Top reasons to study with us
10th for in Mathematics
The Guardian University Guide (2024)
11th for Accounting and Finance in the UK
QS World University Rankings (2023)
13th for Accounting and Finance
The Guardian University Guide (2024)
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 real-world 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 full-time work experience, providing you with invaluable experience and an insight into the real-world 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, 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.
To prepare you for your work placement year, our Careers and Placements Team will provide advice and guidance on: the skills required to create effective CVs, cover letters and applications; tips and techniques on how to make an impact at interviews and assessment centres; how to create a relevant digital profile; and how to research employers and career sectors of interest. In addition, there is great emphasis placed upon developing self-awareness and on how to present yourself in a professional manner to employers. This optional provision will be delivered via a blend of traditional and digital methods including face-to-face workshops, online webinars, e-courses and 1:1 appointments.
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 real-world 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.
The University will use all reasonable effort to support you to find a suitable placement for your studies. While a placement role may not be available in a field or organisation that is directly related to your academic studies or career aspirations, all placement roles offer valuable experience of working at a graduate level and gaining a range of professional skills. If you are unsuccessful in securing a suitable placement for your third year, you will be able to transfer to the equivalent non-placement degree scheme and continue with your studies at Lancaster, finishing your degree after your third year.
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 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
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 Master's-level proficiency in mathematical analysis and concepts, as well as specialist financial knowledge.
The Institute of Mathematics and its Applications is a chartered professional body for mathematicians in the UK. Accreditation means that our degrees demonstrate both a high level of competency and professionalism in the area of mathematics.Learn more about the Institute of Mathematics accreditation
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:
- 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.
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 (either analysis and approaches or applications and interpretations)
BTEC Accepted alongside A level Mathematics grade A and Further Mathematics grade A
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 firstname.lastname@example.org
International foundation programmes
Delivered in partnership with INTO Lancaster University, our one-year tailored foundation pathways are designed to improve your subject knowledge and English language skills to the level required by a range of Lancaster University degrees. Visit the INTO Lancaster University website for more details and a list of eligible degrees you can progress onto.
Lancaster University offers a range of programmes, some of which follow a structured study programme, and some which offer the chance for you to devise a more flexible programme to complement your main specialism.
Information contained on the website with respect to modules is correct at the time of publication, and the University will make every reasonable effort to offer modules as advertised. In some cases changes may be necessary and may result in some combinations being unavailable, for example as a result of student feedback, timetabling, Professional Statutory and Regulatory Bodies' (PSRB) requirements, staff changes and new research. Not all optional modules are available every year.
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.
Convergence and Continuity
This module provides a rigorous overview of real numbers, sequences and continuity. Covering bounds, monotonicity, subsequences, invertibility, and the intermediate value theorem, among other topics, students will become familiar with definitions, theorems and proofs.
Examining a range of examples, students will become accustomed to mathematical writing and will develop an understanding of mathematical notation. Through this module, students will also gain an appreciation of the importance of proof, generalisation and abstraction in the logical development of formal theories, and develop an ability to imagine and ‘see’ complicated mathematical objects.
In addition to learning and developing subject specific knowledge, students will enhance their ability to assimilate information from different presentations of material; learn to apply previously acquired knowledge to new situations; and develop their communication skills.
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.
This course extends ideas of MATH101 from functions of a single real variable to functions of two real variables. The notions of differentiation and integration are extended from functions defined on a line to functions defined on the plane. Partial derivatives help us to understand surfaces, while repeated integrals enable us to calculate volumes.
In mathematical models, it is common to use functions of several variables. For example, the speed of an airliner can depend upon the air pressure and temperature, and the direction of the wind. To study functions of several variables, we introduce rates of change with respect to several quantities. We learn how to find maxima and minima. Applications include the method of least squares. Finally, we investigate various methods for solving differential equations of one variable.
Geometry and Calculus
The main focus of this module is vectors in two and three-dimensional 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 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 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.
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.
This non-credit-bearing module will allow you to identify your current skills level and begin to collect evidence of skills acquisition. It will cover a detailed analysis of the individual in terms of personality, skills, goals, interests and career ideas, and self-development. Skills development will be considered within an organisational context and will practically focus on teamwork, presentation and communication skills and self-reflection.
Series, Integration, and Differentiation
Building on the Convergence and Continuity module, students will explore the familiar topics of integration, and series and differentiation, and develop them further. Taking a different approach, students will learn about the concept of integrability of continuous functions; improper integrals of continuous functions; the definition of differentiability for functions; and the algebra of differentiation.
Applying the skills and knowledge gained from this module, students will tackle questions such as: can you sum up infinitely many numbers and get a finite number? They will also enhance their knowledge and understanding of the fundamental theorem of calculus.
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.
Further Topics in Economics for Managers
This module is designed primarily for business major students looking to understand the macroeconomic environment, the current challenges in the global economy and the impacts of macroeconomic policies on economic activities. The module aims to provide tools, concepts, and models to guide your decision-making.
The topics it covers include analysis of the long- and short-run drivers of economic activity, the developments in the labour and financial market and monetary and fiscal policies. Beyond a review of key theoretical concepts, the course includes the discussion of case studies that show the concrete applications of how economic agents are addressing global issues, such as environmental challenges, financial crisis and debt problems.
The module requires logical thinking and academic writing skills and is only available to students with no prior background in Economics other than ECON 224.
Introduction to Asset Pricing
This module provides a detailed analysis of four key Finance paradigms:
- decision making under uncertainty, including utility theory,
- state preference theory and arbitrage pricing
- capital asset pricing and market equilibrium,
- option pricing.
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.
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.
Principles of Finance
This module covers project evaluation methods, risk, return and the cost of capital (including the capital asset pricing model), corporate financing (including dividend policy and capital structure) and an introduction to options.
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.
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 A-level.
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 A-level, such as estimations of discrete sums of series.
Further possible topics include Stirling's Formula, infinite products and Fourier series.
Research Methods in Management
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 is the science of understanding patterns of population behaviour from data. In the module, this topic will be approached by specifying a statistical model for the data. Statistical models usually include a number of unknown parameters, which need to be estimated.
The focus will be on likelihood-based parameter estimation to demonstrate how statistical models can be used to draw conclusions from observations and experimental data, and linear regression techniques within the statistical modelling framework will also be considered.
Students will come to recognise the role, and limitations, of the linear model for understanding, exploring and making inferences concerning the relationships between variables and making predictions.
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 way to abstractly model various number systems, proving results that can be applied in many different situations, such as number theory and geometry. Familiar examples of rings include the integers, the integers modulation, the rational numbers, matrices and polynomials; several less familiar examples will also be explored.
In this module, students will develop their ability to solve complex mathematical problems using computers. They will learn basic programming techniques, functions and syntax within Python, good programming practice, as well as how to code simple algorithms. Within this module, students will undertake a large programming project in which they will explore a mathematical topic from a range of choices, such as cryptography, error-correcting codes, or finite group theory, allowing them to explore an area of computational mathematics that interests them. Upon successful completion of the module, students will be able to write and debug functions and programs in Python, understand the benefits and limitations of using computers to solve mathematical problems, and produce a report that incorporates text, mathematics, and Python code.
In this module, students will develop their ability to solve complex mathematical problems using computers. They will learn basic programming techniques, functions and syntax within R, good programming practice, as well as how to code simple algorithms. Within this module, students will undertake a large programming project in which they will explore a mathematical modelling topic. The project itself will consolidate learning from the module, and will answer questions about real-world systems such as epidemics or gravitational bodies. Upon successful completion of the module, students will be able to write and debug functions and programs in R, understand the benefits and limitations of using computers to solve mathematical problems, and produce a report that incorporates text, mathematics, and R code.
In this module, students will develop their ability to solve complex mathematical problems using computers. They will learn basic programming techniques, functions and syntax within R, good programming practice, as well as how to code simple algorithms. Within this module, students will undertake a large programming project in which they will explore a mathematical topic from a range of choices, such as Markov chains or Monte Carlo simulations, allowing them to explore an area of computational statistics that interests them. Upon successful completion of the module, students will be able to write and debug functions and programs in R, understand the benefits and limitations of using computers to solve mathematical problems, and produce a report that incorporates text, mathematics, and R code.
