Course overview
- Study period
- Semester 1, 2025 (24/02/2025 - 21/06/2025)
- Study level
- Postgraduate Coursework
- Location
- St Lucia
- Attendance mode
- In Person
- Units
- 2
- Administrative campus
- St Lucia
- Coordinating unit
- Mathematics & Physics School
MATH7333 covers key topics in group theory and ring theory, with a view towards commutative algebra, algebraic number theory and representation theory.
This course covers topics fromﾠ modern algebraﾠ, especially groups and rings.ﾠ This is an essential course for any student wishing to undertake further study in pure mathematics and mathematical physics.
Course requirements
Assumed background
MATH1061 and MATH2301 (or their equivalents).
Prerequisites
You'll need to complete the following courses before enrolling in this one:
Permission of Head of School
Incompatible
You can't enrol in this course if you've already completed the following:
MATH3303 (co-taught)
Jointly taught details
This course is jointly-taught with:
This course is taught jointly with MATH7333 and will share learning activities. The students from MATH7333 have extra questions on their assignments to evaluate students at Level 9 (Masters) of the Australian Qualifications Framework.
Course contact
Course staff
Lecturer
Timetable
The timetable for this course is available on the UQ Public Timetable.
Additional timetable information
There will be no lectures or practicals on public holidays.
Aims and outcomes
On successfulﾠcompletion of this course studentsﾠshould have a solid understanding of the fundamentals of groups, rings and fields.
Learning outcomes
After successfully completing this course you should be able to:
LO1.
Group theory - After completion of this course students should have a solid understanding of the essentials of modern group theory. Topics covered include the three isomorphism theorems, the notion of solvable and simple groups, the JordanHlder theorem and the extension problem.
LO2.
Ring theory - After completion of this course students should have a solid understanding of basic ring theory. Topics covered include ideals, the characteristic of a ring, the isomorphism theorems for rings, domains and integral domains, fraction fields and unique factorsation domains.
Assessment
Assessment summary
| Category | Assessment task | Weight | Due date |
|---|---|---|---|
| Tutorial/ Problem Set |
Assignments
|
30% |
21/03/2025 4:00 pm 11/04/2025 4:00 pm 9/05/2025 4:00 pm 30/05/2025 4:00 pm |
| Quiz |
Quiz 1
|
20% |
24/03/2025 2:00 pm |
| Quiz |
Quiz 2
|
20% |
14/04/2025 2:00 pm |
| Quiz |
Quiz 3
|
30% |
19/05/2025 2:00 pm |
A hurdle is an assessment requirement that must be satisfied in order to receive a specific grade for the course. Check the assessment details for more information about hurdle requirements.
Assessment details
Assignments
- Online
- Mode
- Written
- Category
- Tutorial/ Problem Set
- Weight
- 30%
- Due date
21/03/2025 4:00 pm
11/04/2025 4:00 pm
9/05/2025 4:00 pm
30/05/2025 4:00 pm
Task description
There will be 4 assignments, each worth 7.5%.
Submission guidelines
Submit using Gradescope.
Deferral or extension
You may be able to apply for an extension.
The maximum extension allowed is 7 days. Extensions are given in multiples of 24 hours.
Solutions will be released after 7 days so that is the maximum extension possible.
See ADDITIONAL ASSESSMENT INFORMATION for extension/deferral information relating to this assessment item.
Late submission
A penalty of 10% of the maximum possible mark will be deducted per 24 hours from time submission is due for up to 7 days. After 7 days, you will receive a mark of 0.
Quiz 1
- In-person
- Mode
- Written
- Category
- Quiz
- Weight
- 20%
- Due date
24/03/2025 2:00 pm
Task description
Quiz 1 will be conducted in class.
Submission guidelines
Submit in the lecture.
Deferral or extension
You cannot defer or apply for an extension for this assessment.
If you miss either quiz 1 or 2 for a valid reason (e.g. with a medical certificate), then your other two quizzes will count for more. If you miss two quizzes or more, or if you miss quiz 3, then you must do an oral examination.
Quiz 2
- In-person
- Mode
- Written
- Category
- Quiz
- Weight
- 20%
- Due date
14/04/2025 2:00 pm
Task description
Quiz 2 will be conducted in class.
Submission guidelines
Submit in person in the lecture.
Deferral or extension
You cannot defer or apply for an extension for this assessment.
If you miss either quiz 1 or 2 for a valid reason (e.g. with a medical certificate), then your other two quizzes will count for more. If you miss two quizzes or more, or if you miss quiz 3, then you must do an oral examination.
Quiz 3
- Hurdle
- In-person
- Mode
- Written
- Category
- Quiz
- Weight
- 30%
- Due date
19/05/2025 2:00 pm
Task description
Quiz 3 will be conducted in class.
Hurdle requirements
See COURSE GRADING INFORMATION for the hurdle relating to this assessment item.Submission guidelines
Submit in person in the lecture.
Deferral or extension
You cannot defer or apply for an extension for this assessment.
