Module Catalogue 2021/22

NUS8305 : Mathematical Foundations of Machine Learning

  • Offered for Year: 2021/22
  • Module Leader(s): Dr Mohammed Abdul Hannan
  • Lecturer: Dr Pavan Kumar Naraharisetti
  • Owning School: NUIS
  • Teaching Location: Singapore
Semesters
Semester 2 Credit Value: 20
ECTS Credits: 10.0
Pre Requisites
Pre Requisite Comment

N/A

Co Requisites
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

Learning Outcomes

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 Methods

Please note that module leaders are reviewing the module teaching and assessment methods for Semester 2 modules, in light of the Covid-19 restrictions. There may also be a few further changes to Semester 1 modules. Final information will be available by the end of August 2020 in for Semester 1 modules and the end of October 2020 for Semester 2 modules.

Teaching Activities
Category Activity Number Length Student Hours Comment
Guided Independent StudyAssessment preparation and completion117:0017:00Preparation for quiz
Guided Independent StudyAssessment preparation and completion11:001:00Quiz
Scheduled Learning And Teaching ActivitiesLecture118:0018:00Coursework assignment preparation
Guided Independent StudyAssessment preparation and completion124:0024:00Revision for exam
Guided Independent StudyAssessment preparation and completion12:002:00Final exam
Scheduled Learning And Teaching ActivitiesLecture122:3030:00Lectures
Scheduled Learning And Teaching ActivitiesSmall group teaching121:0012:00Tutorials
Guided Independent StudyIndependent study122:0024:00Lecture follow-up
Guided Independent StudyIndependent study112:0012:00Tutorial preparation
Guided Independent StudyIndependent study160:0060:00Review lecture notes, general reading, background reading, reading specified articles
Total200:00
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.

Reading Lists

Assessment Methods

Please note that module leaders are reviewing the module teaching and assessment methods for Semester 2 modules, in light of the Covid-19 restrictions. There may also be a few further changes to Semester 1 modules. Final information will be available by the end of August 2020 in for Semester 1 modules and the end of October 2020 for Semester 2 modules.

The format of resits will be determined by the Board of Examiners

Exams
Description Length Semester When Set Percentage Comment
Written Examination1202A80Final exam
Other Assessment
Description Semester When Set Percentage Comment
Written exercise2M20Assignment on multiple problems that give an opportunity to apply concepts taught in class. Team report 1500 words per student max
Formative Assessments
Description Semester When Set Comment
Prob solv exercises2M60 mins quiz
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

Timetable

Past Exam Papers

General Notes

N/A

Disclaimer: The information contained within the Module Catalogue relates to the 2021/22 academic year. In accordance with University Terms and Conditions, the University makes all reasonable efforts to deliver the modules as described. Modules may be amended on an annual basis to take account of changing staff expertise, developments in the discipline, the requirements of external bodies and partners, and student feedback. Module information for the 2022/23 entry will be published here in early-April 2022. Queries about information in the Module Catalogue should in the first instance be addressed to your School Office.