68104 Mathematics for Secondary Education - Discrete Mathematics
Warning: The information on this page is indicative. The subject outline for a
particular session, location and mode of offering is the authoritative source
of all information about the subject for that offering. Required texts, recommended texts and references in particular are likely to change. Students will be provided with a subject outline once they enrol in the subject.
Subject handbook information prior to 2025 is available in the Archives.
Credit points: 6 cp
Result type: Grade and marks
There are course requisites for this subject. See access conditions.
Anti-requisite(s): 37181 Discrete Mathematics
Description
This subject gives students the foundation for logical thinking and working, essential for computer scientists and mathematics majors. It covers from scratch the basics of logic, set theory (mathematical notation), functions, counting, proving mathematical statements, analysing the complexity and correctness of algorithms, and some basic number theory.
Contribution to the development of graduate attributes
1. Disciplinary knowledge and its appropriate application
The lectures and workshops will allow students to develop practical and theoretical skills in discrete mathematics.
2. An Enquiry-oriented approach
The collaborative approach to problem formulations and solutions used in the workshops helps students develop skills in idenitifying and evaluating alternative approaches to solving problems.
3. Professional skills and their appropriate application
The ability to work effectively and responsibly in a group is emphasised in the group-based discussion components of the workshops.
6. Communication skills
Presentation of written and oral solutions to problems using appropriate professional language is emphasised in the workshops and assessment. All assessment taks require the appropriate presentation of information, reasoning and conclusions and require students to gain meaning from instructions (written or verbal) and problem statements.
Teaching and learning strategies
Subject delivery (per week): one 2 hour interactive lecture, one 2 hour collaborative "whiteboard workshop". These are delivered on-campus.
The workshops reinforce the content and skills learned, working collaboratively at whiteboards in small groups. They also include a short formative quiz most weeks. The structure of the "whitebord workshops" will be fully explained in the first session.
Canvas will be used to disseminate learning materials in the form of course notes, lecture slides, lecture recordings, homework and worksheets with solutions.
Feedback by rapid return of quiz and test grades, worked solutions available online for assessment tasks, and personal feedback in the whiteboard workshop.
Content (topics)
In this subject we will study the foundations of discrete mathematics. To this end, we will cover:
- basics of propositional logic: truth tables, quantifiers, simple proof structures (direct, indirect)
- mathematical induction, well ordering principle
- formal mathematical notation: set theory, functions
- graph theory, trees
- counting
- pigeonhole principle
- basic number theory, RSA
Assessment
Assessment task 1: In-class quizzes
| Intent: | This assessment task (in-workshop quiz) contributes to the development of the following graduate attributes: 1. disciplinary knowledge and its appropriate application 2. an enquiry-based approach 6. communication skills |
|---|---|
| Type: | Quiz/test |
| Groupwork: | Individual |
| Weight: | 40% |
| Criteria: | Students will be assessed on: accuracy of analysis; clarity of communication. |
Assessment task 2: Assignment
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1. disciplinary knowledge and its appropriate application 2. an enquiry-based approach 3. Professional skills and their appropriate application 6. Communication skills |
|---|---|
| Type: | Exercises |
| Groupwork: | Individual |
| Weight: | 10% |
| Criteria: | Students will be assessed on: accuracy of solution, including determining a correct approach to address the question asked clarity of communication, including neat write-up |
Assessment task 3: Final Examination
| Intent: | This assessment task (formal 2 hour exam) contributes to the development of the following graduate attributes: 1. disciplinary knowledge and its appropriate application 2. an enquiry-oriented approach 6. communication skills |
|---|---|
| Type: | Examination |
| Groupwork: | Individual |
| Weight: | 50% |
| Length: | 2 hours plus 10 minutes reading time. |
| Criteria: | Students will be assessed on: accuracy of solution, including determining a correct approach to address the question asked; clarity of communication |
Minimum requirements
Students must obtain at least 40% of the marks available for the final examination in order to pass this subject. If 40% is not reached, an X grade fail may be awarded for the subject, irrespective of an overall mark greater than 50.
Recommended texts
Any textbook called "Discrete Mathematics" will be useful, for example
- Susanna Epp, Discrete Mathematics with Applications
- Ralf Grimaldi, Discrete and Combinatorial Mathematics, An Applied Introduction
References
Course notes and lecture slides will be provided on Canvas, as the semester progresses.