If you miss either quiz 1 or 2 for a valid reason (e.g. with a medical certificate), then your other two quizzes will count for more. If you miss two quizzes or more, or if you miss quiz 3, then you must do an oral examination.
Course grading
Full criteria for each grade is available in the Assessment Procedure.
| Grade | Description |
|---|---|
| 1 (Low Fail) |
Absence of evidence of achievement of course learning outcomes. Course grade description: Fails to demonstrate most or all of the basic requirements of the course:ﾠ A student will earn a mark of less than 20% if they show a poor knowledge of the basic concepts in the course material. This may include attempts at answering some questions showing an extremely poor understanding of the key concepts. |
| 2 (Fail) |
Minimal evidence of achievement of course learning outcomes. Course grade description: Demonstrates clear deficiencies in understanding and applying fundamental concepts; communicates information or ideas in ways that are frequently incomplete or confusing and give little attention to the conventions of the discipline. To earn a mark of 20% a student must demonstrate some knowledge of the basic concepts in the course material. This includes attempts at expressing their deductions and explanations and attempts to answer a few questions accurately. |
| 3 (Marginal Fail) |
Demonstrated evidence of developing achievement of course learning outcomes Course grade description: Demonstrates superficial or partial or faulty understanding of the fundamental concepts of the field of study and limited ability to apply these concepts; presents undeveloped or inappropriate or unsupported arguments; communicates information or ideas with lack of clarity and inconsistent adherence to the conventions of the discipline. To earn a mark of 45%, a student must demonstrate some knowledge of the basic concepts in the course material. This includes occasional expression of their deductions and explanations, the use of a few appropriate and efficient mathematical techniques and attempts to answer a few questions and tasks accurately and with appropriate justification. They will have demonstrated knowledge of techniques used to solve problems. |
| 4 (Pass) |
Demonstrated evidence of functional achievement of course learning outcomes. Course grade description: Demonstrates adequate understanding and application of the fundamental concepts of the field of study; develops routine arguments or decisions and provides acceptable justification; communicates information and ideas adequately in terms of the conventions of the discipline. To earn a mark of 50%, a student must demonstrate an understanding of the basic concepts in the course material. This includes occasionally expressing their deductions and explanations clearly, the occasional use of appropriate and efficient mathematical techniques and accurate answers to a few questions and tasks with appropriate justification. They will have demonstrated knowledge of techniques used to solve problems and applied this knowledge in some cases. |
| 5 (Credit) |
Demonstrated evidence of proficient achievement of course learning outcomes. Course grade description: Demonstrates substantial understanding of fundamental concepts of the field of study and ability to apply these concepts in a variety of contexts; develops or adapts convincing arguments and provides coherent justification; communicates information and ideas clearly and fluently in terms of the conventions of the discipline. To earn a mark of 65%, a student must demonstrate an adequate understanding of the course material. This includes clear expression of some of their deductions and explanations, the use of appropriate and efficient mathematical techniques in some situations and accurate answers to some questions and tasks with appropriate justification. They will be able to apply mathematical techniques to solve fundamental problems. |
| 6 (Distinction) |
Demonstrated evidence of advanced achievement of course learning outcomes. Course grade description: As for 5, with frequent evidence of originality in defining and analysing issues or problems and in creating solutions; uses a level, style and means of communication appropriate to the discipline and the audience. To earn a mark of 75%, a student must demonstrate a comprehensive understanding of the course material. This includes clear expression of most of their deductions and explanations, the general use of appropriate and efficient mathematical techniques and accurate answers to most questions and tasks with appropriate justification. They will be able to apply mathematical techniques to partially solve problems and provide clear and rigorous justification for their solutions. |
| 7 (High Distinction) |
Demonstrated evidence of exceptional achievement of course learning outcomes. Course grade description: As for 6, with consistent evidence of substantial originality and insight in identifying, generating and communicating competing arguments, perspectives or problem solving approaches; critically evaluates problems, their solutions and implications. To earn a mark of 85%, a student must demonstrate an excellent understanding of the course material.ﾠﾠThis includes clear expression of nearly all their deductions and explanations, the use of appropriate and efficient mathematical techniques and accurate answers to nearly all questions and tasks with appropriate justification. They will be able to apply mathematical techniques to completely solve problems and provide clear, complete and rigorous justification for their solutions. |
Additional course grading information
You need 40% combined on the quizzes to obtain a grade of 4 or higher.
Supplementary assessment
Supplementary assessment is available for this course.
Should you fail a course with a grade of 3, you may be eligible for supplementary assessment. Refer to my.UQ for information on supplementary assessment and how to apply.
Supplementary assessment provides an additional opportunity to demonstrate you have achieved all the required learning outcomes for a course.
If you apply and are granted supplementary assessment, the type of supplementary assessment set will consider which learning outcome(s) have not been met.
Supplementary assessment in this course will be an oral examination. To receive a passing grade of 3S4, you must obtain a mark of 50% or more on the supplementary assessment.
Additional assessment information
Artificial Intelligence
Assessment tasks in this course evaluate students' abilities, skills and knowledge without the aid of generative Artificial Intelligence (AI) or Machine Translation (MT). Students are advised that the use of AI or MT technologies to develop responses is strictly prohibited and may constitute student misconduct under the Student Code of Conduct.
