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.

This module offers an in-depth exploration of artificial intelligence (AI) and its transformative role in the development of advanced software systems. It introduces key theoretical approaches and practical techniques for designing and deploying intelligent technologies, empowering you with the skills to build AI-driven solutions.

Key topics covered include:

  • Introduction to Artificial Intelligence: Understanding the foundations of AI and its significance in modern software development.
  • Theoretical Approaches to AI: Exploring algorithms and models that underpin intelligent systems, such as decision trees, neural networks, and reinforcement learning.
  • Practical AI Implementation: Gaining hands-on experience with AI techniques, including machine learning, natural language processing, and computer vision, through coding exercises and projects.
  • Designing and Deploying Intelligent Systems: Examining methods for building robust, scalable, and ethically sound AI technologies.
  • AI in Various Domains: Critically evaluating how AI is applied across industries such as business, healthcare, education, law, government, and scientific research, along with the ethical and societal implications of these applications.

This module blends theory with practical application, equipping you to develop intelligent systems and critically assess their impact in a wide range of real-world contexts.

Recognition of the need to apply data science applications in organisations.

Establishment of correct selection and application of data science techniques (i.e. data shaping, model type selection, testing and application) in various organisational contexts. 

Application of common machine learning tools (e.g. logistic regression, non-linear model estimation, neural network) in a common development environment (e.g. R, Python, Scala) in preparation for the real world context.

Evaluation of the role of ethics in the application of data science techniques.

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.