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. In some videos I have also included synchronized picture-in-picture (PIP) video of myself, captured using a webcam, displayed in the lower right hand corner. More recently, where available, I have often used resident Echo360 Lecture Capture systems rather than using Camtasia on my laptop.

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 for links to these collections.

Some of my earlier resources are available from

The screencasts below are now in reverse chronological order (approximately).

Foundations of Pure Mathematics

I have taught the introductory (autumn semester) first-year module G11FPM Foundations of Pure Mathematics at Nottingham since autumn 2012. I recorded the videos using the resident Echo360 lecture capture system. There were some teething technical problems, and it wasn’t until autumn 2014 that I had a complete set of videos that I was happy with. (The Lecture 1 recording failed in autumn 2014, but I am happy to use the autumn 2012 version of Lecture 1 in its place.)

The complete set of screencasts is available in various places, including the University of Nottingham’s YouTube playlist at

Measure Theory

In 2012 I recorded a number of my Measure Theory classes as part of the module G14FTA Further Topics in Analysis. One notable feature of some of these recordings is the use of the follow-my-face option in the webcam software. The results are quite interesting, though it may be that the viewer could become a little sea-sick if I move my head up and down too much!

Definitions, Proofs and Examples

In 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

G12MAN Mathematical Analysis 2009-10

My complete module G12MAN Mathematical Analysis (screencasts, lecture notes, etc.) is now available from u-Now. For more details, see the associated blog post

G14FUN Functional Analysis 2009-10

The 2009-10 version of my University of Nottingham Level 4 module G14FUN Functional Analysis is also available in full on u-Now.

Streaming video from the lectures is also available from my blog page

Note that the 2006-7-8 versions of this module are also available from u-Now: see and, specifically,

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

For more information, see the associated blog post at

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 E, all norms on E  are equivalent, along with some consequences of this. This is Theorem 3.8.

The screencast is available at

For more details, and a discussion of some preliminary facts, see the associated blog post at

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

The Baire Category Theorem

In this screencast, available from 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

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

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 \mathbb{R}^d.

There were, originally, three screencasts for this chapter. These screencasts were affected by various incidents! For more details see the associated blog post at

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

For more details on this talk, see the associated post

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, but here is the one I recorded using Camtasia:
Camtasia-recorded screencast (33 minutes, recorded on my tablet laptop)
Riemann integration

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

The topology of \mathbb{R}^d

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

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