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 Financial Mathematics (Industry) BSc Hons (GN1J)
Financial Mathematics (Industry) BSc Hons  2018 Entry
UCAS Code
GN1J
Entry Year
2018
A Level Requirements
AAA
see all requirements
see all requirements
Duration
Full time 4 Year(s)
Course Overview
Drawing on expertise from the Departments of Mathematics and Statistics, Accounting and Finance, and Economics, this degree presents the core elements of finance and maths that underpin the operation of financial markets. Core finance modules provide a thorough grounding in corporate finance, computing, quantitative methods and economics and will be complemented by your mathematics studies.
You will start your degree with modules including Introduction to Accounting and Finance, Discrete Mathematics and Probability. In second year, you will learn subjects such as Advanced Principles of Finance, Introduction to Economics for Managers and Real Analysis. In your third and, for MSci students, fourth years, modules include Corporate Finance, Stochastic Processes, Derivatives Pricing and Assessing Financial Risk.
You will spend your third year in a paid placement with industry before returning to University to complete your degree.
Additionally, MSci students write a substantial dissertation in their fourth year under the supervision of a member of staff from one of the departments. On completion of this degree, they will have Masters level proficiency in mathematical analysis, probability, statistical inference, financial stochastic processes and optimisation.
Entry Requirements
Grade Requirements
A Level AAA including A level Mathematics or Further Mathematics OR AAB including A level Mathematics and Further Mathematics
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 May be accepted alongside A level Mathematics grade A and Further Mathematics grade A
Access to HE Diploma May occasionally be accepted
STEP Paper or the Test of Mathematics for University Admission Please note it is not a compulsory entry requirement to take these tests, but for applicants who are taking any of the papers alongside Mathematics and/or Further Mathematics we may be able to make a more favourable offer. Full details can be found on the Mathematics and Statistics webpage.
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.

Discrete Mathematics
Students are introduced to the basic ideas and notations involved in describing sets and their functions. The module helps students to formalise the idea of the size of a set and what it means to be finite, countably infinite or uncountably finite. For finite sets, we can say that one is bigger than another if it contains more elements. What about infinite sets? Are some infinite sets bigger than others? We develop the tools to answer these questions and other counting problems, such as those involving recurrence relations, e.g. the Fibonacci numbers.
Rather than counting objects, we might be interested in connections between them, leading to the study of graphs and networks – collections of nodes joined by edges. There are many applications of this theory in designing or understanding properties of systems, such as the infrastructure powering the internet, social networks, the London Underground and the global ecosystem.

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.

Geometry and Calculus
The main focus of this course is vectors in two and threedimensional space. We start off with the definition of vectors and we see some applications to finding equations of lines and planes. We then consider some different ways of describing curves and surfaces via equations or parameters, and we use partial differentiation to determine tangent lines and planes, as well as using integration to calculate the length of a curve.
In the second half of the course, we study functions of several variables. When attempting to calculate an integral over one variable, we often substitute one variable for another more convenient one; here we will see the equivalent technique for a double integral, where we have to substitute two variables simultaneously. We also investigate some methods for finding maxima and minima of a function subject to certain conditions.
Finally, we discuss how to calculate the areas of various surfaces and the volumes of various solids.

Introduction to Accounting and Finance
This course provides a comprehensive introduction to the basic concepts and techniques of Accounting and Finance, which include financial accounting, managerial finance, and financial statement analysis.
An important element of this course is that it provides exposure to the business and financial environment within which the discipline of Accounting and Finance operates, using realworld financial data for actual companies.
The course covers concepts, techniques and interpretive skills that relate to the external financial reporting of companies and their relationship to the stock market, and to the use of accounting information for internal management purposes.

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.

