The Times and Sunday Times Good University Guide (2025)
10
10th for Mathematics
The Guardian University Guide (2025)
Develop your mathematical expertise with a solid foundation in economics as you delve into the power of maths and how it underpins economic systems and modelling. You will learn how to apply mathematical and statistical theory to understand how governments, commerce and households shape global economic policies and growth. Studying this combination at Lancaster University means you benefit from a curriculum at the cutting-edge of research across two departments including our renowned Lancaster University Management School, providing you with an outstanding education.
As you progress through the degree, you will develop the knowledge and skills to interpret government policy, analyse economic patterns, and critique business decisions, all of which develop your ability to provide solutions to global problems. As you graduate, you will be prepared for a diverse career in areas such as finance, policymaking, statistics, research, business management and much more.
In Year 1, you will develop a solid grounding in the fundamentals of maths, such as calculus, algebra and statistics along with economics, with two core maths modules and one core economics module. This provides you with a robust foundation in both disciplines and you will begin to hone your critical thinking and analytical skills.
In Year 2, you can choose optional modules in both maths and economics as you shape your degree to align with your career interests. These will be studied alongside core maths and economics modules that continue to build on the fundamentals of Year 1. A highlight of this year is taking part in game theory along with strategic behaviour, where you will work with your classmates to use different types of games to model, analyse and solve real-world strategic situations. Depending on the optional modules you select, you may have the chance to work on fascinating projects such as analysing data about food and living costs; epidemic modelling; or even predicting aftershocks from real earthquake data.
In third year, you will undertake a 12-month placement that will allow you to apply the knowledge and skills that you’ve learnt in Years 1 and 2, and to gain invaluable experience which will make you highly employable when you graduate. You will also submit monthly learning logs reflecting on your experience.
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 for your final year, you will study core modules covering advanced topics in mathematical theory and econometrics, where you will apply statistical modelling to real-world data for economic analysis and decision-making. Your remaining modules can be selected from a wide choice of topics, such as artificial intelligence, where you will learn about large amounts of data and how predictive modelling relates to economic forecasting.
As a graduate of Lancaster you’ll enjoy excellent employment prospects. Your qualification in Economics and Mathematics, along with your problem-solving skills, analytical abilities and organisational expertise, will make you highly desirable to employers.
Former graduates have been taken on as professional economists and economic advisers by the Bank of England, the Civil Service, management consultancies and diverse companies in a wide range of areas.
Your skills are also easily transferable to various roles such as marketing, management, advertising and consultancy.
Lancaster University is dedicated to ensuring you not only gain a highly reputable degree, you also graduate with the relevant life and work-based skills. We are unique in that every student is eligible to participate in The Lancaster Award which offers you the opportunity to complete key activities such as work experience, employability awareness, career development, campus community and social development. Visit our employability section for full details.
Entry requirements
Grade Requirements
A Level AAA including A level Mathematics or Further Mathematics OR AAB including A level Mathematics and Further Mathematics
IELTS 6.0 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 (either analysis and approaches or applications and interpretations)
BTEC May be accepted alongside A level Mathematics and Further Mathematics
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.
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.
Contextual admissions
Contextual admissions could help you gain a place at university if you have faced additional challenges during your education which might have impacted your results. Visit our contextual admissions page to find out about how this works and whether you could be eligible.
Course structure
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.
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 full-year module provides the foundation for your future study in Economics. It is divided into three parts. The first part provides a thorough introduction to Microeconomics (including the theory of demand, costs and pricing under various forms of market structure, and welfare economics). The second part provides a thorough introduction to Macroeconomics (including national income analysis, monetary theory, business cycles, inflation, unemployment, and the great macroeconomic debates).
The third part of the module, taught in parallel with the first two parts, shows how the key Micro- and Macroeconomics ideas can help us understand the world around us. In this part, we will use economic experiments to answer various questions, such as whether economists are selfish. We will analyse whether a sugar tax is a good idea, automation and the minimum wage, the structure, conduct and performance of big technology firms, and use the skills we have learned to analyse inequality, Brexit, and Covid-19. We will also discuss the distinction between transitory inflation and stagflation, central banks’ changing objectives, cryptocurrencies and the financial markets, fiscal and monetary policy responses to the pandemic, the Great Depression and the Great Recession, quantitative easing, currency crises, and the Euro debt crisis. Economics A is taught in conjunction with modules (ECON103 or MATH100, depending on the degree) which provide the quantitative foundations for further study in Economics.
