Mathematics with Finance BSc (Hons)

Many optimisation problems in business and industry can be expressed in the form of a linear programming problem and this is even more apparent with increasing reliance on Artificial Intelligence and Machine Learning.  Businesses and industry use linear programming to determine what to make in order to maximise their profits, Amazon use it to schedule your parcels for delivery and it is also used widely in Game Theory: you can use it to beat your friends at rock-paper-scissors and other games!

In this module, we will study the theoretical background behind the linear programming methods, learn how to express real-world questions as linear programming problems and solve them by hand and using computer programs.  We will also explore some other optimisation methods used in AI and Machine Learning. Topics may include:

• Canonical forms of linear programming problems.
• Theoretical considerations: relevant results from set theory and geometry.
• Integer linear programming.
• Solutions of linear programming models: Simplex and dual simplex methods, Pivot algorithm, and computer-based techniques.
• Degeneracy, cycling, duality.
• Use of a mathematical computer software package, for example, Python, Matlab, Excel etc.
• Application to logistics in transportation and assignment problems, VAM and the Hungarian algorithm.
• Game theory: zero-sum matrix games, multi-phase games.
• Non-linear optimisation techniques in Machine Learning

Stochastic processes serve as essential mathematical models for systems and phenomena exhibiting apparent randomness. Examples encompass diverse scenarios, such as the growth of a bacterial population, fluctuations in electrical current due to thermal noise, or the motion of gas molecules. The applications of stochastic processes span various disciplines, including biology, chemistry, ecology, neuroscience, physics, image processing, signal processing, and financial markets. In order to understand such random behaviour, we introduce and study Markov chains, random walks, Brownian motion and stochastic differential equations. Through these topics, students will not only establish a robust foundation in the principles of stochastic processes but will also gain valuable insights into their diverse applications across numerous domains. The module's goal is to equip students with analytical tools essential for comprehending and modelling complex uncertainties, thereby enhancing their capacity to address real-world challenges in mathematics, statistics, and related fields.

Topics covered include:

• Brief review of Probability Theory via a Measure Theory approach.
• Martingales: Basic definitions, filtrations, stopping times.
• Doob's Martingale inequalities and Convergence Theorem.
• Markov Chains.
• Moment generating functions.
• Characteristic functions.
• Probability generating functions.

The intention of this module is to equip you with the key digital skills required to enhance the understanding of key concepts covered on this course. There will be special emphasis on the operationalisation of the concepts at the work environment, that is, how can technology be used to efficiently implement and enhance the level of productivity of the organisation. The operationalisation agenda required to be actioned from the perspective of the finance manager in using key technologies will the direction of the module. The expectation is that you will develop a broad and holistic understanding of the finance functions in the digital world. You will familiarise yourself with how technologies links various operations of the business activities of an organisation to enhance its value creation.
The module will also cover sustainability concepts and data ethics, focusing on responsible data use, regulatory protections, and ethical impacts of technology in finance. Through these areas, you will gain a broad and practical understanding of how digital tools, sustainability, and ethical thinking combine to enhance value creation in modern finance.

To achieve the intentions of the module, the following indicative contents will covered:

• Data analytics (sources of data, descriptive analytics, predictive analytics and prescriptive analytics)
• Data visualisation techniques.
• Accounting software and information systems.
• Artificial intelligence and automation.
• Emerging technologies within accounting and finance
• Cybersecurity within accounting, finance and banking
• Ms Excel for accounting and finance (Analysis ToolPak and Solver, Pivot Tables-including Power Pivot and Power Query, logical functions - lookups, text functions and financial maths with Ms Excel)
• Decision trees and experimentation
• Sustainability and UN SDGs
• Three pillars of sustainability 
• Regulation and organisational roles in sustainability 
• Data ethics and responsible technology use

The coverage of the above contents will provide a certain degree of mastery in the handling of technologies you require to become a competitive graduate. The value associated with the use of technology to implement key concepts within the accounting, finance and banking courses is immeasurable. For example, the provision of an experiential learning environment will enhance your employability skills thus making you a competitive graduate. 

This module aims to gain understating of credit risk and sustainability in the banking context. It includes understanding of financial difficulties for customers and clients leading to collections and recoveries and losses, and demonstrates the importance of policies and procedures and the PRA requirements on capital adequacy and liquidity for banks. It also covers the growing importance of the societal purpose and practices of sustainability in the banking industry including description of how the types of sustainability today change the way we operate in banking and identifying the key performances indicators in banking that reflect sustainability.

Students will be able to achieve the following learning outcomes by the end of this module:-

1. Understand how credit arrears are formed and the wider impact on the profit and loss account
2. Critically evaluate the regulatory framework within the banking sector and understand how losses, capital adequacy and liquidity have been determined to ensure compliance with PRA regulations.
3. Understand the importance of sustainability in banking including culture, conduct and ethics. 
4. Analyse the relationships between businesses and stakeholders with regards to sustainable practice
5. Interpret the principles and types of sustainability and assess how sustainability is measured within banking organisations.