Numbers and Relations
This module introduces the student to logic and mathematical proofs, with emphasis placed on proving general theorems than on performing calculations. This is because a result which can be applied to many different cases is clearly more powerful than a calculation that deals only with a single specific case.
We take a look at the language and structure of mathematical proofs in general, emphasising how logic can be used to express mathematical arguments in a concise and rigorous manner. These ideas are then applied to the study of number theory, establishing several fundamental results such as Bezout’s Theorem on highest common factors and the Fundamental Theorem of Arithmetic on prime factorisations.
The concept of congruence of integers is introduced to students and they study the idea that a highest common factor can be generalised from the integers to polynomials.

Preparation for Placement
Your preparation your placement year starts with this module which is delivered by the LUMS Careers Team and invited employers. This module will support you in creating suitable CVs, covering letters, application forms and completing psychometric tests. At the end of the module you will have the opportunity to attend a formal assessment centre and an interview with some of the top graduate recruitment teams in the UK.

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.
Core
Year 2

Advanced Principles of Finance
This module provides a detailed analysis of three key finance paradigms: decisionmaking under uncertainty, including utility theory; capital asset pricing and market equilibrium; and option pricing and hedging strategies. Emphasis is placed on financial concepts, theories and models such as portfolio theory, the efficient market hypothesis, and theories of capital structure.

Further Topics in Economics for Managers
The module further develops microeconomic issues relating to labour, organisations and markets, together with macroeconomic issues relating to employment and aggregate demand management.
It examines the essential features of a money economy:
 banking
 the national debt, interest rates, inflation, seigniorage
 the balance of international payments
 fixed and flexible currency exchange rates
 monetary policy
 money and business cycles

Introduction to Economics for Managers
Looking at microeconomic issues relating to markets and firms, and macroeconomic issues relating to money, banking and monetary policy, this module helps you to analyse economic issues from a business perspective. It demonstrates why economic concepts and principles are relevant to business issues by applying introductory economic theory to a range of issues that affect economic aspects of the business environment. Particular emphasis is given to interpreting the economic behaviour of individuals and firms, using theory to interpret events and evaluate policies.

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.

Real Analysis
In this module you’ll take a thorough look at the limits of sequences and convergence of series. You’ll learn to extend the notion of a limit to functions, leading to the analysis of differentiation, including proper proofs of techniques learned at Alevel.
You’ll spend time studying the Intermediate Value Theorem and the Mean Value Theorem, and will discover that they have many applications of widely differing kinds. The next topic is new: sequences and series of functions (rather than just numbers), which again has many applications and is central to more advanced analysis.
Next we put the notion of integration under the microscope. Once it’s properly defined (via limits), you’ll learn how to get from this definition to the familiar technique of evaluating integrals by reverse differentiation. You’ll also explore some applications of integration that are quite different from the ones in Alevel, such as estimations of discrete sums of series.
Further possible topics include Stirling's Formula, infinite products and Fourier series.

Social Research Methods
This course provides students with general knowledge and understanding concerning social research and particular methods and methodologies that lay within the positivist, interpretivist and critical paradigms. The course is aimed at students from across the management school disciplines that are undertaking a year long industrial placement and producing a dissertation upon return to study in their final year. There is also a range of supplementary information regarding the support available once on placement and a link to the sister module OWT.250b.

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

Abstract Algebra
This module builds on the binary operations studies in previous modules, such as addition or multiplication of numbers and composition of functions. Here you’ll select a small number of properties which these and other examples have in common, and use them to define a group.
You’ll also consider the elementary properties of groups. It turns out that several surprisingly elegant results can be proved fairly simply! By looking at maps between groups which 'preserve structure' you’ll discover a way of formalizing (and extending) the natural concept of what it means for two groups to be 'the same'.
Ring theory provides a framework for studying sets with two binary operations: addition and multiplication. This gives us a way to abstractly model various number systems, proving results that can be applied in many different situations, such as number theory and geometry. Familiar examples of rings include the integers, the integers modulation, the rational numbers, matrices and polynomials, but you’ll meet several less familiar examples too.

