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 1

The module explores topics in mathematics which will be used throughout many degree programmes. The module will consider techniques for solving equations, special functions, calculus (differentiation and integration), differential equations, Taylor series, complex numbers and finite and infinite series.

20 credits

Mathematics Core II

The module continues the study of core mathematical topics begun in MS4F1015, which will be used throughout many degree programmes. The module will discuss 2-dimensional co-ordinate geometry, discussing the theory of matrices geometrically and algebraically, and will define and evaluate derivatives and integrals for functions which depend on more than one variable, with an emphasis on functions of two variables.

20 credits

Introduction to Probability and Statistics

The module provides an introduction to the fields of probability and statistics, which form the basis of much of applicable mathematics and operations research. The theory behind probability and statistics will be introduced, along with examples occurring in diverse areas. Some of the computational statistical work may make use of the statistics package R.

20 credits

Numbers and Groups

The module provides an introduction to more specialised Pure Mathematics. The first half of the module will consider techniques of proof, and these will be demonstrated within the study of properties of integers and real numbers. The second semester will study symmetries of objects, and develop a theory of symmetries which leads to the more abstract study of groups.

20 credits

Economics core

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

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

Mathematics core module:

Advanced Calculus and Linear Algebra

Advanced Calculus and Linear Algebra are basic to most further work in pure and applied mathematics and to much of statistics. This course provides the basic tools and techniques and includes sufficient theory to enable the methods to be used in situations not covered in the course.
The material in this course is essential for further study in mathematics and statistics.

20 credits

Mathematics options - choose option A or B:

Option A - 40 credits from:

Algebra

This unit continues the study of abstract algebra begun in MAS114, going further with the study of groups, and introducing the concepts of a ring, which generalises the properties of the integers, and a vector space, which generalises the techniques introduced in linear algebra to many more examples.

As well as demonstrating the interest and power of abstraction, this course is vital to further studies in most of pure mathematics, including algebraic geometry and topology, functional analysis and Galois theory.

20 credits

Analysis

This course is a foundation for the rigorous study of continuity, differentiation and integration of functions of one real variable. As well as providing the theoretical underpinnings of calculus, we develop applications of the theory and examples that show why the rigour is needed, even if we are focused on applications.

The material in this course is vital to further studies in metric spaces, measure theory, parts of probability theory, and functional analysis.

20 credits

Statistical Inference and Modelling

This unit develops methods for analysing data, and provides a foundation for further study of probability and statistics at Level 3. It introduces some standard distributions beyond those met in MAS113, and proceeds with study of continuous multivariate distributions, with particular emphasis on the multivariate normal distribution. Transformations of univariate and multivariate continuous distributions are studied, with the derivation of sampling distributions of important summary statistics as applications. The concepts of likelihood and maximum likelihood estimation are developed. Data analysis is studied within the framework of linear models. There will be substantial use of the software package R.

20 credits

Option B - 40 credits from:

Probability Modelling

The course introduces a number of general models for processes where the state of a system is fluctuating randomly over time. Examples might be the length of a queue, the size of a reproducing population, or the quantity of water in a reservoir. The aim is to familiarize students with an important area of probability modelling.

10 credits

Mathematics and Statistics in Action

This module will demonstrate, in a series of case studies, the use of applied mathematics, probability and statistics in solving a variety of real-world problems. The module 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, as well as simple computer programming, can be used to explore these problems. There will be a mix of individual and group projects, and some projects will involve the use of R or Python, but MAS115 is not a prerequisite.

10 credits

Statistical Inference and Modelling

This unit develops methods for analysing data, and provides a foundation for further study of probability and statistics at Level 3. It introduces some standard distributions beyond those met in MAS113, and proceeds with study of continuous multivariate distributions, with particular emphasis on the multivariate normal distribution. Transformations of univariate and multivariate continuous distributions are studied, with the derivation of sampling distributions of important summary statistics as applications. The concepts of likelihood and maximum likelihood estimation are developed. Data analysis is studied within the framework of linear models. There will be substantial use of the software package R.

20 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 pathway 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

Lectures will provide a bridge from level two core macroeconomic theory and introduce extensions to that theory as well as some new topic areas. They will also equip students to analyse economic issues arising in these topics. Workshops will give students the opportunity to show their understanding of topics and their applications.

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 pathway options - maximum of one from:

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. Macroeconomic new growth theories are considered using empirical evidence. 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

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

Monetary Economics

This module covers monetary theory and monetary policy. It presents several economic models and discusses what monetary policy can and cannot do, as well as an introduction to the New Keynesian model. The module aims to enable students to apply the skills of economic analysis to the conduct of central banks and to the mechanisms underlying the monetary transmission mechanism.

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

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

Economics of Race and Gender

The Economics of Race and Gender will present economic theories as to why discrimination by race and gender occurs, in labour markets and other settings. Empirical evidence will be presented and used to test for such discrimination, as well as to test and evaluate the economic theories put forward to explain its existence.

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

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

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. In this module you will build on and expand your knowledge of microeconomics. Topics will include the relationship between market structure and innovation, the role of firm cooperation and the effects of mergers on innovative activities. The module will also look at the role of intellectual property rights / patent systems and policy interventions. As many innovations in recent years are in the area of digitalisation and platform ecosystems, the module will also provide a short introduction to the economics of platform markets.

20 credits

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

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 follows on from MAS207 'Continuity and Integration', and adapts some of the ideas from that course to the more general setting. 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

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

Differential Geometry

What is differential geometry? In short, it is the study of geometric objects using calculus. In this introductory course, the geometric objects of our concern are curves and surfaces. Besides calculating such familiar quantities as lengths, angles and areas, much of our focus is on how to measure the 'curvature' of a geometric object. The story is relatively simple for curves, but naturally becomes more involved for surfaces - and more interesting too.

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

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

Measure and Probability

The module will give students an additional opportunity to develop skills in modern analysis as well as providing a rigorous foundation for probability theory. In particular it would form a useful precursor or companion course to the Level 4 courses MAS436 (Functional Analysis) and MAS452 (Stochastic Processes and Finance), the latter of which is fundamentally dependent on measure theoretic ideas

10 credits

Bayesian Statistics

This module develops the Bayesian approach to statistical inference. The Bayesian method is fundamentally different in philosophy from conventional frequentist/classical inference and is becoming the approach of choice in many fields of applied statistics. This course will cover both the foundations of Bayesian statistics, including subjective probability, inference, and modern computational tools for practical inference problems, specifically Markov Chain Monte Carlo methods and Gibbs sampling. Applied Bayesian methods will be demonstrated in a series of case studies using the software package R.

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

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

Practical and Applied Statistics

The overall aim of the course is to give students practice in the various stages of dealing with a real problem: objective definition, preliminary examination of data, modelling, analysis, computation, interpretation and communication of results. It could be said that while other courses teach how to do statistics, this teaches how to be a statistician. There will be a series of projects and other exercises directed towards this aim. Projects will be assessed, but other exercises will not.

20 credits