This course introduces students to key concepts and techniques in mathematical physics. Topics will be taken from mathematical areas relevant to contemporary research in mathematical physics, and will typically be either a topic in Algebra or (Differential) Geometry. The course will be mathematical in nature and does not require a background in physics.

Note: Graduate students attend joint classes with undergraduates but will be assessed separately.

Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

1. Explain the fundamental concepts of a special topic in mathematical physics.
2. Demonstrate accurate and efficient use of specific mathematical physics techniques.
3. Demonstrate capacity for mathematical reasoning through analysing, proving and explaining concepts from mathematical physics.
4. Develop in-depth understanding of the material in order to be able to present new material to other students in an intelligible manner, and answer ad-hoc questions

Research-Led Teaching

Lie algebras form a backbone of almost all research in the area of Mathematical Physics, as well as other areas of Mathematics. This course is a first introduction to Lie algebras, providing the student with background knowledge to pursue further (original) research in the area. If time allows, topics on the forefront of present day research (Kac-Moody algebras, Vertex Operator Algebras) will be incorporated.

Required Resources

Lecture notes will be provided via Wattle.

Recommended Resources

The course will be largely based on the textbook by JE Humphreys, "Introduction to Lie algebras and Representation Theory" (Springer 1972), which students may want to consult for clarification of the material.

Recommended student system requirements 

ANU courses commonly use a number of online resources and activities including:

• video material, similar to YouTube, for lectures and other instruction
• two-way video conferencing for interactive learning
• email and other messaging tools for communication
• interactive web apps for formative and collaborative activities
• print and photo/scan for handwritten work
• home-based assessment.

To fully participate in ANU learning, students need:

• A computer or laptop. Mobile devices may work well but in some situations a computer/laptop may be more appropriate.
• Webcam
• Speakers and a microphone (e.g. headset)
• Reliable, stable internet connection. Broadband recommended. If using a mobile network or wi-fi then check performance is adequate.
• Suitable location with minimal interruptions and adequate privacy for classes and assessments.
• Printing, and photo/scanning equipment

For more information please see https://www.anu.edu.au/students/systems/recommended-student-system-requirements

Staff Feedback

Students will be given feedback in the following forms in this course:

• written comments
• verbal comments
• feedback to whole class, groups, individuals, focus group etc.

Student Feedback

ANU is committed to the demonstration of educational excellence and regularly seeks feedback from students. Students are encouraged to offer feedback directly to their Course Convener or through their College and Course representatives (if applicable). Feedback can also be provided to Course Conveners and teachers via the Student Experience of Learning & Teaching (SELT) feedback program. SELT surveys are confidential and also provide the Colleges and ANU Executive with opportunities to recognise excellent teaching, and opportunities for improvement.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	In 2022, this course will cover: Lie Algebras, Representation Theory and Applications, in the context of Mathematical Physics.	The two written assignments, the written open-book examination, and the oral presentation, will assess the topics covered.

Tutorial Registration

Tutorial/Workshop-style sessions, when delivered, will form part of the scheduled lecture hours for this course.

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
Assignment 1	15 %	*	*	1,2,3
Assignment 2	15 %	*	*	1,2,3
Oral Presentation	15 %	*	*	1,3,4
Exam	55 %	02/06/2022	30/06/2022	1,2,3

* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details

Policies

ANU has educational policies, procedures and guidelines , which are designed to ensure that staff and students are aware of the University’s academic standards, and implement them. Students are expected to have read the Academic Integrity Rule before the commencement of their course. Other key policies and guidelines include:

• Academic Integrity Policy and Procedure
• Student Assessment (Coursework) Policy and Procedure
• Special Assessment Consideration Guideline and General Information 
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure
• Code of practice for teaching and learning

Assessment Requirements

The ANU is using Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. For additional information regarding Turnitin please visit the Academic Skills website. In rare cases where online submission using Turnitin software is not technically possible; or where not using Turnitin software has been justified by the Course Convener and approved by the Associate Dean (Education) on the basis of the teaching model being employed; students shall submit assessment online via ‘Wattle’ outside of Turnitin, or failing that in hard copy, or through a combination of submission methods as approved by the Associate Dean (Education). The submission method is detailed below.

Moderation of Assessment

Marks that are allocated during Semester are to be considered provisional until formalised by the College examiners meeting at the end of each Semester. If appropriate, some moderation of marks might be applied prior to final results being released.

Participation

In Semester 1 2022, this course is delivered on campus with adjustments for remote participants. Participants are expected to take part in class sessions to develop their understanding and ability to clearly present the material, both in terms of proving results and working out examples.

Examination(s)

This course includes a final exam, which will be a written, open book exam (access to lecture notes and assignment solutions). The details and mode of delivery for exams will be communicated through the course Wattle site and the ANU final examination timetable.

Please note that, where a date range is used in the Assessment Summary in relation to exams, the due and return date for end of semester exams indicate the approximate timeframe in which the exam will be held and the date official end of Semester results are released on ISIS. Students should consult the course Wattle site and the ANU final examination timetable to confirm the date, time and mode of the exam.

Assessment Task 1

Assignment 1

Written assignment covering part I of the course (Lie algebras: Structure Theory). Tentatively to be distributed during week 6 of the course, and due 2 weeks later (flexible / in discussion with the students).

Assessment Task 2

Assignment 2

Written assignment covering part II of the course (Lie algebras: Representation Theory). Tentatively to be distributed during week 11 of the course, and due 2 weeks later (flexible / in discussion with the students).