Complex Analysis
Complex Analysis has its origins in differential calculus and the study of polynomial equations.
In this module you’ll consider the differential calculus of functions of a single complex variable and study power series and mappings by complex functions. You’ll use integral calculus of complex functions to find elegant and important results, including the fundamental theorem of algebra, and you’ll also use classical theorems to evaluate real integrals.
The module ends with basic discussion of harmonic functions, which play a significant role in physics.

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.

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.

Principles of Finance
This module covers project evaluation methods as well as risk, return and the cost of capital, including the capital asset pricing model. Corporate financing, including dividend policy and capital structure, options, and working capital management will also be investigated.

Project Skills
Project Skills is a module designed to support and develop a range of key technical and professional skills that will be valuable for all career paths. Covering five major components, this module will guide students through and explore:
 Mathematical programmes
 Scientific writing
 Communication and presentation skills
 Short projects
 Group projects
Students will gain an excellent grasp of LaTeX, learning to prepare mathematical documents; display mathematical symbols and formulae; create environments; and present tables and figures.
Scientific writing, communication and presentations skills will also be developed. Students will work on short and group projects to investigate mathematical or statistical topics, and present these in written reports and verbal presentations.
Optional
Year 4

Career Skills in Accounting and Finance
Information for this module is currently unavailable.

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.

Probability Theory
This module is ideal for students who want to develop an analytical and axiomatic approach to the theory of probabilities.
First you’ll examine the notion of a probability space through simple examples featuring both discrete and continuous sample spaces. You’ll then use random variables and the expectation to develop a probability calculus, which you can apply to achieve laws of large numbers for sums of independent random variables.
You’ll also use the characteristic function to study the distributions of sums of independent variables, which have applications to random walks and to statistical physics.
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.

Bond Markets
Fixed income securities are one of the major asset classes, and recent developments in debt markets (bankruptcies and reorganisation of key global players) call for deeper understanding of this key area of the financial spectrum.
This module develops your intellectual and practical understanding of the organisation and structure of bond markets, introducing you to the main problems and issues relevant in the management of interest rate risk and the principles governing the valuation of fixed income securities and their derivatives.

Corporate Finance
This module examines corporate financing and investment decisions, focusing in particular on settings where companies’ assets and liabilities contain embedded options. Topics covered include valuation of options, investment appraisal, valuation of warrants and convertibles, capital structure, and mergers and restructuring.

International Financial and Risk Management
This module provides knowledge that is important to those concerned with financial management in a multinational setting. Areas covered include the relationships between exchange rates, interest rates and inflation rates, forward, futures and options markets, and corporate exchange rate risk management.

Investments
This module covers the fundamental concepts and techniques of modern investment theory and practice. Topics include security analysis, equity and bond portfolio management, asset allocation, performance evaluation, estimation of risk measures and hedging. There is also an emphasis on some of the practical issues in portfolio management.

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.

Quantitative Finance
This module helps you to understand how econometric models can be used to learn about the future behaviour of the prices of financial assets by using information on the history of asset prices and the prices of derivative securities.
It describes time series models for financial market prices and shows how these models can be applied by banks and investors. It covers random walk tests and forecasting price volatility for financial asset prices.

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
Offering unique training in mathematics and finance, your degree opens up excellent employment opportunities in the finance sector. It also prepares you for a wide variety of careers in business.
Many of our graduates enter training contracts with professional accounting firms, while others take up posts in industry or financial institutions. Our alumni have followed a wide variety of career paths, including banking, general and financial management and consulting.
Another popular option is to continue studying for a postgraduate qualification, and you will find that Lancaster offers excellent graduate opportunities and PhD programmes.
Lancaster University is dedicated to ensuring you not only gain a highly reputable degree, but that you also graduate with 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/career development, campus community and social development. Visit our Employability section for full details.
Fees and Funding
Fees
We set our fees on an annual basis and the 2018/19 entry fees have not yet been set.
As a guide, our fees in 2017 were:
UK/EU  Overseas 

