This covers the basic concepts and standard methods of mathematical notation and proof; functions; complex numbers and variables; solution of equations; resolution of inequalities; sequences and series.

This introduces the fundamental concepts of calculus, and develops some of their applications including basic ordinary differential equations.

This gives an introductory treatment of vectors, matrices, geometry, and discrete maths and introduces their application to real-world problems.

The module will provide you with a balanced introduction to economics which will be based on a programme of systematic directed reading, supplemented by experiments and exercises undertaken in tutorials. 

The module uses the innovative CORE (Curriculum Open-Access Resources in Economics) Econ resources, which provides a complete introduction to economics and the economy. CORE Econ teaches about the economy and economics by starting from a question or a problem about the economy - why the advent of capitalism is associated with a sharp increase in average living standards, for example - and then teach the tools of economics that contribute to an answer. This innovative approach ensures that students understand how the tools of economics can help us understand the modern economy. 

The second half of the module is the study of how analytical thinking, scientific method and associated tools can be used to help decision making. This Business Analysis element of the module will provide an overview of where methods and tools are widely used across a large range of industries including the manufacturing, retail, healthcare, financial services, travel, and electronics industries, as well as in local and national government. 

Examples of where Business Analysis is put into practice are: 

• the management of new building projects
• the design of efficient transport systems and plant layouts
• personnel scheduling
• allocation of resources and financial modelling and forecasting

This area of expertise can help to reduce costs, increase revenues, improve customer service, increase efficiency and can even save lives. 

A presentation of some basic ideas and techniques of statistics. This module will also introduce students to the R statistical software.

A module that focuses on communicating mathematics and statistics that will facilitate practical development of communication skills in data analysis, report writing and making presentations.

This module will introduce you to the basic ideas of linear algebra, such as matrices and determinants, vector spaces, bases, eigenvalues and eigenvectors. You'll study various standard methods for solving ordinary differential equations and understand their relevance.

This module will present basic ideas, techniques and results for calculus of two and three variables, along with differentiation and integration over curves, surfaces and volumes of both scalar and vector fields.

This module will present the basic concepts of probability theory and statistical inference and provide you with the tools to appropriately analyse a given data set and effectively communicate the results of such analysis.

This module will introduce you to the R computing environment. It'll enable you to use R to import data and perform statistical tests, allow you to understand the concept of an algorithm and what makes a good algorithm and will equip you for implementing simple algorithms in R.

This module builds upon the macroeconomic foundations established in the first-year Economics module and both extends and deepens analysis. In particular, this module will develop your ability to use key models used to analyse the determination of output in the short run and in the medium run. We'll also cover some topics in the analysis of economic data including correlation and simple regression.

This module builds upon the macroeconomic foundations established in the first-year Economics module and both extends and deepens analysis. In particular, this module will develop your ability to use key models used to analyse the determination of output in the short run and in the medium run. We will also cover some topics in the analysis of economic data including correlation and simple regression.

This module builds on the conceptual framework of Intermediate Microeconomics by introducing you to market imperfections through the lens of game theory. Game theory is an analytical toolbox that allows us to understand decision-making in strategic environments and this module will provide you with a foundation in game theoretic reasoning.

This module also studies how market imperfections create a role for government in markets. In doing so, we'll investigate topics including taxation, education, and crime and punishment. We'll also explore some of these ideas empirically using cross-section data. These empirical methods will open up a new route for you to understand the key taught economic ideas in a real-world context.

In this module, you'll extend your knowledge and understanding of core macroeconomic models and of the econometric methods used to analyse macroeconomic data and develop your ability to apply these models and methods to address some key questions in macroeconomics.

The module covers:

• economic growth
• expectations, demand and policy
• Europe: past, present, and future
• policy rules versus discretion

In addition, econometric methods covered include:

• regression
• unit root testing
• modelling volatility
• cointegration
• error correction

In this module we’ll introduce you to analytical methods for solving ordinary and partial differential equations, so you'll develop an understanding along with technical skills in this area.

