DISCRETE STRUCTURES AND ALGORITHMS

MAT3DSA

2020

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.

School: Engineering and Mathematical Sciences (Pre 2022)

Credit points: 15

Subject Co-ordinator: Tomasz Kowalski

Available to Study Abroad/Exchange Students: Yes

Subject year level: Year Level 3 - UG

Exchange Students: No

Available as Elective: No

Learning Activities: N/A

Capstone subject: Yes

Subject particulars

Subject rules

Prerequisites: MAT2AAL OR MAT2ALC

Co-requisites: N/A

Incompatible subjects: MAT3DS

Equivalent subjects: N/A

Quota Management Strategy: N/A

Quota-conditions or rules: N/A

Special conditions: N/A

Minimum credit point requirement: N/A

Assumed knowledge: N/A

Learning resources

Introduction to Lattices and Order.

Resource Type: Book

Resource Requirement: Prescribed

Author: Davey, B.A. and Priestly, H.A.

Year: 2001

Edition/Volume: 2ND EDN

Publisher: CAMBRIDGE UNIVERSITY PRESS

ISBN: N/A

Chapter/article title: N/A

Chapter/issue: N/A

URL: N/A

Other description: N/A

Source location: N/A

Career Ready

Career-focused: No

Work-based learning: No

Self sourced or Uni sourced: N/A

Entire subject or partial subject: N/A

Total hours/days required: N/A

Location of WBL activity (region): N/A

WBL addtional requirements: N/A

Graduate capabilities & intended learning outcomes

Graduate Capabilities

COMMUNICATION - Communicating and Influencing

DISCIPLINE KNOWLEDGE AND SKILLS

INQUIRY AND ANALYSIS - Creativity and Innovation

INQUIRY AND ANALYSIS - Critical Thinking and Problem Solving

INQUIRY AND ANALYSIS - Research and Evidence-Based Inquiry

PERSONAL AND PROFESSIONAL - Ethical and Social Responsibility

PERSONAL AND PROFESSIONAL - Leadership and Teamwork

Intended Learning Outcomes

01. Implement the basic structure of a simple mathematical proof to prove previously unseen basic mathematical facts from the area.

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.

03. Synthesise content from across the entire subject to tackle unguided problem solving exercises.

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.

05. Self-teach complex mathematical topics and explain them to others in class presentations and written work.

06. Produce short original proofs on fundamental basics of group theory, lattice theory and ordered sets.

07. Reproduce selected longer proofs of key results from the theory of orders and lattice theory.

08. Write short computer code in the package GAP or similar, for exploring properties of small algebraic objects and their application.

Melbourne (Bundoora), 2020, Semester 1, Day

Overview

Online enrolment: Yes

Maximum enrolment size: N/A

Enrolment information: N/A

Subject Instance Co-ordinator: Tomasz Kowalski

Class requirements

Computer LaboratoryWeek: 10 - 22
One 1.00 hour 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 1.00 hour 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 1.00 hour 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	Category	Contribution	Hurdle	%	ILO*
Class presentations equivalent to 500-words.	N/A	N/A	N/A	No	10	SILO1, SILO2, SILO4, SILO5, SILO6
Four written assignments equivalent to 300-words each.	N/A	N/A	N/A	No	30	SILO1, SILO2, SILO3, SILO4, SILO5, SILO6
One 2-hour written exam, with short answer Section A and more detailed problem solving Section B.	N/A	N/A	N/A	No	50	SILO1, SILO2, SILO3, SILO4, SILO7
One report on computer aided exploration equivalent to 800-words.	N/A	N/A	N/A	No	10	SILO1, SILO3, SILO5, SILO8