Mathematics and Economics BSc

The idea of proof is fundamental to all mathematics. We’ll look at mathematical reasoning using techniques from logic to deal with sets, functions, sequences and series.

This module links directly with your study in Calculus and Linear Mathematics. It provides you with the foundations for the broader area of Mathematical Analysis. This includes the rigorous study of the infinite and the infinitesimal.

You will also learn the basics of computer programming. This will give you the chance to use computational algorithms to explore many of the mathematical results you’ll encounter in your core modules.

Your study will include:

• propositional and predicate logic; set theory, countability
• proof: direct, indirect and induction
• sequences and infinite series (convergence and divergence)
• limits and continuity of functions
• programming in Python

How do we define calculus? How is it used in the modern world?

The concept can be explained as the mathematics of continuous change. It allows us to analyse motion and change in time and space.

You will cover techniques for differentiating, integrating and solving differential equations. You’ll learn about the theorems which prove why calculus works. We will explore the theory and how it can be applied in the real world.

Your study will include:

• functions: limits, continuity and differentiability, rules of differentiation
• techniques for integration, fundamental theorem of calculus
• solution of linear and nonlinear differential equations
• multivariate calculus, Lagrange multipliers, stationary points
• multiple integrals, changes of variables, Jacobians

This module gives you the mathematical tools required for later modules which involve modelling with differential equations. These include:

• mathematical physics
• mathematical medicine and biology
• scientific computation

This module aims to provide a means for enabling students to reflect on their personal development and the implications this might have for their future career paths. It will include:

• guidance on recording and evaluating skills
• guidance on careers from the Careers and Employability Service
• information, guidance and advice form a range of graduate employers and alumni

The first semester provides an introduction to microeconomics, including behaviour of firms and households in situations of competitive and imperfectly competitive markets. The second semester provides an introduction to macroeconomics.

Macroeconomics is the study of the aggregate economy, focusing on the cyclical pattern of aggregate output and co-movement of real and monetary aggregates in general equilibrium. A series of basic models used in modern macroeconomics are introduced, with a particular focus on dynamic general equilibrium modeling tools and techniques necessary to build theoretical models.

Vectors, matrices and complex numbers are familiar topics from A level Mathematics and Further Mathematics. Their common feature is linearity. A linear mathematical operation is one which is compatible with addition and scaling.

As well as these topics you’ll study the concept of a vector space, which is fundamental to later study in abstract algebra. We will also investigate practical aspects, such as methods for solving linear systems of equations.

The module will give you the tools to analyse large systems of equations that arise in mathematical, statistical and computational models. For example, in areas such as:

• fluid and solid mechanics
• mathematical medicine and biology
• mathematical finance

Your study will include:

• complex numbers, vector algebra and geometry
• matrix algebra, inverses, determinants
• vector spaces, subspaces, bases
• linear systems of simultaneous equations, Gaussian elimination
• eigenvalues and eigenvectors, matrix diagonalisation
• linear transformations, inner product spaces

What is the importance of probability in the modern world?

It allows us to assess risk when calculating insurance premiums. It can help when making investment decisions. It can be used to estimate the impact that government policy will have on climate change or the spread of disease.

We will look at the theory and practice of discrete and continuous probability. Your study will include:

• sample spaces, events and counting problems
• conditional probability, independence, Bayes’ theorem
• random variables, expectation, variance
• discrete and continuous probability distributions
• multivariate random variables
• sums of random variables, central limit theorem

These topics will help you prepare for later modules in:

• probability methods
• stochastic models
• uncertainty quantification
• mathematical finance

Statistics is concerned with methods for collecting, organising, summarising, presenting and analysing data. It enables us to draw valid conclusions and make reasonable decisions based on the analysis. It can be used to answer a diverse range of questions such as:

• Do the results of a clinical trial indicate that a new drug works?
• Is the HS2 rail project likely to be cost-effective?
• Should a company lend money to a customer with a given credit history?

