Outline

Overview

This unit explores the foundational mathematical ideas of symmetry, structure, and arithmetic in a general algebraic setting. At its core is the study of groups and rings, which appear throughout mathematics in different forms. The first part of the unit focuses on groups, which in a broad sense describe symmetries of shapes, equations, and more. Students learn how to analyse and classify these symmetries, and how group structure reflects underlying mathematical behaviour. The second part turns to rings and ideals, which extend our familiar arithmetic with integers and polynomials. This leads to questions about factorisation and solving equations in new settings. Along the way, students gain practical experience with computer algebra systems, using them to carry out calculations, test ideas and construct and explore examples. Rather than treating algebra as purely abstract, the unit shows how the abstract becomes concrete through computation. The aim is to build both a strong theoretical foundation and a working understanding of how algebraic structures behave in practice.

Unit details and rules

Academic unit	Mathematics and Statistics Academic Operations
Credit points	6
Prerequisites ?	MATH1061 or MATH1961 or MATH1971 or MATH1064 or MATH1964
Corequisites ?	None
Prohibitions ?	MATH2980
Assumed knowledge ?	None
Available to study abroad and exchange students	Yes

Teaching staff

Coordinator	John Voight, john.voight@sydney.edu.au

Assessment

The census date for this unit availability is 31 August 2026

Details
Criteria

Type	Description	Weight	Due	Length	Use of AI
Written exam	Final Exam Exam	60%	Formal exam period	2 hours	AI prohibited
Outcomes assessed:
Out-of-class quiz	Early feedback task Canvas quiz	0%	Week 03 Due date: 20 Aug 2026 at 23:59 Closing date: 24 Aug 2026	8-12 questions	AI allowed
Outcomes assessed:
Written work	Assignment 1 Written work	6%	Week 03 Due date: 20 Aug 2026 at 23:59 Closing date: 30 Aug 2026	3-5 pages	AI allowed
Outcomes assessed:
In-person practical, skills, or performance task or test	Quiz Quiz	15%	Week 07	40 minutes	AI prohibited
Outcomes assessed:
Written work	Assignment 2 Written work	6%	Week 10 Due date: 15 Oct 2026 at 23:59 Closing date: 25 Oct 2026	3-5 pages	AI allowed
Outcomes assessed:
Contribution	Lab Contribution Computational lab: Each participation session counts as 1% for a maximum of 9%.	9%	Weekly	1hr/week	AI allowed
Outcomes assessed:
Contribution	Tutorial Contribution Each participation session counts as 0.5% for a maximum of 4%.	4%	Weekly	1hr/week	AI allowed
Outcomes assessed:
= early feedback task ?

Early feedback task

This unit includes an early feedback task, designed to give you feedback prior to the census date for this unit. Details are provided in the site and your result will be recorded in your Marks page. It is important that you actively engage with this task so that the University can support you to be successful in this unit.

Assessment summary

- Final Exam: Students will complete a written examination during the formal exam period. The exam will comprehensively assess understanding of the unit material.

- Quiz: Students will complete a 40-minute in-person quiz with multiple choice and short answer questions. 听The quiz tests early material from the unit.

- Lab Contribution:听Students will participate in weekly practical computational work using Magma. 听These tasks require students to construct examples, carry out algebraic computations, test ideas, and collaboratively investigate computational methods extending the material covered in lectures. 听Computational lab is assessed on a satisfactory / non-satisfactory basis and reflects your engagement in lab activities. 听It is worth 1 mark per lab, up to 9 workshops. 听This scheme already allows for a small number of absences. 听You should only apply for Special Consideration if you are affected for several workshops. 听Special Consideration is not required for occasional missed classes.

- Tutorial听Contribution: Students will participate in weekly tutorials by working on and discussing problems associated with the lectures. 听Workshop contribution is assessed on a satisfactory / non-satisfactory basis and reflects your engagement in workshop activities. 听It is worth 0.5 mark per workshop class, up to 8 workshops. 听This scheme already allows for a small number of absences. 听You should only apply for Special Consideration if you are affected for several workshops. 听Special Consideration is not required for occasional missed classes.

- Assignment 1: Students will submit a short written assignment of 3鈥�5 pages in Week 3. The assignment focuses on early group-theoretic material and requires clear mathematical writing and logically structured arguments.

- Assignment 2: Students will submit a short written assignment of 3鈥�5 pages in Week 10. The assignment focuses on later material in the unit, including polynomial rings and ideals.

Detailed information for each assessment can be found on Canvas. 听

Assessment criteria

Result name	Mark range	Description
High distinction	85 - 100	The learning outcomes of the unit of study have been demonstrated at an exceptional standard.
Distinction	75 - 84	The learning outcomes of the unit of study have been demonstrated at a very high standard.
Credit	65 - 74	The learning outcomes of the unit of study have been demonstrated at a good standard.
Pass	50 - 64	The learning outcomes of the unit of study have been demonstrated at an acceptable standard.
Fail	0 - 49	The learning outcomes of the unit of study have not been met to a satisfactory standard.听

For more information see guide to grades.

Use of generative artificial intelligence (AI)

You can use generative AI tools for open assessments. Restrictions on AI use apply to secure, supervised assessments used to confirm if students have met specific learning outcomes.

Refer to the assessment table above to see if AI is allowed, for assessments in this unit and check Canvas for full instructions on assessment tasks and AI use.

If you use AI, you must always acknowledge it. Misusing AI may lead to a breach of the听Academic Integrity Policy.

Visit the听Current Students website听for more information on AI in assessments, including听details on how to acknowledge its use.

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 University expects students to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.

Our website听provides information on academic integrity and the resources available to all students. This includes advice on how to avoid common breaches of academic integrity. Ensure that you have completed the听Academic Honesty Education Module (AHEM)听which is mandatory for all commencing coursework students

Penalties for serious breaches can significantly impact your studies and your career after graduation. It is important that you speak with your unit coordinator if you need help with completing assessments.

Visit the听Current Students website听for more information on AI in assessments, including听details on how to acknowledge its use.

Learning support

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听simple extension.鈥� 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鈥檛 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听special consideration or special arrangements.

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

Using AI responsibly

Co-created with students,听听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.

Support for students

The Support for Students Policy听reflects the University鈥檚 commitment to supporting students in their academic journey and making the University safe for students. It is important that you read and understand this policy so that you are familiar with the range of support services available to you and understand how to engage with them.

The University uses email as its primary source of communication with students who need support under the Support for Students Policy. Make sure you check your University email regularly and respond to any communications received from the University.

Learning resources and detailed information about weekly assessment and learning activities can be accessed via Canvas. It is essential that you visit your unit of study Canvas site to ensure you are up to date with all of your tasks.

If you are having difficulties completing your studies, or are feeling unsure about your progress, we are here to help. You can access the support services offered by the University at any time:

Support and Services (including health and wellbeing services, financial support and learning support)
Course planning and administration
Meet with an Academic Adviser

Weekly schedule

WK	Topic	Learning activity
Multiple weeks	Definition and examples of groups and group actions; applications of orbit-stabiliser relation; homomorphisms and quotient groups; Sylow theorems and applications	Lecture (21 hr)
Multiple weeks	Polynomial rings, ideals, quotient rings, the ideal membership problem, Groebner bases, dimension and decision problems for polynomial rings	Lecture (15 hr)
Week 13	Decision problems in abstract algebra and their computational complexity	Lecture (3 hr)
Weekly	Computational aspects of the theory covered in lectures and further examples and applications through interactive worksheets in Magma	Workshop (13 hr)
Weekly	Interactive board tutorial work on problems associated to the lectures	Tutorial (12 hr)

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 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

Learning outcomes

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.

Outcomes
Graduate qualities

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

LO1. Describe groups and group actions as the mathematical language for symmetry
LO2. Describe and compare structural properties of polynomial rings and ideals
LO3. Analyse the structure of groups and group actions, including subgroups, quotient groups, and the orbit-stabiliser relation
LO4. Analyse homomorphisms between groups, including image and kernel
LO5. Evaluate solution sets to polynomial equations using elimination
LO6. Construct examples of groups and rings by hand and by using computer algebra
LO7. Create and communicate clear, logically structured proofs using algebraic reasoning
LO8. Implement, document and apply algorithms in group theory and polynomial arithmetic

Graduate qualities

The graduate qualities are the qualities and skills that all 爆料王 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鈥檚 personal and professional selves in an ethical context.
GQ9	Influence Engaging others in a process, idea or vision.

Outcome map

Learning outcomes	Graduate qualities
Learning outcomes

Responding to student feedback

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

This is the first time this unit has been offered

Disclaimer

Important: the 爆料王 regularly reviews units of study and reserves the right to change the units of study available annually. To stay up to date on available study options, including unit of study details and availability, refer to the relevant handbook.

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

爆料王

Current students

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Early feedback task

Assessment summary

Assessment criteria

Use of generative artificial intelligence (AI)

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Support for students

Weekly schedule

Weekly schedule

Study commitment

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Disclaimer

On this page

Useful links

爆料王

MATH2080: Abstract and Computational Algebra

Semester 2, 2026 [Normal day] - Camperdown/Darlington, Sydney

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Early feedback task

Assessment summary

Assessment criteria

Use of generative artificial intelligence (AI)

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Support for students

Weekly schedule

Weekly schedule

Study commitment

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Disclaimer

On this page

Useful links