Key facts
UNE unit code: PMTH432
*You are viewing the 2025 version of this unit which may be subject to change in future.
- Trimester 2 - On Campus
- Trimester 2 - Online
- Armidale Campus
- Yes
- Yes
- No
- 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 | Dates to be advised. The Intensive School if offered to online and on campus students. Delivery of this Intensive School will be delivered in a hybrid mode. Student can chose to attend either on 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 | 8% | All offerings | Problem-based assignment. |
Assignment 2 | Yes | 8% | All offerings | Problem-based assignment. |
Assignment 3 | Yes | 8% | All offerings | Problem-based assignment. |
Assignment 4 | Yes | 8% | All offerings | Problem-based assignment. |
Mini Project | Yes | 8% | All offerings | Contact your unit coordinator to make arrangements. |
Final Examination | Yes | 60% | All offerings | It is mandatory to pass the Final Examination. The Final Examination consists of two components: a written component conducted via Moodle and an oral component scheduled in consultation with your unit coordinator. Both components will be open book. For the written component you will have 15 minutes reading time, 3 hours to solve the problems and 15 minutes to submit your solutions. Unless there is suspicion of plagiarism you can only improve your mark during the oral component. |
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 is held in the University Library — purchase is optional.
Contemporary Abstract Algebra
ISBN: 9781305657960
Gallian, J.A., Cengage Learning 9th Ed. 2016
Text refers to: All offerings
Discovering Abstract Algebra
ISBN: 9781470464424
John K. Osoinach, Jr., American Mathematical Society 1st Ed. 2021
Text refers to: All offerings
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
A five-star experience
Five Stars,
18 Years in a Row
UNE is the only public uni in Australia awarded 18 straight years of five stars for Overall Experience
Good Universities Guide 2007-2024No.1 in NSW for
Student Experience
QILT (government-endorsed) ranks UNE as the top public NSW uni for Student Experience
QILT Student Experience SurveyFive Stars for
Teaching Quality
UNE rates among the top 20 per cent of universities in Australia for Teaching Quality
Good Universities Guide 2024Studying 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
Register your interest and we'll keep you updated
Why study with us?
I'm grateful to UNE for the opportunities studying has given me, but above all, for making me realise I could actually do it, and giving me a sense of accomplishment.
What happens next?
Got any questions about a course you would like to study? Don’t hesitate to contact us, our Future Student team is standing by to help.
2025 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.