Functional analysis 2010

Abstract

This is a module framework. It can be viewed online or downloaded as a zip file.

As taught Autumn semester 2010.

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.

Suitable for: Undergraduate students Level Four

Dr Joel F. Feinstein School of Mathematical Sciences

Dr Joel Feinstein is an Associate Professor in Pure Mathematics at the University of Nottingham. After reading mathematics at Cambridge, he carried out research for his doctorate at Leeds. He held a postdoctoral position in Leeds for one year, and then spent two years as a lecturer at Maynooth (Ireland) before taking up a permanent position at Nottingham. His main research interest is in functional analysis, especially commutative Banach algebras.

Dr Feinstein has published two case studies on his use of IT in the teaching of mathematics to undergraduates. In 2009, Dr Feinstein was awarded a University of Nottingham Lord Dearing teaching award for his popular and successful innovations in this area.