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 Financial Mathematics (Industry) BSc Hons (GN1J)
Financial Mathematics (Industry) BSc Hons  2019 Entry
UCAS Code
GN1J
Entry Year
2019
A Level Requirements
AAA
see all requirements
see all requirements
Duration
Full time 4 Year(s)
Course Overview
Financial mathematicians are interested in making good decisions in the face of uncertainty. Through our rigorous programme, you will develop the skills and knowledge to become a major decision maker and influencer in your chosen career and gain valuable realworld experience in industry.
Financial maths is about learning to interpret and manipulate data to draw valuable conclusions and make predictions. This is particularly important in business and finance, but the skills gained from this programme are widely applicable and highly sought after. During the course, you will be able to draw on expertise from three specialist departments: Mathematics and Statistics; Accounting and Finance; and Economics. You will also benefit from completing a year of fulltime work experience, providing you with invaluable experience and an insight into the realworld workplace.
During your first year, you will build on your previous knowledge and understanding of mathematical methods and concepts. Modules cover a wide range of topics from calculus, probability and statistics to logic, proofs and theorems. As well as developing your technical knowledge and mathematical skills, you will also enhance your data analysis, problemsolving and quantitative reasoning skills. During this year, you will also receive an introduction to accounting and finance, which will provide you with a comprehensive understanding of the concepts and techniques of the discipline, including financial accounting, managerial finance, and financial statement analysis.
In the second year, you will further develop your knowledge in analysis, probability and statistics. During this year, you will also begin to explore advanced finance and will benefit from modules in economics at managerial level. These will provide you with insight into micro and macroeconomics, and their related issues. You will develop realworld knowledge and experience by applying your analytical skills, interpreting events and evaluating policies. This will be instrumental in developing a career related to banking, finance, international payments and exchange rates, and monetary policy.
The third year will take you away from the academic environment and into the workplace. You will spend this year with one of our partner organisations, putting what you have learnt into practice and gaining experience of a real workplace. This is a fantastic opportunity to see how what you have studied applies to the realworld and gives you the chance to get a taster of a potential career. This experience will be highly beneficial once you begin researching your career and applying for jobs.
Returning to Lancaster in the fourth year to complete your study, you will delve deeper into the theory of probability and will explore the concept of statistical inference. Alongside this, you will build upon the valuable industry and employability skills gained during your placement through a dedicated careersfocused module. This final year will also be highly customisable, allowing you to select from a range of modules to suit your own interests and career aspirations.
MSci Financial Mathematics
In addition to our BSc, we also offer a MSci Financial Mathematics programme that includes an additional year of study and a substantial research project. This programme will provide you with Masterslevel proficiency in mathematical analysis and concepts, as well as specialist financial knowledge.
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
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
Students are provided with an understanding of functions, limits, and series, and knowledge of the basic techniques of differentiation and integration. Examples of functions and their graphs are presented, as are techniques for building new functions from old. Then the notion of a limit is considered along with the main tools of calculus and Taylor Series. Students will also learn how to add, multiply and divide polynomials, and will learn about rational functions and their partial fractions.
The exponential function is defined by means of a power series which is subsequently extended to the complex exponential function of an imaginary variable, so that students understand the connection between analysis, trigonometry and geometry. The trigonometric and hyperbolic functions are introduced in parallel with analogous power series so that students understand the role of functional identities. Such functional identities are later used to simplify integrals and to parametrise geometrical curves.

Discrete Mathematics
An introduction to the basic ideas and notations involved in describing sets and their functions will be given. This 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, it is said that one is bigger than another if it contains more elements. What about infinite sets? Are some infinite sets bigger than others? Students will develop the tools to answer these questions and other counting problems, such as those involving recurrence relations, e.g. the Fibonacci numbers.
The module will also consider the connections between objects, 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. They will see how partial derivatives can help to understand surfaces, while repeated integrals enable them to calculate volumes. The module 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, rates of change are introduced with respect to several quantities. How to find maxima and minima will be explained. Applications include the method of least squares. Finally, various methods for solving differential equations of one variable will be investigated.

