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Unit outline_

OLET1630: Symmetry

Intensive February, 2022 [Online] - Camperdown/Darlington, Sydney

The principle of symmetry appears in architecture, in the arts, in nature. It is often understood as harmony of proportions. But what is the philosophical or mathematical significance of the idea of symmetry? This unit will help clarify this significance by developing the geometric concept of symmetry and by conveying the sensibility to recognise and categorise symmetries in different contexts. The richness, diversity, connectedness, depth and pleasure of the systematic study of symmetry, and indeed of mathematical thinking, is central to this unit. It will not involve grinding through formulas, but instead emphasise the process of thinking, comparing, analysing, understanding and inventing.

Unit details and rules

Academic unit Mathematics and Statistics Academic Operations
Credit points 2
Assumed knowledge


Available to study abroad and exchange students


Teaching staff

Coordinator Stephan Tillmann,
Type Description Weight Due Length
Assignment Project & Project Outline
The project can be an essay, model, computer program or short video.
60% Multiple weeks N/A
Outcomes assessed: LO1 LO2 LO6 LO7
Presentation Presentation
Completion of tasks during workshops and preparation of materials for them.
20% Ongoing Tasks during and before workshops.
Outcomes assessed: LO1 LO7 LO6 LO5 LO4 LO3 LO2
Assignment Reflective Journal
Reflections and practical exercises.
20% Ongoing Ongoing for 5 weeks.
Outcomes assessed: LO4 LO5 LO6 LO1 LO2 LO3

Assessment summary

Detailed information for each assessment can be found on Canvas.

Assessment criteria

The University awards common result grades, set out in the Coursework Policy 2014 (Schedule 1).

As a general guide, a high distinction indicates work of an exceptional standard, a distinction a very high standard, a credit a good standard, and a pass an acceptable standard.

For more information see guide to grades.

Late submission

In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:

  • Deduction of 5% of the maximum mark for each calendar day after the due date.
  • After ten calendar days late, a mark of zero will be awarded.

Academic integrity

The Current Student website  provides information on academic integrity and the resources available to all students. The University expects students and staff to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.  

We use similarity detection software to detect potential instances of plagiarism or other forms of academic integrity breach. If such matches indicate evidence of plagiarism or other forms of academic integrity breaches, your teacher is required to report your work for further investigation.

You may only use artificial intelligence and writing assistance tools in assessment tasks if you are permitted to by your unit coordinator, and if you do use them, you must also acknowledge this in your work, either in a footnote or an acknowledgement section.

Studiosity is permitted for postgraduate units unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission.

Simple extensions

If you encounter a problem submitting your work on time, you may be able to apply for an extension of five calendar days through a simple extension.  The application process will be different depending on the type of assessment and extensions cannot be granted for some assessment types like exams.

Special consideration

If exceptional circumstances mean you can’t complete an assessment, you need consideration for a longer period of time, or if you have essential commitments which impact your performance in an assessment, you may be eligible for special consideration or special arrangements.

Special consideration applications will not be affected by a simple extension application.

Using AI responsibly

Co-created with students, AI in Education includes lots of helpful examples of how students use generative AI tools to support their learning. It explains how generative AI works, the different tools available and how to use them responsibly and productively.

WK Topic Learning activity Learning outcomes
Multiple weeks Reading and Activities on Symmetry guided by online modules on Canvas Independent study (15 hr) LO1 LO3 LO4
Week 03 Applications of symmetry; feedback on individual projects Workshop (3 hr) LO1 LO2 LO6 LO7
Week 05 Advanced topics in the study of symmetry; feedback on individual projects Workshop (3 hr) LO1 LO3 LO4 LO5 LO7

Attendance and class requirements

In order to pass this unit, you must participate in the workshops.

Study commitment

Typically, there is a minimum expectation of 1.5-2 hours of student effort per week per credit point for units of study offered over a full semester. For a 2 credit point unit, this equates to roughly 40-50 hours of student effort in total.

Learning outcomes are what students know, understand and are able to do on completion of a unit of study. They are aligned with the University's graduate qualities and are assessed as part of the curriculum.

At the completion of this unit, you should be able to:

  • LO1. appreciate and understand the scientific and philosophical method of enquiry
  • LO2. understand the symmetries of a diverse range of objects from the arts, nature, chemistry and mathematics
  • LO3. distinguish the different types of symmetries in two and three dimensions
  • LO4. interpret and understand symmetries as mappings
  • LO5. manipulate and compose symmetries and understand their structure as a mathematical group
  • LO6. have a working knowledge of different applications of symmetry and groups in a variety of contexts in science, engineering and the humanities
  • LO7. analyse problems in a team and be able to clearly communicate the findings through both written reports and oral presentations.

Graduate qualities

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course. As a future Sydney graduate, the set of qualities have been designed to equip you for the contemporary world.

GQ1 Depth of disciplinary expertise

Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline.

GQ2 Critical thinking and problem solving

Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem.

GQ3 Oral and written communication

Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context.

GQ4 Information and digital literacy

Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies.

GQ5 Inventiveness

Generating novel ideas and solutions.

GQ6 Cultural competence

Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures. In the Australian context, this includes and celebrates Aboriginal and Torres Strait Islander cultures, knowledge systems, and a mature understanding of contemporary issues.

GQ7 Interdisciplinary effectiveness

Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries.

GQ8 Integrated professional, ethical, and personal identity

An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context.

GQ9 Influence

Engaging others in a process, idea or vision.

Outcome map

Learning outcomes Graduate qualities

This section outlines changes made to this unit following staff and student reviews.

Changes in design of modules and workshops have been implemented as a result of student feedback.

Work, health and safety

We are governed by the Work Health and Safety Act 2011, Work Health and Safety Regulation 2011 and Codes of Practice. Penalties for non-compliance have increased. Everyone has a responsibility for health and safety at work. The University’s Work Health and Safety policy explains the responsibilities and expectations of workers and others, and the procedures for managing WHS risks associated with University activities.


The University reserves the right to amend units of study or no longer offer certain units, including where there are low enrolment numbers.

To help you understand common terms that we use at the University, we offer an online glossary.