£9,250  £17,410 
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
Drawing on expertise from the Departments of Mathematics and Statistics, Accounting and Finance, and Economics, this degree presents the core elements of finance and maths that underpin the operation of financial markets. Core finance modules provide a thorough grounding in corporate finance, computing, quantitative methods and economics and will be complemented by your mathematics studies.
You will start your degree with modules including Introduction to Accounting and Finance, Discrete Mathematics and Probability. In second year, you will learn subjects such as Advanced Principles of Finance, Introduction to Economics for Managers and Real Analysis. In your third and, for MSci students, fourth years, modules include Corporate Finance, Stochastic Processes, Derivatives Pricing and Assessing Financial Risk.
You will spend your third year in a paid placement with industry before returning to University to complete your degree.
Additionally, MSci students write a substantial dissertation in their fourth year under the supervision of a member of staff from one of the departments. On completion of this degree, they will have Masters level proficiency in mathematical analysis, probability, statistical inference, financial stochastic processes and optimisation.

Entry Requirements
Entry Requirements
Grade Requirements
A Level AAA including A level Mathematics or Further Mathematics OR AAB including A level Mathematics and Further Mathematics
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 May be accepted alongside A level Mathematics grade A and Further Mathematics grade A
Access to HE Diploma May occasionally be accepted
STEP Paper or the Test of Mathematics for University Admission Please note it is not a compulsory entry requirement to take these tests, but for applicants who are taking any of the papers alongside Mathematics and/or Further Mathematics we may be able to make a more favourable offer. Full details can be found on the Mathematics and Statistics webpage.
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.

Discrete Mathematics
Students are introduced to the basic ideas and notations involved in describing sets and their functions. The module helps students to formalise the idea of the size of a set and what it means to be finite, countably infinite or uncountably finite. For finite sets, we can say that one is bigger than another if it contains more elements. What about infinite sets? Are some infinite sets bigger than others? We develop the tools to answer these questions and other counting problems, such as those involving recurrence relations, e.g. the Fibonacci numbers.
Rather than counting objects, we might be interested in connections between them, leading to the study of graphs and networks – collections of nodes joined by edges. There are many applications of this theory in designing or understanding properties of systems, such as the infrastructure powering the internet, social networks, the London Underground and the global ecosystem.

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.

Geometry and Calculus
The main focus of this course is vectors in two and threedimensional space. We start off with the definition of vectors and we see some applications to finding equations of lines and planes. We then consider some different ways of describing curves and surfaces via equations or parameters, and we use partial differentiation to determine tangent lines and planes, as well as using integration to calculate the length of a curve.
In the second half of the course, we study functions of several variables. When attempting to calculate an integral over one variable, we often substitute one variable for another more convenient one; here we will see the equivalent technique for a double integral, where we have to substitute two variables simultaneously. We also investigate some methods for finding maxima and minima of a function subject to certain conditions.
Finally, we discuss how to calculate the areas of various surfaces and the volumes of various solids.

Introduction to Accounting and Finance
This course provides a comprehensive introduction to the basic concepts and techniques of Accounting and Finance, which include financial accounting, managerial finance, and financial statement analysis.
An important element of this course is that it provides exposure to the business and financial environment within which the discipline of Accounting and Finance operates, using realworld financial data for actual companies.
The course covers concepts, techniques and interpretive skills that relate to the external financial reporting of companies and their relationship to the stock market, and to the use of accounting information for internal management purposes.

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.

