Students

PHYS8901 – Mathematical Methods in Physics

2026 – Session 1, In person-scheduled-weekday, North Ryde

General Information

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Unit convenor and teaching staff Unit convenor and teaching staff Convener
Daniel Terno
daniel.terno@mq.edu.au
Lecturer
Peter Turner
peter.turner@mq.edu.au
Credit points Credit points
10
Prerequisites Prerequisites
Admission to GradDipResFSE or GradCertResFSE
Corequisites Corequisites
Co-badged status Co-badged status
Unit description Unit description

This unit covers topics in mathematical physics including: differential equations and group theory. The aim is to develop effective problem solving strategies, and where possible, the examples will be taken from the physical sciences. In the first topic the primary focus is on ordinary differential equations covering topics from first order equations and how to classify and solve them, through to higher order equations and more general techniques such as reduction of order, Laplace transforms, Green functions and series solutions. The second topic covers discrete groups and continuous Lie groups and Lie algebras. Group representations are introduced with the examples from Abelian and non-Abelian groups. Irreducible representations, unitary representations, Shur’s Lemma, and orthogonality relations are covered in the context of discrete groups. Compact and non-compact Lie groups and their generating Lie algebras are presented with several examples making the connection between symmetries and conservation laws, e.g. space-time symmetries and the Poincare group.

Learning in this unit enhances student understanding of global challenges identified by the United Nations Sustainable Development Goals (UNSDGs) Quality Education; Industry, Innovation and Infrastructure; Climate Action

Important Academic Dates

Information about important academic dates including deadlines for withdrawing from units are available at https://www.mq.edu.au/study/calendar-of-dates

Learning Outcomes

On successful completion of this unit, you will be able to:

  • ULO1: apply analytic methods for solving linear differential equations.
  • ULO2: describe and use numerical methods for solving ordinary or partial differential equations.
  • ULO3: employ discrete groups, continuous Lie groups and Lie algebras, and representation theory.
  • ULO4: infer discrete and continuous symmetries from the properties of physical systems.
  • ULO5: explain the relations between symmetries and conservation laws.
  • ULO6: analyse differential equations and group theory using Mathematica.

General Assessment Information

REQUIREMENTS TO PASS THE UNIT 

To pass the unit you have to acheave the total sum at least 50 out 100 marks across all the assesments. There are no hurdle requirements.

Attendance and participation

As per  Assessment Policy attendance is not assessed or mandated. Nonetheless, attendance and participation in all classes is very important for student success and is strongly  encouraged. 

Special Consideration

The Special Consideration Policy aims to support students who have been impacted by short-term circumstances or events that are serious, unavoidable and significantly disruptive, and which may affect their performance in assessment.

ASSESMENT TASKS

1. Projects (2x30%, estimated time on task = 22 hours outside of scheduled classes)

Project 1 is intended to reinforce core methods such as variational principles  and Lagrangian mechanics. The latter stages of the task develop into a guided mini-project requiring the derivation of a nonstandard mechanical result—selected specifically for being known to confuse  LLMs. This structure ensures both technical practice and evaluative authenticity.

Project 2 is intended to reinforce core group-theretical methods methods such as permutations and representations. The latter stages of the task develop into a guided mini-project in the area of quantum physics . This structure ensures both technical practice and evaluative authenticity.

2. Oral examination  (40%, estimated time on task = 20 hours outside of scheduled classes, including the examination time)

Oral test of basic understanding of the concepts and their applications. Topics to be examined will be advertised in advance.

Assessment Tasks

Name Weighting Hurdle Due Groupwork/Individual Short Extension AI assisted?
Project 2 30% No 05/06/2026 Individual No Open AI
Project 1 30% No 20/04/2026 Individual No Open AI
Final viva examination 40% No During the University examination period Individual No Observed

Project 2

Assessment Type 1: Portfolio
Indicative Time on Task 2: 22 hours
Due: 05/06/2026
Weighting: 30%
Groupwork/Individual: Individual
Short extension 3: No
AI assisted?: Open

You will complete a structured project to demonstrate understanding of the material in the second half of the unit.
On successful completion you will be able to:
  • employ discrete groups, continuous Lie groups and Lie algebras, and representation theory.
  • infer discrete and continuous symmetries from the properties of physical systems.
  • analyse differential equations and group theory using Mathematica.

