Metric Spaces (U01630)

? Credit Points : 10 ? SCQF Level : 10 ? Acronym : MAT-3-MSp

Optional course for Honours Degrees involving Mathematics and/or Statistics. 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 : Passes at C or better in MAT-2-FoC, MAT-2-SVC, MAT-2-LiA, MAT-2-MAM

? Prohibited combinations : MAT-3-MSpO, similar courses from Mathematics 3 (Hons) prior to 2004-05

Variants

? This course has variants for part year visiting students, as follows

Metric Spaces (VS1) (Semester 1 (Blocks 1-2))

Subject Areas

Home subject area

Specialist Mathematics & Statistics (Honours), (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

All of the following classes

Type	Day	Start	End	Area
Lecture	Monday	10:00	10:50	KB
Lecture	Thursday	10:00	10:50	KB

Summary of Intended Learning Outcomes

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.