 Credits:
| 6 |
| Level:
| Honours (FHEQ level 6) |
| Period: |
Semester 2
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| Assessment:
| EX 100% |
| Supplementary Assessment: | MA30055 Mandatory Extra Work (where allowed by programme regulations) |
| Requisites:
| Before taking this unit you must take MA30041 |
| Description:
| Aims & Learning Objectives:
Aims:
To provide an introduction to the ideas of point-set topology culminating with a sketch of the classification of compact surfaces. As such it provides a self-contained account of one of the triumphs of 20th century mathematics as well as providing the necessary background for the level 4 unit in Algebraic Topology.
Objectives:
To acquaint students with the important notion of a topology and to familiarise them with the basic theorems of analysis in their most general setting. Students will be able to distinguish between metric and topological space theory and to understand refinements, such as Hausdorff or compact spaces, and their applications.
Content:
Topics will be chosen from the following:
Topologies and topological spaces. Subspaces. Bases and sub-bases: product spaces; compact-open topology. Continuous maps and homeomorphisms. Separation axioms. Connectedness. Compactness and its equivalent characterisations in a metric space. Axiom of Choice and Zorn's Lemma. Tychonoff's theorem. Quotient spaces. Compact surfaces and their representation as quotient spaces. Sketch of the classification of compact surfaces.
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Programme availability:
|
MA30055 is Optional on the following programmes:
Department of Computer Science
- USCM-AFB01 : BSc Computing (Full-time) - Year 3
- USCM-AKB01 : BSc Computing (Full-time with Thick Sandwich Placement) - Year 4
- USCM-AFB13 : BSc (hons) Computer Science with Mathematics (Full-time) - Year 3
- USCM-AKB14 : BSc (hons) Computer Science with Mathematics (Full-time with Thick Sandwich Placement) - Year 4
- USCM-AAB14 : BSc (hons) Computer Science with Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
Department of Mathematical Sciences
- USMA-AFB15 : BSc (hons) Mathematical Sciences (Full-time) - Year 3
- USMA-AKB16 : BSc (hons) Mathematical Sciences (Full-time with Thick Sandwich Placement) - Year 4
- USMA-AAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- USMA-AFB13 : BSc (hons) Mathematics (Full-time) - Year 3
- USMA-AKB14 : BSc (hons) Mathematics (Full-time with Thick Sandwich Placement) - Year 4
- USMA-AFB01 : BSc (hons) Mathematics and Statistics (Full-time) - Year 3
- USMA-AKB02 : BSc (hons) Mathematics and Statistics (Full-time with Thick Sandwich Placement) - Year 4
- USMA-AAB02 : BSc (hons) Mathematics and Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- USMA-AAB14 : BSc (hons) Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- USMA-AFB05 : BSc (hons) Statistics (Full-time) - Year 3
- USMA-AKB06 : BSc (hons) Statistics (Full-time with Thick Sandwich Placement) - Year 4
- USMA-AAB06 : BSc (hons) Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- USMA-AFM14 : MMath Mathematics (Full-time) - Year 3
- USMA-AFM14 : MMath Mathematics (Full-time) - Year 4
- USMA-AAM15 : MMath Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- TSMA-AFM09 : MSc Mathematical Sciences (Full-time) - Year 1
- TSMA-APM09 : MSc Mathematical Sciences (Part-time) - Year 1
- TSMA-APM09 : MSc Mathematical Sciences (Part-time) - Year 2
Department of Physics
- USXX-AFB03 : BSc (hons) Mathematics and Physics (Full-time) - Year 3
- USXX-AKB04 : BSc (hons) Mathematics and Physics with Placement (Full-time with Thick Sandwich Placement) - Year 4
- USXX-AAB04 : BSc (hons) Mathematics and Physics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
- USXX-AFM01 : MSci (hons) Mathematics and Physics (Full-time) - Year 3
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