TOPOLOGY AND ANALYSIS

MAT3TA

Not currently offered

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. In particular, they can be applied to problems in the analysis of the real numbers. The subject concludes with a discussion of quotients and products of topological spaces.

SchoolSchool Engineering&Mathematical Sciences

Credit points15

Subject Co-ordinatorGrant Cairns

Available to Study Abroad StudentsYes

Subject year levelYear Level 3 - UG

Exchange StudentsYes

Subject particulars

Subject rules

Prerequisites MAT2ANA or MAT2AAL

Co-requisitesN/A

Incompatible subjectsN/A

Equivalent subjectsN/A

Special conditionsN/A

Readings

Resource TypeTitleResource RequirementAuthor and YearPublisher
ReadingsTopology and AnalysisPrescribedPrinted subject text available from University Bookshop.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:
Critical Thinking (Critical Thinking)
Creative Problem-solving (Creative Problem-solving)
Discipline-specific GCs (Discipline-specific GCs)
Inquiry/ Research (Inquiry/ Research)
Writing (Writing)

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:
Writing (Writing)
Creative Problem-solving (Creative Problem-solving)
Discipline-specific GCs (Discipline-specific GCs)
Critical Thinking (Critical Thinking)

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:
Critical Thinking (Critical Thinking)
Discipline-specific GCs (Discipline-specific GCs)
Creative Problem-solving (Creative Problem-solving)
Writing (Writing)

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:
Critical Thinking (Critical Thinking)
Writing (Writing)
Creative Problem-solving (Creative Problem-solving)
Discipline-specific GCs (Discipline-specific GCs)

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