Numerical Linear Algebra and Optimisation (MATH7234)

Course overview

At the heart of most modern data scientific methods in general, and machine learning in particular, lie computational techniques involving matrices as well as numerical linear algebra and optimisation algorithms. In this course, students will learn about the theory and practical aspects of many fundamental tools from matrix computations, numerical linear algebra and optimisation. In addition to classical applications, most examples will particularly focus on modern large-scale machine learning problems. Implementations will be done using MATLAB/Python. The students will also be exposed to cutting-edge developments including randomised variants of many classical deterministic methods. Students will be taught a range of analytical and algorithmic tools that are employed in research and industry, such as various matrix types, their properties and factorisations, iterative algorithms for matrix computations such as Krylov subspace methods, various eigen-solvers, elements of convex and non-convex analysis, derivative free as well as first and second-order optimisation methods, constrained and unconstrained optimisation algorithms, and introduction to non-smooth and stochastic optimisation.

Numerical Linear Algebra and Optimisation are fundamental to all areas of science, engineering and data analysis that involve computational techniques. In this light, MATH7234 will provide an opportunity to develop the basic and fundamental skills needed to tackle modern computational and data analysis problems.

MATH7234 will cover the following fundamental concepts and techniques:

• Various matrix types and their properties
• Various matrix factorisations
• Iterative algorithms for matrix computations such as Krylov subspace methods
• Elements of convex and non-convex analysis
• First and second-order optimisation methods
• Constrained and unconstrained optimisation algorithms
• Applications in Machine Learning and Scientific Computing

Course requirements

Assumed background

Introductory courses such as MATH2000, MATH2001,ﾠMATH7000 or MATH7502 will cover parts of the prerequisite background. The computational techniques learnt as part of COSC2500 or MATH3201, though not mandatory, are considered helpful background knowledge. Students should have basic computer skills and some level of programming experience in MATLAB/Python is required.

Prerequisites

You'll need to complete the following courses before enrolling in this one:

Knowledge equivalent to MATH7000 or MATH7502.

Recommended prerequisites

We recommend completing the following courses before enrolling in this one:

Knowledge equivalent to COSC7500.

Incompatible

You can't enrol in this course if you've already completed the following:

MATH3204 (co-taught).

Course contact

Course staff

Timetable

The timetable for this course is available on the UQ Public Timetable.

Additional timetable information

All classes will be conducted on campus. Consult your personal timetable for times and locations. Students are expected to attend these sessions inﾠperson unless they have a valid reason for being unable to attend (such as illness).ﾠ

Tutorials start in week 2. If a tutorial session falls on a public holiday, there will be no make-up session. Instead, students are welcome to attend any other session that fits their schedule.

Aims and outcomes

MATH7234 will introduce students to fundamental concepts, tools and techniques from matrix computations and numerical optimization. The course will mainly focus on theoretical developments but it also contains a practical component to provide hands-on learning experience. The programming exercises will be done primarily in MATLAB or Python, but any programming language of your choice may also be used.

Learning outcomes

After successfully completing this course you should be able to:

Assessment

Assessment summary

Assessment details

Assignments

Mode

Written

Category

Tutorial/ Problem Set

Weight

60%

Due date

Assignment 01 16/08/2024 5:00 pm

Assignment 02 6/09/2024 5:00 pm

Assignment 03 4/10/2024 5:00 pm

Assignment 04 25/10/2024 5:00 pm

Task description

Submission guidelines

Each assignment is to be submitted via Blackboard as a single pdf document.

Deferral or extension

You may be able to apply for an extension.

Solutions for assessment item/s will be released 3 calendar days after the assessment is due and as such, an extension after 3 calendar days will not be possible.

See ADDITIONAL ASSESSMENT INFORMATION for extension and deferred examination information relating to this assessment item.

Late submission

A penalty of 10% of the maximum possible mark will be deducted per 24 hours from time submission is due for up to 7 days. After 7 days, you will receive a mark of 0.

You are required to submit assessable items on time. If you fail to meet the submission deadline for any assessment item without an approved extension, a penalty of 10% of the maximum possible mark allocated for the assessment item, or one grade per day if graded on the basis of 1-7, will be deducted per day for up to 3 calendar days, at which point any submission will not receive any marks. Each 24 hour block is recorded from the time the submission is due. 

Final Exam

Mode

Written

Category

Examination

Weight

40%

Due date

End of Semester Exam Period

2/11/2024 - 16/11/2024

Task description

Exam details

Submission guidelines

Deferral or extension

You may be able to defer this exam.

See ADDITIONAL ASSESSMENT INFORMATION for the extension and deferred examination information relating to this assessment item.

Course grading

Full criteria for each grade is available in the Assessment Procedure.

Supplementary assessment

Supplementary assessment is available for this course.

Should you fail a course with a grade of 3, you may be eligible for supplementary assessment. Refer to my.UQ for information on supplementary assessment and how to apply. 