Geometry and Calculus
The main focus of this module is vectors in two and threedimensional space. Starting with the definition of vectors, students will discover some applications to finding equations of lines and planes, then they will consider some different ways of describing curves and surfaces via equations or parameters. Partial differentiation will be used to determine tangent lines and planes, and integration will be used to calculate the length of a curve.
In the second half of the course, the functions of several variables will be studied. When attempting to calculate an integral over one variable, one variable is often substituted for another more convenient one; here students will see the equivalent technique for a double integral, where they will have to substitute two variables simultaneously. They will also investigate some methods for finding maxima and minima of a function subject to certain conditions.
Finally, the module will explain 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 eigenvectors and eigenvalues.
The student will learn how to express a linear transformation of the real euclidean space using a matrix, from which they will be able to determine whether it is singular or not and obtain its characteristic equation and eigenspaces.

Numbers and Relations
The student is introduced to logic and mathematical proofs, with emphasis placed more 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.
The language and structure of mathematical proofs will be explained, highlighting how logic can be used to express mathematical arguments in a concise and rigorous manner. These ideas will then be 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. It then moves on to the selection of appropriate probability models to describe systematic and random variations of discrete and continuous real data sets. Students will learn to implement statistical techniques and to draw clear and informative conclusions.
The module will be supported by the statistical software package ‘R’, which forms the basis of weekly lab sessions. Students will develop a strategic understanding of statistics and the use of associated software, which will underpin the skills needed for all subsequent statistical modules of the degree.
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.
Basic concepts from the first year probability module will be revisited and extended to these to encompass continuous random variables, with students investigating several important continuous probability distributions. Commonly used distributions are introduced and key properties proved, and examples from a variety of applications will be used to illustrate theoretical ideas.
Students will then focus on transformations of random variables and groups of two or more random variables, leading to two theoretical results about the behaviour of averages of large numbers of random variables which have important practical consequences in statistics.

Real Analysis
A thorough look will be taken at the limits of sequences and convergence of series during this module. Students will learn to extend the notion of a limit to functions, leading to the analysis of differentiation, including proper proofs of techniques learned at Alevel.
Time will be spent studying the Intermediate Value Theorem and the Mean Value Theorem, and their many applications of widely differing kinds will be explored. 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, the notion of integration will be put under the microscope. Once it is properly defined (via limits) students will learn how to get from this definition to the familiar technique of evaluating integrals by reverse differentiation. They will 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
The course provides students with general knowledge and understanding concerning social research and particular methods and methodologies that lie within the positivist and interpretivist paradigms. It is primarily aimed at students from across the management school that are planning to undertake an industrial placement and/or a dissertation in their final year of study. This module helps to prepare you to undertake your own research with a view to highlighting different research approaches and techniques that are used in the production of knowledge.
The module provides an insight into the various ways research can be undertaken and the implications of different approaches. We will examine the conceptual and practical complexities of undertaking research in practice. Initially you will be introduced to research methods and that are most commonly employed in business and management research. The module will then examine the methodological approaches and paradigms that are linked with these methods and the assumptions that underpin positivistic and interpretivist approaches. The final part of the module explores how this understanding can be used in writing your research proposal and dissertation.

Statistics II
Statistics is the science of understanding patterns of population behaviour from data. In the module, this topic will be approached by specifying a statistical model for the data. Statistical models usually include a number of unknown parameters, which need to be estimated.
The focus will be on likelihoodbased parameter estimation to demonstrate how statistical models can be used to draw conclusions from observations and experimental data, and linear regression techniques within the statistical modelling framework will also be considered.
Students will come to recognise the role, and limitations, of the linear model for understanding, exploring and making inferences concerning the relationships between variables and making predictions.
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,students will select a small number of properties which these and other examples have in common, and use them to define a group.
They will also consider the elementary properties of groups. By looking at maps between groups which 'preserve structure',a way of formalizing (and extending) the natural concept of what it means for two groups to be 'the same' will be discovered.
Ring theory provides a framework for studying sets with two binary operations: addition and multiplication. This gives students a wayto 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; several less familiar examples will also be explored.

Complex Analysis
Complex Analysis has its origins in differential calculus and the study of polynomial equations. In this module, students will consider the differential calculus of functions of a single complex variable and study power series and mappings by complex functions. They will use integral calculus of complex functions to find elegant and important results and will also use classical theorems to evaluate real integrals.
The first part of the module reviews complex numbers, and presents complex series and the complex derivative in a style similar to calculus. The module then introduces integrals along curves and develops complex function theory from Cauchy's Theorem for a triangle, which is proved by way of a bisection argument. These analytic ideas are used to prove the fundamental theorem of algebra, that every nonconstant complex polynomial has a root. Finally, the theory is employed to evaluate some definite 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
Students will be provided with the foundational results and language of linear algebra, which they will be able to build upon in the second half of Year Two, and the more specialised Year Three modules. This module will give students the opportunity to study vector spaces, together with their structurepreserving maps and their relationship to matrices.
They will consider the effect of changing bases on the matrix representing one of these maps, and will examine how to choose bases so that this matrix is as simple as possible. Part of their study will also involve looking at the concepts of length and angle with regard to vector spaces.

