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Example Unit Outline (refreshed)

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Date: Thursday, 6 August 2026, 9:29 PM

Table of contents

1. Introduction and Assessment Overview

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PMTH332 Abstract Algebra

Trimester 2 2026


This Unit Outline should be read in conjunction with the information contained in the Unit Information and Resources section of this myLearn site. If this is your first unit of study at UNE, please also ensure you have completed the mandatory Academic Integrity Module (AIM).

Introduction

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.


Learning Outcomes

Upon completion of this unit, students will be able to:

  1. demonstrate an understanding of basic topics in Abstract Algebra;
  2. demonstrate a preliminary understanding of central elementary concepts of modern algebra;
  3. continue the unification of earlier material commenced in PMTH213;
  4. develop both theoretical understanding and computational methods;
  5. prepare themselves for further studies in number theory, commutative algebra, Lie algebras, algebraic geometry, representation theory, algebraic topology, homological algebra, category theory; and
  6. illustrate, demonstrate and teach modern mathematics.

Unit specific information can be found on the UNE Handbook: PMTH332


Assessment Summary

Detailed information about each assessment task, including due dates, submission requirements and marking criteria, are available within the Assessments section of this myLearn site.


Assessment Weighting Mandatory Description Offerings Related Learning Outcomes
Assignment 1 5% Yes

Problem-based assignment.

 All 1 2 3 4 5 6
Assignment 2 5% Yes

Problem-based assignment.

 All 1 2 3 4 5 6
Assignment 3 5% Yes

Problem-based assignment.

 All 1 2 3 4 5 6
Assignment 4 5% Yes

Problem-based assignment.

 All 1 2 3 4 5 6
Final Examination - Assurance Task 80% Yes

The final examination is an online, proctored examination. You will handwrite answers and scan and upload them to a submission portal.

 All 1 2 3 4 5 6

Note: Students who do not submit all mandatory ('must complete') assessments will be marked as incomplete and will be unable to pass the unit.
Referencing

Referencing is a way of acknowledging the works of others. If your Unit Coordinator has not specified the required referencing style, you should follow the referencing style used by the subject area in which you are studying. If you have questions about referencing, you should contact the Academic Skills Office or your Unit Coordinator.

Plagiarism

Plagiarism is using the work of other people without appropriate acknowledgement. Plagiarism is a form of academic misconduct under the Student Academic Integrity Policy. Advice on avoiding plagiarism is available from the Academic Skills Office.

Extensions and Late Submission Penalties

Information about extensions and penalties for late submission are available via the Assessment Policy. General guidance on how to apply for an extension can be found at askUNE, though processes may vary between Schools. For more information about School-specific policies and processes related to assessments and extensions, please see the School Information site linked in the Block on the right-hand side of your myLearn site.

Marking, Moderation and Feedback

Information about marking, moderation and feedback is available via the Assessment Policy. Please be aware that assessment tasks in this unit may be marked by someone other than the Unit Coordinator. If more than one marker is involved in marking, moderation of marks will be applied to ensure that the assessment criteria are consistently applied.

Approval of Results by Board of Examiners

Please be aware that marks for assessment tasks displayed through the myLearn site are provided as a guide to your progress in the unit. They are not your official grades for the unit. Results displayed are provisional and subject to change. Official results are available in  myUNE following ratification by the Board of Examiners in the relevant School.

UNE Grade Descriptors

The grading system and descriptors used by UNE are outlined in the Assessment Policy Grading System . Additional information about results and grades can be found at askUNE.

Intensive School

Non-Mandatory Intensive School

This unit has a Non-Mandatory Intensive School. Students may either attend voluntarily, or be provided with alternative activities that achieve the same learning outcomes. Non-Mandatory Intensive Schools require a minimum number of student registrations to run, and will have a cut-off date for registration. More information is available within the Intensive School section of this myLearn site and the Intensive School Procedures.

Intensive schools are for off campus students only, unless specified in the notes.

An intensive school will be held on the following dates (inclusive):

Start Finish Duration Attendance Offerings Notes
13 August 2026 14 August 2026 2 days Non-Mandatory Intensive School 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.

Students are advised to make refundable travel arrangements wherever possible in the event that a Non-Mandatory Intensive School is cancelled or the minimum number of student registrations is not obtained.
Please note that the Armidale campus is located on a hill with steep slopes between some buildings. If this may be difficult for you to navigate, please reach out to your unit coordinator first. You may also contact the Student Accessibility & Wellbeing Office at 02 6773 2897 or accessinclusion@une.edu.au


Unit Outline Created:
09 July 2026 10:04 am

2. Learning Resources and Support

Learning Resources 
Students are expected to purchase Prescribed Materials. Purchase of Recommended Materials is optional - most recommended texts are held in the University Library.  Click here for more information on how and where to buy textbooks, or click on the images below (if present) to find the resource in the UNE Life Campus Books Shop.

Recommended Texts

material thumbnail isbn 9781305657960

Contemporary Abstract Algebra
ISBN: 9781305657960
Gallian, J.A., Cengage Learning 9th ed. 2016
Offerings: All

material thumbnail isbn 9781470464424

Discovering Abstract Algebra
ISBN: 9781470464424
John K. Osoinach, Jr. American Mathematical Society 1st ed 2021
Offerings: All
Referenced Texts

material thumbnail isbn 9780821816462

Algebra
ISBN: 9780821816462
MacLane, S. and Birkhoff, G., American Mathematical Society 3rd ed. 1999
Offerings: All

material thumbnail isbn 9780486471891

Basic Algebra I
ISBN: 9780486471891
Jacobson, N., Freeman 2nd ed. 2009
Offerings: All

Reading List

There may be readings in this unit in addition to those identified here and in the Reading List. Additional readings and resources are normally provided, with the appropriate link, within the unit materials. If you encounter a broken link in your myLearn site, please contact the Unit Coordinator.

Support and Resources

The Unit Coordinator and/or Site Contacts listed in this site are the best people to contact if you have questions about the content of this unit, the assessments and your grades. The best way to contact your Unit Coordinator (e.g. phone, email or direct message) will be indicated in the Unit Information and Resources section. 

There are a range of other support services and resources available to help you succeed in your studies. Click on each of the options below for further information. 


Policies and Information

UNE Policies
All UNE policies and procedures are accessible via the UNE Policy Register. Students should be aware of the following policies in particular:
Teaching and Learning Expectations for Staff and Students

UNE is committed to excellence in teaching and learning by providing a secure, supportive and stimulating environment that facilitates a positive student learning experience. The Teaching and Learning Expectations for Staff and Students includes a list of expectations that have been formulated to build the environment that we wish to create.

Principal Dates 
Important dates for each teaching period, including start and end dates, Census Day, last day to enrol, last day to withdraw without academic penalty and release of results are accessible via the UNE Principal Dates website.