Linear & Abstract Algebra & Number Theory (MATH7307)

Course overview

This course provides an introduction to the basics of linear and abstract algebra (including groups, rings & fields) & elementary number theory. Applications are included, enabling students to apply this knowledge in various fields.

The goal of this course is to give an introduction to number theory, abstract algebra, and linear algebra.

An approximate breakdown by subject is as follows:

Number theory

Divisibility, prime numbers, prime factorisation, modular arithmetic, simultaneous linear congruences, and Euler's theorem.

Abstract algebra

Definition of groups and (normal) subgroups, basic properties. Examples of groups. Lagrange’s theorem. Homomorphisms, isomorphisms, and the homomorphism theorem. Definition of rings and fields, basic properties.

Linear algebra

Definition of an abstract vector space. Subspaces, bases, dimension. Linear transformations, relations with matrices, change of basis. Eigenvalues, eigenvectors, invariant subspaces, diagonalisability, Jordan canonical form.

In the School of Mathematics and Physics we are committed to creating an inclusive and empowering learning environment for all students. We value and respect the diverse range of experiences our students bring to their education, and we believe that this diversity is crucial for fostering a rich culture of knowledge sharing and meaningful exploration. We hold both students and staff accountable for actively contributing to the establishment of a respectful and supportive learning environment.

Bullying, harassment, and discrimination in any form are strictly against our principles and againstﾠUQ Policy,ﾠand will not be tolerated. We have developed aﾠsuite of resourcesﾠto assist you in recognising, reporting, and addressing such behaviour. If you have any concerns about your experience in this course, we encourage you to tell a member of the course teaching team, or alternatively contact an SMP Classroom Inclusivity Champion (see Blackboard for contact details). Our Inclusivity Champions are here to listen, to understand your concerns, and to explore potential actions that can be taken to resolve them. Your well-being and a positive learning atmosphere are of utmost importance to us.

Course requirements

Assumed background

A knowledge of elementary linear algebra, as experienced in MATH1051 or MATH1071, is assumed. Many of the topics covered in MATH1061 are assumed knowledge.ﾠ

Prerequisites

You'll need to complete the following courses before enrolling in this one:

Knowledge equivalent to first year linear algebra and introductory discrete mathematics.

Incompatible

You can't enrol in this course if you've already completed the following:

MATH2301

Restrictions

Enrolment restricted to MCyberSec, GDSc and MSc.

Course contact

Course staff

Timetable

The timetable for this course is available on the UQ Public Timetable.

Additional timetable information

All classes will be conducted on campus. Consult your personal timetable for times and locations. Students are expected to attend these sessions unless they have a valid reason for being unable to attend (such as illness).

ﾠ

Aims and outcomes

The aim of this course is to introduce and develop the basic theory of linear and abstract algebra and of elementary number theory, in a mathematically rigorous way.

Learning outcomes

After successfully completing this course you should be able to:

Assessment

Assessment summary

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

Assignment 1

Mode

Written

Category

Tutorial/ Problem Set

Weight

15%

Due date

11/04/2025 3:00 pm

Task description

Submission guidelines

Assignment 1 must be submitted electronically through Blackboard as a single pdf file. Ensure that your name, student number and tutorial group number appear on the first page of your submission. Make sure that your pdf file is legible and that the file size is not excessive. Use the assignment submission link in Blackboard to submit the pdf file.

Pay careful attention to the general university guidelines on plagiarism. You are welcome to work in small groups, particularly in tutorial classes. However, assignments must be completed individually, so everything you submit must be your own work. Inappropriate copying or excessive collaboration will be taken very seriously.

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.

As solutions will be released 7 days after the due date, there are no extensions beyond 7 days.

See ADDITIONAL ASSESSMENT INFORMATION for further 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.

You are required to submit assessable items on time. If you fail to meet the submission deadline for any assessment item then the listed penalty will be deducted per day for up to 7 calendar days, at which point any submission will not receive any marks unless an extension has been approved. Each 24-hour block is recorded from the time the submission is due. Solutions will be released 7 days after the due date.

Assignment 2

Mode

Written

Category

Tutorial/ Problem Set

Weight

15%

Due date

30/05/2025 3:00 pm

Task description

Submission guidelines

Assignment 2 must be submitted electronically through Blackboard as a single pdf file. Ensure that your name, student number and tutorial group number appear on the first page of your submission. Make sure that your pdf file is legible and that the file size is not excessive. Use the assignment submission link in Blackboard to submit the pdf file.

Pay careful attention to the general university guidelines on plagiarism. You are welcome to work in small groups, particularly in tutorial classes. However, assignments must be completed individually, so everything you submit must be your own work. Inappropriate copying or excessive collaboration will be taken very seriously.

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.

As solutions will be released 7 days after the due date, there are no extensions beyond 7 days.

See ADDITIONAL ASSESSMENT INFORMATION for further 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.

You are required to submit assessable items on time. If you fail to meet the submission deadline for any assessment item then the listed penalty will be deducted per day for up to 7 calendar days, at which point any submission will not receive any marks unless an extension has been approved. Each 24-hour block is recorded from the time the submission is due. Solutions will be released 7 days after the due date.

Final exam

• Hurdle
• Identity Verified
• In-person

Mode

Written

Category

Examination

Weight

60%

Due date

End of Semester Exam Period

7/06/2025 - 21/06/2025

Task description

Hurdle requirements

Exam details

Submission guidelines

Deferral or extension

You may be able to defer this exam.

See ADDITIONAL ASSESSMENT INFORMATION for further extension/deferral information relating to this assessment item.

Project

Mode

Product/ Artefact/ Multimedia, Written

Category

Project

Weight

10%

Due date

30/05/2025 5:00 pm

Task description

Submission guidelines

Submission details will be provided closer to the due date.

Deferral or extension

You may be able to apply for an extension.

The maximum extension allowed is 21 days. Extensions are given in multiples of 24 hours.

The maximum extension is 21 days so that the project can be marked before grades are required to be submitted.

See ADDITIONAL ASSESSMENT INFORMATION for further 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.

Course grading

Full criteria for each grade is available in the Assessment Procedure.

Additional course grading information

Your overall mark is the sum of your two assignment marks, each out of 15, your project out of 10, and your end-of-semester exam mark out of 60.

Supplementary assessment

Supplementary assessment is available for this course.

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

Library resources are available on the UQ Library website.

Learning activities

The learning activities for this course are outlined below. Learn more about the learning outcomes that apply to this course.

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.