Core modules
Advanced Financial Mathematics
In this module you will cover three major topics: continuous time modelling for equity derivatives pricing, pricing interest rate derivatives and credit risk modelling. These will be underpinned by the theory of stochastic processes and stochastic differential equations.
You will gain experience of a topic of considerable contemporary importance, both in research and in terms of how it is applied. You will undertake a group project which will involve independent reading, computer simulations and a written report.
Computational Applied Mathematics
During this module four major topics for the computational solution of problems in applied mathematics are considered.
- approximation theory
- numerical solution of nonlinear problems
- numerical solution of ODEs
- numerical solution of PDEs.
The focus is on formulating and understanding computational techniques with illustrations on elementary models from a variety of scientific applications. Specific contents include: approximation theory, multivariate polynomial approximation, Gauss quadrature, splines, trigonometric polynomials, DFTs, FFTs; numerical solution of (systems of) nonlinear equations; numerical differentiation and numerical solution of ODEs; introduction to PDEs and finite difference methods including error analysis.
Financial mathematics
This module introduces the main concepts of financial mathematics, such as pricing and hedging of financial instruments (forwards, futures, options, swaps) with a focus on discrete models. You will develop your knowledge of probability and stochastic calculus.
The first part of the course introduces the no-arbitrage pricing principle and financial instruments such as forward and futures contracts, bonds and swaps, and options.
The second part of the course considers the pricing and hedging of options and discrete-time discrete-space stochastic processes.
The final part of the module focuses on the Black-Scholes formula for pricing European options and also introduces the Wiener process, Ito integrals and stochastic differential equations.
Scientific Computing and C++
This module provides an introduction to the programming language C++ with a strong emphasis on scientific computing applications. You will study C++ Language: basic types and control structures, program design and implementation, program comprehension and modification, program testing and documentation; pointers, functions, and reference variables. You will also cover classes, inheritance and derived classes; templates, applications, computer roundoff and its effect on the design of algorithms; polynomial interpolations and numerical integration. You will also gain an understanding of computational linear algebra, including direct and iterative methods.
Financial and Computational Mathematics Dissertation
You will carry out a substantial investigation on a topic in financial mathematics and related subjects. The study will be largely self-directed, with oversight and input provided where necessary by a supervisor from the School of Mathematical Sciences. The topic will be chosen from a list of potential projects provided by the school.
The projects will usually contain three components: a finance-related part; mathematical and/or statistical methods and analysis; element of computing either using existing packages or developing new code to simulate and analyse appropriate mathematical models. The balance of the three components will depend on the nature of a particular project.
A training session covering the oral presentation assessment criteria and some elements of good practice will also be included.
Optional stream 1: Mathematics, Statistics and Computing
Optimization
In this module a variety of techniques and areas of mathematical optimization will be covered. You will study topics such as lagrangian methods for optimization, linear programming including the simplex algorithm, dynamic programming both deterministic control problems and stochastic problems. You will also cover network and graph algorithms.
During the module you will gain a rigorous mathematical background and develop the techniques for application through computational examples.
Statistical Foundations
In this module, the fundamental principles and techniques underlying modern statistical and data analysis will be introduced. You will gain experience in using a statistical package and interpreting its output. The course will cover a 'common core' consisting of:
- statistical concepts and methods
- linear models
- probability techniques
- Markov chains
Statistical Machine Learning
This module is a topic at the interface between statistics and computer science, concerning models that can adapt to, and make predictions based on, data. This module builds on the principles of statistical inference and linear regression to introduce a variety of methods of clustering, dimension reduction, regression and classification.
Much of the focus is on the bias-variance trade-off and on methods to measure and compensate for overfitting. The learning approach is hands-on; you will be using R extensively in studying contemporary statistical machine learning methods, and in applying them to tackle challenging real-world applications.
Time Series and Forecasting
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. Methods for model identification for real-time series data will be considered. Techniques for estimating the parameters of a model, assessing its fit and forecasting future values will be developed. You will gain experience of using a statistical package and interpreting its output.
Optional stream 2A: Econometrics
The focus of this stream is on econometrics. It provides advanced knowledge on mathematical and statistical methods applied in economics and finance. Some modules are taught by the School of Economics.
Econometric Theory
Core techniques of econometric theory, including detailed analysis of the multiple linear regression model; large sample theory; asymptotic testing procedures; non-linear techniques; and mis-specification testing will be covered.
Financial and Macro Econometrics
The module extends the coverage of advanced econometric modelling techniques and considers their application through the study of selected topics in finance and macroeconomics, developing familiarity and critical awareness of empirical research in these areas. You will study techniques for the analysis of stationary ARMA processes, Vector Autoregressions (VARs), linear regression models, linear systems of simultaneous equations, cointegration, long-run structural VARs, forecasting, and models of changing volatility. The selected topics include the econometric analysis of business cycle fluctuations, wage, price and (un)employment determination, portfolio choice and stock market returns.
Game Theory
Game theory contains many branches of mathematics (and computing); the emphasis here is primarily algorithmic. The course 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 the mathematical theory of games; exploring the connection between numbers and games, including Sprague-Grundy theory and the reduction of impartial games to Nim.
