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.

This module provides an introduction to finance and accounting, covering:

• the basic concepts and practicalities of corporate finance
• the principles of valuation
• financial management and business investment
• the role and purpose of company accounts and their usefulness
• security analysis
• risk and returns from investments
• personal finance.

At all times the module content will be linked with financial behaviour in the real world.

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 will provide an understanding of the principles and theories relevant to the process of building investment portfolios. It covers practical applications as well as theoretical material and considers the capital asset pricing model (CAPM), market efficiency, and the estimation and evaluation of fund performance measures. It also considers issues in bond portfolio management and equity trading strategies. 

This module looks at the role of the treasurer in a multinational corporation and the main task of managing risk with respect to funding requirements, foreign exchange, liquidity and banking relationships. Also included is the management of country-specific risks for multi-national firms.

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 cover financial markets, institutions, and instruments, process of financing of a corporate entity and some specialist topics (such as convertibles, real options, mergers and acquisitions international project appraisal) that are relevant for corporate decision making.

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.

The finance dissertation is a long piece of academic writing that investigates in detail a particular finance topic in which you have an interest. You will research your chosen subject by critiquing other researcher’s work, discussing relevant theories and/or methodologies, reviewing literature, collecting data and carrying out your own research on this data, usually involving statistical analysis. Once you have produced your results on your data, you will have to interpret what it all means and write it up in an acceptable academic format.

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 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 explores the stochastic discount factor approach to asset pricing. The stochastic discount factor approach provides a general framework for evaluating issues in asset pricing. The aim of the module is to examine a number of theoretical and empirical issues in asset pricing.

This module will cover theories of capital structure, sources of capital (debt and equity), and corporate payout policy at an advanced level. The starting point for this module will be Modigliani-Miller assumptions introduced in Business Finance, and course material will highlight how the relaxation of these assumptions leads to formal models on corporate financing behaviour under imperfect capital markets. The emphasis will be upon the ideas necessary to analyse the firm’s financing decisions. It discusses financial structure and the alternative mechanisms for distributing corporate wealth to shareholders.

This module covers the main topics in the corporate investment and restructuring literature. It's primarily connected with corporate investment, otherwise referred to as real investment. It examines in more detail the theoretical foundations of the principles of optimal investment behaviour, restructuring and the strategic investment positions adopted by firms in practice. It builds significantly on the mergers and acquisitions theories and evidence and also examines the interface between investment and the financing decisions.

This module aims to develop a deep understanding of the main issues in the theory and practice of corporate investment and restructuring policies, and to develop students' initiative and ability to research the relevant literature. It'll emphasise the role of key concepts in finance in explaining and understanding observed corporate investment and restructuring policies, whilst also highlighting their limitations in this respect. This module is based mainly on academic articles that have influenced and directed the current level of understanding of Corporate Investment Policy. 

This module examines the problems associated with specifying financial models in forms which are amenable to estimation and testing with the available data. Consideration is given to the nature of financial data, the methods by which it's compiled and the problems it may present for applied financial analyst. You will be taught techniques of estimation, together with the methods for solving financial model problems. One coursework includes practical experience of applying the techniques to financial data using the econometric software PcGive.

The first aim of this module is to train you in the financial quantitative techniques used for the estimation and testing of financial models. The second aim is to build on and extend aspects of the models covered in other finance modules in order to provide you with skills required to evaluate advanced applied financial research. Therefore, it is assumed that students taking this module are familiar with basic statistics and simple least-squares methods of estimation.

This module builds on your knowledge of finance and your understanding of finance theory developed through the core modules in years 1 to 3. It will introduce you to behavioural finance and provide you with an understanding of the main flaws of traditional finance theory from a behavioural finance viewpoint. This module will allow you to develop the ability to discuss issues arising from violations of the rationality assumption and to enable you to evaluate new theoretical models based on research in psychology.

This module will allow you to appreciate the role of new developments in finance and their possible implications for established views of financial markets. It will provide you with an understanding of the main ideas of behavioural finance. A particular emphasis is placed on understanding the roles of non-rational actions and the development of new financial models that incorporate these. You will engage with up-to-date research and develop a critical view of existing and new finance theories and models.

This module considers financial issues associated with the operation of a firm in the international environment. It will focus on complications that make corporate financial decision harder for internationally oriented firms than domestic firms, like exchange rates and political risk.

Specifically, it will focus on the following issues:

• exchange rate theories and implications for the multinational company
• management of corporate exchange rates exposure
• the evaluation and incorporation of political risk into project evaluation
• the array of corporate financing possibilities in a global market
• the basic issues in international investment analysis, like capital budgeting and cost of capital determination for foreign projects
• methods for evaluating the performance of foreign operations

While this module presents theoretical points of view on the various issues, it uses both empirical academic evidence and discussion of firms' real-world activities to prepare you for careers dealing with financial issues of international corporate operations both at the banking and corporate level. It studies corporate financial decisions in an international setting.

This module covers advanced material in derivatives pricing. We will cover stochastic calculus and its implication in finance. In addition, numerical methods, such as Monte Carlo simulation, the Binomial tree model, and finite difference methods, will be introduced to price basic options. Finally, this course explores portfolio risk management and real option pricing framework. By the end of this course, you will have a good understanding of how derivative contracts work, how they are used and how they are priced. Students will learn how traditional option pricing framework could be used to analyse real investment projects.