In this module you’ll study statistical inference and learn how to analyse, interpret and report data. You’ll learn about the widely used statistical computer language R.

Your study will include:

• exploratory data analysis
• point estimators, confidence intervals
• hypothesis testing
• correlation, statistical inference
• linear regression, chi-squared tests

These first-year topics give you the foundations for later related modules in:

• statistical models and methods
• data analysis and modelling
• statistical machine learning

This module aims to introduce you to the essential skills required for writing as an economist. It will be delivered in conjunction with Libraries, Research and Learning Resources (LRLR), who will cover content on key information skills relating to the library and learning resources.

It will give an introduction to the language of economics and basic research skills and how to write essays and exams. Among the topics covered will be:

• academic integrity and plagiarism
• time management
• writing essays
• writing quantitative projects
• presentation skills
• referencing and using the internet
• revision and examinations

This module covers intermediate microeconomics including general equilibrium analysis; welfare economics; elementary game theory; and strategic behaviour of firms.

This module will address both the fundamental and applied aspects of macroeconomic theory. In particular, the module will focus on:

• introducing the modern theory of expectations and economic dynamics
• using this approach to think about short run fluctuations
• studying the role of macro policy on short run fluctuations

The module will review the so-called modern approach to aggregate demand and aggregate supply. This entails incorporating into the classical approach to aggregate supply and aggregate demand, insights from Keynesian economics. This will serve as a base to discuss the role of macro policy in controlling for fluctuations in output and employment. 

This module covers intermediate microeconomics including general equilibrium analysis; welfare economics; elementary game theory; and strategic behaviour of firms.

The module introduces you to a range of statistical techniques that can be used to analyse the characteristics of univariate economic time series. The basic theoretical properties of time series models are discussed and we consider methods for fitting and checking the adequacy of empirical time series models. Methods of forecasting future values of economic time series are then considered. If reassessment is required, a single examination will replace all failed assessment components of the module.

The module introduces you to a range of statistical techniques that can be used to analyse the characteristics of univariate economic time series. The basic theoretical properties of time series models are discussed and we consider methods for fitting and checking the adequacy of empirical time series models. Methods of forecasting future values of economic time series are then considered. If reassessment is required, a single examination will replace all failed assessment components of the module.

This module will address both the fundamental and applied aspects of macroeconomic theory. In particular, the module will focus on:

• introducing the modern theory of expectations and economic dynamics
• using this approach to think about short run fluctuations
• studying the role of macro policy on short run fluctuations

The module will review the so-called modern approach to aggregate demand and aggregate supply. This entails incorporating into the classical approach to aggregate supply and aggregate demand, insights from Keynesian economics. This will serve as a base to discuss the role of macro policy in controlling for fluctuations in output and employment. 

How can the flight-path of a spacecraft to another planet be planned? How many fish can we catch without depleting the oceans? How long would it take a lake to recover after its pollution is stopped?

The real world is often too complicated to get exact information. Instead, mathematical models can help by providing estimates. In this module, you’ll learn how to construct and analyse differential equations which model real-life applications.

Your study will include:

• modelling with differential equations
• kinematics and dynamics of moving bodies
• Newton’s laws, balance of forces
• oscillating systems, springs, simple harmonic motion
• work, energy and motion

You'll be able to expand on these techniques later in your degree through topics such as:

• black holes, quantum theory
• fluid and solid mechanics
• mathematical medicine and biology
• mathematical finance

In this module you will learn about the theory and applications of functions of a complex variable using a method and applications approach. You will develop an understanding of the theory of complex functions and evaluate certain real integrals using your new skills.

This module is a general introduction to the economic problems of developing countries. The module will cover such topics as:

• the implications of history and expectation
• poverty, income distribution and growth
• fertility and population
• employment, migration and urbanisation
• markets in agriculture
• agricultural household models
• risk and insurance
• famines

This course is an introduction to Fourier series and integral transforms and to methods of solving some standard ordinary and partial differential equations which occur in applied mathematics and mathematical physics.

