I have generated quite a large collection of screencasts in my classes. These are movies, with synchronized sound, captured from my tablet PC, showing everything that I display on the data projector screen during lectures. More recently I have also included synchronized picture-in-picture (PIP) video of myself, captured using a webcam, displayed in the lower right hand corner.
Below are some links to a selection of these screencasts.
Quite a few of my screencasts are also available from various collections provided by the University of Nottingham. See my blog page http://wp.me/PosHB-dd for links to these collections.
Some of my earlier resources are available from
I have recently changed the order of the screencasts below: these are now in reverse chronological order (approximately).
Definitions, Proofs and Examples
This year (2011) I gave five optional examples classes to my second-year G12MAN Mathematical Analysis students on Definitions, Proofs and Examples.
I recorded videos of these classes, to go along with my previous videos on How and why we do mathematical proofs
For more details, and links to the videos, see my blog page
The Uniform Boundedness Principle (Banach-Steinhaus)
In this screencast from my level 4 module G14FUN Functional Analysis I discuss two results, both of which have been called (by various authors) the Banach-Steinhaus Theorem. The stronger of the results is the one which is also called the Uniform Boundedness Principle. The screencast is available from
For more information, see the associated blog post at http://wp.me/posHB-9M
G12MAN Mathematical Analysis 2009-10
G14FUN Functional Analysis 2009-10
Streaming video from the lectures is also available from my blog page http://wp.me/PosHB-8v
Note that the 2006-7-8 versions of this module are also available from u-Now: see http://unow.nottingham.ac.uk/ and, specifically, http://unow.nottingham.ac.uk/resources/resource.aspx?hid=bd32d53b-3c12-ac19-176b-d9e112731951
Hilbert’s Hotel, countable and uncountable infinities
My talk on this is called Beyond Infinity?
The March 2010 edition of this talk is available from
The 2006/7 edition is also available in wmv format:
For more information, see the associated blog post at http://wp.me/posHB-8r
Completeness and equivalence of norms on finite-dimensional spaces
This screencast from G14FUN Functional Analysis includes the proof that for a (real or complex) finite-dimensional vector space , all norms on are equivalent, along with some consequences of this. This is Theorem 3.8.
The screencast is available at http://wirksworthii.nottingham.ac.uk/webcast/maths/G14FUN-09-10/FUN-230210b/
For more details, and a discussion of some preliminary facts, see the associated blog post at http://wp.me/posHB-80
Tychonoff’s theorem on arbitrary products of compact topological spaces
This is covered in two screencasts from my 4th-year module G14FUN: Functional Analysis
For more information, see the associated blog post at http://wp.me/posHB-7C
The Baire Category Theorem
In this screencast, available from http://wirksworthii.nottingham.ac.uk/webcast/maths/G14FUN-09-10/FUN-010210/ I prove the Baire Category Theorem for complete metric spaces: a countable intersection of dense, open subsets of a complete metric space must be dense.
For more information, see the associated blog post at http://wp.me/posHB-7y
Revision of metric and topological spaces
This screencast, available from the web page
is from a revision session on metric and topological spaces. This comes from near the beginning of my module G14FUN Functional Analysis. For more information, see the associated blog post at http://wp.me/posHB-7t
Sequences of functions
Chapter 9 of G12MAN Mathematical Analysis is devoted to pointwise convergence and uniform convergence for sequences of real-valued functions defined on domains in .
There were, originally, three screencasts for this chapter. These screencasts were affected by various incidents! For more details see the associated blog post at http://wp.me/posHB-7j
I have combined these three screencasts into one longer screencast (1 hour 20 minutes), including a few short sections with me talking to my webcam and warning the viewer about the incidents. This video is available from
How We Teach
On Wednesday November 18 2009 I gave one of the seminars in the seminar series How We Teach at the Mathematics Education Centre at Loughborough University. This seminar series is organised by Professor Barbara Jaworski. For more information on this seminar series, contact Professor Jaworski at B.Jaworski@lboro.ac.uk
For more details on this talk, see the associated post http://wp.me/posHB-6P
The title of my talk was Using a tablet PC and screencasts when teaching mathematics (relating to mathematical analysis and proof). There are two versions of the recording, of which one is so far available:
- Camtasia-recorded screencast (33 minutes, recorded on my tablet laptop)
- Full video (86 minutes, produced by the team at Loughborough)
The last chapter (Chapter 11) of my second-year module G12MAN Mathematical Analysis consists of a one-lecture introduction to Riemann integration. For more details, see the associated post at http://wp.me/posHB-6K
The topology of
How and why we do proofs
(See also the University of Nottingham’s Open Courseware U-Now module “How and why we do proofs”, available at http://unow.nottingham.ac.uk/resources/resource.aspx?hid=9ceaa739-b7a0-3c49-fb87-52b6dcb47c5e)