Key facts
UNE unit code: PMTH432
*You are viewing the 2024 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.
Basic Algebra I
ISBN: 9780486471891
Jacobson, N., Freeman 2nd ed. 2009
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
Contemporary Abstract Algebra
ISBN: 9781305657960
Gallian, J.A., Cengage Learning 9th Ed. 2016
Text refers to: All offerings
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