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.
Students will also consider the issue of model choice: in situations where there are multiple models under consideration for the same data, how do we make a justified choice of which model is the 'best'?
The approach taken in this course is just one approach to statistical inference: a contrasting approach is covered in the Bayesian Inference module.

Probability Theory
This module is ideal for students who want to develop an analytical and axiomatic approach to the theory of probabilities.
First the notion of a probability space will be examined through simple examples featuring both discrete and continuous sample spaces. Random variables and the expectation will be used to develop a probability calculus, which can be applied to achieve laws of large numbers for sums of independent random variables.
Students will 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.

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.

Financial 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.

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
The aim is to introduce students to the study designs and statistical methods commonly used in health investigations, such as measuring disease, causality and confounding.
Students will develop a firm understanding of the key analytical methods and procedures used in studies of disease aetiology, appreciate the effect of censoring in the statistical analyses, and use appropriate statistical techniques for time to event data.
They will look at both observational and experimental designs and consider various health outcomes, studying a number of published articles to gain an understanding of the problems they are investigating as well as the mathematical and statistical concepts underpinning inference.

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
The concept of generalised linear models (GLMs), which have a range of applications in the biomedical, natural and social sciences, and can be used to relate a response variable to one or more explanatory variables, will be explored. The response variable may be classified as quantitative (continuous or discrete, i.e. countable) or categorical (two categories, i.e. binary, or more than categories, i.e. ordinal or nominal).
Students will come to understand the effect of censoring in the statistical analyses and will use appropriate statistical techniques for lifetime data. They will also become familiar with the programme R, which they will have the opportunity to use in weekly workshops.

Stochastic Processes
Important examples of stochastic processes, and how these processes can be analysed, will be the focus of this module.
As an introduction to stochastic processes, students will look at the random walk process. Historically this is an important process, and was initially motivated as a model for how the wealth of a gambler varies over time (initial analyses focused on whether there are betting strategies for a gambler that would ensure they won).
The focus will then be on the most important class of stochastic processes, Markov processes (of which the random walk is a simple example). Students will discover how to analyse Markov processes, and how they are used to model queues and populations.

Time series analysis
Modern statistics is characterised by computerintensive methods for data analysis and development of new theory for their justification. In this module students will become familiar with topics from classical statistics as well as some from emerging areas.
Time series data will be explored through a wide variety of sequences of observations arising in environmental, economic, engineering and scientific contexts. Time series and volatility modelling will also be studied, and the techniques for the analysis of such data will be discussed, with emphasis on financial application.
Another area the module will focus on is some of the techniques developed for the analysis of multivariates, such as principal components analysis and cluster analysis.
Lastly,students will spend time looking at 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
Financial maths graduates are very versatile, having indepth specialist knowledge and a wealth of skills. Through this degree, you will graduate with a comprehensive skill set, including data analysis and manipulation, logical thinking, problemsolving and quantitative reasoning, as well as adept knowledge of the discipline. As a result, financial mathematicians are sought after in a range of industries. However, graduates of this programme are ideally placed to forge rewarding careers in the business and finance, and government sectors.
The starting salary for many financial maths graduate roles is highly competitive, and career options include:
 Actuary
 Data Analyst
 Finance Manager
 Financial Analyst
 Insurance Underwriter
 Investment Analyst
 Market Researcher
Alternatively, you may wish to undertake postgraduate study at Lancaster and pursue a career in research and teaching.
Fees and Funding
Fees
We set our fees on an annual basis and the 2019/20 entry fees have not yet been set.
As a guide, our fees in 2018 were:
UK/EU  Overseas 

£9,250  £18,195 
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
For full details of the University's financial support packages including eligibility criteria, please visit our fees and funding page
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
Financial mathematicians are interested in making good decisions in the face of uncertainty. Through our rigorous programme, you will develop the skills and knowledge to become a major decision maker and influencer in your chosen career and gain valuable realworld experience in industry.
Financial maths is about learning to interpret and manipulate data to draw valuable conclusions and make predictions. This is particularly important in business and finance, but the skills gained from this programme are widely applicable and highly sought after. During the course, you will be able to draw on expertise from three specialist departments: Mathematics and Statistics; Accounting and Finance; and Economics. You will also benefit from completing a year of fulltime work experience, providing you with invaluable experience and an insight into the realworld workplace.
During your first year, you will build on your previous knowledge and understanding of mathematical methods and concepts. Modules cover a wide range of topics from calculus, probability and statistics to logic, proofs and theorems. As well as developing your technical knowledge and mathematical skills, you will also enhance your data analysis, problemsolving and quantitative reasoning skills. During this year, you will also receive an introduction to accounting and finance, which will provide you with a comprehensive understanding of the concepts and techniques of the discipline, including financial accounting, managerial finance, and financial statement analysis.
In the second year, you will further develop your knowledge in analysis, probability and statistics. During this year, you will also begin to explore advanced finance and will benefit from modules in economics at managerial level. These will provide you with insight into micro and macroeconomics, and their related issues. You will develop realworld knowledge and experience by applying your analytical skills, interpreting events and evaluating policies. This will be instrumental in developing a career related to banking, finance, international payments and exchange rates, and monetary policy.
The third year will take you away from the academic environment and into the workplace. You will spend this year with one of our partner organisations, putting what you have learnt into practice and gaining experience of a real workplace. This is a fantastic opportunity to see how what you have studied applies to the realworld and gives you the chance to get a taster of a potential career. This experience will be highly beneficial once you begin researching your career and applying for jobs.
Returning to Lancaster in the fourth year to complete your study, you will delve deeper into the theory of probability and will explore the concept of statistical inference. Alongside this, you will build upon the valuable industry and employability skills gained during your placement through a dedicated careersfocused module. This final year will also be highly customisable, allowing you to select from a range of modules to suit your own interests and career aspirations.
MSci Financial Mathematics
In addition to our BSc, we also offer a MSci Financial Mathematics programme that includes an additional year of study and a substantial research project. This programme will provide you with Masterslevel proficiency in mathematical analysis and concepts, as well as specialist financial knowledge.

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
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
Students are provided with an understanding of functions, limits, and series, and knowledge of the basic techniques of differentiation and integration. Examples of functions and their graphs are presented, as are techniques for building new functions from old. Then the notion of a limit is considered along with the main tools of calculus and Taylor Series. Students will also learn how to add, multiply and divide polynomials, and will learn about rational functions and their partial fractions.
The exponential function is defined by means of a power series which is subsequently extended to the complex exponential function of an imaginary variable, so that students understand the connection between analysis, trigonometry and geometry. The trigonometric and hyperbolic functions are introduced in parallel with analogous power series so that students understand the role of functional identities. Such functional identities are later used to simplify integrals and to parametrise geometrical curves.

Discrete Mathematics
An introduction to the basic ideas and notations involved in describing sets and their functions will be given. This 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, it is said that one is bigger than another if it contains more elements. What about infinite sets? Are some infinite sets bigger than others? Students will develop the tools to answer these questions and other counting problems, such as those involving recurrence relations, e.g. the Fibonacci numbers.
The module will also consider the connections between objects, 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. They will see how partial derivatives can help to understand surfaces, while repeated integrals enable them to calculate volumes. The module 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, rates of change are introduced with respect to several quantities. How to find maxima and minima will be explained. Applications include the method of least squares. Finally, various methods for solving differential equations of one variable will be investigated.

Geometry and Calculus
The main focus of this module is vectors in two and threedimensional space. Starting with the definition of vectors, students will discover some applications to finding equations of lines and planes, then they will consider some different ways of describing curves and surfaces via equations or parameters. Partial differentiation will be used to determine tangent lines and planes, and integration will be used to calculate the length of a curve.
In the second half of the course, the functions of several variables will be studied. When attempting to calculate an integral over one variable, one variable is often substituted for another more convenient one; here students will see the equivalent technique for a double integral, where they will have to substitute two variables simultaneously. They will also investigate some methods for finding maxima and minima of a function subject to certain conditions.
Finally, the module will explain 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 eigenvectors and eigenvalues.
The student will learn how to express a linear transformation of the real euclidean space using a matrix, from which they will be able to determine whether it is singular or not and obtain its characteristic equation and eigenspaces.

