Explaining mathematics

For more posts about our maths taster sessions (https://tinyurl.com/uonmathstaster), see https://tinyurl.com/uonmathstasterposts

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:

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For more posts about our maths taster sessions (https://tinyurl.com/uonmathstaster), see https://tinyurl.com/uonmathstasterposts

We have a maths masterclass coming up on June 14^th (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!

For more posts about our maths taster sessions (https://tinyurl.com/uonmathstaster), see https://tinyurl.com/uonmathstasterposts

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

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

See https://wordpress.com/blog/2022/05/19/your-website-looks-great-so-should-your-emails/

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

Sets and their characteristic functions, Part 1

But I hadn’t had time to add the follow-up yet. So here is a sneak preview!

Another observation which can be helpful is the following. Suppose that and are elements of . Then , and this will be even even if and only if it is zero, i.e., if and only if . In terms of modular arithmetic, working modulo , for and in , we have

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

Since characteristic functions only take the values or , we have the following extension of the above. Let and be subsets of . 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?)

for all , we have

for all , we have

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

Let and be integer-valued functions defined on $X$. We say that is congruent to modulo , and write if (and only if), for all , we have

In other words, we require to be even for all .

To be continued!

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.

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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).

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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!)

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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!)

Autogenerated captions	What I think I really said (or tried to say)
… et cerebral llamas	… extended real numbers
… topology or eggs	… topology on X
… bomb umbrella sets	… non-Borel sets

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.

I have mentioned our University of Nottingham Mathematics YouTube channel at https://tinyurl.com/uonmathsyt (have you subscribed to our YouTube channel yet?) and our Taster Sessions PlayList at https://tinyurl.com/UoNMathsTaster-YT

But the University of Nottingham also has its own channel at https://www.youtube.com/c/uniofnottingham

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For more posts about our maths taster sessions, see https://explainingmaths.wordpress.com/?s=Taster+Sessions

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

Please follow this link to subscribe to our Mathematics Newsletter: UoN Maths News: https://tinyurl.com/uonmathsnews

– Taster Lectures give you a taste of what a maths lecture at the University of Nottingham is really like, often based on content that we teach our first-year students. These are mainly suitable for Year 12/13 A level maths students.

– Popular Maths Talks give you the opportunity to hear one of our university teachers talk about an exciting mathematical topic, and how it links to the maths we teach at Nottingham. This could range from how to use mathematics in the fight against Covid-19, to climate change predictions. These are still most suitable for Year 12/13 A level maths students. Younger pupils such as Year 10-11 GCSE maths students who are considering taking maths A level will also find them of interest.

See all posts about the UoN maths newsletter

Hi everyone,
I have made a few tweaks to the first issue of the newsletter at https://tinyurl.com/uonmathsnewsVol-1-1 (but you might need to refresh the page or clear your cache to see the new version). I think that the maths looks a bit better in the revised version.

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If you saw my last post here you will know that I recently took advantage of editing our UoN maths newsletter to write an article about Alice Roth and Swiss cheeses.

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