## Taster Sessions Update 16, July 1st 2022

You may be interested in a free, in-person event with some maths taster sessions at the University of Nottingham under the auspices of the Advanced Mathematics Support Programme:

Moving on with Maths
July 7th 2022, 1-4:30PM
University of Nottingham

See https://tinyurl.com/UoNMowM for full details and how to book a place. Or you can use this QR code:

If you have missed some of our previous maths taster sessions, you can watch recordings of most of these, as well as some of our other maths talks. See https://tinyurl.com/uonmathstasterposts

If you know of anyone else who might be interested in this information, it would be great if you could pass this information on!

Best wishes,
Joel Feinstein

Study with us: https://tinyurl.com/mathscourseuon
Maths Taster Sessions: https://tinyurl.com/uonmathstaster

## University of Nottingham Open Days

The University of Nottingham has Open Days for potential undergraduate applicants tomorrow and Saturday, June 24-25 2022 (and also on September 10 and October 15).

Perhaps you have students or know others who might be interested?

https://www.nottingham.ac.uk/open-days/

## Taster Sessions Update 15b (reminder), June 14th 2022

This is a reminder of today’s free maths masterclass (live, online, on Teams), part of a series of University of Nottingham Science Masterclasses (June 13-16 2022). You need register to watch these masterclasses on Teams.
See https://tinyurl.com/uonsciencemasterclass for full details and to book a place. From that page:

## Taster Sessions Update 15, June 1st 2022

We have a maths masterclass coming up on June 14th (live, online, on Teams) as part of a series of University of Nottingham Science Masterclasses (June 13-16 2022). See https://tinyurl.com/uonsciencemasterclass for full details and to book a place. Here is a QR code you can use.

From that page:

Find out more about our areas of study and put your questions to the experts in our interactive online masterclasses.

Our teaching staff are experts in their field. Watch the masterclass presentation as they show you a taster of what it’s like to study at the University of Nottingham. You can also find out more about the careers our graduates go into.

Maths masterclass

Tuesday 14 June, 4.30-5.45pm

Speaker: Professor Theo Kypraios (https://tinyurl.com/uonmathskypraios)

Maths: Using social media to discover data patterns

Finding insights and patterns in large datasets at scale and at speed happens all the time. This session uses real-life examples to show how statisticians extract useful information from data to solve a problem. We will discuss how university-level mathematics and statistics enable us to detect the occurrence of a major disruptive event based on data from social media.

If you have missed some of our previous maths taster sessions, you can watch recordings of most of these, as well as some of our other maths talks. See https://tinyurl.com/uonmathstasterposts

If you know of anyone else who might be interested in this information, it would be great if you could pass this information on!

## Taster Sessions Update 14, May 29th 2022

In case you missed any of last year’s maths taster sessions (https://tinyurl.com/uonmathstaster), we now have playlists on YouTube and on MediaSpace. We have also included a few extra maths sessions in those playlists that you may find interesting.

Our YouTube maths taster sessions playlist is at https://tinyurl.com/uonmathstaster-yt, and the MediaSpace playlist is at https://tinyurl.com/uonmathstaster-mpl

## New WordPress email template

I recently received a notification from WordPress that they had updated the template used for sending emails out to subscribers to WordPress blogs.

I am curious to see how a bit of maths looks like in the new email template. So I should write something. (I’m subscribed to my own blog so I’ll see what the email looks like!)

I have a draft somewhere of something I was going to write about characteristic functions, counting and the inclusion/exclusion principle. Ah I see I already published Part 1 at

Another observation which can be helpful is the following. Suppose that $s$ and $t$ are elements of $\{0,1\}$. Then $s-t \in \{-1,0,1\}$, and this will be even even if and only if it is zero, i.e., if and only if $s=t$. In terms of modular arithmetic, working modulo $2$, for $s$ and $t$ in $\{0,1\}$, we have

$s=t \Leftrightarrow s \equiv t~~(\mathrm{mod}~2)\,.$

Here the forward implication is trivial, but the backward implication uses the restriction on $s$ and $t$.