Mathematics for Engineering Management
This module examines and classifies various (non-statistical) management and operational research problems and their formulation and techniques for solution.
Techniques introduced and used concentrate on operations research problems such as linear programming (LP), dynamic programming and nonlinear programming problems. You will gain an understanding of graphical solution to simple LP problems along with the use of simplex method for the numerical/computational solution of LP problems.
Time Series Econometrics
The module covers fundamental properties of time series and various classes of stochastic processes. Issues in estimation and forecasting of time series models; concepts of contemporary interest to time series econometricians are also covered.
Optional stream 2B: Microeconomics
The focus of this stream is on microeconomics, with economics and finance modules offered by the School of Economics. They are complemented by modules providing advanced knowledge on mathematical methods offered by the School of Mathematical Sciences.
Economics of Corporate Finance
This module offers you an introduction to the economics of corporate finance. It is designed to provide you with the basic theoretical background in this area that is necessary for any applied work. Emphasis is placed on the analysis of simple models and their applications.
The module covers a variety of topics with substantial time devoted for covering issues directly related to the financial needs of firms, such as capital structure, credit rationing and corporate governance.
The module also examines the role of financial intermediaries analyzing bank failures and, consequently, the scope for banking regulations. The last part of the module looks closely at the relationship between the financial sector and the real economy thus offering the background for any applied work related to the link between financial development and economic fluctuations.
Game Theory
Game theory contains many branches of mathematics (and computing); the emphasis here is primarily algorithmic. The course 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 the mathematical theory of games; exploring the connection between numbers and games, including Sprague-Grundy theory and the reduction of impartial games to Nim.
Mathematics for Engineering Management
This module examines and classifies various (non-statistical) management and operational research problems and their formulation and techniques for solution.
Techniques introduced and used concentrate on operations research problems such as linear programming (LP), dynamic programming and nonlinear programming problems. You will gain an understanding of graphical solution to simple LP problems along with the use of simplex method for the numerical/computational solution of LP problems.
Microeconomics: Consumer and Firm Behaviour
This module covers foundations of consumer theory, decision-making under risk, elements of the theory of imperfect competition, and incomplete information in markets.
Macroeconomics: Economic Cycles, Frictions and Policy
The module lays the foundations of macroeconomic models with the use of very stylized one and two-period models in which consumers, firms and governments interact in the goods and factor markets. You will also study the determinants of long-run economic growth. The overarching question that we will consider is: why are some countries so much richer than others?
We will study several mechanisms that can potentially account for these differences, namely, capital accumulation, knowledge production and institutions. Finally, we will embed the consumption and labour supply decision studied at the beginning of the semester into a dynamic stochastic general equilibrium model of the macroeconomy. The standard real business cycle (RBC) model developed by Kydland and Prescott will be considered alongside the investment decision of firms, and you will spend some time studying the search and matching model of unemployment of Mortensen and Pissarides.
Monetary Theory and Practice
This module covers monetary aspects of advanced macroeconomics. It focuses on the theory and practice of central banking, monetary policy and control. It covers concepts such as time inconsistency, the problem of inflation bias with solutions, credibility, transparency and accountability of monetary institutions. You will also cover inflation targeting and price stability, the choice of instruments for monetary policy and their control, and finally monetary transmission. You will combine some theory with evidence and practice. Students that take this module typically aim to work in central banks, financial institutions or government.
Optional stream 2C: Big data economics
This stream is focused towards the growth in big data and being able to interpret the outputs from an economic perspective. Some modules are taught by the School of Economics.
Big Data Economics
This module will focus on advanced Big Data methods and their applications in various economics problems. Topics of the module include:
- nonlinear models
- tree-based models
- support vector machines
- unsupervised learning and applications in international trade
- household finance
- macro forecasting
- labor economics
- text analysis
Game Theory
Game theory contains many branches of mathematics (and computing); the emphasis here is primarily algorithmic. The course 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 the mathematical theory of games; exploring the connection between numbers and games, including Sprague-Grundy theory and the reduction of impartial games to Nim.
Machine Learning for Economics
This module is intended as an introduction of the methodology and implementation of machine learning methods used widely in economic analysis; the module provides an introduction to the analysis of large datasets, with more up to date Big Data methods introduced later as natural developments. Topics will include:
- an introduction to statistical computing
- generating random variables and random processes
- Monte Carlo integration and variance reduction; high performance computing
- multivariate linear regression
- classification
- resampling methods
- linear model selection and regularization
Mathematics for Engineering Management
This module examines and classifies various (non-statistical) management and operational research problems and their formulation and techniques for solution.
Techniques introduced and used concentrate on operations research problems such as linear programming (LP), dynamic programming and nonlinear programming problems. You will gain an understanding of graphical solution to simple LP problems along with the use of simplex method for the numerical/computational solution of LP problems.
The above is a sample of the typical modules we offer but is not intended to be construed and/or relied upon as a definitive list of the modules that will be available in any given year. Modules (including methods of assessment) may change or be updated, or modules may be cancelled, over the duration of the course due to a number of reasons such as curriculum developments or staffing changes. Please refer to the
module catalogue for information on available modules. This content was last updated on Monday 28 November 2022.