37181 Discrete Mathematics
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Credit points: 6 cp
Result type: Grade and marks
Anti-requisite(s): 35111 Applications of 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.
Subject learning objectives (SLOs)
Upon successful completion of this subject students should be able to:
| 1. | Solve simple problems in discrete mathematics and apply this knowledge to solve selected problems arising in other parts of science, in engineering and business |
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| 2. | Understand and apply knowledge of discrete mathematics and its theoretical underpinnings by constructing logical, clearly presented and justified arguments incorporating deductive reasoning |
| 3. | Identify where the basic concepts of discrete mathematics are useful in addressing a real world problem |
| 4. | Engage in group discussions to decide upon the appropriate choice of techniques from discrete mathematics to describe a wide variety of problems from fields including the physical sciences, engineering and business |
Course intended learning outcomes (CILOs)
This subject also contributes specifically to the development of following course intended learning outcomes:
- Demonstrate theoretical and technical knowledge of mathematical sciences including calculus, discrete mathematics, linear algebra, probability, statistics and quantitative management. (1.1)
- Evaluate mathematical and statistical approaches to problem solving, analysis, application, and critical thinking to make mathematical arguments, and conduct experiments based on analytical, numerical, statistical, algorithms to solve new problems. (2.1)
- Work autonomously or in teams to demonstrate professional and responsible analysis of real-life problems that require application of mathematics and statistics. (3.1)
- Design creative solutions to contemporary mathematical sciences-related issues by incorporating innovative methods, reflective practices and self-directed learning. (4.1)
- Use succinct and accurate presentation of reasoning and conclusions to communicate mathematical solutions, and their implications, to a variety of audiences, using a variety of approaches. (5.1)
Contribution to the development of graduate attributes
1.0 Disciplinary knowledge
The lectures and workshops will allow students to develop practical and theoretical skills in discrete mathematics.
2.0 Research, inquiry and critical thinking
The collaborative approach to problem formulations and solutions used in the tutorials helps students develop skills in identifying and evaluating alternative approaches to solving problems.
3.0 Professional, ethical, and social responsibility
The ability to work effectively and responsibly in a group is emphasised in the group-based discussion components of the tutorials.
4.0 Reflection, innovation, creativity
Constructing a mathematical proof, making conjectures, constructing counterexamples require students to develop their mathematical/logical creative sides. Reflecting on whether a proof you have written is really correct, if it could be done more efficiently, if it could be made more general, is another important skill that will be developed in this subject.
5.0 Communication
Presentation of written and oral solutions to problems using appropriate professional language is emphasised in the tutorials and assessment. All assessment tasks 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): recorded lecture materials on CANVAS, one 1.5 hour workshop delivered on-campus, one 1.5 hour collaborative "whiteboard tutorial" delivered on-campus.
The weekly workshop bridges across from the delivery of content in the lecture recordings to the student led learning in the tutorials.
The tutorials reinforce the content and skills learned, working collaboratively at whiteboards in small groups. The structure of the "whiteboard 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 marked quizzes (LPC), worked solutions available online after each assessment task, and immediate feedback from peers and tutor in the whiteboard tutorial.
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
- counting, pigeonhole principle
- basic number theory, RSA
- graph theory, trees, applications
Assessment
Assessment task 1: Learning Progress Checks
| Intent: | This assessment task contributes to the development of the following graduate attributes: 2.0 research, inquiry and critical thinking 4.0 reflection, innovaton, creativity 5.0 communication |
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| Objective(s): | This assessment task addresses subject learning objective(s): 1, 2 and 3 This assessment task contributes to the development of course intended learning outcome(s): 2.1, 4.1 and 5.1 |
| Type: | Quiz/test |
| Groupwork: | Individual |
| Weight: | 40% |
| Length: | In class LPC: 30 minutes. |
| Criteria: | Students will be assessed on: accuracy of analysis; clarity of communication. |
Assessment task 2: Tutorial Active Participation
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1.0 disciplinary knowledge 3.0 professional, ethical, and social responsibility 4.0 reflection, innovation, creativity 5.0 communication |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1, 2, 3 and 4 This assessment task contributes to the development of course intended learning outcome(s): 1.1, 3.1, 4.1 and 5.1 |
| Type: | Exercises |
| Groupwork: | Group, individually assessed |
| Weight: | 10% |
| Criteria: | Students will be assessed on: regular and active participation; accuracy of solution/proof, including determining a correct approach to address the question asked; evidence of effective and positive team-work. |
Assessment task 3: Summative Achievement Check
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1.0 disciplinary knowledge 2.0 research, inquiry and critical thinking 5.0 communication |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1, 2 and 3 This assessment task contributes to the development of course intended learning outcome(s): 1.1, 2.1 and 5.1 |
| Type: | Examination |
| Groupwork: | Individual |
| Weight: | 50% |
| Length: | 2 hours writing/working time. Additional time will be given for download/scanning/upload. |
| 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 need to attain at least 50/100 overall in order to pass this subject.
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
Subject materials will be provided on Canvas.