Key facts
UNE unit code: PMTH432
*You are viewing the 2026 version of this unit which may be subject to change in future.
- Trimester 2 - On Campus
- Trimester 2 - Online
- Armidale Campus
- Yes
- Yes
- Yes
- 6
Unit information
Abstraction makes mathematics widely applicable, and algebra makes computation possible. Building on your foundation in linear algebra, this unit will extend your understanding of the central concepts of modern algebra, fostering your independence and creativity.
This unit will introduce you to the theory of groups and rings. You will explore basic properties, subgroups and subrings, quotient structures, products of groups and rings, and isomorphism theorems.
You will meet key results such as the Fundamental Theorem of Finitely Generated Abelian Groups and the Sylow Theorems as well as cyclic groups, polynomial rings and fields of quotients.
Seize the opportunity to boost your theoretical understanding, your ability to construct proofs and your communication of complex concepts to prepare for further studies in advanced mathematics.
In PMTH432, a mini project chosen in negotiation with your supervisor will provide you with additional opportunities at a more advanced level.
Offerings
For further information about UNE's teaching periods, please go to Principal Dates.
| Teaching period | Mode/location |
|---|---|
| Trimester 2 | On Campus, Armidale Campus |
| Trimester 2 | Online |
*Offering is subject to availability
Intensive schools
| Start | Finish | Duration | Attendance | Offerings | Notes |
|---|---|---|---|---|---|
| TBA | TBA | 2 days | Non-Mandatory Intensive School | All offerings | The Intensive School is offered to online and on campus students. Delivery of this Intensive School will be delivered in a hybrid mode. Students can choose to attend either online or on campus in Armidale. |
Enrolment rules
Notes
Please refer to the student handbook for current details on this unit.
Unit coordinator(s)
Learning outcomes
Upon completion of this unit, students will be able to:
- demonstrate an understanding of advanced topics in algebra;
- demonstrate an understanding of central concepts of modern algebra;
- develop advanced theoretical understanding and computational methods;
- prepare themselves for further studies in number theory, commutative algebra, Lie algebras, algebraic geometry, representation theory, algebraic topology, homological algebra, category theory;
- apply their knowledge and communication skills to illustrate, demonstrate and teach modern mathematics; and
- demonstrate autonomy, well-developed judgement and adaptability to critically analyse and evaluate information and transmit solutions to complex problems.
Assessment information
Assessments are subject to change up to 8 weeks prior to the start of the teaching period in which you are undertaking the unit.
| Title | Must Complete | Weight | Offerings | Assessment Notes |
|---|---|---|---|---|
| Assignment 1 | Yes | 4% | All offerings | Problem-based assignment. |
| Assignment 2 | Yes | 4% | All offerings | Problem-based assignment. |
| Assignment 3 | Yes | 4% | All offerings | Problem-based assignment. |
| Assignment 4 | Yes | 4% | All offerings | Problem-based assignment. |
| Final Examination - Assurance Task | Yes | 80% | All offerings | It is mandatory to pass the Final Examination. |
| Mini Project | Yes | 4% | All offerings | Supervised extension topic |
Learning resources
Textbooks are subject to change up to 8 weeks prior to the start of the teaching period in which you are undertaking the unit.
Note: Recommended material may be held in the University Library — purchase is optional.
Discovering Abstract Algebra
ISBN: 9781470464424
John K. Osoinach, Jr., American Mathematical Society 1st Ed. 2021
Text refers to: All offerings
Contemporary Abstract Algebra
ISBN: 9781305657960
Gallian, J.A., Cengage Learning 9th Ed. 2016
Text refers to: All offerings
Note: Referenced material may be held in the University Library — purchase is optional.
Algebra
ISBN: 9780821816462
MacLane, S. and Birkhoff, G., American Mathematical Society 3rd ed. 1999
Text refers to: All offerings
Basic Algebra I
ISBN: 9780486471891
Jacobson, N., Freeman 2nd ed. 2009
Text refers to: All offerings
Excellence in experience, equity and employability
Five Stars,
20 Years in a Row
UNE is the only public uni in Australia awarded 20 straight years of five stars for Overall Experience.
Good Universities Guide 2007-2026
Five Stars for
Social Equity
UNE rates among the top 20% of universities nationally and is #1 in NSW for Social Equity.
Good Universities Guide 2026
Five Stars for
Graduate Employment
UNE rates among the top 20% of universities for Graduate Full-Time Employment and Starting Salary.
Good Universities Guide 2026 (Undergraduate)
Diamond-Rated Digital Learning
UNE’s leadership in digital learning earned the highest ‘Diamond’ rating in a peer review.
ASCILITE TELAS 2025
Studying online
At UNE we know it takes more than just being online to be a great online university. It takes time and experience. We pioneered distance education for working adults back in the 1950s, so we’ve been doing this longer than any other Australian university.
We understand the challenges faced by busy adults studying at home. We know that a vital part of online study is your engagement with the learning community. Communication with your classmates, teaching staff and university support staff will enhance your study experience and ensure that your skills extend beyond the subject matter. UNE’s teaching staff are experts in their field which is why UNE consistently receives five stars from students for teaching quality, support and overall experience.*
*The Good Universities Guide
Stay connected
Join our mailing list for updates and helpful tips to support your study plans. You can unsubscribe at any time.
- •Course updates and important changes as they happen
- •Key dates for intakes, deadlines, and enrolment steps
- •Application guidance, including supporting documentation requirements
- •Next steps and what to expect after you apply or enquire
Ready to stay in the loop?
GET IN TOUCH
Why study with us?
UNE’s flexibility and support made the transition smooth and helped me find a great balance between academic responsibilities and personal growth. It was the perfect place to study education while staying true to my rural roots.
What happens next?
Got a question about a course you'd like to study? Contact our Future Student Team for help.
2026 applications are now open. The application process only takes 20 minutes to complete. Don’t delay, apply now!
Your start date is based on the study period you choose to apply for.
