Module Catalogue 2024/25

Pre Requisite Comment

N/A

Co Requisite Comment

N/A

Aims

This module aims to provide fundamental knowledge and skills in mathematics related to Machine Learning and Data Analytics so that students can either build their Machine Learning tools in the future or use existing tools with confidence since they would know the “science behind” such tools. This is done by teaching linear, non-linear models in addition to ordinary differential equations and statistical models.

Outline Of Syllabus

1.       Introduction
a.       Mathematical modelling.
b.       Simulation – Optimisation.
c.       Digital Twin and Machine Learning.
2.       First Principles models
a.       Linear algebra including eigenvalues and eigenvectors.
b.       First and second-order systems.
3.       System of systems: series
4.       Optimisation and Parameter Estimation
5.       Lean Data and Design of Experiments
6.       Statistics
a.       PCA and Model Reduction.
b.       Mathematics of Statistical Process Control

Intended Knowledge Outcomes

At the end of the module, students should:
• Have knowledge of how physical systems can be modelled as a system of linear,
nonlinear and differential equations.
• Be able to discriminate between first principles models and data-based models.
• Be able to choose the right mathematical models and justify the selection.
• Have the knowledge of the differences between Modelling, Simulation, Optimisation
for Parameter Estimation and Optimisation for System Design.
• Use the knowledge and determine the best path forward. Be able to justify the plan

Intended Skill Outcomes

At the end of the module, students should be able to:
• Determine which of linear, nonlinear, differential equations or statistical models
are required to model a system in addition to being able to solve these problems.
• Generate mathematical models given the description of a system.
• Compare first principles models and data-based models and determine which is appropriate
for a given system.
• Choose the correct mathematical method to get a satisfactory outcome. Be able to conclude
and defend that the outcome is satisfactory.

Teaching Rationale And Relationship

Teaching is conducted via lectures and tutorial with small group discussions during class. This is complemented with self-study and preparation of tutorial solutions, coursework/project and final examination in order to provide feedback on student learning. Teaching materials are made available to the students online in order for self-study and preparation at their own pace. Tutorial classes enable students to ask questions and clarify any doubts.

Due to the emerging Covid-19 situation, it is likely that some or all of the classes are conducted online. Attendance will be taken irrespective of whether the class is online or face-to-face, and students are expected to switch on their camera for online classes.

Assessment Rationale And Relationship

Coursework assignment provides students more time to think about a larger problem and provide solutions to it. It also allows them to work as a team to handle more significant problems. The quiz allows the students to test the knowledge gained thus far and better plan the rest of the study. The written exam enables students to demonstrate understanding and apply knowledge and skills learnt to solve engineering problems using known mathematical methods

General Notes

N/A