Metric Spaces (Ord) (U01644)

? Credit Points : 10 ? SCQF Level : 9 ? Acronym : MAT-3-MSpO

Syllabus summary: Countable sets; open and closed subsets of R; analysis on Rk, open and closed sets; metric spaces, open and closed sets, limits, continuity, equivalent metrics, path-connectedness; completeness, contraction mapping theorem and applications; compactness.

Entry Requirements

? Pre-requisites : MAT-2-FoC, MAT-2-SVC, MAT-2-LiA, MAT-2-MAM or MAT-2-am3, MAT-2-mm3, MAT-2-am4, MAT-2-mm4 or MAT-2-mi3, MAT-2-mi4

? Prohibited combinations : MAT-3-MSp

Subject Areas

Home subject area

Specialist Mathematics & Statistics (Ordinary), (School of Mathematics, Schedule P)

Delivery Information

? Normal year taken : 3rd year

? Delivery Period : Semester 1 (Blocks 1-2)

? Contact Teaching Time : 2 hour(s) per week for 11 weeks

First Class Information

Date	Start	End	Room	Area	Additional Information
18/09/2007	10:00	11:00	Lecture Theatre C, JCMB	KB

All of the following classes

Type	Day	Start	End	Area
Lecture	Tuesday	10:00	10:50	KB
Lecture	Friday	10:00	10:50	KB

Summary of Intended Learning Outcomes

The following are the learning objectives for the Honours version, MAT-3-MSp; for this (Ordinary) version there is more emphasis on the technical, rather than conceptual elements, which will be reflected by a different examination.

1. Facility in working with concrete metric spaces based upon Rk and C[a,b] (with various metrics) and the discrete metric.
2. An ability to perform simple abstract arguments involving metric spaces.
3. An ability to demonstrate an understanding of notions such as openness, closedness, continuity, completeness, equivalence of metrics, compactness and path-connectedness as applied in the context of general and specific metric spaces.
4. An appreciation of the contraction mapping theorem and some of its easier applications.