Numbers and Relations
The student is introduced to logic and mathematical proofs, with emphasis placed more 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.
The language and structure of mathematical proofs will be explained, highlighting how logic can be used to express mathematical arguments in a concise and rigorous manner. These ideas will then be 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. It then moves on to the selection of appropriate probability models to describe systematic and random variations of discrete and continuous real data sets. Students will learn to implement statistical techniques and to draw clear and informative conclusions.
The module will be supported by the statistical software package ‘R’, which forms the basis of weekly lab sessions. Students will develop a strategic understanding of statistics and the use of associated software, which will underpin the skills needed for all subsequent statistical modules of the degree.
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.
Basic concepts from the first year probability module will be revisited and extended to these to encompass continuous random variables, with students investigating several important continuous probability distributions. Commonly used distributions are introduced and key properties proved, and examples from a variety of applications will be used to illustrate theoretical ideas.
Students will then focus on transformations of random variables and groups of two or more random variables, leading to two theoretical results about the behaviour of averages of large numbers of random variables which have important practical consequences in statistics.

Real Analysis
A thorough look will be taken at the limits of sequences and convergence of series during this module. Students will learn to extend the notion of a limit to functions, leading to the analysis of differentiation, including proper proofs of techniques learned at Alevel.
Time will be spent studying the Intermediate Value Theorem and the Mean Value Theorem, and their many applications of widely differing kinds will be explored. 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, the notion of integration will be put under the microscope. Once it is properly defined (via limits) students will learn how to get from this definition to the familiar technique of evaluating integrals by reverse differentiation. They will 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
The course provides students with general knowledge and understanding concerning social research and particular methods and methodologies that lie within the positivist and interpretivist paradigms. It is primarily aimed at students from across the management school that are planning to undertake an industrial placement and/or a dissertation in their final year of study. This module helps to prepare you to undertake your own research with a view to highlighting different research approaches and techniques that are used in the production of knowledge.
The module provides an insight into the various ways research can be undertaken and the implications of different approaches. We will examine the conceptual and practical complexities of undertaking research in practice. Initially you will be introduced to research methods and that are most commonly employed in business and management research. The module will then examine the methodological approaches and paradigms that are linked with these methods and the assumptions that underpin positivistic and interpretivist approaches. The final part of the module explores how this understanding can be used in writing your research proposal and dissertation.

Statistics II
Statistics is the science of understanding patterns of population behaviour from data. In the module, this topic will be approached by specifying a statistical model for the data. Statistical models usually include a number of unknown parameters, which need to be estimated.
The focus will be on likelihoodbased parameter estimation to demonstrate how statistical models can be used to draw conclusions from observations and experimental data, and linear regression techniques within the statistical modelling framework will also be considered.
Students will come to recognise the role, and limitations, of the linear model for understanding, exploring and making inferences concerning the relationships between variables and making predictions.
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,students will select a small number of properties which these and other examples have in common, and use them to define a group.
They will also consider the elementary properties of groups. By looking at maps between groups which 'preserve structure',a way of formalizing (and extending) the natural concept of what it means for two groups to be 'the same' will be discovered.
Ring theory provides a framework for studying sets with two binary operations: addition and multiplication. This gives students a wayto 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; several less familiar examples will also be explored.

Complex Analysis
Complex Analysis has its origins in differential calculus and the study of polynomial equations. In this module, students will consider the differential calculus of functions of a single complex variable and study power series and mappings by complex functions. They will use integral calculus of complex functions to find elegant and important results and will also use classical theorems to evaluate real integrals.
The first part of the module reviews complex numbers, and presents complex series and the complex derivative in a style similar to calculus. The module then introduces integrals along curves and develops complex function theory from Cauchy's Theorem for a triangle, which is proved by way of a bisection argument. These analytic ideas are used to prove the fundamental theorem of algebra, that every nonconstant complex polynomial has a root. Finally, the theory is employed to evaluate some definite 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
Students will be provided with the foundational results and language of linear algebra, which they will be able to build upon in the second half of Year Two, and the more specialised Year Three modules. This module will give students the opportunity to study vector spaces, together with their structurepreserving maps and their relationship to matrices.
They will consider the effect of changing bases on the matrix representing one of these maps, and will examine how to choose bases so that this matrix is as simple as possible. Part of their study will also involve looking at the concepts of length and angle with regard to vector spaces.

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.
Students will also consider the issue of model choice: in situations where there are multiple models under consideration for the same data, how do we make a justified choice of which model is the 'best'?
The approach taken in this course is just one approach to statistical inference: a contrasting approach is covered in the Bayesian Inference module.

