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

http://www.maths.nott.ac.uk/personal/jff/Teaching/TeachingResources.html

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

http://explainingmaths.wordpress.com/definitions-proofs-and-examples/

**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

http://wirksworthii.nottingham.ac.uk/webcast/maths/G14FUN-09-10/FUN-260310b/

For more information, see the associated blog post at http://wp.me/posHB-9M

**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 http://wp.me/posHB-7S

**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 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

http://wirksworthii.nottingham.ac.uk/webcast/maths/Beyond-Infinity-March-2010/

The 2006/7 edition is also available in wmv format:

**Beyond Infinity?** (wmv file, 2006-7 edition)

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

http://wirksworthii.nottingham.ac.uk/webcast/maths/G14FUN-09-10/FUN-090210/

and

http://wirksworthii.nottingham.ac.uk/webcast/maths/G14FUN-09-10/FUN-120210a/

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

http://wirksworthii.nottingham.ac.uk/webcast/maths/G14FUN-09-10/FUN-290110/

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

http://wirksworthii.nottingham.ac.uk/webcast/maths/G12MAN-09-10/Chapter9/

**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)

**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 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)

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