with some useful computer tools.
The statistical topics covered are sampling, introductory data analysis and presentation, index numbers, probability, the use of some important probability distributions, confidence intervals and hypothesis tests for means and proportions, regression analysis with two variables. The computing side of the module introduces the use of word processing, spreadsheet software for statistical calculations, PowerPoint for presentations and management reports.
Available to students taking degrees in the departments of Accounting and Finance, Economics, Management Science and Mathematics, and to incoming exchange students with collegelevel Mathematics.
Core
Year 2

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.

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, fixedpoint iteration, higher dimensions, first and second derivatives, nonparametric 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.

Intermediate Microeconomics II
This module builds on learning gained in Intermediate Microeconomics 1 (ECON220), developing on the theories and concepts covered as well as focusing on a range of new topics.
Topics include:

analysis of monopoly behaviour and regulation

price and quantity setting in duopoly markets

introduction to game theory and strategic behaviour by firms

auctions (including a study of eBay)

general equilibrium and welfare economics
The module is normally taken in conjunction with ECON220.


Linear Algebra II
This module will give you the opportunity to study vector spaces, together with their structurepreserving maps and their relationship to matrices.
You’ll 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 your study will also involve looking at the concepts of length and angle with regard to vector spaces.

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

Speciallystructured linear programs

Integer and mixedinteger programming

Heuristics for largescale problems


Probability II
Probability provides the theoretical basis for statistics and is of interest in its own right.
You’ll revisit basic concepts from the first year probability module, and extend these to encompass continuous random variables, investigating several important continuous probability distributions.
You’ll 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 this module we approach this problem by specifying a statistical model for the data. Statistical models usually include a number of unknown parameters, which need to be estimated.
You’ll focus on likelihoodbased parameter estimation to demonstrate how statistical models can be used to draw conclusions from observations and experimental data, and also considering linear regression techniques within the statistical modelling framework.
Core

Intermediate Macroeconomics I
This module is designed to extend the knowledge of macroeconomics principles you acquired in Year 1.
Topics include:

classical and Keynesian views

the role of money

real balance and wealth effects

government budgetary constraints

monetary policy in the UK

models of exchange rate determination
Although the main focus of the module is on macroeconomic theory, this is taught within the context of current events in the international macroeconomic environment. You are encouraged to use your knowledge of macroeconomic theory to gain a better understanding of current macroeconomic events and issues.


Intermediate Macroeconomics I
This module is designed to extend the knowledge of macroeconomics principles you acquired in Year 1.
Topics include:

classical and Keynesian views

the role of money

real balance and wealth effects

government budgetary constraints

monetary policy in the UK

models of exchange rate determination
Although the main focus of the module is on macroeconomic theory, this is taught within the context of current events in the international macroeconomic environment. You are encouraged to use your knowledge of macroeconomic theory to gain a better understanding of current macroeconomic events and issues.

Optional
Year 3

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.
You’ll 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.
Core

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.

Financial Mathematics
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 BlackScholes 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
 BlackScholes formula
Throughout the module, students will learn key financial maths skills, such as constructing binomial tree models; determining associated riskneutral probability; performing calculations with the BlackScholes formula; and proving various steps in the derivation of the BlackScholes 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 realworld; improve their written and oral communication skills; and develop their critical thinking.

Medical Statistics: study design and data analysis
This module aims to introduce students to the study designs and statistical methods commonly used in health investigations, such as measuring disease, study design, causality and confounding.
You’ll 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 you’re investigating as well as the mathematical and statistical concepts underpinning inference.

Multivariate Statistics in 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 highdimensional 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.

Statistical Models
This module explores the concept of generalized 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. 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). You’ll also become familiar with the programme R, which you’ll have the opportunity to use in weekly workshops.

Stochastic Processes
This module covers important examples of stochastic processes, and how these processes can be analysed.
As an introduction to stochastic processes you’ll 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).
You’ll then focus on the most important class of stochastic processes, Markov processes (of which the random walk is a simple example). You’ll discover how to analyse Markov processes, and how they are used to model queues and populations.