This module will:

• review the concepts of probability distributions and how to work with these
• present approaches to parameter estimation, focusing on maximum likelihood estimation, bootstrap estimation, and properties of estimators
• present hypothesis testing procedures, including classical likelihood ratio tests and computer-based methods for testing parameter values, and goodness-of-fit tests
• introduce and provide understanding of the least squares multiple regression model, general linear model, transformations and variable selection procedures
• present use of R functions for regression and interpretation of R output

This module will introduce functions of a complex variable, define concepts such as continuity, differentiability, analyticity, line integration, singular points, etc. You will examine some important properties of such functions and consider some applications of them, for example, conformal mappings and the evaluation of real integrals using the Residue Theorem. You will also be introduced to Fourier and Laplace transform methods for solving linear ordinary differential equations and convolution type integral equations.

In this module we'll introduce basic algebraic structures, with particular emphasis on those pertaining to finite dimensional linear spaces and deepen your understanding of linear mappings. We'll also provide an introduction to inner product spaces and bilinear forms.

This module will motivate the need for numerical algorithms to approximate the solution of problems that can’t be solved with pen and paper. You’ll develop your skills in performing detailed analysis of the performance of numerical methods and will continue to develop your skills in the implementation of numerical algorithms using R.

You'll be introduced to the basic concepts of random phenomena evolving in time, from two complementary points of view: probabilistic modelling and data-driven analysis. Presentation of underlying ideas of simple stochastic processes, time series models, and the associated probability theory and statistical techniques will be covered. In addition to applications of the methods to financial and economic systems, including modelling, data analysis, and forecasting.

This module provides you with experience of the skills required to undertake project work, and to communicate the findings in written and oral form using a variety of sources, such as books, journals and the internet. You will undertake an individual research project, researching a mathematical or statistical topic and writing a short report on it.

You will write a dissertation on an aspect of economics.

You will be provided with a range of applied statistical techniques that can be used in professional life. This module provides you with the fundamental principles of statistical modelling through experimental design and multivariate analysis.

In this module you'll be introduced to a range of modern statistical methods and practices used in industry, commerce and research, and you will develop skills in your application and presentation.

20 credits

This module will cover the fundamental statistical methods necessary for the application of classical statistical methods to data collected for health care research. There will be an emphasis on the use of real data and the interpretation of statistical analyses in the context of the research hypothesis under investigation.

Topics covered will include:

• survival analysis
• analysing categorical data using hypothesis tests
• experimental Design and sampling
• clinical measurement

In this module, you’ll get an introduction to ideas in mathematics and statistics that can be used to model real systems, with an emphasis on the valuation of financial derivatives. The module places equal emphasis on deterministic analysis (calculus, differential equations) and stochastic analysis (Brownian motion, birth and death processes).  In both cases, in addition to theoretical analysis, appropriate computational algorithms are introduced. 

The first half of the module introduces general modeling and simulation tools, and the second half focuses on the specific application of valuing financial derivatives, including the celebrated Black-Scholes theory.

In the third-year econometrics module, you will have learned about regression in both cross-sectional data and time series data contexts. This module extends that knowledge in three ways.

First, for cross-sectional data, the module deals with regression techniques where the dependent variable may be restricted or limited in some way. In such cases, the regression model as taught in the third-year module is not appropriate; this module develops models that are similar in spirit to the standard regression model but can handle all of these cases.

A second purpose of Applied Econometrics is to develop regression methods that can be used when you have panel data - consisting of both cross-sectional and time-series dimensions.

Third, the module will build on the introduction to the econometrics of time series data studied previously by developing two classes of models. One class consists of models that can accommodate multiple long-run equilibrium relationships among a set of possibly non-stationary variables. A second class consists of methods for modeling volatility.

Risk and uncertainty are ubiquitous in everyday life and they affect the way in which economic agents make their choices. This module will start analysing how modern economic theory deals with uncertainty and the way people make their decisions under uncertainty. Attitude towards risk, decision-making under uncertainty, and the role of insurance and financial markets will be covered in the first part of the module.

The second part will present the foundation of the Economics of Information. Building on the first part of this module and on the game theoretic framework covered in third-year microeconomics, the study of Economics of Information will provide tools for the analysis of economic situations and contracting issues when either monitoring is imperfect or information is asymmetric.