The course describes the solution of ordinary differential equations using series and introduces Fourier series and Fourier and Laplace transforms, with applications to differential equations and signal analysis. Standard examples of partial differential equations are introduced and solution using separation of variables is discussed.

This module generalises and builds upon the econometric techniques covered in the year one module, Mathematical Economics and Econometrics. This will involve introducing a number of new statistical and econometric concepts, together with some further development of the methodology that was introduced in year one. The multivariate linear regression model will again provide our main framework for analysis.

This module introduces you to a range of statistical techniques that can be used to analyse the characteristics of univariate economic time series. The basic theoretical properties of time series models are discussed and we consider methods for fitting and checking the adequacy of empirical time series models. Methods of forecasting future values of economic time series are then considered.

This module will look at:

• market failure and the need for environmental policy - the Coase theorem
• instruments of environmental policy - efficiency advantages of market instruments
• applications of market instruments, especially the EU Emission Trading Scheme
• fisheries - the open access problem and rights-based policies
• valuation of the benefits of environmental policy
• biodiversity and its benefits
• international trade in polluting goods
• mobile capital: race to the bottom?

This module provides a foundation in behavioural economics and the role of experimental methods in economics. The traditional approach in economics is to explain market outcomes and economic decision-making using simple theoretical models based on perfectly rational, self-interested agents who maximise their wellbeing by carefully weighing up the costs and benefits of different alternatives. Behavioural economics, on the other hand, aspires to relax these stringent assumptions and develop an understanding of how real people actually make decisions.

The module will introduce you to behavioural and experimental economics, discuss these fields from a methodological perspective and examine several areas of economic analysis in which they are applied. This will include individual choice under risk and uncertainty, decision-making in strategic situations and competition in markets.

This module will offer an introduction to some theoretical concepts related to the allocation of risk by financial institutions. Then it will apply these concepts to the analysis of financial and banking crises.

Pure mathematics at university is typically very different to the pure mathematics you've learnt at school or college. You'll use the language of sets, functions and relations to study some very abstract mathematical ideas.

In this module, we'll develop the skills of reading and writing the language of pure mathematics. You will learn techniques to build mathematical proofs in an abstract setting.

Your study will include:

• the language of set theory
• relations and functions
• rational and irrational numbers
• modular arithmetic
• prime factorisation

These topics will provide you with the basics you need for subsequent modules in algebra, number theory and group theory.

This module provides an economic analysis of the theory and practice of organisation of firms and industries. It explores the nature of competition among firms and their behaviour in various markets, with the specific emphasis on imperfectly competitive markets. Tools for both empirical and theoretical approaches to the analysis of industries are covered.

Starting from a detailed analysis of market structures, the module goes on to discuss various aspects of firms' behaviour and their influence on market outcome. Among the behaviours covered in the module are price discrimination, vertical integration, advertising, research and development activities and entry and exit of firms. Government regulation of industries is also discussed.

This module is an introduction to international trade theory and policy. It covers the core trade theories under perfect and imperfect competition and applies them to understanding the pattern of trade, gains from trade and modern topics like foreign outsourcing. On the policy side, it examines the effects of different government trade policy instruments and the role of international trade agreements.

This module introduces basic techniques in numerical methods and numerical analysis which can be used to generate approximate solutions to problems that may not be amenable to analysis. Specific topics include:

• Implementing algorithms in Matlab
• Discussion of errors (including rounding errors)
• Iterative methods for nonlinear equations (simple iteration, bisection, Newton, convergence)
• Gaussian elimination, matrix factorisation, and pivoting
• Iterative methods for linear systems, matrix norms, convergence, Jacobi, Gauss-Siedel
• Interpolation (Lagrange polynomials, orthogonal polynomials, splines)
• Numerical differentiation & integration (Difference formulae, Richardson extrapolation, simple and composite quadrature rules)
• Introduction to numerical ODEs (Euler and Runge-Kutta methods, consistency, stability) 

This module provides an introduction to the economics of the labour market. We will look at some basic theories of how labour markets work and examine evidence to see how well these theories explain the facts.