Numbers and Relations
This module introduces the student to logic and mathematical proofs, with emphasis placed on proving general theorems than on performing calculations. This is because a result which can be applied to many different cases is clearly more powerful than a calculation that deals only with a single specific case.
We take a look at the language and structure of mathematical proofs in general, emphasising how logic can be used to express mathematical arguments in a concise and rigorous manner. These ideas are then applied to the study of number theory, establishing several fundamental results such as Bezout’s Theorem on highest common factors and the Fundamental Theorem of Arithmetic on prime factorisations.
The concept of congruence of integers is introduced to students and they study the idea that a highest common factor can be generalised from the integers to polynomials.

Preparation for Placement
Your preparation your placement year starts with this module which is delivered by the LUMS Careers Team and invited employers. This module will support you in creating suitable CVs, covering letters, application forms and completing psychometric tests. At the end of the module you will have the opportunity to attend a formal assessment centre and an interview with some of the top graduate recruitment teams in the UK.

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.
Core
Year 2

Advanced Principles of Finance
This module provides a detailed analysis of three key finance paradigms: decisionmaking under uncertainty, including utility theory; capital asset pricing and market equilibrium; and option pricing and hedging strategies. Emphasis is placed on financial concepts, theories and models such as portfolio theory, the efficient market hypothesis, and theories of capital structure.

Further Topics in Economics for Managers
The module further develops microeconomic issues relating to labour, organisations and markets, together with macroeconomic issues relating to employment and aggregate demand management.
It examines the essential features of a money economy:
 banking
 the national debt, interest rates, inflation, seigniorage
 the balance of international payments
 fixed and flexible currency exchange rates
 monetary policy
 money and business cycles

Introduction to Economics for Managers
Looking at microeconomic issues relating to markets and firms, and macroeconomic issues relating to money, banking and monetary policy, this module helps you to analyse economic issues from a business perspective. It demonstrates why economic concepts and principles are relevant to business issues by applying introductory economic theory to a range of issues that affect economic aspects of the business environment. Particular emphasis is given to interpreting the economic behaviour of individuals and firms, using theory to interpret events and evaluate policies.

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.

Real Analysis
In this module you’ll take a thorough look at the limits of sequences and convergence of series. You’ll learn to extend the notion of a limit to functions, leading to the analysis of differentiation, including proper proofs of techniques learned at Alevel.
You’ll spend time studying the Intermediate Value Theorem and the Mean Value Theorem, and will discover that they have many applications of widely differing kinds. The next topic is new: sequences and series of functions (rather than just numbers), which again has many applications and is central to more advanced analysis.
Next we put the notion of integration under the microscope. Once it’s properly defined (via limits), you’ll learn how to get from this definition to the familiar technique of evaluating integrals by reverse differentiation. You’ll also explore some applications of integration that are quite different from the ones in Alevel, such as estimations of discrete sums of series.
Further possible topics include Stirling's Formula, infinite products and Fourier series.

Social Research Methods
This course provides students with general knowledge and understanding concerning social research and particular methods and methodologies that lay within the positivist, interpretivist and critical paradigms. The course is aimed at students from across the management school disciplines that are undertaking a year long industrial placement and producing a dissertation upon return to study in their final year. There is also a range of supplementary information regarding the support available once on placement and a link to the sister module OWT.250b.

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

Abstract Algebra
This module builds on the binary operations studies in previous modules, such as addition or multiplication of numbers and composition of functions. Here you’ll select a small number of properties which these and other examples have in common, and use them to define a group.
You’ll also consider the elementary properties of groups. It turns out that several surprisingly elegant results can be proved fairly simply! By looking at maps between groups which 'preserve structure' you’ll discover a way of formalizing (and extending) the natural concept of what it means for two groups to be 'the same'.
Ring theory provides a framework for studying sets with two binary operations: addition and multiplication. This gives us a way to abstractly model various number systems, proving results that can be applied in many different situations, such as number theory and geometry. Familiar examples of rings include the integers, the integers modulation, the rational numbers, matrices and polynomials, but you’ll meet several less familiar examples too.

