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Module MA2223: Metric spaces

Credit weighting (ECTS)
5 credits
Semester/term taught
Michaelmas term 2016-17
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 in a 2-hour examination in Trinity term. Continuous assessment will contribute 15% to the final grade for the module at the annual examination session, with the examination counting for the remaining 85%. Supplemental exams if required will consist of 100% exam.