Topology and Advanced Analysis (L7) (803G1)
15 credits, Level 7 (Masters)
Topology has a central role in all of mathematics and having a proper understanding of its basic ideas, concepts and main results is essential as part of a good mathematics degree.
You will be introduced to basic concepts and properties of Topological Spaces. Various applications to Functional Analysis, Real and Complex Analysis will be discussed and there will be a fair balance between theory and examples.
Topics include separation axioms, metrisability, compactness and coverings, total boundedness, nets and Lebesgue numbers, Arzela-Ascoli theorem and compactness in function spaces, Montel's theorem and normal families, Tychonoff's theorem and infinite products and upon time allowing the Banach-Alaoglu theorem and compactness in weak-star topologies.
20%: Coursework (Portfolio, Problem set)
80%: Examination (Unseen examination)
Contact hours and workload
This module is approximately 150 hours of work. This breaks down into about 33 hours of contact time and about 117 hours of independent study. The University may make minor variations to the contact hours for operational reasons, including timetabling requirements.
We regularly review our modules to incorporate student feedback, staff expertise, as well as the latest research and teaching methodology. We’re planning to run these modules in the academic year 2023/24. However, there may be changes to these modules in response to COVID-19, staff availability, student demand or updates to our curriculum. We’ll make sure to let our applicants know of material changes to modules at the earliest opportunity.
This module is offered on the following courses: