Economics and Mathematics BSc

Economics core module:

Economic Analysis and Policy

This is a compulsory module for all single and dual honours students in Economics. The module provides students with an introduction to microeconomic and macroeconomic analysis together with examples of their application in order to develop students' understanding of the roles of both in economic policy making.

40 credits

Mathematics core modules:

Mathematics Core

Mathematics Core covers topics which continue school mathematics and which are used throughout the degree programmes: calculus and linear algebra, developing the framework for higher-dimensional generalisation.  This material is central to many topics in subsequent courses.  At the same time, small-group tutorials with the Academic Tutor aim to develop core skills, such as mathematical literacy and communication, some employability skills and problem-solving skills.

40 credits

Foundations of Pure Mathematics

The module aims to give an overview of basic constructions in pure mathematics; starting from the integers, we develop some theory of the integers, introducing theorems, proofs, and abstraction.  This leads to the idea of axioms and general algebraic structures, with groups treated as a principal example.  The process of constructing the real numbers from the rationals is also considered, as a preparation for “analysis”, the branch of mathematics where the properties of sequences of real numbers and functions of real numbers are considered.

20 credits

Probability and Data Science

Probability theory is branch of mathematics concerned with the study of chance phenomena. Data science involves the handling and analysis of data using a variety of tools: statistical inference, machine learning, and graphical methods. The first part of the module introduces probability theory, providing a foundation for further probability and statistics modules, and for the statistical inference methods taught here. Examples are presented from diverse areas, and case studies involving a variety of real data sets are discussed. Data science tools are implemented using the statistical computing language R.

20 credits

Economics core

Econometrics

The aim of this module is to consolidate the statistical theory covered in earlier modules for economists, introduce students to the role of econometrics in economic analysis and to give an introduction to the conduct of empirical work in econometrics.

20 credits

Intermediate Microeconomics

This module builds on Level 1 modules in microeconomics and mathematical economics, using the mathematical training to allow a more rigorous investigation of the principles of microeconomics. It aims to develop an understanding and ability to undertake economic analysis of models of the behaviour and interaction of economic agents (consumers, firms and government) in a market economy, the functioning of different types of industries, decision making under uncertainty and economic welfare.

20 credits

Intermediate Macroeconomics

The aims of this course are to provide firm grounding in the analytical tools of modern macroeconomics; to use these tools to understand critically the conduct of economic policy nationally and internationally. The course builds on level 1 modules in macroeconomics. The main subject areas covered are: Basic macroeconomic models: consumption/leisure choice, closed economy one period-macro models, models of search and unemployment; Savings, investment and government deficits: consumption/savings choice (two-period model), credit market imperfections, real intertemporal model with investment; Money and business cycles: flexible price models, New Keynesian economics (sticky prices), inflation; International macroeconomics: international trade, money in open economy; Economic growth: Malthus and Solow growth models, convergence, endogenous growth model.

20 credits

Mathematics core modules - students must take a minimum of 40 credits and a maximum of 50 credits from this group

Mathematics Core II

Building on Level 1 Mathematics Core, Mathematics Core II will focus on foundational skills and knowledge for both higher mathematics and your future life as a highly skilled, analytically-astute worker.  Mathematical content will focus on topics that are vital for all areas of the mathematical sciences (pure, applied, statistics), such as vector calculus and linear algebra.  This will help develop your analytic and problem solving skills.  Alongside this, you will continue to develop employability skills, building on Level 1 Core.  Finally, there will be opportunities to learn and reflect on social, ethical, and historical aspects of mathematics, which will enrich your understanding of the importance of mathematics in the modern world.

30 credits

Analysis and Algebra

This module will build on the theory built in Level 1 'Foundations of Pure Mathematics', focusing on the twin pillars of analysis and algebra.  These are not only fundamental for pure mathematics at higher levels, but provide rigorous theory behind core concepts that are used throughout the mathematical sciences.  Whilst to some extent you have been doing analysis and algebra since you were at school, here you will be going much deeper.  You will examine why familiar tools, like differentiation and integration, actually work.  Familiar objects, such as vectors, differential operators, and matrices, will be unpacked; powerful, formal properties of these objects proved.  Ultimately, this rigorous foundation will enable you to extend these tools and concepts to tackle a far greater set of problems than before.

20 credits

Statistical Inference and Modelling

Statistical inference and modelling are at the heart of data science, a field of rapidly-growing importance in the modern word.  This module develops methods for analysing data, and provides a foundation for further study of probability and statistics at higher Levels.  You will learn about a range of standard probability distributions beyond those met at Level 1, including multivariate distributions. You will learn about sampling theory and summary statistics, and their relation to data analysis. You will discover how to parametrise various types of statistical model, learn techniques for determining whether one model is 'better' than another for understanding a dataset, and learn how to ascertain how good a statistical model is at explaining trends in data. The software package R will be used throughout.

20 credits

Mathematics options - student must take between one and two modules from this group

Stochastic Modelling

Many things about life are unpredictable.  Consequently, it often makes sense to incorporate some randomness in mathematical models of natural and physical processes. Such models are called 'stochastic models' and are the study object of this module.  We will learn about a number of general models for processes where the state of a system is fluctuating randomly over time. Examples might include the length of a queue, the size of a reproducing population, or the quantity of water in a reservoir. We will cover various techniques for analysis of such models, setting the student up for further study of stochastic processes and probability at levels 3 and 4.

10 credits

Group Theory

A group is one of the most foundational objects in mathematics.  It just consists of a set, together with a way of combining two objects in that set to create another object in an internally-consistent fashion.  Familiar examples abound: integers with addition, real numbers with multiplication, symmetries of the square, and so on.  In this module, you will learn about formal properties of groups in general, including famous results like the orbit-stabiliser theorem.  You will also learn about important foundational examples, such as number, matrices, and symmetries.  You will learn how the general framework of groups allows you to prove theorems that pertain to all these examples in one go.  This provides a great example of the power and beauty of abstraction, a feature of pure mathematics that underlies the entire module.

10 credits

Mathematics and Statistics in Action

In this project module, you will investigate one or more case studies of using mathematics and statistics for solving empirical (i.e. 'real world') problems. These case studies will illustrate the process of mathematical and statistical modelling, whereby real-world questions are translated to mathematical and/or statistical questions. Students will see how techniques learned earlier in their degree can be used to explore these problems. There will be a mix of individual and group projects to choose from, and some projects may  involve the use of R or Python, but 'MPS115 Mathematical Investigations Skills' is not a prerequisite. Students will be expected to work independently (either individually or in a small group). However, the topic and scope of each piece of project work will be clearly defined by the lecturer in charge of the topic.

10 credits

Analysis

This module will build on the theory built in Level 1 'Foundations of Pure Mathematics', focusing specifically on analysis.  This provides rigorous theory behind core concepts that are used throughout the mathematical sciences.  Whilst to some extent you have been doing analysis since you were at school, in the form of calculus, here you will be going much deeper.  You will examine why familiar tools, like differentiation and integration, actually work.  This allows powerful, formal properties of these objects to be proved.  Ultimately, this rigorous foundation will enable you to extend these tools and concepts to tackle a far greater set of problems than before.

10 credits

Economics core

Further Econometrics

This module is designed to introduce students to a number of important advanced topics in econometrics. The aims of the module are to provide: an overview of modern econometric methodology; an introduction to further econometric techniques; and an introduction to applied econometric research methods. The module will cover topics in both microeconometrics and times series econometrics.

20 credits

Economics methodological options - one or two from:

Further Mathematical Methods for Economics

This module aims to build upon a basic knowledge of mathematical economics, introducing and explaining some of the more advanced mathematical techniques which are prevalent in modern economics and to show how they can be applied to intermediate economic analysis and discussions. By the end of the module students should be able to demonstrate an understanding of, and be able to apply in a variety of economic situations, the principles of univariate and multivariate calculus; linear algebra; constrained and unconstrained optimisation and comparative static analysis (with and without the use of linear algebra); basic inequality constrained optimisation; maximum value functions and the envelope theorem. It is assumed that students enrolling onto this module can rearrange equations, solve simultaneous equations, undertake multivariate calculus and solve economic problems including basic constrained optimisation.

