also available in 2018
A Level Requirements
see all requirements
see all requirements
Full time 3 Year(s)
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.
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. Over the three years, you will be able to draw on expertise from three specialist departments: Mathematics and Statistics; Accounting and Finance; and Economics.
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, problem-solving 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 real-world 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.
During your third year, you will delve deeper into the theory of probability and will explore the concept of statistical inference. Alongside this, you will gain valuable industry and employability skills through a dedicated careers-focused 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
As well as offering a BSc, we also offer a four year MSci Financial Mathematics degree. During the course of this programme, you have the option to graduate after three years with a BSc, or progress onto an advanced fourth year and complete an MSci. This additional year features Masters-level modules and a dissertation.
BSc Financial Mathematics (Industry)
Alternatively, you may wish to apply for our BSc Financial Mathematics (Industry) programme, which will offer you the opportunity to spend a year working with one of our partner organisations. This year in industry will provide you with invaluable experience and insight into the real-world workplace and will allow you to try out a possible career pathway.
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.
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 email@example.com
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.
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.
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.
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.
The main focus of this course is vectors in two and three-dimensional 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.
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 real-world 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.
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.
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.
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.
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.
This module provides a detailed analysis of three key finance paradigms: decision-making 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.
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:
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 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.
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 A-level.
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 A-level, such as estimations of discrete sums of series.
Further possible topics include Stirling's Formula, infinite products and Fourier series.
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 likelihood-based 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.
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.
Information for this module is currently unavailable.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Modern statistics is characterised by computer-intensive 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 Change-Point Methods, which include traditional as well as some recently developed techniques for the detection of change in trend and variance.
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.
Financial maths graduates are very versatile, having in-depth 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, problem-solving 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:
Alternatively, you may wish to undertake postgraduate study at Lancaster and pursue a career in research and teaching.
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:
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:
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.
Typical time in lectures, seminars and similar per week during term time
Average assessment by coursework