Mathematics and Economics BSc

During this module you will build on your theoretical knowledge of statistical inference by a practical implementation of the generalised linear model. You will progress to enhance your understanding of statistical methodology including the analysis of discrete and survival data. You will also be trained in the use of a high-level statistical computer program.

This module provides an introduction to coding theory in particular to error-correcting codes and their uses and applications. You’ll learn cryptography, including classical mono- and polyalphabetic ciphers.  There will also be a focus on modern public key cryptography and digital signatures, their uses and applications.

The aim of Discrete Mathematics is the study of discrete and finite rather than continuous quantities. This includes counting problems, graphs and other quantities parametrised by integers.

As such Discrete Mathematics is of great importance for various branches of Pure Mathematics, Mathematical Physics, Statistics and Computer Sciences.

The course will cover a range of Discrete Mathematics topics, including:

• an introduction to advanced aspects of combinations and permutations
• ordinary and exponential generating functions
• recurrence relations and applications to counting problems
• graphs
• digraphs
• Eulerian and Hamiltonian trails
• planar graphs
• graph colouring
• trees
• minimum spanning tree algorithms

Game theory contains many branches of mathematics (and computing); the emphasis here is primarily algorithmic. The module starts with an investigation into normal-form games, including strategic dominance, Nash equilibria, and the Prisoner’s Dilemma. We look at tree-searching, including alpha-beta pruning, the ‘killer’ heuristic and its relatives. It then turns to mathematical theory of games; exploring the connection between numbers and games, including Sprague-Grundy theory and the reduction of impartial games to Nim.

You will explore the concepts of discrete time Markov chains to understand how they used. We will also provide an introduction to probabilistic and stochastic modelling of investment strategies, and for the pricing of financial derivatives in risky markets.

You will gain well-rounded knowledge of contemporary issues which are of importance in research and workplace applications.

This module involves the application of mathematics to a variety of practical, open-ended problems - typical of those that mathematicians encounter in industry and commerce.

Specific projects are tackled through workshops and student-led group activities. The real-life nature of the problems requires you to develop skills in model development and refinement, report writing and teamwork. There are various streams within the module, for example:

• Pure Mathematics
• Applied Mathematics
• Data Analysis
• Mathematical Physics

This ensures that you can work in the area that you find most interesting.

A metric space generalises the concept of distance familiar from Euclidean space. It provides a notion of continuity for functions between quite general spaces. The module covers:

• metric spaces
• topological spaces
• compactness
• separation properties like Hausdorffness and normality
• Urysohn’s lemma
• quotient and product topologies, and connectedness

Finally, Borel sets and measurable spaces are introduced.

This module is concerned with the analysis of multivariate data, in which the response is a vector of random variables rather than a single random variable. A theme running through the module is that of dimension reduction.

Key topics to be covered include:

• principal components analysis
• modelling and inference for multivariate data
• classification of observation vectors into sub-populations using a training sample
• canonical correlation analysis
• factor analysis
• methods of clustering
• multidimensional scaling

In this module a variety of techniques and areas of mathematical optimisation will be covered including Lagrangian methods for optimisation, simplex algorithm linear programming and dynamic programming. You’ll develop techniques for application which can be used outside the mathematical arena. 

This module is concerned with the two main theories of statistical inference, namely classical (frequentist) inference and Bayesian inference.

You will explore the following topics in detail:

• sufficiency
• estimating equations
• likelihood ratio tests
• best-unbiased estimators

There is special emphasis on the exponential family of distributions, which includes many standard distributions such as the normal, Poisson, binomial and gamma.

This module will develop your knowledge of discrete-time Markov chains by applying them to a range of stochastic models. You will be introduced to Poisson and birth-and-death processes. You will then move onto more extensive studies of epidemic models and queuing models, with introductions to component and system reliability.

This module generalises and builds upon the material covered in the Econometric Theory I and II. In the first part of the module, we study large sample, or asymptotic, theory. This is needed in order to obtain tractable results about the behaviour of estimators and tests when the standard modelling assumptions - which frequently cannot be verified in practice - are relaxed.

The second part of the module continues the time series analysis taken in Econometric Theory II, with the emphasis on the behaviour of typical economic time series, and the implications of that behaviour in practical analysis, such as the construction of models linking economic time series. The key issues addressed will be the identification of non-stationarity through the construction of formal tests and the implications for modelling with non-stationary data.

Particular attention will be paid to the contributions of Sir Clive Granger to the spurious regression problem and to cointegration analysis, for which he was ultimately awarded the Nobel Prize.

This module discusses aspects of some of the main sub-areas of experimental and behavioural economics. This includes applications related to individual decision-making, strategic behaviour and market behaviour.

The module encourages reflection on both the role of experiments in economics and the assumptions that economics does (and should) make about people’s motivations. Both experimental economics and behavioural economics are still comparatively new fields within the wider discipline.

The module considers their potential and main achievements, relative to more traditional economic techniques. It encourages development of critical skills and reflection on specific research contributions in experimental and behavioural economics.

This module adopts a broad focus on factors influencing growth and development, concentrating on core economic policy areas and the role of international organisations.

Topics covered include macroeconomic policies, in particular exchange rates and the role of the IMF; aid policy and the World Bank, effects of aid on growth, macroeconomic and fiscal policy, and poverty; trade policy and performance and the WTO; economic reforms and growth experiences in East Asia, China and Africa; human development and the UN Sustainable Development Goals.

