Topics in Mathematical Physics (MATH4108)

Course overview

Mathematical structures and symmetries of physical systems. Illustrative examples may be drawn from classical and quantum many-body systems, integrable and (quasi-)exactly solvable models, conformal field theory, and supersymmetry.

The goal of this course is to give an introduction to a range of topics in Mathematical Physics that are relevant to modern research in this field.

The first part of the course will look into an introduction to the mathematical methods used to develop and analyse integrable models in classical and quantum mechanics, particularly many-body systems. Students will study a variety of applications of algebraic structures and methods to such systems.

The second part of the course will look into statistical field theories that arise from the continuum limit of lattice models. This complementary part of the course will introduce concepts related to field theory, such as the notion of fields and their symmetry transformations under different symmetry groups, an introduction to critical phenomena, renormalisation in field theory, renormalisation group theory, and integrable classical field theory, if time permits, at the end.

In the School of Mathematics and Physics we are committed to creating an inclusive and empowering learning environment for all students. We value and respect the diverse range of experiences our students bring to their education, and we believe that this diversity is crucial for fostering a rich culture of knowledge sharing and meaningful exploration. We hold both students and staff accountable for actively contributing to the establishment of a respectful and supportive learning environment.

Bullying, harassment, and discrimination in any form are strictly against our principles and against UQ Policy, and will not be tolerated. We have developed a suite of resources to assist you in recognising, reporting, and addressing such behaviour. If you have any concerns about your experience in this course, we encourage you to tell a member of the course teaching team, or alternatively contact an SMP Classroom Inclusivity Champion (see Blackboard for contact details). Our Inclusivity Champions are here to listen, to understand your concerns, and to explore potential actions that can be taken to resolve them. Your well-being and a positive learning atmosphere are of utmost importance to us.

Course requirements

Assumed background

A basic understanding of the principles of quantum mechanics and related algebraic methods (e.g. Lie algebras, representation theory) as presented in MATH3103. It is expected that students will have some experience with complex analysis, as presented in MATH3401.

Prerequisites

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

MATH3401

Companion or co-requisite courses

You'll need to complete the following courses at the same time:

MATH3103

Incompatible

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

MATH4104, MATH4106

Course contact

Course staff

Timetable

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

Additional timetable information

Applied classes will begin in week 2 and will run for the first part of the course, till Wednesday of week 7 included. The second part of the course will be a combined lecture and applied class style, with a reading component for the students.

There will be no activities on public holidays. Alternative arrangements will be made and communicated via Blackboard 

All classes will be conducted on campus. Consult your personal timetable for times and locations. Students are expected to attend these sessions in person unless they have a valid reason for being unable to attend (such as illness). Important: if you are ill, then do not attend any classes in person. Alternative arrangements can be organised – consult Blackboard for details. 

Aims and outcomes

The aim of this course is to introduce a variety of topics and techniques relevant to research in mathematical physics. This includes concepts and techniques in the context of quantum integrable systems and field theories. Throughout the course, the student should be able to demonstrate how these concepts and techniques may be exploited in the analysis of certain systems to gain insights into physical properties. 

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% 10% for each assignment

Due date

Assignment 1: 21/08/2025 5:00 pm

Assignment 2: 11/09/2025 5:00 pm

Assignment 3: 9/10/2025 5:00 pm

Assignment 4: 30/10/2025 5:00 pm

Task description

Submission guidelines

All assignments have to be submitted exclusively in digital form on 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.

Solutions for assessment item/s are planned to be released 7 days after the assessment is due and as such, an extension after 7 days will not be possible. 

See ADDITIONAL ASSESSMENT INFORMATION for the 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. 

In-Semester Exam

• Identity Verified
• In-person

Mode

Written

Category

Examination

Weight

30%

Due date

15/09/2025 - 26/09/2025

Confirmation of the date, time, and venue will be communicated to students by the end of week 3 of the semester. 

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. 

End of Semester Exam

• Identity Verified
• In-person

Mode

Written

Category

Examination

Weight

30%

Due date

End of Semester Exam Period

8/11/2025 - 22/11/2025

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

To pass this course, students will be required to demonstrate a detailed understanding of course material together with a range of associated skills independent of Artificial Intelligence (AI) and Machine Translation (MT) tools.

For assessment tasks that are completed in-person (including examinations) termed “secure assessment”, the use of generative Artificial Intelligence (AI) or Machine Translation (MT) tools will not be permitted unless otherwise advised. Any attempted use of AI or MT may constitute student misconduct under the Student Code of Conduct.

Other non-secure assessment tasks (such as assignments) are designed to help you develop your understanding and skills, and to prepare you for secure assessment. You are thus generally encouraged to complete such assessment without the use of AI/MT, unless explicitly advised to the contrary in the assessment item. In any event, if you choose to use such tools, then you must clearly reference any such use within your submitted work. A failure to reference AI or MT use may constitute student 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.

ﾠ

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.

Additional learning resources information

See the information given in the library learning resources. Some lecture notes will also be provided. Many other resources are available in the library and online which may also be of benefit. These will be mentioned during class where appropriate, and lecture notes and whiteboard notes from the lectures will be uploaded on blackboard.

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 for Students Policy and Procedure

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