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Unit information: Metric Spaces in 2015/16

Please note: you are viewing unit and programme information for a past academic year. Please see the current academic year for up to date information.

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 Professor. van den Berg
Open unit status Not open

MATH11006 Analysis 1 and MATH11521 Further Topics in Analysis



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.

Intended learning outcomes

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.

Teaching details

Lectures and problem classes.

Assessment Details

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

J.C. Burkill & H. Burkill, A second course in mathematical analysis, Cambridge University Press, Cambridge

I. Kaplansky, Set theory and metric spaces, Chelsea Publishing Company, New York.

W. Rudin, Principles of Mathematical Analysis, McGraw-Hill.

W. A. Sutherland, Introduction to metric and topological spaces, Clarendon Press, Oxford.