Discrete Mathematics and Computing Projects
In this module, students will learn the basics of producing a mathematical project, getting to grips with the fundamentals of scientific writing and working within a scientific environment. They will learn how to utilise LaTeX for presenting mathematical formulae, using it to create a report on a given mathematical topic. Students will also undertake a group presentation and deliver it to the class, as well as collaborating with peers (under the direction of a supervisor) to produce a report on an area within the discrete mathematics and computing strands of mathematics, such as Ramsey's theorem, the birth of computer science, and Game theory. Upon successful completion of the module, students will be able to produce documents which accurately and effectively communicate scientific material, and be able to work independently under supervision and as part of a small group.
Dynamics and Analysis Projects
In this module, students will learn the basics of producing a mathematical project, getting to grips with the fundamentals of scientific writing and working within a scientific environment. They will learn how to utilise LaTeX for presenting mathematical formulae, using it to create a report on a given mathematical topic. Students will also undertake a group presentation and deliver it to the class, as well as collaborating with peers (under the direction of a supervisor) to produce a report on an area within the dynamics and analysis strands of mathematics, such as continued fractions, branching processes, and Kepler's laws. Upon successful completion of the module, students will be able to produce documents which accurately and effectively communicate scientific material, and be able to work independently under supervision and as part of a small group.
Geometry and Algebra Projects
In this module, students will learn the basics of producing a mathematical project, getting to grips with the fundamentals of scientific writing and working within a scientific environment. They will learn how to utilise LaTeX for presenting mathematical formulae, using it to create a report on a given mathematical topic. Students will also undertake a group presentation and deliver it to the class, as well as collaborating with peers (under the direction of a supervisor) to produce a report on an area within the geometry and algebra strands of mathematics, such as symmetry in music, error-correcting codes, and counting equivalent patterns. Upon successful completion of the module, students will be able to produce documents which accurately and effectively communicate scientific material, and be able to work independently under supervision and as part of a small group.
Linear Algebra II
Students will be provided with the foundational results and language of linear algebra, which they will be able to build upon in the second half of Year Two, and the more specialised Year Three modules. This module will give students the opportunity to study vector spaces, together with their structure-preserving maps and their relationship to matrices.
They will consider the effect of changing bases on the matrix representing one of these maps, and will examine how to choose bases so that this matrix is as simple as possible. Part of their study will also involve looking at the concepts of length and angle with regard to vector spaces.
Modelling and Probability Projects
In this module, students will learn the basics of producing a mathematical project, getting to grips with the fundamentals of scientific writing and working within a scientific environment. They will learn how to utilise LaTeX for presenting mathematical formulae, using it to create a report on a given mathematical topic. Students will also undertake a group presentation and deliver it to the class, as well as collaborating with peers (under the direction of a supervisor) to produce a report on an area within the modelling and probability strands of mathematics, such as Markov chains, beyond the Central Limit Theorem, and epidemic modelling. Upon successful completion of the module, students will be able to produce documents which accurately and effectively communicate scientific material, and be able to work independently under supervision and as part of a small group.
Placement Year Work-Based Learning
You will spend this year working in a graduate-level placement role. This is an opportunity to gain experience in an industry or sector that you might be considering working in once you graduate.
Our Careers and Placements Team will support you during your placement with online contact and learning resources.
You will undertake a work-based learning module during your placement year which will enable you to reflect on the value of the placement experience and to consider what impact it has on your future career plans.
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.
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.
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.
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.
