Financial Mathematics BSc

This core module is designed to consolidate A-level material and explore topics in mathematics that you'll use throughout your degree. You'll also be introduced to core skills, such as mathematical literacy, communication and problem-solving.  

Throughout this module you'll develop a strong foundation in core mathematics. You'll consider techniques for solving equations, special functions, calculus, vectors, complex numbers, and finite and infinite series.

This core module is designed to further develop your knowledge of the core mathematics you'll use across your degree.

You'll learn about two-dimensional coordinate geometry, discussing the theory of matrices geometrically and algebraically. You'll also define and evaluate derivatives and integrals for functions that depend on more than one variable, with an emphasis on functions of two variables.

Throughout this module you'll continue to develop your employability skills, exploring the career options open to mathematics graduates. You'll also work with your coursemates to undertake a group project on sustainability.

Probability theory is branch of mathematics concerned with the study of chance phenomena. Data science involves the handling and analysis of data using a variety of tools: statistical inference, machine learning, and graphical methods. The first part of the module introduces probability theory, providing a foundation for further probability and statistics modules, and for the statistical inference methods taught here. Examples are presented from diverse areas, and case studies involving a variety of real data sets are discussed. Data science tools are implemented using the statistical computing language R.

This module collects together a number of the most useful topics for future modules in financial mathematics. The first semester will cover some computing, using Python to write simple programmes and LaTeX to write mathematical documents.  The second semester is given to analysis, a branch of pure mathematics with applications in financial mathematics.  The two semesters are independent of each other.

This module introduces you to the fundamental principles of microeconomic theory, focusing on the behaviour and decision-making processes of individuals, households, and firms. You will gain a solid understanding of key microeconomic concepts, such as choice theory, market structures, consumer behavior, and firm decision-making. The module explores the practical application of microeconomic analysis to contemporary policy issues. This module provides you with the foundations in microeconomics required for advanced study.

This module introduces you to the foundations of macroeconomic theory and analysis. You will explore how economies operate at the aggregate level and develop the analytical tools needed to understand key economic indicators such as interest rates, national output, inflation, unemployment, and exchange rates. A central focus will be on understanding how these variables interact and influence one another over the short and long run. Through real-world examples and policy applications, you will learn how macroeconomic analysis informs and shapes economic decision-making and policy evaluation in both national and global contexts. Topics covered will include the determination of output and employment and the role of fiscal and monetary policy. By the end of this module, you will be equipped to evaluate the effectiveness of monetary and fiscal policies and understand the complex dynamics shaping economic outcomes in national and global contexts.

In this module, you will develop a solid foundation in financial management, equipping you with the knowledge and analytical skills needed to make informed financial decisions. You will explore key principles, theories, and techniques used in the field, and learn how to apply them through relevant calculations and real-world scenarios. You will also examine contemporary issues and developments in the financial markets, helping you understand the broader context in which financial decisions are made. This module is designed to prepare you for more advanced study in years 2 and 3 and is aligned with the foundation-level content of professional accounting qualifications.

This module introduces you to the core techniques of Management Accounting, with a focus on its application in business decision-making, financial planning, and performance evaluation. You will develop an understanding of key concepts such as cost classification, budgeting, costing methods, and capital investment appraisal. The module highlights the role of the management accountant in providing valuable insights through cost analysis, supporting both short- and long-term decisions, and enhancing organisational performance through behavioral and responsibility accounting. Additionally, you will explore the integration of management accounting with social, environmental and sustainability indicators, and their impact on both financial and non-financial outcomes, ensuring that future decisions align with sustainable business practices.

Linear algebra and calculus are fundamental to most advanced work in pure and applied mathematics and to much of statistics.

This module will provide you with basic tools and techniques from linear algebra and calculus. You'll also develop an understanding of the theory underpinning these, enabling you to use these methods in a variety of situations beyond the module.

Building on your first year, you'll also continue to develop employability skills throughout this module.

This module will develop your understanding of theory covered in first year modules. 

You'll explore analysis, which underpins core concepts across the mathematical sciences.  You'll examine why familiar tools, like differentiation and integration, actually work, allowing us to prove their formal properties. This rigorous foundation in analysis will enable you to tackle more complex problems in the future.

