Introduces the concept of topology and its applications. The course includes topological spaces and related constructions and properties, connectedness and its applications, as well as compactness and related properties.
Unit contentComplex Analysis (Topics 1 to 5)
1. Theory of sets – sets and operations
2. Theory of sets – functions and relations
3. Metric spaces – metric spaces and continuity
4. Metric spaces – limits, open and closed sets, subspaces and equivalence
5. Topological spaces – spaces and functions
6. Topological spaces – subspaces, products, identification topologies
7. Connectedness – introduction and applications
8. Connectedness – components and local connectedness, path-connected spaces
9. Compactness – compact topological spaces, subsets and products
10. Compactness – compact metric spaces, Bolzano-Weierstrass property, surfaces by identification
Unit Learning Outcomes express learning achievement in terms of what a student should know, understand and be able to do on completion of a unit. These outcomes are aligned with the graduate attributes. The unit learning outcomes and graduate attributes are also the basis of evaluating prior learning.
Learning outcomes and graduate attributes
|On completion of this unit, students should be able to:||GA1||GA2||GA3||GA4||GA5||GA6||GA7|
|1||correctly use concepts and techniques of topology in known contexts||Intellectual rigour||Knowledge of a discipline|
|2||correctly apply concepts and techniques of topology to new contexts||Intellectual rigour||Creativity||Knowledge of a discipline|
|3||effectively communicate mathematical ideas, processes and results at different levels of formality||Intellectual rigour||Knowledge of a discipline||Communication and social skills|
Teaching and assessment
Commonwealth Supported courses
For information regarding Student Contribution Amounts please visit the Student Contribution Amounts.
Commencing 2015 Commonwealth Supported only. Student contribution band: 2
Please check the international course and fee list to determine the relevant fees.