Financial Mathematics 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

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

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

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

This module provides an introduction to the fundamental concepts of finance and will help you:

• understand that there is a relationship between the risk of an investment and the expected returns
• understand the concept of the time value of money and be able to calculate the present value of a single and multiple future cash flows
• to be able to apply NPV to project appraisal in realistic situations
• understand the fundamental ideas or portfolio theory and be able to apply the CAPM
• to be able to estimate cost of capital for equity (CAPM and dividend growth model) and bonds (market value and IRR)

Introducing you to the nature and purpose of financial accounting, you’ll study key accounting concepts, the impact of accounting policy selection, accounting standards and the recording and collating of accounting information. Accounting reports, eg income statements, balance sheets and cash flow statements will be developed from accounting data and you’ll gain an understanding of some contemporary accounting issues.

This module introduces:

• cost concepts and allocation of manufacturing overheads
• absorption and variable costing
• cost-volume-profit analysis
• relevant costing
• budgeting 

This module introduces you to the microeconomic theory of the market and the firm. Topics covered include:

• market demand
• supply and equilibrium
• firm production and costs
• market structure
• perfect competition
• monopolistic competition
• oligopoly and monopoly

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) 

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.

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 will equip you with valuable skills needed for graduate employment. You will work on two group projects based on open-ended mathematical topics agreed by your group. You will also work independently to improve your communication skills and learn how to summarise technical mathematical data for a general audience. You will be provided with some commercial and business awareness and explore how to use your mathematical sciences degree for your future career.

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.

The module provides you with a knowledge and understanding of key practical applications of finance using standard computer software. Students taking the module are assumed to have prior background knowledge of financial markets and financial econometrics.

It equips you with computational and programming skills, allowing you to analyse financial data, build financial models and solve complex financial problems. The module will also integrate application areas in finance which have already been introduced, or which are being introduced concurrently. Topics include:

• Basic R commands
• analysing and visualising financial data
• modelling and forecasting financial time-series
• applications relevant to asset pricing and portfolio analysis

The module will introduce you to the corporate investment and financing decision as well as the interaction between the investment and financing decision.

The module addresses the application of financial reporting principles in preparing financial statements in accordance with International Financial Reporting Standards, for a range of transactions and economic events.

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.

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 involves the application of mathematics to a variety of practical, open-ended problems, typical of those that mathematicians encounter in the financial industry. You will examine specific projects through workshops and student-led group activities. The real-life nature of the problems enables you to develop skills in model development and refinement, report writing and teamwork. 

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.

In this module you will explore two main concepts of statistical inference; classical (frequentist) and Bayesian. Topics such as sufficiency, estimating equations, likelihood ratio tests and best-unbiased estimators will be discussed in detail. You will gain knowledge of the theory and concepts underpinning contemporary research in statistical inference and methodology.

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 concentrates on the major investment and financing decisions made by managers within a firm.

This module uses a combination of lectures and group work to develop your understanding of financial reporting, the links between strategic and financial management, and the ways in which the stock market responds to financial information. The module involves detailed study and critical analysis of the financial strategy and performance of a major UK quoted company. 

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.

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.