Indictive contents:-

• Financial analysis of credit losses.
• Understanding arrears and losses.
• Collections and recoveries practices.
• Policies and procedures.
• Financial conduct authority policies and regulations in banking and finance including PRA, capital adequacy and stress testing.
• Why sustainable finance, ethics and conduct are important in banking.
• Business and its stakeholders.
• Principles of sustainability.
• The types of sustainability (human, social, economic, environmental).
• Finance practices and KPIs reflecting sustainability.
• Industry case studies.

This module provides a structured, university-level work placement for 4, 5 or 7 weeks (optional timeframe decided on a 1 2 1 basis) as one continuous block / period with a placement provider (i.e. industry apprioprate sector). It is designed to enhance your professional skills in a real-world job setting.

The placement can either be organised by you or with support from university staff.

All work placements within this module must be university-level; this means:

• Undertaking high-skilled work commensurate with level 5 study (e.g. report writing, attending meetings, delivering presentations, producing spreadsheets, writing content on webpages, social media, marketing services/products etc)
• Physically placed (albeit part of it can be hybrid) within an employer setting in one continuous block / period for 4, 5 or 7 weeks for a minimum of 140-147 hours over the course of the entire work placement

Where applicable, your existing part-time employer can be approached/used as the placement provider, if the high-skilled work.

• criterion above is fulfilled for the full duration of the placement.
• All quality assurances/agreements provided by the University are adhered to, by you and the employer.

The work placement context may not necessarily, reflect your degree discipline per se, but rather, it will give you an enriched experience to enhance your professional skills in a real-world job setting.

This is an experiential learning opportunity that incorporates 35 teaching contact hours/lectures to prepare for the 150 contract hours. L5 students can use all their skills learned to date on an actual real-world (external business) client-driven project, working in teams and producing an artefact. 

You are also expected to undertake around 215 hours of self-study.

This module not only gives them enhanced skills but the opportunity to work for a real client thus giving them a valuable CV and LInkedIn entry as work experience that can contribute to their employability portfolio. 

You will collaborate in teams and produce full client documentation alongside a reflection of their expereince and this all give some much needed contemplation of their skills to date and how to use them. 

The module will provide the opportunity to further develop your language skills, building on your previous learning at advanced level. The second half of the module includes a placement abroad or, alternatively, a project on a sustainability issue in a target language country. The first half of the module will prepare you for placements abroad where appropriate as well as a deeper understanding of sustainability in target language contexts. Students of more than one language may take one language in the first half of the module and spend their time abroad developing a different language. 

The module will provide the opportunity to further develop your language skills, building on your previous learning at intermediate level. The first half of the module includes intensive taught sessions in interactive workshop mode which will prepare you for placements abroad or self-directed language development. The second half of the module includes an placement abroad or, alternatively, a project on a business or tourism issue in a target language country. Students of more than one language may take one language in the first half of the module and spend their time abroad developing a different language. 

The module will provide the opportunity to further develop your language skills, building on your previous learning at beginner level. The first half of the module includes intensive taught sessions in interactive workshop mode which will prepare you for placements abroad or self-directed language development. The second half of the module includes a placement abroad or, alternatively, a project on a cultural issue in a target language country. Students of more than one language may take one language in the first half of the module and spend their time abroad developing a different language. 

• The multiple facets of global citizenship
• Ethical engagement and practice
• The United Nations Sustainable Development Goals
• Cross-cultural issues and sensitivity
• Intercultural communication
• Culture shock
• Cultural adjustment
• Self- assessment of needs: identification of the range of transferable skills, competencies and attitudes employees need and employers expect graduates to possess-with a strong focus on understanding the intercultural competencies (ICC) needed to live and work abroad.
• Critical analysis/evaluation of individual requirements in relation to culture/cultural adjustment/culture shock/visas/medical.
• Critical analysis/evaluation of skills already acquired in relation to key skills related to ICC.
• Devising strategies to improve one’s own prospects of working abroad in the future.
• Devising an action plan to address gaps in transferable skills based on organisational analysis and sector opportunities.

Part A:      

Preparation for Experiential Overseas Learning will take place at the University of Chester during level 5 and will include:  

• The multiple facets of Global citizenship
• Ethical engagement and practice
• Cross-cultural issues and sensitivity
• Intercultural communication

Theories, models and strategies of learning

• Theories and models Intercultural competence
• Theories and models of Integration and Multiculturalism
• Critical thinking skills and models of Reflection

• Experiential learning models
• Self-directed experiential learning

Personal and placement-related skills

• Enhanced independence
• Improved command of multicultural behaviour
• Increased knowledge and confidence in their individual facets of personal identity
• Effective time management and organisational skills
• Project management – working away from University and independent study
• Self-management and personal development
• Team building and team work

Part B:            Overseas

Students will engage in experiential learning activities overseas for at least 150 hours 

Year in Industry placement year for computing students. 

This is a placement module where students acquire a 1 year paid work placement related to their area of study.

Full attendance at the work placement and University-scheduled events is mandatory.

The placement hours stated for this module are only the minimum required hours for this module, it is likely most placements will last for 9 months - 12 months and exceed the minimum 1,180 placements hours.

