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

This module explores the fundamental ethics and principles of artificial intelligence and understanding how it impacts on society, specifically examining the ethical, social and technical challenges posed by AI systems. As part of this module, students will develop their understanding of key ethical principles, the societal impact of AI and will evaluate how human factors can influence system design/model development and potentially perpetuate human biases. This module will also explore different governance approaches and legislative requirements for AI and will examine the diverse strategies for mitigating discrimination and bias in AI based systems.

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.

This module provides a comprehensive introduction to data analytics, focusing on foundational concepts and practical applications. Students will develop essential skills to analyse data, solve real-world problems, and explore the rapidly growing field of big data analytics. The key perspectives are:

• Introduction to the data analytics process, including data collection, cleaning, analysis, visualisation, and interpretation.
• Hands-on experience with data analytics tools and techniques.
• Exploring big data analytics concepts, including scalable data processing and analysis.
• Promoting ethical decision-making and effective communication in data-driven contexts.

The data analytics process covers :

• Identifying business problems and defining objectives.
• Collecting and cleaning raw data for analysis.
• Performing exploratory data analysis (EDA) to uncover patterns.
• Visualising and interpreting results to derive actionable insights.

The statistical and analytical thinking aspect includes: 

• Measures of central tendency and dispersion.
• Regression analysis and correlation.
• Data modelling and simulation.

The tools and techniques component covers:

• cleaning and preprocessing using Python or R.
• SQL for querying and managing databases.
• Data visualisation using tools like Tableau, Power BI, Matplotlib and Apache Superset
• Introduction to big data ecosystem.

The big data analytics aspect addresses:

• Scalable data storage and processing.
• Analysing large datasets with distributed systems.
• Leveraging machine learning for big data insights.
• Real-time analytics and stream processing.

The ethical and professional skills aspect encompasses:

• Ethical issues in data privacy and security.
• Effective communication of data insights through storytelling.
• Collaboration and teamwork in data projects.
• Presentation and reporting of analytics outcomes.

Choose one of the following:

1. Professional Placement (40 Credits) Optional
2. Term abroad (40 Credits) Optional
3. One of the following Language options

Advanced Language Development and Global Sustainability (40 Credits) Optional

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. 

Developing Intercultural Literacy and Cross-Cultural Skills (40 Credits) Optional

• 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.

Experiential Overseas Learning (40 Credits) Optional

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 

Post Beginner Language Development and Global Cultures (40 Credits) Optional

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. 

Upper Intermediate Language Development and Global Employability (40 Credits) Optional

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. 

Or you can choose ONE of the following:

• University Placement Year Optional
• Subject Placement Year Optional
• International University Placement Year Optional