Functional Analysis begins with a marriage of linear algebra and metric topology. These work together in a highly effective way to elucidate problems arising from differential equations. Solutions are sought in an infinite dimensional space of functions.

This module paves the way by establishing the principal theorems (all due in part to the great Polish mathematician Stefan Banach) and exploring their diverse consequences. Topics to be covered will include:

• norm topology and topological isomorphism;

• boundedness of operators;

• compactness and finite dimensionality;

• extension of functionals;

• weak*-compactness;

• sequence spaces and duality;

• basic properties of Banach algebras.

This resource includes mp4 screencasts (videos from classes with synchronized sound) of each of the lectures.

Supporting documents and media such as written notes, annotated slides, audio podcasts, problems, question sheets and solutions are available from a previous version of the module: functional analysis 2006 to 2008

Suitable for: Undergraduate students Level Four