Algebraic Methods of Mathematical Physics (MATH7133)

Course overview

Algebraic structures and their representations of relevance to contemporary mathematical physics, including Lie algebras and their applications to quantum mechanics.

This course is an introduction to algebraic methods used in mathematical physics to describe symmetries mathematically and solve problems in quantum mechanics. Focus will be on Lie algebras and their representation theory, including some applications, but with the aim of developing an understanding of the associated algebraic structures and approaches more generally.

Course requirements

Assumed background

A sound working knowledge of linear algebra is assumed.

A basic understanding of the theory of quantum mechanics is desirable but not essential.

Prerequisites

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

Permission of Head of School/

Incompatible

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

MATH3103 (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.
• If you are ill, do not attend any classes or tutorials in person.
• No tutorials in Week 1.

Aims and outcomes

The aim of this course is to develop the basic theory of Lie algebras and their representations and to use this to formulate algebraic approaches for the analysis of physical systems, specifically in the context of quantum mechanical models. A key element in this approach is to describe the symmetries of a given physical system in terms of an algebraic structure such as a Lie algebra. In this manner,ﾠinsights into the physical aspects of the systemﾠare gained by exploiting known properties of the symmetry algebra through its representation theory.

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

40% or 0%

Due date

Assignment 1: 23/08/2024 4:00 pm

Assignment 2: 13/09/2024 4:00 pm

Assignment 3: 11/10/2024 4:00 pm

Assignment 4: 25/10/2024 4:00 pm

Learning outcomes

L01, L02, L03, L04, L05

Task description

Submission guidelines

Assignments must be submitted electronically through Blackboard.

Deferral or extension

You may be able to apply for an extension.

The maximum extension allowed is 7 days. Extensions are given in multiples of 24 hours.

Assignment solutions will be released a week after the assignment is due. 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, then the listed penalty will be deducted per day for up to 7 calendar days, at which point any submission will not receive any marks unless an extension has been approved. Each 24-hour block is recorded from the time the submission is due.

Final Exam

Mode

Written

Category

Examination

Weight

60% or 100%

Due date

End of Semester Exam Period

2/11/2024 - 16/11/2024

Learning outcomes

L01, L02, L03, L04, L05

Task description

Exam details

Submission guidelines

Deferral or extension

You may be able to defer this exam.

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

Course grading

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

Additional course grading information

A student's overall mark is the larger of

(1) the sum of their assignment marks out of 40 and their end-of-semester exam mark out of 60,

and

(2) their end-of-semester exam mark out of 100.

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

No discussions about incorrect or missing assignment marks will be entertained more than two weeks after the marks of a given assignment have been released.

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 timeframe 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.
• An extension for an assessment item due within the teaching period in which the course is offered, must not exceed four weeks in total. If you are incapacitated for a period exceeding four weeks of the teaching period, you are advised to apply for Removal of Course.
• 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.
• 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.
• 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

Library resources are available 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.