Functional Analysis (L.7) (851G1)
15 credits, Level 7 (Masters)
This module serves as an introduction to the abstract area of Functional Analysis. You will study the theory of Banach and Hilbert spaces, fundamental results concerning linear functions on these spaces such as the open mapping and closed graph theorems, the uniform boundedness principle, and the Hahn-Banach theorem.
Functional Analysis studies vector spaces endowed with certain special structures (normed and inner product spaces), as well as the linear functions between them. These structures generalise those found in Euclidean spaces but, unlike Euclidean spaces and their linear functions studied in Linear Algebra, the spaces considered here need not be finite-dimensional.
These infinite-dimensional vector spaces include many examples that are important for applications, and their study gives rise to the theory of Functional Analysis which forms the theoretical foundation for most of the mathematical analysis and theory of partial differential equations underpinning the mathematical treatment of models in applied science.
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: