Advanced Mathematics University of Nottingham

 Courses

A selection of recordings of more specialized talks, typically for those with background equivalent to at least a BSc in mathematics.

 video
The Baire Category Theorem  Dr Joel Feinstein
This is a lecture from Dr Feinstein's 4thyear module G14FUN Functional Analysis.
See also Dr Feinstein's blog at http://explainingmaths.wordpress.com/ and, in particular, the associated blog post at http://wp.me/posHB7y In this screencast, Dr Feinstein proves the Baire Category Theorem for complete metric spaces  a countable intersection of dense, open subsets of a complete metric space must be dense.
This material is suitable for those with a knowledge of metric space topology and, in particular, dense subsets and complete metrics. 
 video
The weak star topology and the BanachAlaoglu theorem
This is a lecture from Dr Feinstein's 4thyear module G14FUN Functional Analysis.
See also Dr Feinstein's blog at http://explainingmaths.wordpress.com/ and, in particular, the Functional Analysis screencasts blog page at http://wp.me/PosHB8v
In this screencast, Dr Feinstein introduces the weak topology on a normed space and the weak star topology on the dual space. He then proves the BanachAlaoglu theorem, that the closed unit ball of the dual space is weak star compact.
This material is suitable for those with a basic knowledge of normed spaces and their duals, and of infinite products of topological spaces, including Tychonoff's theorem on arbitrary products of compact topological spaces. 
 video
The Uniform Boundedness Principle  Dr Joel Feinstein
This is a lecture from Dr Feinstein's 4thyear module G14FUN Functional Analysis.
See also Dr Feinstein's blog at http://explainingmaths.wordpress.com/ and, in particular, the Functional Analysis screencasts blog page at http://wp.me/PosHB8v
In this screencast, Dr Feinstein discusses two famous results concerning collections of bounded linear operators, one of which is a corollary of the other. Both of these results have been called the BanachSteinhaus Theorem (by various authors). The stronger of these two results is the one which is also known as the Uniform Boundedness Principle.
This material is suitable for those with a good background knowledge of metric spaces and normed spaces. In particular, the student should know about bounded (continuous) linear operators between normed spaces, and the Baire Category Theorem for complete metric spaces. 
 video
iPod version  The Baire Category Theorem  Dr Joel Feinstein
This is a lecture from Dr Feinstein's 4thyear module G14FUN Functional Analysis. See also Dr Feinstein's blog at http://explainingmaths.wordpress.com/ and, in particular, the associated blog post at http://wp.me/posHB7y In this screencast, Dr Feinstein proves the Baire Category Theorem for complete metric spaces  a countable intersection of dense, open subsets of a complete metric space must be dense. This material is suitable for those with a knowledge of metric space topology and, in particular, dense subsets and complete metrics.

 video
iPod version  The weak star topology and the BanachAlaoglu theorem
This is a lecture from Dr Feinstein's 4thyear module G14FUN Functional Analysis. See also Dr Feinstein's blog at http://explainingmaths.wordpress.com/ and, in particular, the Functional Analysis screencasts blog page at http://wp.me/PosHB8v In this screencast, Dr Feinstein introduces the weak topology on a normed space and the weak star topology on the dual space. He then proves the BanachAlaoglu theorem, that the closed unit ball of the dual space is weak star compact. This material is suitable for those with a basic knowledge of normed spaces and their duals, and of infinite products of topological spaces, including Tychonoff's theorem on arbitrary products of compact topological spaces.

 video
iPod version  The Uniform Boundedness Principle  Dr Joel Feinstein
This is a lecture from Dr Feinstein's 4thyear module G14FUN Functional Analysis.
See also Dr Feinstein's blog at http://explainingmaths.wordpress.com/ and, in particular, the Functional Analysis screencasts blog page at http://wp.me/PosHB8v
In this screencast, Dr Feinstein discusses two famous results concerning collections of bounded linear operators, one of which is a corollary of the other. Both of these results have been called the BanachSteinhaus Theorem (by various authors). The stronger of these two results is the one which is also known as the Uniform Boundedness Principle.
This material is suitable for those with a good background knowledge of metric spaces and normed spaces. In particular, the student should know about bounded (continuous) linear operators between normed spaces, and the Baire Category Theorem for complete metric spaces.