The traditional academic programme structure is not applicable. The placement content is freely structured and determined by negotiation between the student, placement supervisor and host organisation. It is generally informed by the aims and learning outcomes and by the objective of optimising added value for both the host organisation and the student experience

Preparation for the year abroad will take place in Chester during level 5 and will include:

• Cross-cultural issues and sensitivity
• Host-country orientation, study methods– economic, political and social reality of the country
• Orientation specific to exchange – health, education, gender issues
• The United Nations Sustainable Development Goals
• Practical matters relating to living and studying in the wider world

Theories, models and strategies of learning

• Critical thinking skills, experiential learning and models of reflection

Personal and placement-related transversal skills

• Effective self-motivation and independent resourcefulness
• Effective time management and organisational skills
• Project management – working away from University and independent study
• Self-management and personal development

Whilst abroad:

You will undertake study at one of the University of Chester's partner universities or undertake and approved work placement or virtual placement. If you are a student,  it is expected that you will choose a series of modules at the university abroad which must be agreed by the host institution and the Module Leader. you must supply details of you modules on a learning agreement within 4 weeks of arrival at the host university.

Quality Control is an important application of statistical theory and methods. Since the industrial revolution, factories have needed to find ways to manufacture high quality products while minimising cost to maintain a competitive edge. From monitoring an automotive production line to stop out-of-control processes, to sampling techniques in the food production industries designed to minimise food waste, quality control procedures form a key part of the modern manufacturing process.

In this module you will learn the techniques companies employ to achieve the above. Topics for this module may include:

• Introduction to quality control: summary of relevant probability theory and probability distributions.
• Methods and philosophy of statistical process control.
• Control charts for variables: mean, median and range charts, special charts.
• Control charts for attributes: p-charts, np-charts, u-charts, c-charts.
• Process capability studies.
• Acceptance control charts.
• Acceptance sampling: single, double, and sequential sampling plans, rectifying inspections.
• Modified control limits.
• Cumulative sum techniques: CUSUM Charts, V-Masks, Tabular CUSUM.

Numerical analysis is the exploration of algorithms that rely on numerical approximation; this is invaluable for the study of many complicated problems, where an exact solution is very difficult, or even impossible to obtain.  Its applications extend across mathematics, physical sciences and engineering, and, in the 21st century, have expanded into life sciences, social sciences, medicine, business, and even the arts.  This module serves as an introduction to the fundamental techniques and methodologies for solving mathematical problems using numerical methods and equips students with the skills needed to analyse, design, and implement numerical algorithms effectively across a broad range of mathematical problems.

The topics include:

• Solving nonlinear equations, finding roots, Newton iteration and related methods.
• Introduction to optimisation, optimisation of functions of several variables, with and without constraints.
• Interpolation and approximations: Lagrange interpolation, Hermite interpolations,
• Numerical integration and differentiation: Trapezoidal method, Simpson method.
• Solutions of ordinary differential equations: Euler method, Runge-Kutta method, multistep methods, stability, convergence.
• Solution techniques for partial differential equations including the heat equation.
• Implementation and programming, e.g., Python, MATLAB.
• Error analysis: developing an understanding of the sources of error in numerical computations and methods for analysing and controlling numerical errors.

The aim of this module is to examine strategic finance issues faced by multinational companies from an international perspective. It focuses on how these companies operate within the global financial environment. Students will learn to identify and analyze the various forms and sources of business risks that multinational companies encounter.

Specifically, the module aims to:

1. To enable students to critically evaluate the international financial environment of a multinational corporation, including financial institutions, financial markets and exchange rate systems.

2. To critically examine and evaluate the principal concepts in the theory and practice of international financial management.

3. To analyse, apply and evaluate financial strategies through application of relevant analytical tools to examine and assess major issues and developments in international financial management.

4. To provide a critical understanding of the principles of risk exposures and the management of its international financial operations

On successful completion of this module students should be able to:

1. Analyse the environment in which international financial management is undertaken and discuss the structure of a MNC.

2. Critically assess the operations of the currency and derivatives markets and theories of exchange rate determination.

3. Define, assess and apply techniques and methods to evaluate and manage exposures and risks deriving from international business.

4. Apply the principal concepts, theories and appropriate tools in international financial management and reflect upon contemporary thinking to analyse and evaluate the international financial strategies of organisations, capital structure and financing of MNCs.

5. Assess a wide body of empirical research literature on contemporary issues relating to international financial management and critically appraise it. 

The module aims to develop students' ability to apply financial models and related advanced analytical techniques to inform business decisions and to evaluate possible decision outcomes in a competitive business environment.

This module will include topics such as, but not limited to:

• Principles of business and financial planning
• Introduction to financial modelling for business finance
• Techniques of quantitative and qualitative financial analysis
• Decision Making under risk and uncertainty
• Analysing and interpreting the financial performance

The project is an opportunity for you to explore deeply an area of mathematics of your choice.  This may be a topic not already covered in the degree, or you may explore in more depth a topic covered before.

You will engage with mathematical literature, seeking out material and learning for yourself, supported by regular meetings with your project supervisor.  You will develop skills of self-discipline and project management, and study the art of mathematical writing and communication.

You will negotiate with tutors the precise title and objectives for the project.