50011

Computational Techniques

Module aims

In this module you will have the opportunity to study additional mathematical topics that form prerequisites for later third and fourth year modules in areas such as computer graphics, machine learning and computational finance. The focus is on how mathematical methods can be applied to complex computational problems.

Learning outcomes

Upon successful completion of this module you will be able to:

• apply advanced topics in linear algebra to problems in machine learning and deep learning,
• be able to understand and implement mathematical methods in image processing, graphics and computational finance
• use vector calculus to solve computational optimisation problems
• solve problems in linear programming

Module syllabus

The indicative module content is as follows:

Vector and matrix norms, Generalised eigenvectors, Jordan normal form, Singular Value Decomposition, Dimensionality Reduction, Positive definite matrices, Cholesky factorisation, Normal Equations, Least Square Method, QR-decomposition, Householder transform, QR algorithm, LU-decomposition, Conditions of a matrix, Iterative solution of linear systems of equations, Jacobi method, Gauss-Seidel method, Iterative computation of eigenvectors, Power method, Inverse iteration, Rayleigh Quotient, Steepest descent method, Conjugate method, Linear programming.

Teaching methods

The module will be taught through lectures, backed up by unassessed, formative, exercises, that you will solve in-class. There will be one or more assessed coursework exercises designed to reinforce your understanding of the material. Small-group tutorials will be organised, which you can engage in on an optional basis.

An online web service will be used as an open online discussion forum for the module.

Assessments

There will be one or more assessed coursework exercises which collectively count for 20% of the marks for the module. There will be a final written exam, which counts for the remaining 80% of the marks.

Written feedback will be given on the assessed exercises will be returned through department's online platform. If you elect to attend the small-group tutorials then you will also get regular additional verbal feedback and will benefit from the group discussions.

Reading list

Module leaders

Dr Calvin Tsay
Professor Abbas Edalat