This module covers:

• saving, focusing on how agents make intertemporal decisions about their savings and wealth accumulation
• saving puzzles and household portfolios, focusing on credit markets and credit markets' imperfections, and why do households hold different kinds of assets
• asset allocation and asset pricing, focusing on intertemporal portfolio selection, asset pricing and the equity premium puzzle
• bond markets and fixed income securities
• the term structure of interest rates
• the role of behavioural finance in explaining stock market puzzles

This module provides an advanced economic analysis of the theory of organisation of firms and industries. It will analyse a variety of market structures related to the degree of market competition with a special emphasis on imperfectly competitive markets. It will also analyse issues related to the internal organisation of firms.

This module looks at:

• trade policy
• economic policy for trade and international factor mobility
• theory and evidence
• trade policy and imperfect competition
• trade and distortions
• the political economy of protection
• trade policy reform

This module covers:

• models of intra-industry trade
• trade policy in oligopolistic industries
• multinational enterprises
• testing trade theories
• the WTO and "new issues"

This module covers an economic analysis of the labour market, with an emphasis on policy implications and institutional arrangements.

This module is intended to provide an introduction to mathematical techniques used in economics. In particular, examples of economic issues that can be analysed using mathematical models will be discussed in detail.

Particular attention will be given to providing an intuitive understanding of the logic behind the formal results presented.

This module covers:

• dynamic general equilibrium models, focusing on how the time path of consumption, and saving, is determined by optimising agents and firms that interact on competitive markets
• growth in dynamic general equilibrium, focusing on the Solow model and the data, and the role played by accumulation of knowledge (endogenous innovation) in explaining long run growth
• Real Business Cycles (RBC), focusing on how the RBC approach accounts for business cycle fluctuations, and what links short run fluctuations and growth processes

This module will cover topics in advanced microeconomics and decision theory. The precise content may vary from year to year, but the module will start from the basis established by the Microeconomic Theory module.

This module provides a rigorous introduction to formal models of money in the macroeconomy. Following this, applications for areas of central banking, finance and international macroeconomics will be explored.

This module covers: 

• Foundations:
  • The rational political individual?
  • Voter participation
  • Collective action and the role of the state
• Core Political Economy:
  • The economic approach to politics
  • Political aspects of economics: rights and the limits of the state
  • Political aspects of economics: inequality and the duties of the state
• Political Economy in Action:
  • Political economy in action: some current issues in political economy

An independent research project, involving the application of techniques of economic analysis to a self-chosen research topic and the presentation of a written report. There will be lectures to provide general guidance on economic research methods and writing an undergraduate dissertation in economics.

Topics include:

• introduction to the dissertation
• types of dissertation
• literature reviews
• sources of data
• writing up your dissertation
• data entry and data management
• an introduction to STATA
• descriptive statistics
• practical issues in regression analysis
• model selection
• endogeneity bias

This module will introduce you to economic policy analysis. It will focus on the role played by different institutional rules in shaping the behaviour of elected governments by providing incentives to elected governments.

This module will introduce students to economic policy analysis, using examples from environmental economics and international trade.  The first part of the module is about climate change. We first examine the practice of discounting future outcomes. We will look at the evidence for climate change in the past and predictions for future damage. Combining this with information about abatement options and costs, we can devise a globally optimal policy path, depending on the discount rate. Finally, we will trace actual climate change negotiations, evaluate climate change policy and examine why it is so difficult for countries to agree on greenhouse gas emission reductions. 

The second part of the module will focus on the issues around and methods for policy evaluation. We also draw some lessons for policy prescription/design. There is an increasing consensus as to the appropriate methods for evaluation but the topic of policy prescription remains contentious. It considers the main empirical methods of policy evaluation and the fundamental question of evaluation studies (what would have happened if the policy had not been undertaken). It discusses trade liberalization and exporting firms. This allows us to think about aggregate outcomes for policy change using evidence from microdata. It considers the question of whether there is systematic, reliable evidence that government policies stimulate growth in the long run and if so what those policies are. This topic is used to explore the issue of policy prescription.

This module will provide an introduction to international monetary issues, including the determination of exchange rates and international spill-over effects. 

This module focuses on a range of econometric methods used in policy evaluation and in the identification and estimation of causal effects. Topics to be covered include:

• potential outcomes framework
• regression analysis and matching
• instrumental variables
• difference-in-differences
• regression discontinuity

You'll learn how to use numerical techniques for determining the approximate solution of ordinary and partial differential equations where a solution cannot be found through analytical methods alone. You will also cover topics in numerical linear algebra, discovering how to solve very large systems of equations and find their eigenvalues and eigenvectors using a computer.

Time Series Analysis

The module will introduce some major themes of the economic analysis of government. Using the tools of modern microeconomic theory, it will explore how government institutions are designed, how they could be designed better, and how they shape economic policy. 

This module covers the following:

Static numerical methods

• Numerical solution methods
• Numerical static optimisation methods
• Applications: resource allocation, computable general equilibrium

Dynamic numerical optimisation

• Discrete dynamic programming
• Implementation of the methods
• Applications: optimal growth, rational expectations, asset management

Agent-based economic modelling

• Foundations of agent-based modelling
• Basics of computer programming
• Applications: evolutionary games, markets