This module introduces students to changepoint detection motivated by its applicability in a variety of different settings. Changepoints are sudden, and often unexpected shifts in the behaviour of a physical, biological, industrial or financial process. Students will understand the importance of identifying these shifts, and the module will cover the fundamental concepts within changepoint detection, the key approaches to At Most One Change (AMOC), and multiple changepoint identification. Students will explore key challenges around model selection concepts and techniques through a variety of models used in real-world applications, including changes in mean, variance, and regression. Successful completion of this module will see students be able to understand the importance of changepoint methodology, communicate technical ideas, critically evaluate approaches to solve problems, and make conclusions based on evidence in relation to a real-world problem.
This course equips students with the knowledge to apply corporate finance theory to real-world situations. It builds on and extends the concepts covered in the basic financial management courses and introduces advanced topics in Corporate Finance. The major topics covered include capital budgeting, capital structure, corporate valuation, real options, equity financing for startups, IPOs, leasing, short term financing, merger and acquisitions, and corporate governance
This module introduces students to two classes of continuous-time, dynamic compartmental models that describe the time evolution of natural systems such as epidemics, biological reactions in a cell, and the interactions between populations of predators and prey in an environment: Markov jump processes (MJPs) and ordinary differential equations (ODEs).
Students will examine model formulation in numerous real-world scenarios, delve into some tractable and partially-tractable examples, and use numerical simulation as a general method for visualising and classifying behaviour. Students will also examine stationary distributions and large n limits in order to further their understanding of MJPs, and find and examine stationary points and their stability to get to grips with ODEs, allowing students to justify their use within a variety of real-world processes. Upon successful completion of this module, students will be able to construct a mathematical model using real-world evidence.
The objective of this module is to offer a practical introduction to the workings of today’s financial markets and institutions built on a theoretical base. Moving beyond the descriptions and definitions provided by other textbooks and UK university courses in the field, this module encourages students to understand the connection between the theoretical concepts and their real-world applications.
Topics include foreign exchange, stock markets, bond markets, derivatives, central banks' monetary policy and financial crises. We also look at how trading in financial markets takes place. This module prepares students for successful careers in the financial services industry or successful interactions with financial institutions, whatever their future careers.
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.
The aim of this module is to equip students with the tools necessary to enable them to make the core investment management decisions that managers face on a daily basis as well as the knowledge as to where they can find the information necessary to apply those tools. This course is an introduction to investment analysis, with emphasis on the pricing of equity securities. This course covers fundamental concepts and key issues in asset pricing; modern portfolio theory and its applications; equilibrium theories of asset pricing; portfolio performance evaluation; mutual funds and hedge funds. It provides an entry point to advanced-level subjects and foundational knowledge on the valuation and arbitrage of investment assets.
Using the classical problem of data classification as a running example, this module covers mathematical representation and visualisation of multivariate data; dimensionality reduction; linear discriminant analysis; and Support Vector Machines. While studying these theoretical aspects, students will also gain experience of applying them using R.
An appreciation for multivariate statistical analysis will be developed during the module, as will an ability to represent and visualise high-dimensional data. Students will also gain the ability to evaluate larger statistical models, apply statistical computer packages to analyse large data sets, and extract and evaluate meaning from data.
This module provides an introduction to mathematical cryptography, introducing students to a range of methods of encryption, from the more classical forms (such as Caesar Shift, Vigenère and Enigma), to more contemporary methods of encrypting data (eg. RSA, El Gamal and Knapsack). During this module, students will consider the advantages, disadvantages, and efficiency of the different cryptographical approaches. They will also explore examples of potential attacks on these hard problems (e.g. Trial Division, Fermat’s method, Pollard rho, Dixon, Baby-step giant-step, Index calculus), and demonstrate attacks in situations where bad key generation or implementation has occurred. The module will culminate in a brief introduction to Post-Quantum Cryptography, the theory of lattices, tough problems, and how these lead to schemes that are considered impenetrable to both classical and quantum computers. Successful completion of this module will see students be able to formulate real-world problems in mathematical formality, and recognise the applications of cryptography to other mathematical fields, such as Algebra and Number Theory.
Mathematics for Stochastic Finance
This module formally introduces students to the discipline of financial mathematics, providing them with an understanding of some of the maths that is used in the financial and business sectors.
