| 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 |
MATH11006 Analysis 1 and MATH11521 Further Topics in Analysis |
| Co-requisites |
None |
| School/department | School of Mathematics |
| Faculty | Faculty of Science |
Unit aims
To introduce metric and topological spaces and to extend some theorems about convergence and continuity in the case of sequences of real numbers and real-valued functions of one real variable.
General Description of the Unit
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 and 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 & Integration, Advanced Topics in Analysis, and Functional Analysis.
Additional unit information can be found at http://www.maths.bristol.ac.uk/study/undergrad/current_units/index.html
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.
Lectures and problem classes.
100% examination
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.
Reading and references are available at http://www.maths.bristol.ac.uk/study/undergrad/current_units/index.html