You'll extend your understanding of ideas from calculus to higher dimensions, considering differentiation of functions of many variables as linear transformations.

You'll also have opportunities to reflect on social, ethical, and historical aspects of mathematics, enriching your understanding of the importance of mathematics in the modern world.

Statistical inference and modelling are at the heart of data science, a field of rapidly-growing importance in the modern word.  This module develops methods for analysing data, and provides a foundation for further study of probability and statistics at higher Levels.  You will learn about a range of standard probability distributions beyond those met at Level 1, including multivariate distributions. You will learn about sampling theory and summary statistics, and their relation to data analysis. You will discover how to parametrise various types of statistical model, learn techniques for determining whether one model is 'better' than another for understanding a dataset, and learn how to ascertain how good a statistical model is at explaining trends in data. The software package R will be used throughout.

This module examines stochastic processes. These are models of natural and physical processes that incorporate randomness, to reflect the way that life can change unpredictably over time. 

You'll explore a number of general models for processes where the state of a system is fluctuating randomly. This might include the length of a queue, the size of a reproducing population, or the amount of payouts on insurance policies. 

You'll learn various techniques for the analysis of these models, preparing you for further study of stochastic processes and probability in later years.

This module is designed to give you an introduction into the econometric skills you will need for a successful career in applied economic research. Throughout this module, you will build a strong foundation in interpreting econometric outputs, crucial for understanding academic literature and policy reports. You will learn fundamental theoretical knowledge, such as ordinary least squares, supported by economic intuition and mathematical reasoning. You will learn statistical software, gaining an understanding of reproducible coding, in order to develop and apply such skills to answer economic research questions by analysing real-world data using appropriate statistical and econometric techniques. This process will also introduce you to ethical research practices. This module will train you in the core competencies you need to perform rigorous econometric and economic research.

This module builds on Level 1 modules in microeconomics and mathematical economics, using the mathematical training to allow a more rigorous investigation of the principles of microeconomics. It aims to develop an understanding and ability to undertake economic analysis of models of the behaviour and interaction of economic agents (consumers, firms and government) in a market economy, the functioning of different types of industries, decision making under uncertainty and economic welfare.

The aims of this course are to provide firm grounding in the analytical tools of modern macroeconomics; to use these tools to understand critically the conduct of economic policy nationally and internationally. The course builds on level 1 modules in macroeconomics. The main subject areas covered are: Basic macroeconomic models: consumption/leisure choice, closed economy one period-macro models, models of search and unemployment; Savings, investment and government deficits: consumption/savings choice (two-period model), credit market imperfections, real intertemporal model with investment; Money and business cycles: flexible price models, New Keynesian economics (sticky prices), inflation; International macroeconomics: international trade, money in open economy; Economic growth: Malthus and Solow growth models, convergence, endogenous growth model.

This module aims to provide knowledge and understanding of key management issues in corporate finance with a focus on a broad range of issues including corporate investment and the financing of such investments. Students will critically assess various analytical techniques in relation to specific corporate finance applications and develop a knowledge of key board-level considerations.

The function of financial management is the acquisition and use of funds for investment purposes. Thus, this unit focuses on ways of raising and deploying investment finance, the institutions involved, and the tools and techniques that are used when making financial decisions. Financial decisions are not isolated from the rest of society, so the module also considers perspectives on the relationship between finance and society and the prospective impact of financial decisions on other parties.

This advanced module is designed for students seeking to specialise in finance. You will build upon foundational principles of financial management to develop a rigorous understanding of the theories and practices central to modern corporate finance. You will gain a robust foundation for subsequent advanced study and develop the ability to analyse the complex financial landscape in which firms operate, with particular emphasis on digital tools and strategic decision-making. You will focus on firm-level financial decision-making and its strategic impact. You will examine advanced theories and analytical techniques related to company valuation, investment appraisal, and the determination of optimal capital structure and dividend policy. In addition, you will investigate the impact of contemporary issues, such as asymmetric information, on firm strategy and valuation. Digitalisation and practical application are central to your learning experience. You will develop proficiency in industry-standard digital tools, including MS Excel for financial modelling and analysis, PowerPoint for the professional presentation of financial insights, and the Bloomberg Terminal for financial data extraction and market intelligence. Through hands-on engagement with these platforms, you will learn to translate complex theoretical models into actionable financial insights using real-world data and real-life case studies. Strong emphasis is placed on applying theoretical frameworks to address practical financial problems. Through the analysis of contemporary case studies and business scenarios in collaborative group settings, you will develop key capabilities in financial modelling, data-driven decision-making, and professional communication. This applied approach, combined with the development of digital literacy, will strengthen the essential competencies required for a career in finance, including rigorous analytical reasoning, strategic thinking, proficiency with financial technology platforms, and the effective communication of complex financial information to diverse stakeholders.