This module is intended to show how economic theory can be used to analyse individual behaviour when information is not complete and decisions are risky. In particular, it will be applied to economic and business problems but also social interaction issues. In addition, the relevance of incentives and information in many economic environments will be highlighted, with particular emphasis on situations in which moral hazard and adverse selection problems arise.

This module is useful in enhancing your understanding of other modules and will be of particular use for your dissertation. Moreover, you will gain key skills in strategic thinking and the analysis of information asymmetries that will be useful both in further study and employment.

This module aims to provide you with the required tools to understand current macroeconomic issues, such as the interactions between the banking sector and monetary policy; or the policy responses to the global financial crisis. Throughout the module, the analytical usefulness of the theoretical models taught is illustrated with real-world examples.

This module will examine fundamental topics in Labour Economics. The primary goal is for you to learn how economists view the world of work and pay. The focus is on applications rather than theory. Topics include human capital and signaling, discrimination, the effect of technology on the wage structure, and income inequality. Along the way, you will gain insights into data analysis and empirical methods. These are highly marketable skills that tend to be entry requirements for consulting jobs, government work, and many other sectors.

In this module you'll get an introduction to ideas in mathematics and statistics that can be used to model real systems, with an emphasis on the valuation of financial derivatives. This module places equal emphasis on deterministic analysis (calculus, differential equations) and stochastic analysis (Brownian motion, birth and death processes). In both cases, in addition to theoretical analysis, appropriate computational algorithms are introduced.

The first half of the module introduces general modelling and simulation tools, and the second half focuses on the specific application of valuing financial derivatives, including the celebrated Black-Scholes theory.

This module will present the main results in Functional Analysis. You will also be introduced to linear operators on Banach and Hilbert spaces and study applications to integral and differential equations.

In this module you'll be introduced to the theory of Newtonian fluids and its application to flow problems and the dynamics of waves on water and in other contexts.

In this module you'll be presented with the basic theory and practice of finite element methods and polynomial and piecewise polynomial approximation theory.

In this module, you'll learn the application of mathematical models to a variety of problems in biology, medicine, and ecology. The module will show:

• the application of ordinary differential equations to simple biological and medical problems
• the use of mathematical modelling in biochemical reactions
• the application of partial differential equations in describing spatial processes such as cancer growth and pattern formation in embryonic development
• the use of delay-differential equations in physiological processes.

The marine population modelling element will introduce the use of difference models to represent population processes through applications to fisheries, and the use of coupled ODE system to represent ecosystems. Practical work will include example class case studies that will explore a real-world application of an ecosystem model.

This module will demonstrate the central role network theory plays in mathematical modelling. It'll also show the intimate connection between linear algebra and graph theory and how to use this connection to develop a sound theoretical understanding of network theory. Finally, it'll apply this theory as a tool for revealing structure in networks.

This module will investigate the actions firms can take in markets with the aim of maintaining their market power by deterring the entry of additional firms. A modern approach recognises that each firm faces competing firms that all have similar motives.

After briefly reviewing industry market structures to provide the basis of the analysis, issues of entry deterrence will be considered, including the role of advertising, issues associated with research and development, anti-trust, and both vertical integration and horizontal mergers. The module will conclude with an investigation of regulatory measures that can be put in place to limit anti-competitive strategies and consider the role of competition policy.

Behavioural Economics offers alternative theories that merge psychological insights with economic theory and are based on experimental and other evidence. These theories attempt to provide a better explanation of real-world behaviour.

This module is concerned with exploring these behavioural theories with the aim of providing you with an expanded toolkit with which to approach ‘real-world Economics’ that is based on the burgeoning Behavioural Economics literature that has emerged over the past two or three decades. You will then be able to extend much of your previously learned knowledge in microeconomics in various directions that take into account more realistic ways of modelling how individuals behave.

This module will provide you with an introduction to Natural Resource Economics, Environmental Economics, and Energy Economics, establishing connections between the economics and the policy aspects of the module topics. It focuses on the contributions of Economics to understanding environmental, energy, and natural resource problems, their causes, and the design of effective public policies to counteract them.