Your time in the second year is equally split between mathematics and economics. In both subjects there is a wide range of modules to choose from.
You can specialise in different areas of maths with economics. In total you must take 60 credits of mathematics and 60 credits of economics. This specialisation allows you to focus on areas that interest you and which may be relevant for a future career perhaps in finance or data analytics.
Subject to your interests, you can tailor your stream with the following module choice combinations.
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
Differential Equations and Fourier Analysis
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.
Econometric Theory I
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.
Econometric Theory II
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.
Environmental and Resource Economics
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?
Experimental and Behavioural Economics
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.
Foundations of Pure Mathematics
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.
Introduction to Scientific Computation
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:
- 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.
Probability Models and Methods
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.
Public Sector Economics
This module looks at:
- public finances in the UK
- market failures
- fundamental theorems of welfare economics
- social welfare functions
- public goods
- natural monopolies
- public choice
- social insurance: social security, taxation and equity
- excess burden of taxation and tax incidence
Statistical Models and Methods
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.