20 credits

Advanced Microeconomics

This module is designed to further develop students' understanding of core microeconomic principles by exploring a number of advanced topics in microeconomics. The course material will be predominately theoretical with a substantial mathematical component and some evaluation of empirical evidence. Indicative topics include: decision-making under uncertainty; insurance markets, principal-agent theory, risk aversion and risky asset holdings; cooperative and non-cooperative bargaining; economics of sporting contests.

20 credits

Advanced Macroeconomics

This module is designed to cover topics which illustrate and amplify the core teaching in macroeconomics at level two. Topics include Dynamic general equilibrium theory of consumption and saving, Consumption theory, Macroeconomic Risk, Real business cycle and fiscal policy, Financial frictions and credit constraints, Nominal economy and monetary policy, Economic growth and finance.

20 credits

Modern Finance

The aim of this module is to introduce some of the main principles of modern finance. This is an analytical module which reflects the quantitative nature of the subject and each topic is developed from first principles. The topics covered include: the time value of money and its applications; risk return and diversification; introduction to portfolio selection; the capital asset pricing model (CAPM) and its use; and an introduction to the role of utility theory in finance and company capital structure. The aims of the module are to: Provide an introduction to portfolio theory, i.e., the concept of financial risk and behaviour of rational, risk-averse investors; Leading to a general equilibrium picture of financial asset returns and prices; Explore corporate financial decision making in the major areas of Capital Structure (the mix of equity and debt financing used to finance the firm's investments); Introduce students to concepts of Stock Market Efficiency and Option Pricing, considering in particular alternative pricing models.

20 credits

Game Theory for Economists

Game theory is the study of decision problems which involve more than one agent. Given the prevalence of such problems in economics, game theory has become a very important methodological tool in many of its fields, including industrial economics, political economy and international trade. This module aims at equipping students with the core knowledge of game theory as used in economics, with special emphasis on applications and examples, rather than pure theory.

20 credits

Economics applied options - maximum of one from:

International Trade

The first part of the course will cover neoclassical trade theories in which countries trade following their comparative advantage. The second part of the course deals with more recent trade theories based on economies of scale and/or imperfect competition that helps us to explain some recent patterns observed in the data. The third part of the course is an introduction to trade policy and the political economy of trade policy.

20 credits

Urban Economics

Urban economics is concerned with understanding the spatial form of cities and the spatial distribution of economic activities within a country, making use of theoretical models and empirical evidence. Three fundamental questions are: (1) Why are economic activities within a country so unequally distributed across space? (2) Why do cities, and more broadly agglomerations of firms and workers, emerge and in what locations? (3) What are the consequences of unequal distribution of activities for productivity, innovation and wages? This module covers topics such as:- Why do cities exist and why do firms cluster?- What determines equilibrium city size and features of the urban system?- City growth, spatial transformation and the implications for productivity, knowledge and wages.- Real Estate economics and the housing market.- Diseconomies in cities: Urban location, land rents and land use patterns.- Unequal distribution of economic activities and levelling-up.- Transportation economics.- Urbanisation in developing countries.

20 credits

Health Economics

Economics is the study of how society allocates its scarce resources across competing alternatives. This notion of scarcity is as relevant in the health care sector as it is elsewhere and, thus, it is important that the resources available to health and health care are used in the best possible ways. This course will: look at how best should be defined in the context of health care; consider the roles that market forces and governments might play in achieving the sector's objectives; and discuss what information is needed so that resources can be deployed where they will do the most good. The aims of the module are: 1. To enable students to develop a critical understanding of the basis of health economics.
2. To introduce students to the health economists' toolkit, the ways in which it can be used in to inform health care resource allocation, and its limitations.

20 credits

Economic Analysis of Inequality and Poverty

This module will cover the economic theories used for the analysis of inequality and poverty.
The theories will be backed by evidence from both the developed and the developing countries. The module starts off by a discussion of issues around measurement of inequality and poverty; the different measures that are used and the inherent assumptions behind these measures. We then move on to explain the existing global trends in inequality and poverty. Different theories are used to explain these trends; for example: role of human capital, poverty traps etc. Finally we discuss the policy response of different countries to address the issues of inequality and poverty, drawing on the specific examples of welfare programmes in the developed countries and the conditional cash transfers in the developing countries.