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.
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.
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.
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.
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.
Core
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This module helps you improve your strategic thinking. Over the course of this module, you will learn how to use ‘games’ to model strategic situations in the real world, and how to analyse and find out solutions to these games in situations in which players are intelligent and rational. Games including “normal form games”, “extensive form games”, “Bayesian games”, “repetitive games”, and “games with correlation device” will be introduced. Opportunities for playing games with the lecturer and other students will also be provided. The module requires a basic knowledge of algebra, calculus, and economics.
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.
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.
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.
Optional
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This module uses the tools of economics to study various macroeconomic variables (inflation, consumption, output, unemployment) and particularly their short-run and long-run dynamics. It covers topics related to fiscal policy and the sustainability of public debt in the intermediate run. In addition, students will study unemployment and labour market dynamics and more in general economic stability in the short run.
The module requires algebra, elementary calculus, logical thinking and general problem-solving ability.
Markets consist of individual buyers and sellers, each facing choices. A buyer must decide what, and how much, to purchase. A seller must decide how much to produce, how to produce it, and what price to charge. But how are these choices made? In this course, we will explore this question formally, with the aid of economic models. The topics include consumer choice, profit maximization and cost minimization. The module requires a basic knowledge of algebra and calculus.
By the end of the course, you will improve your logical thinking and problem-solving abilities.
Core
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Students will spend their third year working on a graduate level placement to gain valuable experience in an industry or sector that they might aspire to work in once they graduate. They will be supported by the Faculty Placements Team and the Careers Team in securing their own placement.
Core
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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.
This module introduces up-to-date quantitative econometric methods used in applied research/empirical work. We will discuss various economic applications, including “returns to schooling” and “the effect of minimum wages on employment”. The module will also provide students with the data analytical skills necessary to conduct applied research in economics/policy analysis using popular statistical software, STATA. Key topics include linear regression, instrumental variables, causal inferences, binary choice models, panel data, time series modelling, and forecasting.
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.
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.
Optional
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Behavioural Economics is the interface between economics and psychology. It is one of the fastest-growing fields in economics, and since the past decade, it is regarded as a standard tool for policymaking. The course will survey the empirical tools used by behavioural economists and in particular lab and field experiments. We will explore behavioural biases affecting economic and financial decision making, and the role of trust and cooperation in teamwork. We will discuss models and experimental results explaining how we make decisions in various contexts such as choice under uncertainty, intertemporal choice or decision making in a social framework.
This module introduces up-to-date knowledge and understanding of the quantitative analysis of economic data based on machine learning and big data methods. We will overview statistical learning and how to use statistical software R for adequate use of data visualisation and manipulation techniques.
Key topics include linear regression, classification, resampling methods (cross-validation and the Bootstrap), Ridge Regression and The Lasso, Tree-Based Methods (Decision Tree, Bootstrap Aggregation (Bagging) and Random Forests), Support Vector Machines, Deep Learning and Neural Networks.
Fees and funding
Our annual tuition fee is set for a 12-month session, starting in the October of your year of study.
We set our fees on an annual basis and the 2025/26 home undergraduate
entry fees have not yet been set.
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.
College fees
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 2025, the fee is £40 for undergraduates and research students and £15 for students on one-year courses.
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.
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.
Home fees are subject to annual review, and may be liable to rise each year in line with UK government policy. International fees (including EU) are reviewed annually and are not fixed for the duration of your studies. Read more about fees in subsequent years.
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
You will be automatically considered for our main scholarships and bursaries when you apply, so there's nothing extra that you need to do.
You may be eligible for the following funding opportunities, depending on your fee status:
Unfortunately no scholarships and bursaries match your selection, but there are more listed on scholarships and bursaries page.
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We also have other, more specialised scholarships and bursaries - such as those for students from specific countries.
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.
Our historic city is student-friendly and home to a diverse and welcoming community. Beyond the city you'll find a stunning coastline and the picturesque Lake District.
