Course overview
- Study period
- Semester 2, 2024 (22/07/2024 - 18/11/2024)
- Study level
- Undergraduate
- Location
- St Lucia
- Attendance mode
- In Person
- Units
- 2
- Administrative campus
- St Lucia
- Coordinating unit
- Mathematics & Physics School
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 fundamentalﾠtoﾠall areas of science, engineering and data analysis that involve computational techniques. In this light, MATH3204 will provide an opportunity to develop the basic and fundamental skills needed to tackle modern computational and data analysis problems.
MATH3204 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:
MATH2000 or MATH2001 or MATH2901 or MATH7000 or MATH7502
Recommended prerequisites
We recommend completing the following courses before enrolling in this one:
COSC2500 or COSC7500
Incompatible
You can't enrol in this course if you've already completed the following:
MATH7234 (co-taught).
Course contact
Tutor
Mr Alexander Lim
Tutor
Mr Jacob Westerhout
Tutor
Mr Joseph Wilson
Course staff
Lecturer
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
MATH3204 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 choiceﾠmay also be used.
Learning outcomes
After successfully completing this course you should be able to:
LO1.
Frame an appropriate optimisation formulation for a scientific, engineering, machine learning and data analysis problem .
LO2.
Select an appropriate algorithm, or modify an exiting method to obtain a variant, that is effective and efficient for a given optimisation problem.
LO3.
Given a matrix computation problem, select and appropriately modify an effective numerical linear algebra routine
LO4.
Understand the derivation, convergence analysis, and expected performance of various methods in numerical linear algebra and optimisation.
LO5.
Translate numerical methods into computer algorithms and code
LO6.
Demonstrate written communication skills appropriate for scientific reports.
Assessment
Assessment summary
| Category | Assessment task | Weight | Due date |
|---|---|---|---|
| Tutorial/ Problem Set | Assignments | 60% |
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 |
| Examination | Final Exam | 40% |
End of Semester Exam Period 2/11/2024 - 16/11/2024 |
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
Four assignments involve both theoretical and programming questions. Each assignment is equally weighted, contributing 15% towards your total mark.
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
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
Problems will be drawn from ideas and concepts covered during the lectures and practicals. Students will be expected to apply the ideas discussed in the course. The questions will be mainly about theoretical aspects, but understanding of the numerical and empirical properties of the methods could also be tested.
Exam details
| Planning time | 10 minutes |
|---|---|
| Duration | 120 minutes |
| Calculator options | (In person) Casio FX82 series only or UQ approved and labelled calculator |
| Open/closed book | Closed Book examination - specified written materials permitted |
| Materials | One A4 sheet of handwritten or typed notes, double sided, is permitted |
| Exam platform | Paper based |
| Invigilation | Invigilated in person |
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.
| Grade | Description |
|---|---|
| 1 (Low Fail) |
Absence of evidence of achievement of course learning outcomes. Course grade description: The student demonstrates very limited understanding of the theory of the topics listed in the course outline above and of the basic concepts in the course material. This includes attempts at answering some questions but demonstrating very limited understanding of the key concepts. Students will receive this grade if their final mark is less than 20%. |
| 2 (Fail) |
Minimal evidence of achievement of course learning outcomes. Course grade description: The student demonstrates limited understanding of the theory of the topics listed in the course outline above and demonstrates limited knowledge of the relevant mathematical techniques used to solve problems. This includes attempts at expressing their deductions and explanations and attempts to answer a few questions accurately. Students will receive this grade if their final mark is at least 20% but less than 45%. |
| 3 (Marginal Fail) |
Demonstrated evidence of developing achievement of course learning outcomes Course grade description: The student demonstrates some understanding of the theory of the topics listed in the course outline above and demonstrates some knowledge of the relevant mathematical techniques used to solve problems, yet fails to satisfy all of the basic requirements for a pass. Students will receive this grade if their final mark is at least 45% but less than 50%. |
| 4 (Pass) |
Demonstrated evidence of functional achievement of course learning outcomes. Course grade description: The student demonstrates an understanding of the theory of the topics listed in the course outline above and demonstrates a knowledge of the relevant mathematical techniques used to solve problems. Students will receive this grade if their final mark is at least 50% but less than 65%. |
| 5 (Credit) |
Demonstrated evidence of proficient achievement of course learning outcomes. Course grade description: The student demonstrates a good understanding of the theory of the topics listed in the course outline above and can apply the relevant mathematical techniques to solve problems. Students will receive this grade if their final mark is at least 65% but less than 75%. |
| 6 (Distinction) |
Demonstrated evidence of advanced achievement of course learning outcomes. Course grade description: The student demonstrates a comprehensive understanding of the theory of the topics listed in the course outline above and is proficient in applying the relevant mathematical techniques to solve both theoretical and practical problems. Students will receive this grade if their final mark is at least 75% but less than 85%. |
| 7 (High Distinction) |
Demonstrated evidence of exceptional achievement of course learning outcomes. Course grade description: The student demonstrates an excellent understanding of the theory of the topics listed in the course outline above and is highly proficient in applying the relevant mathematical techniques to solve both theoretical and practical problems. Students will receive this grade if their final mark is 85% or higher. |
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.
Filter activity type by
Please select
| Learning period | Activity type | Topic |
|---|---|---|
Multiple weeks From Week 1 To Week 13 |
Lecture |
Understanding Fundamental Concepts |
Multiple weeks From Week 2 To Week 13 |
Tutorial |
Further Discussions, Problem Solving, Programming MATH3204 contains scheduled tutorial sessions. During these sessions, students will get a chance to work on their assignments and get direct help from the tutors on both the theoretical and programming components. |
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.