20 credits

Education Economics

The amount of education possessed by individuals will influence their decisions in future. Education relates to issues such as health and labour market decisions. This module examines the demand for and provision of education, incorporating a mixture of economic theory such as human capital; rates of return to further and higher education and course type all of which directly relate to the labour market. The graduate labour market is analysed, incorporating changes in the provision of higher education and an understanding of the rationale for the introduction of top-up fees. A final section considers schools, analysing and evaluating issues such as class size reduction, competition and selection, the performance of teachers, and the importance of pupils' family backgrounds, all in terms of their effect on pupil performance.

20 credits

Political Economy

Important economic processes cannot be fully understood without taking into account political and institutional factors and governments' political motivations. This module introduces insights from politics into the study of public policy and economic performance. In particular, it aims to give students: 1. an opportunity for interdisciplinary study within the undergraduate economics degree; 2. familiarity with the modern literature in theoretical and applied political economy; 3. an opportunity to develop their research skills through research-oriented assignments.

20 credits

Environmental Economics

Economic choices shape nature just as nature can shape our choices. This module provides students with the opportunity to apply economic concepts and methods to issues related to the use and management of the environment and natural resources. The module explores issues, arguments and analysis of market failure in the protection of the environment. It also offers public policy responses to issues of sustainability and climate change.

20 credits

Behavioural Economics

Standard economic models can successfully model human behaviour. However, the strong assumptions required of economic actors in those models will make systematic mispredictions in some contexts. Behavioural economics tries to overcome the systematic mispredictions by adopting non-standard assumptions, often inspired by insights from other disciplines. The module will discuss empirical evidence that underpins these non-standard assumptions, and will reflect on how insights from behavioural economics can be relevant in real life.

20 credits

Economics of Race and Gender

The Economics of Race and Gender first presents an overview of differential outcomes by gender and ethnicity in the UK labour market and discusses the possible drivers of these differences.  It then presents economic theories of discrimination in labour markets before discussing the strategies that economists use to test for discrimination in the real world.  

20 credits

The Economics of Innovation

The aim of this module is to provide an overview of the economics of innovation. The module will study firms' incentives to invest in innovation and the resulting policy implications. Expanding your knowledge of microeconomics this module will include the relationship between market structure and innovation, the role of firm cooperation and the effects of mergers on innovative activities. We will also look at the role of intellectual property rights / patent systems and policy interventions. As many innovations in recent years are in the areas of digitalization, artificial intelligence, and big data, the module will also cover those topics.

20 credits

Development Economics

It takes the average worker in the UK less than ten days to produce the same amount of output as the average worker in the Democratic Republic of Congo produces over the course of an entire year. Earning the minimum wage in the UK easily puts you in the top 10% of earners worldwide. This module uses a mix of theory and empirics to seek to understand where these enormous gaps in standards of living between countries come from and how they evolve over time.

20 credits

Mathematics options - 60 credits from example optional modules such as:

Complex Analysis

It is natural to use complex numbers in algebra, since these are the numbers we need to provide the roots of all polynomials. In fact, it is equally natural to use complex numbers in analysis, and this course introduces the study of complex-valued functions of a complex variable. Complex analysis is a central area of mathematics. It is both widely applicable and very beautiful, with a strong geometrical flavour. This course will consider some of the key theorems in the subject, weaving together complex derivatives and complex line integrals. There will be a strong emphasis on applications. Anyone taking the course will be expected to know the statements of the theorems and be able to use them correctly to solve problems.

10 credits

Financial Mathematics

The discovery of the Capital Asset Pricing Model by William Sharpe in the 1960's and the Black-Scholes option pricing formula a decade later mark the beginning of a very fruitful interaction between mathematics and finance. The latter obtained new powerful analytical tools while the former saw its knowledge applied in new and surprising ways. (A key result used in the derivation of the Black-Scholes formula, Ito's Lemma, was first applied to guide missiles to their targets; hence the title 'rocket science' applied to financial mathematics). This course describes the mathematical ideas behind these developments together with their application in modern finance.