Particular attention will be given to the relationship between the theory, empirical evidence and government policy. The module will refer especially to the UK labour market, but reference will also be made to other developed economies.

In this module you will build on the foundation of knowledge gained from your core year one modules in Analytical and Computational Foundations and Calculus. You will learn to follow a rigorous approach needed to produce concrete proof of your workings.

Groups, rings and fields are abstract structures which underpin many areas of mathematics. For example, addition of integers fits the structure of a group. However, by analysing the general concept of a group, our proofs are relevant to many other areas of mathematics.

You will build on your understanding of Foundations of Pure Mathematics. Together we will develop a deeper knowledge of abstract algebraic structures, particularly groups. This provides the foundation for subsequent modules in abstract algebra and number theory.

Your study will include:

• symmetries
• groups, cyclic groups, Lagrange’s theorem
• rings and fields
• integer arithmetic, Euclid’s algorithm
• polynomial arithmetic, factorisation

This module will address both the fundamental and applied aspects of macroeconomic theory. In particular, the module will focus on:

• introducing the modern theory of expectations and economic dynamics
• using this approach to think about short run fluctuations
• studying the role of macro policy on short run fluctuations

The module will review the so-called modern approach to aggregate demand and aggregate supply. This entails incorporating into the classical approach to aggregate supply and aggregate demand, insights from Keynesian economics. This will serve as a base to discuss the role of macro policy in controlling for fluctuations in output and employment. 

This module covers intermediate microeconomics including general equilibrium analysis; welfare economics; elementary game theory; and strategic behaviour of firms.

This module will provide a foundation for the monetary economics modules in the third year and is a complement to financial economics for the second and third years. It will cover topics such as the definitions and role of money, portfolio choice, financial markets and banks, central banks and monetary policy, and the monetary transmission mechanism. 

Under these headings the module will address issues of theory, policy and practice relating to recent experience in the UK and other countries. The module will feature some current debates and controversies based on recent events.

This module is concerned with the effect of political and institutional factors on economic variables as well as with the study of politics using the techniques of economics.

This module will give you an introduction to the theory of probability and random variables, with particular attention paid to continuous random variables. Fundamental concepts relating to probability will be discussed in detail, including well-known limit theorems and the multivariate normal distribution. You will then progress onto complex topics such as transition matrices, one-dimensional random walks and absorption probabilities.

This module looks at:

• public finances in the UK
• market failures
• fundamental theorems of welfare economics
• social welfare functions
• externalities
• public goods
• natural monopolies
• public choice
• social insurance: social security, taxation and equity
• excess burden of taxation and tax incidence

The first part of this module provides an introduction to statistical concepts and methods and the second part introduces a wide range of techniques used in a variety of quantitative subjects. The key concepts of inference including estimation and hypothesis testing will be described as well as practical data analysis and assessment of model adequacy.

This course aims to give students a sound grounding in the application of both differential and integral calculus to vectors, and to apply vector calculus methods and separation of variables to the solution of partial differential equations. The module is an important pre-requisite for a wide range of other courses in Applied Mathematics.

In this module you will build on your theoretical knowledge of statistical inference by a practical implementation of the generalised linear model. You will move on 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 course provides an introduction to coding theory in particular to error-correcting codes and their uses and applications. It also provides an introduction to to cryptography, including classical mono- and polyalphabetic ciphers as well as modern public key cryptography and digital signatures, their uses and applications.

This module involves the application of probability and statistics to a variety of practical, open-ended problems, typical of those that statisticians encounter in industry and commerce. Specific projects are tackled through workshops and student-led group activities.