Supplementary assessment provides an additional opportunity to demonstrate you have achieved all the required learning outcomes for a course.  

If you apply and are granted supplementary assessment, the type of supplementary assessment set will consider which learning outcome(s) have not been met.  

Supplementary assessment in this course will be a 2-hour examination similar in style to the end-of-semester examination. To receive a passing grade of 3S4, you must obtain a mark of 50% or more on the supplementary assessment. 

Additional assessment information

Artificial Intelligence

The assessment tasks in this course evaluate students’ abilities, skills and knowledge without the aid of Artificial Intelligence (AI). Students are advised that the use of AI technologies to develop responses is strictly prohibited and may constitute misconduct under the Student Code of Conduct.

Applications for Extensions to Assessment Due Dates

Extension requests are submitted online via my.UQ – applying for an extension. Extension requests received in any other way will not be approved. Additional details associated with extension requests, including acceptable and unacceptable reasons, may be found at my.UQ.

Please note:

• Requests for an extension to an assessment due date must be submitted through your my.UQ portal and you must provide documentation of your circumstances, as soon as it becomes evident that an extension is needed. Your application must be submitted on or before the assessment item's due date and time.
• Applications for extension can take time to be processed so you should continue to work on your assessment item while awaiting a decision. We recommend that you submit any completed work by the due date, and this will be marked if your application is not approved. Should your application be approved, then you will be able to resubmit by the agreed revised due date.
• If an extension is approved, you will be notified via your my.UQ portal and the new date and time for submission provided. It is important that you check the revised date as it may differ from the date that you requested.
• If the basis of the application is a medical condition, applications should be accompanied by a medical certificate dated prior to the assignment due date. If you are unable to provide documentation to support your application by the due date and time you must still submit your application on time and attach a written statement (Word document) outlining why you cannot provide the documentation. You must then upload the documentation to the portal within 24 hours.
• If an extension is being sought on the basis of exceptional circumstances, it must be accompanied by supporting documentation (eg. Statutory declaration).
• For extensions based on a SAP you may be granted a maximum of 7 days (if no earlier maximum date applies). See the Extension or Deferral availability section of each assessment for details. Your SAP is all that is required as documentation to support your application. However, additional extension requests for the assessment item will require the submission of additional supporting documentation e.g., a medical certificate. All extension requests must be received by the assessment due date and time.
• Students may be asked to submit evidence of work completed to date. Lack of adequate progress on your assessment item may result in an extension being denied.
• If you have been ill or unable to attend class for more than 14 days, you are advised to carefully consider whether you are capable of successfully completing your courses this semester. You might be eligible to withdraw without academic penalty - seek advice from the Faculty that administers your program.
• There are no provisions for exemption from an assessment item within UQ rules. If you are unable to submit an assessment piece then, under special circumstances, you may be granted an exemption, but may be required to submit alternative assessment to ensure all learning outcomes are met.

Applications to defer an exam

In certain circumstances you can apply to take a deferred examination for in-semester and end-of-semester exams. You'll need to demonstrate through supporting documentation how unavoidable circumstances prevented you from sitting your exam. If you can’t, you can apply for a one-off discretionary deferred exam.

Deferred Exam requests are submitted online via mySi-net. Requests received in any other way will not be approved. Additional details associated with deferred examinations, including acceptable and unacceptable reasons may be found at my.UQ.

Please note:

• Applications can be submitted no later than 5 calendar days after the date of the original exam.
• There are no provisions to defer a deferred exam. You need to be available to sit your deferred examination.
• Your deferred examination request(s) must have a status of "submitted" in mySI-net to be assessed.
• All applications for deferred in-semester examinations are assessed by the relevant school. Applications for deferred end-of-semester examinations are assessed by the Academic Services Division.
• You’ll receive an email to your student email account when the status of your application is updated.
• If you have a medical condition, mental health condition or disability and require alternative arrangements for your deferred exam you’ll need to complete the online alternative exam arrangements through my.UQ. This is in addition to your deferred examinations request. You need to submit this request on the same day as your request for a deferred exam or supplementary assessment. Contact Student Services if you need assistance completing your alternative exam arrangements request.

Learning resources

You'll need the following resources to successfully complete the course. We've indicated below if you need a personal copy of the reading materials or your own item.

Library resources

Find the required and recommended resources for this course on the UQ Library website.

Learning activities

The learning activities for this course are outlined below. Learn more about the learning outcomes that apply to this course.

Policies and procedures

University policies and procedures apply to all aspects of student life. As a UQ student, you must comply with University-wide and program-specific requirements, including the:

• Student Code of Conduct Policy
• Student Integrity and Misconduct Policy and Procedure
• Assessment Procedure
• Examinations Procedure
• Reasonable Adjustments - Students Policy and Procedure

Learn more about UQ policies on my.UQ and the Policy and Procedure Library.