Applications for Extensions to Assessment Due Dates
Extension requests are submitted online via my.UQ – applying for an extension. Extension requests received in any other way will not be approved. Additional details associated with extension requests, including acceptable and unacceptable reasons, may be found at my.UQ.
Please note:
- Requests for an extension to an assessment due date must be submitted through your my.UQ portal and you must provide documentation of your circumstances, as soon as it becomes evident that an extension is needed. Your application must be submitted on or before the assessment item's due date and time.
- Applications for extension can take time to be processed so you should continue to work on your assessment item while awaiting a decision. We recommend that you submit any completed work by the due date, and this will be marked if your application is not approved. Should your application be approved, then you will be able to resubmit by the agreed revised due date.
- If an extension is approved, you will be notified via your my.UQ portal and the new date and time for submission provided. It is important that you check the revised date as it may differ from the date that you requested.
- If the basis of the application is a medical condition, applications should be accompanied by a medical certificate dated prior to the assignment due date. If you are unable to provide documentation to support your application by the due date and time you must still submit your application on time and attach a written statement (Word document) outlining why you cannot provide the documentation. You must then upload the documentation to the portal within 24 hours.
- If an extension is being sought on the basis of exceptional circumstances, it must be accompanied by supporting documentation (eg. Statutory declaration).
- For extensions based on a SAP you may be granted a maximum of 7 days (if no earlier maximum date applies). See the Extension or Deferral availability section of each assessment for details. Your SAP is all that is required as documentation to support your application. However, additional extension requests for the assessment item will require the submission of additional supporting documentation e.g., a medical certificate. All extension requests must be received by the assessment due date and time.
- Students may be asked to submit evidence of work completed to date. Lack of adequate progress on your assessment item may result in an extension being denied.
- If you have been ill or unable to attend class for more than 14 days, you are advised to carefully consider whether you are capable of successfully completing your courses this semester. You might be eligible to withdraw without academic penalty - seek advice from the Faculty that administers your program.
- There are no provisions for exemption from an assessment item within UQ rules. If you are unable to submit an assessment piece then, under special circumstances, you may be granted an exemption, but may be required to submit alternative assessment to ensure all learning outcomes are met.
Applications to defer an exam
In certain circumstances you can apply to take a deferred examination for in-semester and end-of-semester exams. You'll need to demonstrate through supporting documentation how unavoidable circumstances prevented you from sitting your exam. If you can’t, you can apply for a one-off discretionary deferred exam.
Deferred Exam requests are submitted online via mySi-net. Requests received in any other way will not be approved. Additional details associated with deferred examinations, including acceptable and unacceptable reasons may be found at my.UQ.
Please note:
- Applications can be submitted no later than 5 calendar days after the date of the original exam.
- There are no provisions to defer a deferred exam. You need to be available to sit your deferred examination.
- Your deferred examination request(s) must have a status of "submitted" in mySI-net to be assessed.
- All applications for deferred in-semester examinations are assessed by the relevant school. Applications for deferred end-of-semester examinations are assessed by the Academic Services Division.
- You’ll receive an email to your student email account when the status of your application is updated.
- If you have a medical condition, mental health condition or disability and require alternative arrangements for your deferred exam you’ll need to complete the online alternative exam arrangements through my.UQ. This is in addition to your deferred examinations request. You need to submit this request on the same day as your request for a deferred exam or supplementary assessment. Contact Student Services if you need assistance completing your alternative exam arrangements request.
Learning resources
You'll need the following resources to successfully complete the course. We've indicated below if you need a personal copy of the reading materials or your own item.
Library resources
Find the required and recommended resources for this course on the UQ Library website.
Additional learning resources information
The most important resource for the course is to attend lectures and take your own notes. You may find the following books helpful:
"Abstract Algebra" by D.S. Dummit and R.M. Foote
"Algebra" by M. Artin
"Introduction to Abstract Algebra" by W.K. Nicholson (An e-version of this book is available at the UQ library)
"Modern Algebra, An Introduction" by J.R. Durbin
Learning activities
The learning activities for this course are outlined below. Learn more about the learning outcomes that apply to this course.
Filter activity type by
Please select
| Learning period | Activity type | Topic |
|---|---|---|
Multiple weeks |
Lecture |
Lecture classes Three traditional black/whiteboard lectures per week. Students are expected to actively participate by taking notes, asking questions, and by answering weekly homework problems. |
Practical |
Practicals During the practical students can work on the assignment problems (some of which are deliberately hard and require assistance from the tutor). |
Policies and procedures
University policies and procedures apply to all aspects of student life. As a UQ student, you must comply with University-wide and program-specific requirements, including the:
- Student Code of Conduct Policy
- Student Integrity and Misconduct Policy and Procedure
- Assessment Procedure
- Examinations Procedure
- Reasonable Adjustments - Students Policy and Procedure
Learn more about UQ policies on my.UQ and the Policy and Procedure Library.