Complex Analysis
Complex Analysis has its origins in differential calculus and the study of polynomial equations.
In this module you’ll consider the differential calculus of functions of a single complex variable and study power series and mappings by complex functions. You’ll use integral calculus of complex functions to find elegant and important results, including the fundamental theorem of algebra, and you’ll also use classical theorems to evaluate real integrals.
The module ends with basic discussion of harmonic functions, which play a significant role in physics.

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.

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.

Principles of Finance
This module covers project evaluation methods as well as risk, return and the cost of capital, including the capital asset pricing model. Corporate financing, including dividend policy and capital structure, options, and working capital management will also be investigated.

Project Skills
Project Skills is a module designed to support and develop a range of key technical and professional skills that will be valuable for all career paths. Covering five major components, this module will guide students through and explore:
 Mathematical programmes
 Scientific writing
 Communication and presentation skills
 Short projects
 Group projects
Students will gain an excellent grasp of LaTeX, learning to prepare mathematical documents; display mathematical symbols and formulae; create environments; and present tables and figures.
Scientific writing, communication and presentations skills will also be developed. Students will work on short and group projects to investigate mathematical or statistical topics, and present these in written reports and verbal presentations.
Optional
Year 4

Career Skills in Accounting and Finance
Information for this module is currently unavailable.

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.

Probability Theory
This module is ideal for students who want to develop an analytical and axiomatic approach to the theory of probabilities.
First you’ll examine the notion of a probability space through simple examples featuring both discrete and continuous sample spaces. You’ll then use random variables and the expectation to develop a probability calculus, which you can apply to achieve laws of large numbers for sums of independent random variables.
You’ll also use the characteristic function to study the distributions of sums of independent variables, which have applications to random walks and to statistical physics.
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.

Bond Markets
Fixed income securities are one of the major asset classes, and recent developments in debt markets (bankruptcies and reorganisation of key global players) call for deeper understanding of this key area of the financial spectrum.
This module develops your intellectual and practical understanding of the organisation and structure of bond markets, introducing you to the main problems and issues relevant in the management of interest rate risk and the principles governing the valuation of fixed income securities and their derivatives.

Corporate Finance
This module examines corporate financing and investment decisions, focusing in particular on settings where companies’ assets and liabilities contain embedded options. Topics covered include valuation of options, investment appraisal, valuation of warrants and convertibles, capital structure, and mergers and restructuring.

International Financial and Risk Management
This module provides knowledge that is important to those concerned with financial management in a multinational setting. Areas covered include the relationships between exchange rates, interest rates and inflation rates, forward, futures and options markets, and corporate exchange rate risk management.

Investments
This module covers the fundamental concepts and techniques of modern investment theory and practice. Topics include security analysis, equity and bond portfolio management, asset allocation, performance evaluation, estimation of risk measures and hedging. There is also an emphasis on some of the practical issues in portfolio management.

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.

Quantitative Finance
This module helps you to understand how econometric models can be used to learn about the future behaviour of the prices of financial assets by using information on the history of asset prices and the prices of derivative securities.
It describes time series models for financial market prices and shows how these models can be applied by banks and investors. It covers random walk tests and forecasting price volatility for financial asset prices.

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
Offering unique training in mathematics and finance, your degree opens up excellent employment opportunities in the finance sector. It also prepares you for a wide variety of careers in business.
Many of our graduates enter training contracts with professional accounting firms, while others take up posts in industry or financial institutions. Our alumni have followed a wide variety of career paths, including banking, general and financial management and consulting.
Another popular option is to continue studying for a postgraduate qualification, and you will find that Lancaster offers excellent graduate opportunities and PhD programmes.
Lancaster University is dedicated to ensuring you not only gain a highly reputable degree, but that you also graduate with 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/career development, campus community and social development. Visit our Employability section for full details.

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.
As a guide, our fees in 2017 were:
UK/EU Overseas £9,250 £17,410 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
24%
Average time in lectures, seminars and similar
48%
Average assessment by coursework