Assessment Task 3

Oral Presentation

Students will be required to select a topic involving new material (additional to the course content) for their oral presentation, in consultation with the course convener, and then develop in-depth understanding of that material in order to be able to present it to other students in an intelligible manner, and answer ad-hoc questions. Presentations will be scheduled to occur near the end of the course. The mode of delivery of the presentations may be determined by the social distancing and travel restriction conditions in place at the time, and could potentially be in-person or over Zoom. Further details of this task will be provided early during the course delivery, via Wattle.

Assessment Task 4

Exam

Written open-book exam (access to lecture notes and assignment solutions), during the regular exam period.

Academic Integrity

Academic integrity is a core part of the ANU culture as a community of scholars. The University’s students are an integral part of that community. The academic integrity principle commits all students to engage in academic work in ways that are consistent with, and actively support, academic integrity, and to uphold this commitment by behaving honestly, responsibly and ethically, and with respect and fairness, in scholarly practice.

The University expects all staff and students to be familiar with the academic integrity principle, the Academic Integrity Rule 2021, the Policy: Student Academic Integrity and Procedure: Student Academic Integrity, and to uphold high standards of academic integrity to ensure the quality and value of our qualifications.

The Academic Integrity Rule 2021 is a legal document that the University uses to promote academic integrity, and manage breaches of the academic integrity principle. The Policy and Procedure support the Rule by outlining overarching principles, responsibilities and processes. The Academic Integrity Rule 2021 commences on 1 December 2021 and applies to courses commencing on or after that date, as well as to research conduct occurring on or after that date. Prior to this, the Academic Misconduct Rule 2015 applies.

 

The University commits to assisting all students to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. All coursework students must complete the online Academic Integrity Module (Epigeum), and Higher Degree Research (HDR) students are required to complete research integrity training. The Academic Integrity website provides information about services available to assist students with their assignments, examinations and other learning activities, as well as understanding and upholding academic integrity.

Online Submission

You will be required to agree to a declaration as part of the submission of your assignments, that will record your understanding of ANU academic integrity principles. Submission of assignments will either be via a Wattle assignment tool or by email: further details will be provided on the course Wattle site. Please keep a copy of tasks completed for your records. MATH6211 does not use Turnitin, having been granted an exemption.

Hardcopy Submission

For some forms of assessment (hand written assignments, art works, laboratory notes, etc.) hard copy submission is appropriate when approved by the Associate Dean (Education). Hard copy submissions must utilise the Assignment Cover Sheet. Please keep a copy of tasks completed for your records.

Late Submission

Late submission permitted. Late submission of assessment tasks without an extension are penalised at the rate of 5% of the possible marks available per working day or part thereof. Late submission of assessment tasks is not accepted after 10 working days after the due date, or on or after the date specified in the course outline for the return of the assessment item. Late submission is not accepted for take-home examinations.

Referencing Requirements

The Academic Skills website has information to assist you with your writing and assessments. The website includes information about Academic Integrity including referencing requirements for different disciplines. There is also information on Plagiarism and different ways to use source material.

Returning Assignments

Assignments to be returned via email.

Extensions and Penalties

Extensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure. Extensions may be granted for assessment pieces that are not examinations or take-home examinations. If you need an extension, you must request an extension in writing on or before the due date. If you have documented and appropriate medical evidence that demonstrates you were not able to request an extension on or before the due date, you may be able to request it after the due date.

Resubmission of Assignments

Not permitted.

Privacy Notice

The ANU has made a number of third party, online, databases available for students to use. Use of each online database is conditional on student end users first agreeing to the database licensor’s terms of service and/or privacy policy. Students should read these carefully. In some cases student end users will be required to register an account with the database licensor and submit personal information, including their: first name; last name; ANU email address; and other information.
In cases where student end users are asked to submit ‘content’ to a database, such as an assignment or short answers, the database licensor may only use the student’s ‘content’ in accordance with the terms of service – including any (copyright) licence the student grants to the database licensor. Any personal information or content a student submits may be stored by the licensor, potentially offshore, and will be used to process the database service in accordance with the licensors terms of service and/or privacy policy.
If any student chooses not to agree to the database licensor’s terms of service or privacy policy, the student will not be able to access and use the database. In these circumstances students should contact their lecturer to enquire about alternative arrangements that are available.

Distribution of grades policy

Academic Quality Assurance Committee monitors the performance of students, including attrition, further study and employment rates and grade distribution, and College reports on quality assurance processes for assessment activities, including alignment with national and international disciplinary and interdisciplinary standards, as well as qualification type learning outcomes.

Since first semester 1994, ANU uses a grading scale for all courses. This grading scale is used by all academic areas of the University.

Support for students

The University offers students support through several different services. You may contact the services listed below directly or seek advice from your Course Convener, Student Administrators, or your College and Course representatives (if applicable).

• ANU Health, safety & wellbeing for medical services, counselling, mental health and spiritual support
• ANU Access and inclusion for students with a disability or ongoing or chronic illness
• ANU Dean of Students for confidential, impartial advice and help to resolve problems between students and the academic or administrative areas of the University
• ANU Academic Skills and Learning Centre supports you make your own decisions about how you learn and manage your workload.
• ANU Counselling Centre promotes, supports and enhances mental health and wellbeing within the University student community.
• ANUSA supports and represents undergraduate and ANU College students
• PARSA supports and represents postgraduate and research students