Unit name | Metric Spaces |
---|---|
Unit code | MATH20006 |
Credit points | 20 |
Level of study | I/5 |
Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
Unit director | Dr. Viveka Erlandsson |
Open unit status | Not open |
Pre-requisites |
MATH10011 Analysis and MATH10010 Introduction to Proofs and Group Theory |
Co-requisites |
None |
School/department | School of Mathematics |
Faculty | Faculty of Science |
Lecturers: Viveka Erlandsson and Asma Hassannezhad
Unit Aims
To introduce the notion of metric spaces and extend several theorems and concepts about the real numbers and real valued functions, such as convergence and continuity, to the more general setting of these spaces.
Unit Description
This course generalizes some theorems about convergence and continuity of functions from the Level 4 unit Analysis 1, and develops a theory of convergence and uniform convergence in any metric space. Topics will include basic topology (open, closed, compact, connected sets), continuity of functions, completeness, the contraction mapping theorem and applications, compactness and connectedness.
Relation to Other Units
This unit is a member of a sequence of analysis units at levels 5, 6 and 7. It is a prerequisite for Measure Theory and Integration, Advanced Topics in Analysis, and Functional Analysis.
At the end of the course the student should know and understand the definitions and theorems (and their proofs) and should be able to use the ideas of the course in unseen situations.
The unit will be taught through a combination of
90% Timed, open-book examination 10% Coursework
Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.
If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.
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