Through this module you'll hone the skills and knowledge required of a graduate-level professional.

You'll undertake extended project work, which will include relating project work to the literature, setting project aims and objectives, planning and carrying out the work, and reporting it using disciplinary conventions.

You'll investigate how your academic studies relate to either research, society, or industry. You'll develop an understanding of where your degree could lead you and reflect on your career ambitions.You'll also undertake activities to develop the professional skills needed to complete applications for employment or further study.

This module covers statistical ideas that are important in medicine and the actuarial sector. 

You'll learn about the design and statistical analysis of clinical trials used to license new drugs. These trials have their own distinct methodology, due to ethical and regulatory constraints involved in experimentation on human subjects.

You'll develop an understanding of survival analysis, which involves analysing 'time-to-event' data. An example of this could include how long an individual lives and the factors that may increase or decrease life expectancy.

You'll also explore statistical methods with actuarial applications, such as extreme value theory (EVT), which considers the likelihood and magnitude of rare events.

Throughout the module you'll implement statistical methodologies using packages in the programming language R.

A stochastic process is a mathematical model for phenomena unfolding dynamically and unpredictably over time. This module studies two classes of stochastic process particularly relevant to financial phenomena: martingales and diffusions. The module develops the properties of these processes and then explores their use in Finance. A key problem considered is that of the pricing of a financial derivative such as an option giving the right to buy or sell a stock at a particular price at a future time. What is such an option worth now? Martingales and stochastic integration are shown to give powerful solutions to such questions.

In this module you will further your understanding of core microeconomic principles by exploring a number of advanced topics in microeconomics. The course material you will encounter will be predominately theoretical with a substantial mathematical component and some evaluation of empirical evidence. Indicative topics include: auctions; decision making under uncertainty; dynamic efficiency; imperfect competition and common ownership; matching and assignment.

It is essential for you as an economist to understand and be able to apply econometric techniques because it will allow you to rigorously analyse data to test economic theories, measure real-world effects, and produce credible evidence to inform decisions and policy. In this module you will study a number of advanced topics in econometrics. In the first half of the module you will learn how to implement recent developments in time series econometrics. In the second half of the module you will learn how to model microeconometric outcomes using cross-section and panel data techniques. The module will have a strong practical element and you will learn how to use relevant econometric computer packages. This module will be particularly useful if you are interested in how to test economic theories and/or model economic behaviour. 

In this module you will explore modern macroeconomic theory and its application to key economic challenges facing policymakers and society. The module is framed within the dynamic general equilibrium (DGE) tradition that underpins much contemporary research and policy analysis, providing a coherent framework for understanding aggregate behaviour and policy design.

You will begin by building a benchmark DGE model, using it to learn how such models are constructed, solved, and interpreted. You will then extend this framework to study issues such as macroeconomic uncertainty, pandemics and policy responses, ageing and pension sustainability, inequality and redistribution, secular stagnation, unconventional monetary policy, and the government expenditure multiplier.

By the end of the module, you will will be able to analyse macroeconomic policy debates using modern theoretical tools and communicate policy-relevant insights.

This module introduces the core principles of finance and develops your ability to apply them in both corporate and investment contexts. Using an analytical approach, with key ideas developed from foundational principles, it examines risk and return, portfolio theory, the Capital Asset Pricing Model, and the associated empirical evidence. It also explores corporate financing decisions, especially capital structure, leverage, firm value, and financial risk. Further topics include market efficiency, behavioural finance, and the use of derivatives in risk management. By engaging with readings, quizzes, and class discussion, you will build both conceptual understanding and the ability to evaluate the applications and limitations of financial theories, with emphasis on critically evaluating competing views on asset pricing, investors' behaviour, and financial decision-making.