10 credits

Machine Learning

Machine learning lies at the interface between computer science and statistics. The aims of machine learning are to develop a set of tools for modelling and understanding complex data sets. It is an area developed recently in parallel between statistics and computer science. With the explosion of 'Big Data', statistical machine learning has become important in many fields, such as marketing, finance and business, as well as in science. The module focuses on the problem of training models to learn from training data to classify new examples of data.

10 credits

Medical Statistics

This course comprises sections on Clinical Trials and Survival Data Analysis. The special ethical and regulatory constraints involved in experimentation on human subjects mean that Clinical Trials have developed their own distinct methodology. Students will, however, recognise many fundamentals from mainstream statistical theory. The course aims to discuss the ethical issues involved and to introduce the specialist methods required. Prediction of survival times or comparisons of survival patterns between different treatments are examples of paramount importance in medical statistics. The aim of this course is to provide a flavour of the statistical methodology developed specifically for such problems, especially with regard to the handling of censored data (eg patients still alive at the close of the study). Most of the statistical analyses can be implemented in standard statistical packages.

10 credits

Metric Spaces

This unit explores ideas of convergence of iterative processes in the more general framework of metric spaces. A metric space is a set with a distance function which is governed by just three simple rules, from which the entire analysis follows. The course ends with the Contraction Mapping Theorem, which guarantees the convergence of quite general processes; there are applications to many other areas of mathematics, such as to the solubility of differential equations.

10 credits

Bayesian Statistics

This module develops the Bayesian approach to statistical inference. The Bayesian method is fundamentally different to the approach taken in earlier statistics courses. It is a more general and more powerful approach, and it is widely used, but it relies on modern computers for much of its implementation. It is based on the idea that if we take a (random) statistical model, and condition this model on the event that it generated the data that we actually observed, then we will obtain a better model. This course covers the foundations of Bayesian statistics and the incorporation of prior beliefs, as well as computational tools for practical inference problems, specifically Markov Chain Monte Carlo and Gibbs sampling. Computational methods will be implemented using R and Python.

10 credits

Combinatorics

Combinatorics is the mathematics of selections and combinations. For example, given a collection of sets, when is it possible to choose a different element from each of them? That simple question leads to Hall's Theorem, a far-reaching result with applications to counting and pairing problems throughout mathematics.

10 credits

Game Theory

The module will give students the opportunity to apply previously acquired mathematical skills to the study of Game Theory and to some of the applications in Economics.

10 credits

Topics in Number Theory

In this module we study intergers, primes and equations. Topics covered include linear and quadratic congruences, Fermat Little Theorem and Euler's Theorem, the RSA cryptosystem, Quadratic Reciprocity, perfect numbers, continued fractions and others.

10 credits

Graph Theory

A graph is a simple mathematical structure consisting of a collection of points, some pairs of which are joined by lines. Their basic nature means that they can be used to illustrate a wide range of situations. The aim of this course is to investigate the mathematics of these structures and to use them in a wide range of applications.

10 credits

Operations Research

Mathematical Programming is the title given to a collection of optimisation algorithms that deal with constrained optimisation problems. Here the problems considered will all involve constraints which are linear, and for which the objective function to be maximised or minimised is also linear. These problems are not continuously differentiable; special algorithms have to be developed. The module considers not only the solution of such problems but also the important area of post-optimality analysis; i.e. given the solution can one answer questions about the effect of small changes in the parameters of the problem (such as values of the cost coefficients)?

10 credits

Sampling Theory and Design of Experiments

The results of sample surveys through opinion polls are commonplace in newspapers and on television. The objective of the Sampling Theory section of the module is to introduce several different methods for obtaining samples from finite populations. Experiments which aim to discover improved conditions are commonplace in industry, agriculture, etc. The purpose of experimental design is to maximise the information on what is of interest with the minimum use of resources. The aim of the Design section is to introduce some of the more important design concepts.