Probability Theory
This module is ideal for students who want to develop an analytical and axiomatic approach to the theory of probabilities.
First the notion of a probability space will be examined through simple examples featuring both discrete and continuous sample spaces. Random variables and the expectation will be used to develop a probability calculus, which can be applied to achieve laws of large numbers for sums of independent random variables.
Students will 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.

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.

Financial 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.

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
The aim is to introduce students to the study designs and statistical methods commonly used in health investigations, such as measuring disease, causality and confounding.
Students will develop a firm understanding of the key analytical methods and procedures used in studies of disease aetiology, appreciate the effect of censoring in the statistical analyses, and use appropriate statistical techniques for time to event data.
They will look at both observational and experimental designs and consider various health outcomes, studying a number of published articles to gain an understanding of the problems they are investigating as well as the mathematical and statistical concepts underpinning inference.

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
The concept of generalised linear models (GLMs), which have a range of applications in the biomedical, natural and social sciences, and can be used to relate a response variable to one or more explanatory variables, will be explored. The response variable may be classified as quantitative (continuous or discrete, i.e. countable) or categorical (two categories, i.e. binary, or more than categories, i.e. ordinal or nominal).
Students will come to understand the effect of censoring in the statistical analyses and will use appropriate statistical techniques for lifetime data. They will also become familiar with the programme R, which they will have the opportunity to use in weekly workshops.

Stochastic Processes
Important examples of stochastic processes, and how these processes can be analysed, will be the focus of this module.
As an introduction to stochastic processes, students will look at the random walk process. Historically this is an important process, and was initially motivated as a model for how the wealth of a gambler varies over time (initial analyses focused on whether there are betting strategies for a gambler that would ensure they won).
The focus will then be on the most important class of stochastic processes, Markov processes (of which the random walk is a simple example). Students will discover how to analyse Markov processes, and how they are used to model queues and populations.

Time series analysis
Modern statistics is characterised by computerintensive methods for data analysis and development of new theory for their justification. In this module students will become familiar with topics from classical statistics as well as some from emerging areas.
Time series data will be explored through a wide variety of sequences of observations arising in environmental, economic, engineering and scientific contexts. Time series and volatility modelling will also be studied, and the techniques for the analysis of such data will be discussed, with emphasis on financial application.
Another area the module will focus on is some of the techniques developed for the analysis of multivariates, such as principal components analysis and cluster analysis.
Lastly,students will spend time looking at 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
Financial maths graduates are very versatile, having indepth specialist knowledge and a wealth of skills. Through this degree, you will graduate with a comprehensive skill set, including data analysis and manipulation, logical thinking, problemsolving and quantitative reasoning, as well as adept knowledge of the discipline. As a result, financial mathematicians are sought after in a range of industries. However, graduates of this programme are ideally placed to forge rewarding careers in the business and finance, and government sectors.
The starting salary for many financial maths graduate roles is highly competitive, and career options include:
 Actuary
 Data Analyst
 Finance Manager
 Financial Analyst
 Insurance Underwriter
 Investment Analyst
 Market Researcher
Alternatively, you may wish to undertake postgraduate study at Lancaster and pursue a career in research and teaching.

Fees and Funding
Fees and Funding
Fees
We set our fees on an annual basis and the 2019/20 entry fees have not yet been set.
As a guide, our fees in 2018 were:
UK/EU Overseas £9,250 £18,195 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
For full details of the University's financial support packages including eligibility criteria, please visit our fees and funding page
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
Download the latest Mathematics & Statistics brochure, featuring all of the information you could need. The includes detailed course information about each of our courses.
Our Courses
Our courses offer academic excellence. We have 3 singlehonours degrees and 10 combinedhonours degrees. We have focused our courses in the first two years, so you can choose from a wide range of third and fourthyear topics. Our academic research shapes our courses with the latest developments.
Friendly and Collaborative
The department has around 50 academic staff and 500 undergraduate students. Throughout your course, you will have weekly workshops and marked assignments. You will have opportunity to discuss each topic and get feedback from expert tutors. We also offer onetoone sessions during lecturers' office hours, so you soon get to know us and vice versa.
Supportive Environment
You will receive the support you need to achieve your full academic potential. We are a friendly department and foster a supportive learning environment. You will have an academic tutor who will assist you throughout your degree. We also encourage you to attend our weekly Maths Café, lead by fellow students.
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12.9 hours
Typical time in lectures, seminars and similar per week during term time
31%
Average assessment by coursework