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Unit Summary

Unit type

UG Coursework Unit

Credit points

12

AQF level

7

Level of learning

Advanced

Former School/College

Former School of Education

Pre-requisites

have completed MAT10722 - Complex Analysis

Unit aim

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 content

Complex 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

Learning outcomes

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.

GA1: Intellectual rigour, GA2: Creativity, GA3: Ethical practice, GA4: Knowledge of a discipline, GA5: Lifelong learning, GA6: Communication and social skills, GA7: Cultural competence
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

On completion of this unit, students should be able to:

  1. correctly use concepts and techniques of topology in known contexts
    • GA1: Intellectual rigour
    • GA4: Knowledge of a discipline
  2. correctly apply concepts and techniques of topology to new contexts
    • GA1: Intellectual rigour
    • GA2: Creativity
    • GA4: Knowledge of a discipline
  3. effectively communicate mathematical ideas, processes and results at different levels of formality
    • GA1: Intellectual rigour
    • GA4: Knowledge of a discipline
    • GA6: Communication and social skills