Topology and Advanced Analysis (G1026)
15 credits, Level 6
This module will introduce you to some of the basic concepts and properties of topological spaces. The subject of topology has a central role in all of Mathematics and having a proper understanding of its concepts and main theorem is essential as part of an undergraduate mathematics curriculum.
Topics that will be covered in this module include:
- topological spaces
- base and sub-base
- separation axioms
- compactness and coverings
- total boundedness
- Lebesgue numbers and Epsilon-nets
- sequential compactness
- Arzela-Ascoli Theorem
- Montel's theorem
- infinite products
- box and product topologies
- Tychonov Theorem.
20%: Coursework (Problem Set)
80%: Examination (Unseen examination)
Contact hours and workload
This module is 150 hours of work. This breaks down into 33 hours of contact time and 117 hours of independent study.
This module is running in the academic year 2019/20. We also plan to offer it in future academic years. It may become unavailable due to staff availability, student demand or updates to our curriculum. We’ll make sure to let our applicants know of such changes to modules at the earliest opportunity.