Students will begin to encounter financial terminology and will study both European and American option pricing. The module will cover these in relation to discrete and continuous financial models, which include binomial, finite market and Black-Scholes models.
Students will also explore mathematical topics, some of which may be familiar, specifically in relation to finance. These include:
- Conditional expectation
- Stopping times
- Brownian motion
- Black-Scholes formula
Throughout the module, students will learn key financial maths skills, such as constructing binomial tree models; determining associated risk-neutral probability; performing calculations with the Black-Scholes formula; and proving various steps in the derivation of the Black-Scholes formula. They will also be able to describe basic concepts of investment strategy analysis, and perform price calculations for stocks with and without dividend payments.
In addition, to these subject specific skills and knowledge, students will gain an appreciation for how mathematics can be used to model the real-world; improve their written and oral communication skills; and develop their critical thinking.
Medical Statistics: study design and data analysis
The aim is to introduce students to the study designs and statistical methods commonly used in health investigations, such as measuring disease, causality and confounding.
Students will develop a firm understanding of the key analytical methods and procedures used in studies of disease aetiology, appreciate the effect of censoring in the statistical analyses, and use appropriate statistical techniques for time to event data.
They will look at both observational and experimental designs and consider various health outcomes, studying a number of published articles to gain an understanding of the problems they are investigating as well as the mathematical and statistical concepts underpinning inference.
This module is designed as an introduction to econometric and time series methods for the analysis and research of financial assets and capital markets relationships. The focus will be on the analysis of financial data and econometric methods for modelling of financial time series, risk management and forecasting. The key objectives are to i) explain how econometric methods can be used to learn about the behaviour of financial assets; ii) endow students with practical experience of analysing financial data useful for research and practical work in the quantitative finance industry using basic statistical software packages; and iii) endow students with the relevant quantitative skills for advanced studies in MSc programmes.
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 computer-intensive methods for data analysis and development of new theory for their justification. In this module students will become familiar with topics from classical statistics as well as some from emerging areas.
Time series data will be explored through a wide variety of sequences of observations arising in environmental, economic, engineering and scientific contexts. Time series and volatility modelling will also be studied, and the techniques for the analysis of such data will be discussed, with emphasis on financial application.
Another area the module will focus on is some of the techniques developed for the analysis of multivariates, such as principal components analysis and cluster analysis.
Lastly,students will spend time looking at Change-Point Methods, which include traditional as well as some recently developed techniques for the detection of change in trend and variance.
Fees and funding
We set our fees on an annual basis and the 2025/26 entry fees have not yet been set.
As a guide, our fees in 2024/25 were:
There may be extra costs related to your course for items such as books, stationery, printing, photocopying, binding and general subsistence on trips and visits. Following graduation, you may need to pay a subscription to a professional body for some chosen careers.
Specific additional costs for studying at Lancaster are listed below.
Lancaster is proud to be one of only a handful of UK universities to have a collegiate system. Every student belongs to a college, and all students pay a small college membership fee which supports the running of college events and activities. Students on some distance-learning courses are not liable to pay a college fee.
For students starting in 2023 and 2024, the fee is £40 for undergraduates and research students and £15 for students on one-year courses. Fees for students starting in 2025 have not yet been set.
Computer equipment and internet access
To support your studies, you will also require access to a computer, along with reliable internet access. You will be able to access a range of software and services from a Windows, Mac, Chromebook or Linux device. For certain degree programmes, you may need a specific device, or we may provide you with a laptop and appropriate software - details of which will be available on relevant programme pages. A dedicated IT support helpdesk is available in the event of any problems.
The University provides limited financial support to assist students who do not have the required IT equipment or broadband support in place.
Study abroad courses
In addition to travel and accommodation costs, while you are studying abroad, you will need to have a passport and, depending on the country, there may be other costs such as travel documents (e.g. VISA or work permit) and any tests and vaccines that are required at the time of travel. Some countries may require proof of funds.
Placement and industry year courses
In addition to possible commuting costs during your placement, you may need to buy clothing that is suitable for your workplace and you may have accommodation costs. Depending on the employer and your job, you may have other costs such as copies of personal documents required by your employer for example.
