mat3dsa discrete structures
DISCRETE STRUCTURES AND ALGORITHMS
MAT3DSA
2017
Credit points: 15
Subject outline
This capstone mathematics subject covers an array of fundamental concepts from discrete mathematics and algebra as well as developing fundamental skills for both further mathematics and for mathematics in the workplace. The subject is a continuation and expansion of MAT2AAL, with a deeper treatment of the theory of groups embellished by applications to counting, games and patterns. Around two thirds of the subject concerns ordered sets and lattices, and their role in mathematical foundations, algebra, information analysis and computer science.
SchoolSchool Engineering&Mathematical Sciences
Credit points15
Subject Co-ordinatorTomasz Kowalski
Available to Study Abroad StudentsYes
Subject year levelYear Level 3 - UG
Exchange StudentsYes
Subject particulars
Subject rules
Prerequisites MAT2ALC or MAT2AAL
Co-requisitesN/A
Incompatible subjects MAT3DS
Equivalent subjectsN/A
Special conditionsN/A
Learning resources
Readings
| Resource Type | Title | Resource Requirement | Author and Year | Publisher |
|---|---|---|---|---|
| Readings | Introduction to Lattices and Order. | Prescribed | Davey, B.A. and Priestly, H.A. 2001 | 2ND EDN, CAMBRIDGE UNIVERSITY PRESS |
Graduate capabilities & intended learning outcomes
01. Implement the basic structure of a simple mathematical proof to prove previously unseen basic mathematical facts from the area.
- Activities:
- Repeated instruction in lectures.
- Related graduate capabilities and elements:
- Ethical Awareness(Ethical Awareness)
- Creative Problem-solving(Creative Problem-solving)
- Critical Thinking(Critical Thinking)
- Writing(Writing)
02. Write medium length proofs and explanations to the level that their work can be used as part of the assignment solutions for other students.
- Activities:
- Repeated instruction in lectures.
- Related graduate capabilities and elements:
- Discipline-specific GCs(Discipline-specific GCs)
- Critical Thinking(Critical Thinking)
- Writing(Writing)
- Ethical Awareness(Ethical Awareness)
- Creative Problem-solving(Creative Problem-solving)
03. Synthesise content from across the entire subject to tackle unguided problem solving exercises.
- Activities:
- Several lengthy problem solving questions are demonstrated in lectures. One or two are then analysed in groups by students, with staff guidance.
- Related graduate capabilities and elements:
- Inquiry/ Research(Inquiry/ Research)
- Ethical Awareness(Ethical Awareness)
- Writing(Writing)
- Creative Problem-solving(Creative Problem-solving)
- Discipline-specific GCs(Discipline-specific GCs)
- Critical Thinking(Critical Thinking)
04. Present a clear board-presentation of selected parts of core content of the subject to the rest of the class, including responses to any questions.
- Activities:
- Repeated instruction in lectures. Students are required to deliver some of the core content, overseen by the lecturer. Presentation tips are provided to students in advance, and feedback is provided to the individual student after each presentation.
- Related graduate capabilities and elements:
- Discipline-specific GCs(Discipline-specific GCs)
- Critical Thinking(Critical Thinking)
- Writing(Writing)
- Speaking(Speaking)
- Teamwork(Teamwork)
05. Self-teach complex mathematical topics and explain them to others in class presentations and written work.
- Activities:
- Approaches discussed in lectures. Lectures also expose students to similar style critical analysis of printed notes and subject text. Two classes containing exploratory tutorials on unseen material.
- Related graduate capabilities and elements:
- Critical Thinking(Critical Thinking)
- Teamwork(Teamwork)
- Inquiry/ Research(Inquiry/ Research)
- Quantitative Literacy/ Numeracy(Quantitative Literacy/ Numeracy)
06. Produce short original proofs on fundamental basics of group theory, lattice theory and ordered sets.
- Activities:
- Repeated instruction in lectures.
- Related graduate capabilities and elements:
- Creative Problem-solving(Creative Problem-solving)
- Ethical Awareness(Ethical Awareness)
- Writing(Writing)
- Discipline-specific GCs(Discipline-specific GCs)
- Critical Thinking(Critical Thinking)
07. Reproduce selected longer proofs of key results from the theory of orders and lattice theory.
- Activities:
- Numerous longer proofs are carefully analysed in lectures. Students told to learn the key tricks involved (the rest of the proofs require only general understanding of basic proof structure, as in ILO1). This builds toward a repertoire of deeper proof ideas that can possibly be implemented in future creative problem solving situations.
- Related graduate capabilities and elements:
- Writing(Writing)
- Creative Problem-solving(Creative Problem-solving)
- Discipline-specific GCs(Discipline-specific GCs)
- Ethical Awareness(Ethical Awareness)
08. Write short computer code in the package GAP or similar, for exploring properties of small algebraic objects and their application.
- Activities:
- In computer lab classes, there will be numerous examples of computer code for students to explore and adjust. In addition, the algebraic properties explored will relate to exercises performed in other classes in the subject.
- Related graduate capabilities and elements:
- Ethical Awareness(Ethical Awareness)
- Inquiry/ Research(Inquiry/ Research)
- Creative Problem-solving(Creative Problem-solving)
- Critical Thinking(Critical Thinking)
- Quantitative Literacy/ Numeracy(Quantitative Literacy/ Numeracy)
- Discipline-specific GCs(Discipline-specific GCs)
Subject options
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Melbourne, 2017, Semester 1, Day
Overview
Online enrolmentYes
Maximum enrolment sizeN/A
Enrolment information
Subject Instance Co-ordinatorTomasz Kowalski
Class requirements
Computer LaboratoryWeek: 10 - 22
One 1.0 hours computer laboratory every two weeks on weekdays during the day from week 10 to week 22 and delivered via face-to-face.
"Fortnightly (odd weeks)"
LectureWeek: 10 - 22
Three 1.0 hours lecture per week on weekdays during the day from week 10 to week 22 and delivered via face-to-face.
"Hybrid Lecture/Presentation Classes"
TutorialWeek: 10 - 22
One 1.0 hours tutorial every two weeks on weekdays during the day from week 10 to week 22 and delivered via face-to-face.
"Help Class fortnightly (even weeks)"
Assessments
| Assessment element | Comments | % | ILO* |
|---|---|---|---|
| Class presentations equivalent to 500-words. | 10 | 01, 02, 04, 05, 06 | |
| Four written assignments equivalent to 300-words each. | 30 | 01, 02, 03, 04, 05, 06 | |
| One 2-hour written exam, with short answer Section A and more detailed problem solving Section B. | 50 | 01, 02, 03, 04, 07 | |
| One report on computer aided exploration equivalent to 800-words. | 10 | 01, 03, 05, 08 |