DISCRETE STRUCTURES AND ALGORITHMS

MAT3DSA

2018

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

Readings

Resource TypeTitleResource RequirementAuthor and YearPublisher
ReadingsIntroduction to Lattices and Order.PrescribedDavey, B.A. and Priestly, H.A. 20012ND 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
Creative Problem-solving
Critical Thinking
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
Critical Thinking
Writing
Ethical Awareness
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
Ethical Awareness
Writing
Creative Problem-solving
Discipline-specific GCs
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
Critical Thinking
Writing
Speaking
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
Teamwork
Inquiry/ Research
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
Ethical Awareness
Writing
Discipline-specific GCs
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
Creative Problem-solving
Discipline-specific GCs
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
Inquiry/ Research
Creative Problem-solving
Critical Thinking
Quantitative Literacy/ Numeracy
Discipline-specific GCs

Subject options

Select to view your study options…

Start date between: and    Key dates

Melbourne, 2018, Semester 1, Day

Overview

Online enrolmentYes

Maximum enrolment sizeN/A

Enrolment information

Subject Instance Co-ordinatorTomasz Kowalski

Class requirements

Computer Laboratory Week: 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)"

Lecture Week: 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"

Tutorial Week: 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 elementComments% 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