Since characteristic functions only take the values $0$ or $1$, we have the following extension of the above. Let $A$ and $B$ be subsets of $X$. Then (I must find a better way to write multiline LaTeX with alignment in WordPress! Perhaps they allow this by now and I just haven’t noticed?)

$A = B \Leftrightarrow \chi_A = \chi_B$

$\Leftrightarrow$ for all $x \in X$, we have $\chi_A(x)=\chi_B(x)$

$\Leftrightarrow$ for all $x \in X$, we have $\chi_A(x)\equiv\chi_B(x)~~(\mathrm{mod}~2)\,.$

Here it is convenient to bring in some new terminology to save some writing.

Let $f$ and $g$ be integer-valued functions defined on $X$. We say that $f$ is congruent to $g$ modulo $2$, and write $f \equiv g ~~(\mathrm{mod}~2)$ if (and only if), for all $x \in X$, we have

$f(x)\equiv g(x) ~~(\mathrm{mod}~2)\,.$

In other words, we require $f(x)-g(x)$ to be even for all $x \in X$.

To be continued!

## Measure Theory playlists on MediaSpace and YouTube

I have now finished correcting the captions of my 15 Measure Theory episodes. This material was one of the chapters from the Level 4 module Further Topics in Analysis, as I taught it back in 2011-12.

My Measure Theory page on this blog now links to the MediaSpace versions of these videos, which should also be viewable in China (in case you have contacts in China who want to see these!). They have also been released on the main University of Nottingham YouTube channel.

## Regularity conditions for Banach function algebras

On this blog I usually talk about mathematics topics suitable for maths undergraduates, maths A-level students or (sometimes) GCSE maths students. I have been involved in maths outreach for far younger school students. And at the other extreme I do give research seminars for specialists in my area of Functional Analysis (Commutative Banach Algebras).

## Measure Theory captions finally complete

Well, it took a lot of time, and a lot of laughter, but I have finally finished correcting the auto-generated captions for my Measure Theory videos: 15 episodes on MediaSpace, with 14 so far published with corrected captions on YouTube. The last episode will soon be published on YouTube with corrected captions.

## Maths videos on MediaSpace

Because it can be hard for people in China to access YouTube, many University of Nottingham videos are also available through MediaSpace. (See https://mediaspace.nottingham.ac.uk/)

For example, most of my old Measure Theory videos are available there (12 out of 15 so far. I’m still correcting captions for the last few!)

## Captions for Measure Theory and Beyond Infinity

After a long break, I have returned to correcting the subtitles/captions for some of my older videos!

I think that there is a convention that captions are for the same language, and subtitles are for a different language. (If that’s right then the people who published lots of my videos in China have provided English captions and Chinese subtitles.)

I started with making minor corrections to the captions for the Virtually Nottingham edition of Beyond Infinity (the most recent edition of my talk about Hilbert’s Hotel, with quite a long Q&A session afterwards). It looks like my corrections have been incorporated already, but I don’t yet know whether this was automatic or else very efficient work by a colleague!

Now I’m back to my old Measure Theory videos. You may remember that (perhaps due to a combination of me speaking too fast, and questionable audio quality) there were a lot of very funny errors in the automatically generated captions. I know that I went over the top with that list! But let me reveal some of the answers. (I’ll add some more later when I can remember the answers myself!)

Of course, I keep finding more, but I’ll resist posting most of them (unless more are requested).

Still, I just can’t resist telling you that “the Bogan’s robots” are supposed to be de Morgan’s laws!

I’ll let you know when the new versions of the Measure Theory videos with captions are released on YouTube.

## University of Nottingham Maths Taster Sessions YouTube Playlist

Thanks to my colleague Jamie Walton, we now have a UoN Maths Taster Sessions PlayList on YouTube at https://tinyurl.com/UoNMathsTaster-YT

The Playlist description currently says:

We have been running a series of Taster Lectures and Popular Maths Talks. You can find more information, including how to join us live for future taster sessions, at this link: https://tinyurl.com/uonmathstaster