Discrete Mathematics (MATH7861)

Course overview

Propositional & predicate logic, valid arguments. Elementary set theory. Elementary graph theory. Relations & functions, categories. Induction & recursive definitions. Counting methods (pigeonhole, inclusion/exclusion). Introductory probability. Binary operations, semi-groups, groups, fields. Applications of finite fields. Elementary number theory.

This course provides an introduction to discrete mathematics. It is likely to be useful for students who are planning on studying more mathematics, those intending to teach, and also for those enrolled in computer science, engineering, science and information technology.

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

There is no particular assumed background, apart from a level of mathematical sophistication such as that developed by completing a senior secondary mathematics subject such as General Mathematics or Mathematical Methods. Year 10 level algebra skills, such as factoring polynomials and simplifying algebraic fractions, will be required.

Incompatible

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

MATH1061 (co-taught), MATH1081

Course contact

Course staff

Timetable

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

Additional timetable information

The three lectures per week (no repeats) will be conducted on campus at the times and locations advertised in your personal timetable. ﾠAll lectures (except Lecture 1) will have associated pre-work that you are expected to complete before attending the lecture.ﾠ Lectures themselves will be focused on problem-solving and applying the concepts seen in pre-work. All students are expected to attend these sessions in person unless they have a valid reason for being unable to attend (such as illness). If you are unable to attend a lecture, you can catch up by watching the lecture recording available in Blackboard.

Your weekly applied class will be conducted on campus – consult your personal timetable for times and locations. You should attend at least one applied class per week, but you may attend more if you like. Sign up for ONE applied class time, and this applied class time will be your designated applied class, although you may choose to attend other applied classes if there is space available. Note that applied classes start in Week 2.

Friday 3rd of April and Monday 4th of May are public holidays. There are no lectures or applied classes on these days. If your designated applied class falls on a public holiday, you should plan to attend a different applied class in that week.ﾠ

Aims and outcomes

The broad aim of this course is to provide students with a solid basis for mathematical reasoning and the opportunity to apply this reasoning to problems in mathematics.

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

Applied Classes Exercises

• In-person

Mode

Written

Category

Tutorial/ Problem Set

Weight

40% The best 8 out of 12 will count for assessment.

Due date

Week 2 2/03/2026 - 6/03/2026

Week 3 9/03/2026 - 13/03/2026

Week 4 16/03/2026 - 20/03/2026

Week 5 23/03/2026 - 27/03/2026

Week 6 30/03/2026 - 2/04/2026

Week 7 13/04/2026 - 17/04/2026

Week 8 20/04/2026 - 24/04/2026

Week 9 27/04/2026 - 1/05/2026

Week 10 5/05/2026 - 8/05/2026

Week 11 11/05/2026 - 15/05/2026

Week 12 18/05/2026 - 22/05/2026

Week 13 25/05/2026 - 29/05/2026

The exercises are to be completed during the weekly Applied Classes, except in Week 1. If you cannot attend your scheduled applied class, you may attend another applied class that week. Information about all available applied classes will be provided on the course website.

Learning outcomes

L01, L02, L03, L04, L05

Task description

Submission guidelines

Submit your work in person during an Applied Class. You may attend any applied class, not only the one listed on your timetable.

Deferral or extension

You cannot defer or apply for an extension for this assessment.

If you miss your scheduled Applied Class, you may attend any other Applied Class that week. Submissions are not accepted outside the week in which the work is set.

Extensions or deferrals are not available for this assessment, as all work is completed in class.

If you are unable to submit the exercise in a week for any reason then you will receive 0 marks for that Applied Class. However, we automatically count your best 8 out 12 Applied Class marks so it is possible to miss up to 4 Applied Classes and still receive full marks. If you miss more than 4 Applied Classes then you are advised to carefully consider whether you are capable of successfully completing your courses this semester.

Assignment

Mode

Written

Category

Essay/ Critique

Weight

5%

Due date

Due Date: Friday April 24 at 4:00 pm.

Learning outcomes

L01, L02, L03, L04, L05

Task description

Submission guidelines

Submit PDF via course website

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 for assessment item will be released 7 days after the assessment is due and as such, an extension after 7 days will not be possible.

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.

Solutions for assignments will be released 7 days after the assessment is due and as such, late submission after 7 days from the original time submission is due will not be possible, regardless of approved extensions.

End of Semester examination

• Hurdle
• Identity Verified
• In-person

Mode

Written

Category

Examination

Weight

55%

Due date

End of Semester Exam Period

6/06/2026 - 20/06/2026

Other conditions

Secure.

See the conditions definitions

Learning outcomes

L01, L02, L03, L04

Task description

Hurdle requirements

Exam details

Submission guidelines

Deferral or extension

You may be able to defer this exam.

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

Course grading

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

Additional course grading information

Note the final exam hurdles for each grade.

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. 

Supplementary assessment in this course will be a 2-hour examination similar in style to the end-of-semester examination. To receive a passing grade of 3S4, you must obtain a mark of 50% or more on the supplementary assessment.

Additional assessment information

Calculators: Only approved non-programmable calculators will be allowed for student use in examinations. With the exception of the Casio fx-82 series, all calculators must have an official "Approved" label attached. Please see the website https://my.uq.edu.au/services/manage-my-program/exams-and-assessment/sitting-exam/approved-calculatorsﾠ for more information.

Artificial Intelligence

To pass this course, students will be required to demonstrate a detailed understanding of course material together with a range of associated skills independent of Artificial Intelligence (AI) and Machine Translation (MT) tools.

For assessment tasks that are completed in-person (including examinations) termed “secure assessment”, the use of generative Artificial Intelligence (AI) or Machine Translation (MT) tools will not be permitted unless otherwise advised. Any attempted use of AI or MT may constitute student misconduct under the Student Code of Conduct.

Other non-secure assessment tasks (such as assignments) are designed to help you develop your understanding and skills, and to prepare you for secure assessment. You are thus generally encouraged to complete such assessment without the use of AI/MT, unless explicitly advised to the contrary in the assessment item. In any event, if you choose to use such tools, then you must clearly reference any such use within your submitted work. A failure to reference AI or MT use 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

Additional support for the material in MATH1061 is available in the First Year Learning Centre for Mathematics. Casual academics will be available each weekday, starting in week 1, in rooms 442 and 443 of building 67. There is no need to make an appointment, just drop-in with your discrete mathematics questions.

An online discussion board for the course will also be made available, which will be monitored by course staff and fellow students.ﾠ A link to the online discussion board will be provided on Blackboard.

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 for Students Policy and Procedure
• AI for Assessment Guide

Learn more about UQ policies on my.UQ and the Policy and Procedure Library.