Time series analysis
Modern statistics is characterised by computerintensive methods for data analysis and development of new theory for their justification. In this module you’ll become familiar with topics from classical statistics as well as some from emerging areas.
You’ll explore time series data through a wide variety of sequences of observations arising in environmental, economic, engineering and scientific contexts. You’ll also study time series and volatility modelling, where we’ll discuss the techniques for the analysis of such data with emphasis on financial application.
Another area you’ll focus on is some of the techniques developed for the analysis of multivariates, such as principal components analysis and cluster analysis. Lastly you’ll spend time looking at ChangePoint Methods, which include traditional as well as some recently developed techniques for the detection of change in trend and variance.
Optional
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. 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 visit our Teaching and Learning section.
Information contained on the website with respect to modules is correct at the time of publication, but changes may be necessary, for example as a result of student feedback, Professional Statutory and Regulatory Bodies' (PSRB) requirements, staff changes, and new research.
Careers
Careers
Our graduates enter a wide array of jobs and careers, from mainstream human resource management in both public and private corporations to management consultancy and roles in the media and marketing. Others set up businesses on their own, both at home and abroad.
The degree also opens up opportunities for further study, with recent graduates undertaking studies towards professional recruitment practice and Masters in Human Resource and Knowledge Management.
Lancaster University is dedicated to ensuring you not only gain a highly reputable degree, you also graduate with the relevant life and work based skills. We are unique in that every student is eligible to participate in The Lancaster Award which offers you the opportunity to complete key activities such as work experience, employability awareness, career development, campus community and social development. Visit our Employability section for full details.
Lancaster Management School has an award winning careers team to provide a dedicated careers and placement service offering a range of innovative services for management school students. Our high reputation means we attract a wide range of leading global employers to campus offering you the opportunity to interact with graduate recruiters from day 1 of your degree.
Fees and Funding
Fees
We set our fees on an annual basis and the 2018/19 entry fees have not yet been set.
Channel Islands and the Isle of Man
Some science and medicine courses have higher fees for students from the Channel Islands and the Isle of Man. You can find more details here: Island Students.
Funding
Lancaster University's priority is to support every student to make the most of their life and education and we have committed £3.7m in scholarships and bursaries. Our financial support depends on your circumstances and how well you do in your A levels (or equivalent academic qualifications) before starting study with us.
Scholarships recognising academic talent:
 An Academic Scholarship of £2,000 for the first year of study for fulltime UK, Channel Islands and Isle of Man students who achieve A*,A*,A in their A level examinations (or equivalent academic qualifications) and who place Lancaster as their firm choice. This is awarded regardless of household income.
 An Access Scholarship of £1,000 for each year of study for all UK students with household incomes of less than £42,600 who achieve A level grades of A*,A, A in their A level examinations (or the equivalent academic qualifications). In addition, students from household incomes of less than £42,600 who achieve higher entry grades of A*, A*, A (or equivalent academic qualifications), who place Lancaster as their firm choice will also be awarded our £2,000 Academic Scholarship in their first year of study.
Continuation of the Access Scholarship is subject to satisfactory academic progression.
Students may be eligible for both the Academic and Access Scholarship if they meet the requirements for both.
 An Excellence Scholarship which forms part of the Unconditional Offer Scheme for full time UK, Channel Islands and Isle of Man applicants with outstanding academic profiles within a number of academic departments.
Bursaries for life, living and learning:
 A Lancaster bursary of £1,000 for each year of study for all students from the UK with a household income of less than £42,600.
Students from the UK eligible for a bursary package will also be awarded our Academic Scholarship and/or Access Scholarship if they meet the criteria detailed above.
Any financial support that you receive from Lancaster University will be in addition to government support that might be available to you (eg fee loans) and will not affect your entitlement to these.
For full details of the University's financial support packages including eligibility criteria, please visit our fees and funding page
Please note that this information relates to the funding arrangements for 2017, which may change for 2018.
Students also need to consider further costs which may include books, stationery, printing, photocopying, binding and general subsistence on trips and visits. Following graduation it may be necessary to take out subscriptions to professional bodies and to buy business attire for job interviews.

