Due to the exciting course changes we have planned for 2022 entry onwards, please check this page again later so that you have the most up to date information.
Two thirds of the first year is devoted to mathematics, with the remainder devoted to financial topics.
Core modules
Analytical and Computational Foundations
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
Business 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)
Calculus
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
Fundamentals of Financial and Management Accounting
This module covers:
- key accounting concepts
- the impact of accounting policy selection
- the recording and collating of accounting information, including double entry bookkeeping
- preparation of financial statement from accounting data
- cost concepts and allocation of manufacturing overheads
- absorption and variable costing
- cost-volume-profit analysis
- relevant costing
- budgeting
Insurance in a Risky World
The module examines how insurance markets operate to satisfy commercial and individual customers' demand for protection against risk, and would usually include:
- introduction to insurance
- private and social insurance
- the historical development of insurance
- why buy property/liability insurance
- why buy life, health and pensions insurance
- the supply of insurance
- Lloyd's and the London Insurance Market
- how is insurance distributed to consumers
- the role of insurance in the economy
- international aspects of insurance
- insurance and catastrophes
Linear Mathematics
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
Probability
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
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
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 Friday 02 September 2022.
You will study a total of 120 credits. 100 credits will be maths modules and the remaining 20 are financial-based modules.
Core modules
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.
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)
Mathematical Analysis
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.
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.
Professional Skills for Mathematicians
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.
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.
Vector Calculus
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.
Optional
You must choose between 20 credits from the following:
Economic Principles
This module introduces you to the microeconomic theory of the market, firm and consumer, and to the nature and scope of the macroeconomic policy agenda, developing the analytical frameworks necessary for the evaluation of policy instruments. The module enables you to understand the economic arguments that underlie different views and to evaluate relevant arguments.
Topics include: market demand, supply and equilibrium; firm production and costs; market structure (perfect competition, oligopoly, monopoly); consumer theory; market failure; asymmetric information; externalities; aggregate demand; money and interest rates; aggregate supply; unemployment and inflation; balance of payments and exchange rates.
This module provides you with the opportunity to apply for CIMA accreditation in the CIMA paper: Fundamentals of Business Economics. It also provides you with the foundations to build upon in quantitative and econometric modules which provides you with the opportunity to apply for additional CIMA accreditation.
Corporate Finance
This module concentrates on the major investment and financing decisions made by managers within a firm.
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
Three-quarters of the year is spent studying more advanced mathematical topics relevant to finance with the remainder being chosen from a range of financial modules.
The compulsory group project allows you to consolidate your mathematical knowledge and understanding whilst gaining experience of working collaboratively to solve complex problems.
Core modules
Mathematical Finance
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.
Vocational Financial Mathematics
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.
Mathematics Group Projects
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.
Optional mathematics modules
You must take 50 credits from the following:
Coding and Cryptography
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.
Game Theory
Game theory contains many branches of mathematics (and computing); the emphasis here is primarily algorithmic. The module 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 mathematical theory of games; exploring the connection between numbers and games, including Sprague-Grundy theory and the reduction of impartial games to Nim.
Optimisation
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.
Scientific Computation and Numerical Analysis
You will learn how to use numerical techniques for determining the approximate solution of ordinary and partial differential equations where a solution cannot be found through analytical methods alone. You will also cover topics in numerical linear algebra, discovering how to solve very large systems of equations and find their eigenvalues and eigenvectors using a computer.
Statistical Inference
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.
Stochastic Models
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.
Time Series Analysis
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.
Optional finance modules
You must take 30 credits from the following:
Financial Economics
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.
Financial Markets: Theory and Computation
This module examines the workings of the major financial markets. Markets for equity and debt are dealt with (money and foreign exchange markets are also the focus) as are markets for derivative instruments. The module covers the key theoretical models of modern finance, key market conventions and mechanisms, financial risk management with derivative instruments.
International Finance
This module discusses and analyses the management of the international finance function of firms. Typical issues include:
- foreign exchange markets
- foreign exchange and other international risks
- international financial markets
- international investment decisions
- foreign trade
Risk, Information and Insurance
This module examines individual decision-making under conditions of risk and uncertainty, and investigates the effectiveness of insurance as a means of controlling risk.
Risk Management Decisions
This module will introduce the different aspects of corporate risk and examine how the risk of fortuitous loss may affect the various stakeholders in the operations of firms.
Risk Management Processes
This module will discuss the processes utilised by corporate enterprises to manage the risk of fortuitous loss. Once corporate risks have been identified and their impact on the firm measured, risk management attempts to control the size and frequency of loss, and to finance those fortuitous losses which do occur.
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