Metric spaces are sets equipped with a notion of distance. This module examines how important ideas and concepts of real analysis can be extended to the more general setting of metric spaces.
This module provides a foundation for further study in a wide range of mathematical topics, including analysis, topology, measure theory, geometry and dynamical systems.
A Recognise whether a given structure forms a metric space.
B Work effectively with subsets of a metric space and determine the diameter, boundary, interior or closure.
C Prove results concerning continuous maps between metric spaces.
D Demonstrate whether or not a given metric space is connected, compact or complete.
E Use the Banach contraction mapping theorem to identify fixed points.
F Solve mathematical problems using the formalism of metric spaces.
This module will be delivered mainly through a combination of formal lectures and tutorials.