Unit information: Metric Spaces in 2020/21

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

Description including Unit Aims

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.

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 Information

The unit will be taught through a combination of

• synchronous online and, if subsequently possible, face-to-face lectures
• asynchronous online materials, including narrated presentations and worked examples
• guided asynchronous independent activities such as problem sheets and/or other exercises
• synchronous weekly group problem/example classes, workshops and/or tutorials
• synchronous weekly group tutorials
• synchronous weekly office hours

Assessment Information

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.

Reading and References

Recommended

• J.C. Burkill and H. Burkill, A Second Course in Mathematical Analysis, Cambridge University Press, 2002
• Irving Kaplansky, Set Theory and Metric Spaces, Chelsea Publishing Company, 1977
• Walter Rudin, Principles of Mathematical Analysis, McGraw-Hill, 1976
• W. A. Sutherland, Introduction to Metric and Topological Spaces, Clarendon Press, 2009