Project 1

Assessment Type 1: Portfolio
Indicative Time on Task 2: 22 hours
Due: 20/04/2026
Weighting: 30%
Groupwork/Individual: Individual
Short extension 3: No
AI assisted?: Open

You will complete a structured project to demonstrate understanding of the material in the first half of the unit.
On successful completion you will be able to:
  • apply analytic methods for solving linear differential equations.
  • describe and use numerical methods for solving ordinary or partial differential equations.
  • explain the relations between symmetries and conservation laws.
  • analyse differential equations and group theory using Mathematica.

Final viva examination

Assessment Type 1: Examination
Indicative Time on Task 2: 20 hours
Due: During the University examination period
Weighting: 40%
Groupwork/Individual: Individual
Short extension 3: No
AI assisted?: Observed

Final viva examination covering all content from the unit.
On successful completion you will be able to:
  • apply analytic methods for solving linear differential equations.
  • describe and use numerical methods for solving ordinary or partial differential equations.
  • employ discrete groups, continuous Lie groups and Lie algebras, and representation theory.
  • infer discrete and continuous symmetries from the properties of physical systems.
  • explain the relations between symmetries and conservation laws.
  • analyse differential equations and group theory using Mathematica.

1 If you need help with your assignment, please contact:

  • the academic teaching staff in your unit for guidance in understanding or completing this type of assessment
  • the Writing Centre for academic skills support.

2 Indicative time-on-task is an estimate of the time required for completion of the assessment task and is subject to individual variation.

3 An automatic short extension is available for some assessments. Apply through the Service Connect Portal.

Delivery and Resources

Detailed reading guides and lecture notes will be provided

Policies and Procedures

Macquarie University policies and procedures are accessible from Policy Central (https://policies.mq.edu.au). Students should be aware of the following policies in particular with regard to Learning and Teaching:

Students seeking more policy resources can visit Student Policies (https://students.mq.edu.au/support/study/policies). It is your one-stop-shop for the key policies you need to know about throughout your undergraduate student journey.

To find other policies relating to Teaching and Learning, visit Policy Central (https://policies.mq.edu.au) and use the search tool.

Student Code of Conduct

Macquarie University students have a responsibility to be familiar with the Student Code of Conduct: https://students.mq.edu.au/admin/other-resources/student-conduct

Results

Results published on platform other than eStudent, (eg. iLearn, Coursera etc.) or released directly by your Unit Convenor, are not confirmed as they are subject to final approval by the University. Once approved, final results will be sent to your student email address and will be made available in eStudent. For more information visit connect.mq.edu.au or if you are a Global MBA student contact globalmba.support@mq.edu.au

Academic Integrity

At Macquarie, we believe academic integrity – honesty, respect, trust, responsibility, fairness and courage – is at the core of learning, teaching and research. We recognise that meeting the expectations required to complete your assessments can be challenging. So, we offer you a range of resources and services to help you reach your potential, including free online writing and maths support, academic skills development and wellbeing consultations.

Student Support

Macquarie University provides a range of support services for students. For details, visit http://students.mq.edu.au/support/

Academic Success

Academic Success provides resources to develop your English language proficiency, academic writing, and communication skills.

The Library provides online and face to face support to help you find and use relevant information resources. 

Student Services and Support

Macquarie University offers a range of Student Support Services including:

Student Enquiries

Got a question? Ask us via the Service Connect Portal, or contact Service Connect.

IT Help

For help with University computer systems and technology, visit http://www.mq.edu.au/about_us/offices_and_units/information_technology/help/. 

When using the University's IT, you must adhere to the Acceptable Use of IT Resources Policy. The policy applies to all who connect to the MQ network including students.

Unit information based on version 2026.02 of the Handbook