Course Overview
Course Overview
The MORSE scheme at Lancaster is specifically designed for numerate students wishing to pursue careers in industry, commerce, finance and the public sector. It provides knowledge and key skills in areas that are in great demand and emphasises the application of those ideas in the real world.
The programme equips you with competencies in a variety of quantitative and analytical subjects. Creating strong foundations in mathematics, operations research, statistics and economics in the first year of study, the programme then allows you to tailor your personal programme, whether this is by developing your knowledge in all areas or specialising in those topics that you see as most relevant to your future career. These might be in pure mathematics, statistics, business analytics, economics or management topics. Taught by our worldclass Departments of Mathematics and Statistics, Economics, and Management Science the programme offers a wide range of choice for students, all of which focus on applying mathematical knowledge and theory in a practical context.

Entry Requirements
Entry Requirements
Grade Requirements
A Level AAA
Subject Requirement A level Mathematics grade A
GCSE Mathematics grade B, English Language grade C
IELTS 6.5 overall with at least 5.5 in each component. For other English language qualifications we accept, please see our English language requirements webpages.
Other Qualifications
International Baccalaureate 36 points overall with 16 points from the best 3 Higher Level subjects including 6 in Mathematics HL
BTEC Considered alongside A level Mathematics grade A
Access to HE Diploma May occasionally be accepted
We welcome applications from students with a range of alternative UK and international qualifications, including combinations of qualification. Further guidance on admission to the University, including other qualifications that we accept, frequently asked questions and information on applying, can be found on our general admissions webpages.
Contact Admissions Team + 44 (0) 1524 592028 or via ugadmissions@lancaster.ac.uk

Course Structure
Course Structure
Many of Lancaster's degree programmes are flexible, offering students the opportunity to cover a wide selection of subject areas to complement their main specialism. You will be able to study a range of modules, some examples of which are listed below.
Year 1

Calculus
This module provides the student with an understanding of functions, limits, and series, and knowledge of the basic techniques of differentiation and integration. We introduce examples of functions and their graphs, and techniques for building new functions from old. We then consider the notion of a limit and introduce the main tools of calculus and Taylor Series. Students will also learn how to add, multiply and divide polynomials, and be introduced to 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 module extends the theory of calculus from functions of a single real variable to functions of two real variables. Students will learn more about the notions of differentiation and integration and how they extend from functions defined on a line to functions defined on the plane. We see how partial derivatives help us to understand surfaces, while repeated integrals enable us to calculate volumes. Students will also investigate complex polynomials and use De Moivre’s theorem to calculate complex roots.
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, temperature and wind direction. 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.

Introduction to Management Science / Operational Research
Management science is used in all major organisations in industry, commerce, finance and government. Its application might involve welldefined problems, such as reducing the cost of a complex goods distribution network, or more nebulous problems, such as improving patient care in hospital. Techniques based on mathematics and statistics can be extremely powerful in helping to solve these organisational problems.
Five such techniques will be introduced:
 forecasting
 linear programming
 decision analysis
 simulation
 stock control
The module emphasises not only how to apply techniques, but also when (and when not) to apply them. There is a stress on practical examples of using the techniques.
You will work on two challenging case studies based on real problems. These provide the opportunity to apply concepts and techniques of problem solving, making recommendations and reporting results. To take this module you must also be taking one of MSCI 101, 100 or MNGT130.

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 equation and eigenvectors and eigenvalues.

Mathematics (Part I subject)
Information for this module is currently unavailable.

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 and 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, and this underpins the skills needed for all subsequent statistical modules of the degree.

Statistics and Computing for Management
This module is designed to give you an introduction to probability and statistics and to make you familiar with some useful computer tools.
The statistical topics covered are sampling, introductory data analysis and presentation, index numbers, probability, the use of some important probability distributions, confidence intervals and hypothesis tests for means and proportions, regression analysis with two variables. The computing side of the module introduces the use of word processing, spreadsheet software for statistical calculations, PowerPoint for presentations and management reports.
Available to students taking degrees in the departments of Accounting and Finance, Economics, Management Science and Mathematics, and to incoming exchange students with collegelevel Mathematics.
Core
Year 2

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.

