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Module MA2223: Metric spaces
- Credit weighting (ECTS)
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5 credits
- Semester/term taught
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Michaelmas term 2013-14
- Contact Hours
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11 weeks, 3 lectures including tutorials per week
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- Lecturer
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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 rigourous mathematical arguments using apporopriate 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
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- 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
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- Recommended Reading
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- Introduction to metric and topological spaces, W.A. Sutherland. Oxford University Press, 1975;
- Metric Spaces, E.T. Copson. Cambridge University Press, 1968;
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- Assessment Detail
- This module will be examined in a 2-hour examination in Trinity term. Continuous assessment will contribute 5% to the final grade for the module at the annual
examination session. Supplemental exams if required will consist of 100% exam.