DISCRETE STRUCTURES AND ALGORITHMS

MAT3DSA

2021

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.

SchoolEngineering and Mathematical Sciences

Credit points15

Subject Co-ordinatorTomasz Kowalski

Available to Study Abroad/Exchange StudentsYes

Subject year levelYear Level 3 - UG

Available as ElectiveNo

Learning ActivitiesN/A

Capstone subjectYes

Subject particulars

Subject rules

PrerequisitesMAT2AAL OR MAT2ALC

Co-requisitesN/A

Incompatible subjectsMAT3DS

Equivalent subjectsN/A

Quota Management StrategyN/A

Quota-conditions or rulesN/A

Special conditionsN/A

Minimum credit point requirementN/A

Assumed knowledgeN/A

Readings

Introduction to Lattices and Order.

Resource TypePrescribed

Resource RequirementN/A

AuthorDavey, B.A. and Priestly, H.A.

Year2001

Edition/Volume2ND EDN

PublisherCAMBRIDGE UNIVERSITY PRESS

ISBNN/A

Chapter/article titleN/A

Chapter/issueN/A

URLN/A

Other descriptionN/A

Source locationN/A

Career Ready

Career-focusedNo

Work-based learningNo

Self sourced or Uni sourcedN/A

Entire subject or partial subjectN/A

Total hours/days requiredN/A

Location of WBL activity (region)N/A

WBL addtional requirementsN/A

Graduate capabilities & intended learning outcomes

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.
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.

Subject options

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Start date between: and    Key dates

Melbourne (Bundoora), 2021, Semester 1, Day

Overview

Online enrolmentYes

Maximum enrolment sizeN/A

Subject Instance Co-ordinatorTomasz Kowalski

Class requirements

Computer LaboratoryWeek: 10 - 22
One 1.00 h 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 h 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 h 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 elementCommentsCategoryContributionHurdle% ILO*
Class presentations equivalent to 500-words.N/AN/AN/ANo10 SILO1, SILO2, SILO4, SILO5, SILO6
Four written assignments equivalent to 300-words each.N/AN/AN/ANo30 SILO1, SILO2, SILO3, SILO4, SILO5, SILO6
One 2-hour written exam, with short answer Section A and more detailed problem solving Section B.N/AN/AN/ANo50 SILO1, SILO2, SILO3, SILO4, SILO7
One report on computer aided exploration equivalent to 800-words.N/AN/AN/ANo10 SILO1, SILO3, SILO5, SILO8