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, fixedpoint iteration, higher dimensions, first and second derivatives, nonparametric 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.

Intermediate Microeconomics II
This module builds on learning gained in Intermediate Microeconomics 1 (ECON220), developing on the theories and concepts covered as well as focusing on a range of new topics.
Topics include:

analysis of monopoly behaviour and regulation

price and quantity setting in duopoly markets

introduction to game theory and strategic behaviour by firms

auctions (including a study of eBay)

general equilibrium and welfare economics
The module is normally taken in conjunction with ECON220.


Linear Algebra II
This module will give you the opportunity to study vector spaces, together with their structurepreserving maps and their relationship to matrices.
You’ll 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 your study will also involve looking at the concepts of length and angle with regard to vector spaces.

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

Speciallystructured linear programs

Integer and mixedinteger programming

Heuristics for largescale problems


Probability II
Probability provides the theoretical basis for statistics and is of interest in its own right.
You’ll revisit basic concepts from the first year probability module, and extend these to encompass continuous random variables, investigating several important continuous probability distributions.
You’ll 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 this module we approach this problem by specifying a statistical model for the data. Statistical models usually include a number of unknown parameters, which need to be estimated.
You’ll focus on likelihoodbased parameter estimation to demonstrate how statistical models can be used to draw conclusions from observations and experimental data, and also considering linear regression techniques within the statistical modelling framework.
Core

Intermediate Macroeconomics I
This module is designed to extend the knowledge of macroeconomics principles you acquired in Year 1.
Topics include:

classical and Keynesian views

the role of money

real balance and wealth effects

government budgetary constraints

monetary policy in the UK

models of exchange rate determination
Although the main focus of the module is on macroeconomic theory, this is taught within the context of current events in the international macroeconomic environment. You are encouraged to use your knowledge of macroeconomic theory to gain a better understanding of current macroeconomic events and issues.


Intermediate Macroeconomics I
This module is designed to extend the knowledge of macroeconomics principles you acquired in Year 1.
Topics include:

classical and Keynesian views

the role of money

real balance and wealth effects

government budgetary constraints

monetary policy in the UK

models of exchange rate determination
Although the main focus of the module is on macroeconomic theory, this is taught within the context of current events in the international macroeconomic environment. You are encouraged to use your knowledge of macroeconomic theory to gain a better understanding of current macroeconomic events and issues.

Optional
Year 3

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.
You’ll 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.
Core

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.

Financial Mathematics
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 BlackScholes 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
 BlackScholes formula
Throughout the module, students will learn key financial maths skills, such as constructing binomial tree models; determining associated riskneutral probability; performing calculations with the BlackScholes formula; and proving various steps in the derivation of the BlackScholes 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 realworld; improve their written and oral communication skills; and develop their critical thinking.

Medical Statistics: study design and data analysis
This module aims to introduce students to the study designs and statistical methods commonly used in health investigations, such as measuring disease, study design, causality and confounding.
You’ll 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 you’re investigating as well as the mathematical and statistical concepts underpinning inference.

Multivariate Statistics in 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 highdimensional 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.

Statistical Models
This module explores the concept of generalized 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. 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). You’ll also become familiar with the programme R, which you’ll have the opportunity to use in weekly workshops.

Stochastic Processes
This module covers important examples of stochastic processes, and how these processes can be analysed.
As an introduction to stochastic processes you’ll 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).
You’ll then focus on the most important class of stochastic processes, Markov processes (of which the random walk is a simple example). You’ll discover how to analyse Markov processes, and how they are used to model queues and populations.

