mat4top topology
TOPOLOGY
MAT4TOP
2019
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.
SchoolSchool Engineering&Mathematical Sciences
Credit points15
Subject Co-ordinatorYuri Nikolayevsky
Available to Study Abroad StudentsYes
Subject year levelYear Level 4 - UG/Hons/1st Yr PG
Exchange StudentsYes
Subject particulars
Subject rules
Prerequisites MAT3DS OR MAT3AC
Co-requisitesN/A
Incompatible subjects MAT3TA
Equivalent subjectsN/A
Special conditionsN/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.
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.
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.
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.
Subject options
Select to view your study options…
Melbourne, 2019, Semester 2, Day
Overview
Online enrolmentNo
Maximum enrolment sizeN/A
Enrolment information
Subject Instance Co-ordinatorYuri 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 |