What is my fee status?
The fee that you pay will depend on whether you are considered to be a home or international student. Read more about how we assign your fee status.
Fees in subsequent years
Fees are set by the UK Government annually, and subsequent years' fees may be subject to increases. Read more about fees in subsequent years.
Fees for study abroad and work placements
We will charge tuition fees to Home undergraduate students on full-year study abroad/work placements in line with the maximum amounts permitted by the Department for Education. The current maximum levels are:
- Students studying abroad for a year: 15% of the standard tuition fee
- Students taking a work placement for a year: 20% of the standard tuition fee
International students on full-year study abroad/work placements will be charged the same percentages as the standard International fee.
Please note that the maximum levels chargeable in future years may be subject to changes in Government policy.
Scholarships and bursaries
Details of our scholarships and bursaries for students starting in 2025 are not yet available. You can use our scholarships for 2024-entry applicants as guidance.
Accounting and Finance
- Accounting and Finance BSc Hons : N400
- Accounting and Finance (Industry) BSc Hons : N401
- Accounting and Management BSc Hons : NN24
- Accounting and Management (Industry) BSc Hons : NN25
- Accounting, Finance and Mathematics BSc Hons : NG41
- Accounting, Finance and Mathematics (Industry) BSc Hons : NG42
- Economics and Finance BSc Hons : NL31
- Economics and Finance (Industry) BSc Hons : NL32
- Finance BSc Hons : N300
- Finance (Industry) BSc Hons : N301
- Mathematics with Finance BSc Hons : GN13
Mathematics and Statistics
- Chinese Studies and Mathematics BA Hons : T1G1
- Computer Science and Mathematics BSc Hons : GG14
- Computer Science and Mathematics MSci Hons : GG1K
- Computer Science and Mathematics (Placement Year) Bsc Hons : GG1L
- French Studies and Mathematics BA Hons : GR11
- German Studies and Mathematics BA Hons : GR12
- Mathematics BSc Hons : G100
- Mathematics MSci Hons : G101
- Mathematics (Placement Year) BSc Hons : G102
- Mathematics (Study Abroad) MSci Hons : G103
- Mathematics and Philosophy BA Hons : GV15
- Mathematics and Philosophy (Placement Year) BA Hons : GV16
- Mathematics with Finance BSc Hons : GN13
- Mathematics with Statistics BSc Hons : G1G3
- Mathematics with Statistics MSci Hons : G1GJ
- Mathematics with Statistics (Placement Year) BSc Hons : GCG3
- Mathematics with Statistics (Study Abroad) MSci Hons : G1GH
- Mathematics, Operational Research, Statistics and Economics (MORSE) BSc Hons : GLN0
- Mathematics, Operational Research, Statistics and Economics (MORSE) (Industry) BSc Hons : GLN1
- Spanish Studies and Mathematics BA Hons : GR14
- Theoretical Physics with Mathematics BSc Hons : F3GC
- Theoretical Physics with Mathematics MSci Hons : F3G1
- Theoretical Physics with Mathematics (Study Abroad) MSci Hons : F3G5
The information on this site relates primarily to 2025/2026 entry to the University and every effort has been taken to ensure the information is correct at the time of publication.
The University will use all reasonable effort to deliver the courses as described, but the University reserves the right to make changes to advertised courses. In exceptional circumstances that are beyond the University’s reasonable control (Force Majeure Events), we may need to amend the programmes and provision advertised. In this event, the University will take reasonable steps to minimise the disruption to your studies. If a course is withdrawn or if there are any fundamental changes to your course, we will give you reasonable notice and you will be entitled to request that you are considered for an alternative course or withdraw your application. You are advised to revisit our website for up-to-date course information before you submit your application.
More information on limits to the University’s liability can be found in our legal information.
Our Students’ Charter
We believe in the importance of a strong and productive partnership between our students and staff. In order to ensure your time at Lancaster is a positive experience we have worked with the Students’ Union to articulate this relationship and the standards to which the University and its students aspire. View our Charter and other policies.
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