Module MA2223: Metric Spaces
- Credit weighting (ECTS)
- 5 credits
- Semester/term taught
- Michaelmas term 2012-13
- Contact Hours
- 11 weeks, 3 lectures including tutorials per week
- Lecturer
- Prof. Sergey Mozgovoy
- Learning Outcomes
- On successful completion of this module, students will be able to:
- Accurately recall definitions, state theorems and produce proofs on topics in metric spaces normed vector spaces and topological spaces;
- Construct rigorous mathematical arguments using appropriate concepts and terminology from the module, including open, closed and bounded sets, convergence, continuity, norm equivalence, operator norms, completeness, compactness and connectedness;
- Solve problems by identifying and interpreting appropriate concepts and results from the module in specific examples involving metric, topological and /or normed vector spaces;
- Construct examples and counterexamples related to concepts from the module which illustrate the validity of some prescribed combination of properties;
- Module Content
-
- Metric spaces (including open and closed sets, continuous maps and complete metric spaces);
- Normed vector spaces (including operator norms and norms on finite dimensional vector spaces);
- Topological properties of metric spaces (including Hausdorff, connected and compact spaces);
- Module Prerequisite
- Recommended Reading
-
- Introduction to metric and topological spaces, W.A. Sutherland. Oxford University Press, 1975;
- Metric Spaces, E.T. Copson. Cambridge University Press, 1968;
Assessment Detail
This module will be examined jointly with MA2224 in a 3-hour examination in Trinity term, except that those taking just one of the two modules will have a 2 hour examination. Continuous assessment will contribute 5% to the final grade for the module at the annual examination session. The annual continuous assessment mark will be carried over for the supplemental exams.