This advanced-level module provides a rigorous and comprehensive foundation in modern corporate finance and asset pricing theory. It explores a range of sophisticated topics central to financial decision-making within firms and the functioning of capital markets. Key themes include debt and equity financing, financing and investment decisions under asymmetric information, managerial incentives and executive compensation, mergers and acquisitions, and the interplay between market efficiency and behavioural biases. In addition to these core areas, the module examines the pricing and strategic use of financial derivatives, such as forward and futures contracts, options, warrants, and convertible securities in corporate settings. You will engage with both classical theories and contemporary empirical debates, cultivating the analytical and critical thinking skills required to assess complex corporate financial decisions and navigate dynamic financial environments.

This module introduces the core principles of finance and develops your ability to apply them in both corporate and investment contexts. Using an analytical approach, with key ideas developed from foundational principles, it examines risk and return, portfolio theory, the Capital Asset Pricing Model, and the associated empirical evidence. It also explores corporate financing decisions, especially capital structure, leverage, firm value, and financial risk. Further topics include market efficiency, behavioural finance, and the use of derivatives in risk management. By engaging with readings, quizzes, and class discussion, you will build both conceptual understanding and the ability to evaluate the applications and limitations of financial theories, with emphasis on critically evaluating competing views on asset pricing, investors' behaviour, and financial decision-making.

Over the last thirty years, the worldwide derivatives market has grown enormously in size and importance. This growth is due in part to the long-term consequences of the now famous option pricing formula developed by Black, Scholes and Merton and published in 1973 and the increase in the volatility of many financial instruments over the last 30 years. Futures and options, which are both derivative securities, are increasingly used by many participants in financial markets. This includes bankers, fund managers, security and currency traders in the world's major financial centres, but also increasingly extends to the finance departments of public and private sector organizations. This module aims to provide an introduction to the pricing and use of some of the basic types of derivative securities. Reflecting the subject, the module is analytical in nature. All concepts are taught from first principles. The course is self-contained to a large extent and includes lectures on the underlying financial economics as well as necessary mathematics and statistics.

This module will develop your understanding of the Bayesian approach to statistical inference, which is fundamentally different to the approach taken in earlier statistics modules.

The Bayesian method is more general and more powerful. While widely used, it relies on modern computers for much of its implementation.  It's based on the idea that if we take a (random) statistical model, and condition this model on the event that it generated the data that we actually observed, then we will obtain a better model.

Through this module, you'll explore the foundations of Bayesian statistics and the incorporation of prior beliefs. You'll study the computational tools important in modern applied statistics, including those important for Bayesian inference such as Markov Chain Monte Carlo. You'll also learn to implement computational methods using R and Python.

This module introduces two important areas of modern statistics.

Time series are observations made in time, for which the time aspect is potentially important for understanding and use. You'll be introduced to modern methods of time series analysis and forecasting, as applied in economics and finance, environmental sciences, medical and social sciences. You'll gain practical techniques for data analysis and a firm basis for practical modelling.

Generalised linear models extend linear models, such as regression-type models, in order to accommodate non-normal (non-Gaussian) observations. Through this module, you'll be introduced to generalised linear models and explore inference, including model building and goodness of fit. 

You'll also learn to implement computational methods using a programming language such as R.

In this module, you'll study two topics in operations research, which involve developing strategies to make decisions about the optimal ways to respond to certain situations. 

You'll explore game theory, learning about optimal responses to competitive situations.

You'll also study optimisation, by finding and analysing optimal solutions to certain kinds of mathematical problems.

Through this module, you'll develop an understanding of strategies with far-reaching applications, from engineering and computing to economics and business management.

This module provides a practical toolkit for modelling and understanding complex datasets by integrating modern AI tools. 

Bridging computer science, statistics, and physics, you'll learn to implement industry-standard algorithms, from linear models to deep neural networks, using Python and modern libraries like Keras and scikit-learn.

You'll not only learn to code, but also effectively co-pilot with AI agents for debugging and code generation, preparing you for the future of technical work.

We'll focus on intuition and implementation. You'll learn to understand when to use a method, how to implement it, and why it works, enabling you to solve real-world problems in science, finance, and business.