10 credits

Time Series

Time series are observations made in time, for which the time aspect is potentially important for understanding and use. The course aims to give an introduction to modern methods of time series analysis and forecasting as applied in economics, engineering and the natural, medical and social sciences. The emphasis will be on practical techniques for data analysis, though appropriate stochastic models for time series will be introduced as necessary to give a firm basis for practical modelling. Appropriate computer packages will be used to implement the methods.

10 credits

Generalised Linear models

This module introduces the theory and application of generalised linear models. These models can be used to investigate the relationship between some quantity of interest, the 'dependent variable', and one more 'explanatory' variables; how the dependent variable changes as the explanatory variables change. The term 'generalised' refers to the fact that these models can be used for a wide range of different types of dependent variable: continuous, discrete, categorical, ordinal etc. The application of these models is demonstrated using the programming language R.

10 credits

Codes and Cryptography

The word 'code' is used in two different ways. The ISBN code of a book is designed in such a way that simple errors in recording it will not produce the ISBN of a different book. This is an example of an 'error-correcting code' (more accurately, an error-detecting code). On the other hand, we speak of codes which encrypt information - a topic of vital importance to the transmission of sensitive financial information across the internet. These two ideas, here labelled 'Codes' and 'Cryptography', each depend on elegant pure mathematical ideas: codes on linear algebra and cryptography on number theory. This course explores these topics, including the real-life applications and the mathematics behind them.

10 credits

Knots and Surfaces

The course studies knots, links and surfaces in an elementary way. The key mathematical idea is that of an algebraic invariant: the Jones polynomial for knots, and the Euler characteristic for surfaces. These invariants will be used to classify surfaces, and to give a practical way to place a surface in the classification. Various connections with other sciences will be described.

10 credits

Mathematical Physics

Linear algebra: matrices and vectors; eigenvalue problems; matrix diagonalisation; vector spaces; transformation of basis; rotation matrices; tensors; Lie groups; Noether's theorem. Complex analysis: analytic functions; contour integration; Cauchy theorem; Taylor and Laurent series; residue theorem; application to evaluating integrals; Kronig-Kramers relations; conformal mapping; application to solving Laplace's equation.

10 credits

Probability and Random Graphs

Random graphs were studied by mathematicians as early as the 1950s. The field has become particularly important in recent decades as modern technology gives rise to a vast range of examples, such as social and communication networks, or the genealogical relationships between organisms. This course studies a range of models of random trees, graphs and networks, alongside probabilistic ideas that are needed to analyse their different properties. The precise material covered in this module may vary according to the lecturer's interests.

10 credits

Stochastic Processes and Finance

A stochastic process is a mathematical model for phenomena unfolding dynamically and unpredictably over time. This module studies two classes of stochastic process particularly relevant to financial phenomena: martingales and diffusions. The module develops the properties of these processes and then explores their use in Finance. A key problem considered is that of the pricing of a financial derivative such as an option giving the right to buy or sell a stock at a particular price at a future time. What is such an option worth now? Martingales and stochastic integration are shown to give powerful solutions to such questions.

20 credits

Undergraduate Ambassadors Scheme in Mathematics

This module provides an opportunity for Level Three students to gain first hand experience of mathematics education through a mentoring scheme with mathematics teachers in local schools. Typically, each student will work with one class for half a day every week for 11 weeks. The classes will vary from key stage 2 to sixth form. Students will be given a range of responsibilities from classroom assistant to the organisation and teaching of self-originated special projects. Only a limited number of places are available and students will be selected on the basis of their commitment and suitability for working in schools.

20 credits

Skills Development in Mathematics and Statistics

This module consolidates skills development across a number of areas of the mathematics curriculum, allowing students choice from a range of application areas in mathematics and statistics.  Students will complete a portfolio, comprising a range of outputs from project work, group work, and evidence of professional skills development.  Possible areas of mathematics include statistical investigations, history of mathematics, mathematical modelling, and sustainability, while the outputs might take the form of written projects, for example.  The module will involve considerable independent study, but staff will be available to guide you in your work.

20 credits