Time series analysis
Modern statistics is characterised by computerintensive methods for data analysis and development of new theory for their justification. In this module you’ll become familiar with topics from classical statistics as well as some from emerging areas.
You’ll explore time series data through a wide variety of sequences of observations arising in environmental, economic, engineering and scientific contexts. You’ll also study time series and volatility modelling, where we’ll discuss the techniques for the analysis of such data with emphasis on financial application.
Another area you’ll focus on is some of the techniques developed for the analysis of multivariates, such as principal components analysis and cluster analysis. Lastly you’ll spend time looking at ChangePoint Methods, which include traditional as well as some recently developed techniques for the detection of change in trend and variance.
Optional
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. 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 visit our Teaching and Learning section.
Information contained on the website with respect to modules is correct at the time of publication, but changes may be necessary, for example as a result of student feedback, Professional Statutory and Regulatory Bodies' (PSRB) requirements, staff changes, and new research.

Calculus

Careers
Careers
Our graduates enter a wide array of jobs and careers, from mainstream human resource management in both public and private corporations to management consultancy and roles in the media and marketing. Others set up businesses on their own, both at home and abroad.
The degree also opens up opportunities for further study, with recent graduates undertaking studies towards professional recruitment practice and Masters in Human Resource and Knowledge Management.
Lancaster University is dedicated to ensuring you not only gain a highly reputable degree, you also graduate with the relevant life and work based skills. We are unique in that every student is eligible to participate in The Lancaster Award which offers you the opportunity to complete key activities such as work experience, employability awareness, career development, campus community and social development. Visit our Employability section for full details.
Lancaster Management School has an award winning careers team to provide a dedicated careers and placement service offering a range of innovative services for management school students. Our high reputation means we attract a wide range of leading global employers to campus offering you the opportunity to interact with graduate recruiters from day 1 of your degree.

Fees and Funding
Fees and Funding
Fees
We set our fees on an annual basis and the 2018/19 entry fees have not yet been set.
Channel Islands and the Isle of Man
Some science and medicine courses have higher fees for students from the Channel Islands and the Isle of Man. You can find more details here: Island Students.
Funding
Lancaster University's priority is to support every student to make the most of their life and education and we have committed £3.7m in scholarships and bursaries. Our financial support depends on your circumstances and how well you do in your A levels (or equivalent academic qualifications) before starting study with us.
Scholarships recognising academic talent:
 An Academic Scholarship of £2,000 for the first year of study for fulltime UK, Channel Islands and Isle of Man students who achieve A*,A*,A in their A level examinations (or equivalent academic qualifications) and who place Lancaster as their firm choice. This is awarded regardless of household income.
 An Access Scholarship of £1,000 for each year of study for all UK students with household incomes of less than £42,600 who achieve A level grades of A*,A, A in their A level examinations (or the equivalent academic qualifications). In addition, students from household incomes of less than £42,600 who achieve higher entry grades of A*, A*, A (or equivalent academic qualifications), who place Lancaster as their firm choice will also be awarded our £2,000 Academic Scholarship in their first year of study.
Continuation of the Access Scholarship is subject to satisfactory academic progression.
Students may be eligible for both the Academic and Access Scholarship if they meet the requirements for both.
 An Excellence Scholarship which forms part of the Unconditional Offer Scheme for full time UK, Channel Islands and Isle of Man applicants with outstanding academic profiles within a number of academic departments.
Bursaries for life, living and learning:
 A Lancaster bursary of £1,000 for each year of study for all students from the UK with a household income of less than £42,600.
Students from the UK eligible for a bursary package will also be awarded our Academic Scholarship and/or Access Scholarship if they meet the criteria detailed above.
Any financial support that you receive from Lancaster University will be in addition to government support that might be available to you (eg fee loans) and will not affect your entitlement to these.
For full details of the University's financial support packages including eligibility criteria, please visit our fees and funding page
Please note that this information relates to the funding arrangements for 2017, which may change for 2018.
Students also need to consider further costs which may include books, stationery, printing, photocopying, binding and general subsistence on trips and visits. Following graduation it may be necessary to take out subscriptions to professional bodies and to buy business attire for job interviews.
The Department
29%
Average time in lectures, seminars and similar
32%
Average assessment by coursework