The real-life nature of the problems requires students to develop skills in model development and refinement, report writing and teamwork. Students will have an opportunity to apply a variety of statistical methods and knowledge learned in previous modules.

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A graph (in the sense used in Graph Theory) consists of vertices and edges, each edge joining two vertices. Graph Theory has become increasingly important recently through its connections with computer science and its ability to model many practical situations. 

Topics covered in the course include:

• paths and cycles
• the resolution of Euler’s Königsberg Bridge Problem
• Hamiltonian cycles
• trees and forests
• labelled trees,
• the Prüfer correspondence
• planar graphs
• Demoucron et al. algorithm
• Kruskal's algorithm
• the Travelling Salesman's problem
• the statement of the four-colour map theorem
• colourings of vertices
• chromatic polynomial
• colourings of edges.

This module gives an introduction into some basic ideas of functional analysis with an emphasis on Hilbert spaces and operators on them.

Many concepts from linear algebra in finite dimensional vector spaces (e.g. writing a vector in terms of a basis, eigenvalues of a linear map, diagonalisation etc.) have generalisations in the setting of infinite dimensional spaces making this theory a powerful tool with many applications in pure and applied mathematics

In this module the concepts of discrete time Markov chains are explored and used to provide an introduction to probabilistic and stochastic modelling for 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 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.

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, whose purpose is to identify the main modes of variation in a multivariate dataset; modelling and inference for multivariate data, including multivariate regression data, based on the multivariate normal distribution; classification of observation vectors into sub-populations using a training sample; canonical correlation analysis, whose purpose is to identify dependencies between two or more sets of random variables. Further topics to be covered include factor analysis, methods of clustering and 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 course is concerned with the two main theories of statistical inference, namely classical (frequentist) inference and Bayesian inference. 

Topics such as sufficiency, estimating equations, likelihood ratio tests and best-unbiased estimators are explored in detail. There is special emphasis on the exponential family of distributions, which includes many standard distributions such as the normal, Poisson, binomial and gamma.

In Bayesian inference, there are three basic ingredients: a prior distribution, a likelihood and a posterior distribution, which are linked by Bayes' theorem. Inference is based on the posterior distribution, and topics including conjugacy, vague prior knowledge, marginal and predictive inference, decision theory, normal inverse gamma inference, and categorical data are pursued.

Common concepts, such as likelihood and sufficiency, are used to link and contrast the two approaches to inference. You will gain experience of the theory and concepts underlying much contemporary research in statistical inference and methodology.

In this module you 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 and then you will move onto more extensive studies of epidemic models and queuing models with introductions to component and system reliability.

This module will provide a general introduction to the analysis of data that arise sequentially in time. Several commonly-occurring models will be discussed and their properties derived, along with methods for model identification for real-time series data. You will develop techniques for estimating the parameters of a model, assessing its fit and forecasting future values. You will also gain experience of using a statistical package and interpreting its output.

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

For this module you will carry out a major individual research project based on issues and concepts investigated on the course so far as well as your own research interests. Your work will demonstrate your skill for primary research, critical argumentation and understanding of scholarly research. You will also be supported by individual supervision, resources such as film databases, and workshops on research methods throughout the semester.

The below are examples of recent dissertation topics, chosen by students across Film and Television Studies and International Media and Communications Studies:

• The BBC and its evolving position within a changing British society
• Coraline: The issue of fidelity in adaptation
• Barbie and girl power: Commodified feminism and its discourses of traditional femininity
• Social media and the fitness culture: A case study of social dynamics on Instagram
• Farewell Mr Colonizer: Depiction of former European colonial nations in cinema
• Women’s fashion as an expression of essentialist values in the UK

This module is worth 40 credits.

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 cover post-crisis monetary policy; controlling money markets with excess reserves; spill-overs of QE; effects of QE on asset and credit markets; low real equilibrium interest rates; uncertainty in monetary policy.

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