TOPOLOGY

MAT4TOP

2020

Credit points: 15

Subject outline

This subject begins with a careful discussion of the various set theoretical results that are required for the subsequent material. This is followed by a discussion of the theory of metric spaces. The most basic properties of open sets in metric spaces can be used to motivate a more generally applicable definition of open sets, which leads to the idea of a topological space. A study of fundamental concepts in the theory of topological spaces such as compactness and connectedness yields results of very general application. The subject concludes with a treatment of quotients and products of topological spaces.

SchoolEngineering and Mathematical Sciences

Credit points15

Subject Co-ordinatorYuri Nikolayevsky

Available to Study Abroad/Exchange StudentsYes

Subject year levelYear Level 4 - UG/Hons/1st Yr PG

Available as ElectiveNo

Learning ActivitiesN/A

Capstone subjectNo

Subject particulars

Subject rules

PrerequisitesN/A

Co-requisitesN/A

Incompatible subjectsMAT3TA

Equivalent subjectsN/A

Quota Management StrategyN/A

Quota-conditions or rulesN/A

Special conditionsN/A

Minimum credit point requirementN/A

Assumed knowledgeN/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. Read and explain highly abstract formulations in modern mathematics.
02. Implement basic ideas in point set topology, particularly connectedness and compactness, in basic proofs.
03. Produce new topological spaces from given ones using the topological constructions of products and quotients.
04. Communicate mathematical arguments clearly and succinctly in the form of a written mathematical proof.

Subject options

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Start date between: and    Key dates

Melbourne (Bundoora), 2020, Semester 2, Day

Overview

Online enrolmentNo

Maximum enrolment sizeN/A

Subject Instance Co-ordinatorYuri Nikolayevsky

Class requirements

Lecture Week: 31 - 43
Two 1.00 h lecture per week on weekdays during the day from week 31 to week 43 and delivered via face-to-face.

Assessments

Assessment elementCommentsCategoryContributionHurdle% ILO*
5 fortnightly written assignments - 1500 words (300 words each)N/AN/AN/ANo30 SILO1, SILO2, SILO3, SILO4
One 2-hour written exam - 2000 wordsN/AN/AN/ANo50 SILO1, SILO2, SILO3, SILO4
Student classroom presentations - 1000 wordsN/AN/AN/ANo20 SILO1, SILO2, SILO3, SILO4