TOPOLOGY
MAT4TOP
2017
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 atreatment of quotients and products of topological spaces.
School: School Engineering&Mathematical Sciences
Credit points: 15
Subject Co-ordinator: Yuri Nikolayevsky
Available to Study Abroad Students: Yes
Subject year level: Year Level 4 - UG/Hons/1st Yr PG
Exchange Students: Yes
Subject particulars
Subject rules
Prerequisites: MAT3DS OR MAT3AC
Co-requisites: N/A
Incompatible subjects: MAT3TA
Equivalent subjects: N/A
Special conditions: N/A
Graduate capabilities & intended learning outcomes
01. Read and explain highly abstract formulations in modern mathematics.
- Activities:
- Discussed and demonstrated in lectures. Related problems solved by students in practice classes. Assignment questions, with feedback.
- Related graduate capabilities and elements:
- Quantitative Literacy/ Numeracy(Quantitative Literacy/ Numeracy)
- Speaking(Speaking)
- Ethical Awareness(Ethical Awareness)
- Writing(Writing)
- Inquiry/ Research(Inquiry/ Research)
- Creative Problem-solving(Creative Problem-solving)
- Critical Thinking(Critical Thinking)
- Discipline-specific GCs(Discipline-specific GCs)
02. Implement basic ideas in point set topology, particularly connectedness and compactness, in basic proofs.
- Activities:
- Discussed and demonstrated in lectures. Related problems solved by students in practice classes. Assignment questions, with feedback.
- Related graduate capabilities and elements:
- Critical Thinking(Critical Thinking)
- Creative Problem-solving(Creative Problem-solving)
- Speaking(Speaking)
- Writing(Writing)
- Inquiry/ Research(Inquiry/ Research)
- Discipline-specific GCs(Discipline-specific GCs)
03. Produce new topological spaces from given ones using the topological constructions of products and quotients.
- Activities:
- Discussed and demonstrated in lectures. Related problems solved by students in practice classes. Assignment questions, with feedback.
- Related graduate capabilities and elements:
- Creative Problem-solving(Creative Problem-solving)
- Discipline-specific GCs(Discipline-specific GCs)
- Speaking(Speaking)
- Writing(Writing)
- Inquiry/ Research(Inquiry/ Research)
- Critical Thinking(Critical Thinking)
04. Communicate mathematical arguments clearly and succinctly in the form of a written mathematical proof.
- Activities:
- Discussed and demonstrated in lectures. Related problems solved by students in practice classes. Assignment questions, with feedback.
- Related graduate capabilities and elements:
- Writing(Writing)
- Inquiry/ Research(Inquiry/ Research)
- Speaking(Speaking)
- Discipline-specific GCs(Discipline-specific GCs)
- Critical Thinking(Critical Thinking)
- Creative Problem-solving(Creative Problem-solving)
Melbourne, 2017, Semester 2, Day
Overview
Online enrolment: No
Maximum enrolment size: N/A
Enrolment information:
Subject Instance Co-ordinator: Yuri Nikolayevsky
Class requirements
LectureWeek: 31 - 43
Two 1.0 hours lecture per week on weekdays during the day from week 31 to week 43 and delivered via face-to-face.
Assessments
| Assessment element | Comments | % | ILO* |
|---|---|---|---|
| 5 fortnightly written assignments | 30 | 01, 02, 03, 04 | |
| one 2-hour written exam | 50 | 01, 02, 03, 04 | |
| student classroom presentations | 20 | 01, 02, 03, 04 |