Computational Techniques

Module aims

To improve the analytic skills to the level required for engineering and financial applications.

To develop the students' abilities needed for problem solving in linear algebra.

Learning outcomes

  1. Understanding of the principles of linear algebra and its application in ML/AI, engineering and finance.
  2. Introduction to transforms and their use in image processing, engineering and probability/statistics.
  3. Introduction to functions of several variables and optimisation.

Module syllabus

  • Eigenvalues, eigenvectors and their generalisation
  • Jordan form
  • Singular value decomposition, with applications
  • LU and QR decompositions
  • Spectral Decomposition
  • Least Squares Method
  • Cholesky factorisation, with applications
  • Iterative methods for solving linear systems
  • Vector and matrix norms and condition numbers
  • Metric spaces and convergence, application to linear equation solvers
  • Laplace and Fourier transforms, with applications
  • Functions of several variables
  • Method of conjugate gradients and its role in optimisation

Teaching methods

Lectures and small group tutorials.               

Assessments

Examination and approximately 7 small, regular courseworks.                

Module leaders

Professor Abbas Edalat
Professor Peter Harrison