Foundations of Pure Mathematics (FPM) archives

Videos are available from 2014-15, 2018-19 and 2019-20 editions of Foundations of Pure Mathematics (FPM)

The complete set of videos from the 2014-15 edition of Foundations of Pure Mathematics (FPM) is available on YouTube and iTunes. And I have opened up some of the Echo360 recordings (also known as “Echoes”) from previous years. These have the (possible) advantage that you have two separate windows, one with the screen recording (the “screencast”) and one with the footage of me. These windows can be resized or hidden according to your taste! Another nice feature of these Echoes is that you can change the speed of the video if you find my pace either too slow or too fast. (This often varies from student to student, from lecture to lecture, and also within lectures). If you click on the settings cog near the bottom right of the video window, and click on the speed (default 1), there are plenty of options!

I don’t advise anyone to watch several versions of every class! But if there is a specific point you are interested in, then there is a possibility that I did say something different about it each year.

The 2018-19 edition of FPM is available at

The syllabus in 2018-19 was essentially the same as in 2014-15. But the syllabus then changed slightly in 2019-20. The main difference now is that the last topic from 2014-15 and 2018-19 (on countability and uncountability) is no longer in the syllabus for this module. Instead there is further coverage of equivalence relations and modular arithmetic, and some material on the Euclidean Algorithm for integers (See the new material in lectures 7b and 9b)

The 2019-20 edition of FPM is available at

Note that, because of industrial action, not all classes in 2019-20 were given live, so the set of videos is incomplete. However the new material is there, in lectures 7b and 9b.

Please let me know if there are problems with these links!

Virtually Nottingham

In view of the coronavirus crisis, the University of Nottingham is running many online activities over the summer. This includes “Virtually Nottingham” (see There are live talks and recorded catch-up sessions. I contributed a “mini-lecture” to this on Tuesday 7th July 2020 with a new edition of my take on Hilbert’s Hotel, “Beyond Infinity?”. Thanks to Helen Preston for converting my original pdf file (produced using LaTeX) into a suitable PowerPoint presentation.

The main talk was pre-recorded this time, but I was live for the Q&A. I look forward to seeing the combined video in due course via the catch-up page

My most popular video

Of all of my videos published anywhere that I know of, the one which has the most views appears to be this one in China:

(This may not be viewable in all countries, but is currently working here. It was unavailable for a few months in the UK, but I noticed that it came back after Brexit, so maybe it is unavailable in the EU!)

[Notes added: On 18/6/20 I noticed that I couldn’t watch the video on that site any more: they were asking you to download an app, which I haven’t tried myself. However, as of 2/8/20 it seems to be available directly from that site again.]

It’s the “About this module” introductory class from my old Mathematical Analysis module (2009-10). At the time of writing it has had 261,000 views.

I don’t know why this one is so much more “popular” than all the other videos. But generally, when I have a series (sequence?) of videos, the first one in the series is always the most popular. And I suppose lots of people may search for Mathematical Analysis.

I am very impressed by the work they must have put in to add subtitles (English and Chinese) to lots of my videos! So far I know about subtitled versions (Chinese and English) in China for Mathematical Analysis and for Functional Analysis. If any more turn up, please let me know!

Funny auto-generated subtitles

As I gradually edit subtitles for my Measure Theory videos, I should make a note of some of the funnier errors in the auto-generated subtitles. A challenge (often impossible) for the reader is to try to work out what I really said. But as a hint, the topic is measure theory, including the extended real line, sigma algebras (also known as sigma fields), Borel sets, measures, etc.
These are all genuine attempts by the software to generate text from what I said. But, to be fair, the sound quality of these recordings isn’t great, and I don’t always speak slowly and clearly enough to give the software a real chance.

Here are some of my favourites so far. (There are many more which I didn’t write down and have now forgotten.)

I haven’t kept a systematic set of “solutions” to these, but they are mostly in order of appearance in my Measure Theory videos. So hopefully I can still work out what (I think) I really said if I need to!

Continue reading

Measure Theory videos on YouTube

As newly mentioned in a (new) note added at the end of my previous post
and also now mentioned at the top of my Measure Theory blog page, the University of Nottingham is now beginning to release my Measure Theory videos on YouTube. See the playlist at

The plan is to release about two episodes per week. If you are impatient, all the videos are already available from the blog page above. At the time of writing, I am still in the process of making subtitles/closed captions available for those. The versions released on YouTube will/do have subtitles available.

Subtitles for Measure Theory videos

I am considering publishing my Measure Theory videos (as available on ) on some of the official University of Nottingham channels. However, the latest rules say that University of Nottingham videos must have subtitles available.

The recommendation is that I upload the videos to MediaSpace. There is a facility there to auto-generate captions. I have tried this, and the results were better than I expected, but still very funny! So, as a holiday treat, I have been doing some corrections by hand. I found that it took me several hours to correct the subtitles/captions for the first 14-minute recording. But I think I am getting faster now!

If you look on  you will see that, of the 15 Measure Theory recordings, parts 6 and 7 now have subtitles available (you click the [cc] closed captions button under the video to turn these on or off). Part 1 also now has a two versions, and the version on MediaSpace has subtitles available.

Please let me know whether you find the subtitles helpful!

Note added 20/4/20: I am continuing to correct subtitles on more episodes, but it is hard work! Gradually more episodes will be available on MediaSpace (and I’ll link to those from the above blog page). Also, the University of Nottingham will release about two episodes a week on YouTube: see the playlist at

Time for a break!

Right, it is now the end of term. Time for the Easter Break, I suppose!

I’m going to miss the online teaching a bit. It’s been quite interesting getting everything working. And it helps that (at least for me) the recordings have started working properly in Microsoft Teams.

I’m mostly happy with my setup now, in case I have to do a lot more of this. Of course, I am broadcasting from my living room, so random family members and/or pets may be audible at times. In particular, our dog Lily sometimes gets overexcited and starts barking, and I can’t do much about that. Fortunately my wife and children can usually help distract her or tempt her out of the room.

Technically, most things are working well now. In today’s class, my Surface Pro was clearly thinking about something else again, because there was some lag between writing with the tablet pen and the digital ink actually appearing. But I did forget to restart the tablet this morning, so I have to take some of the blame! Otherwise, my main technical issues now are caused by the pen’s side button: the way I hold the pen, I find it hard to avoid pressing this button unintentionally. I must have another look to see if I can deactivate it.

I have at least deactivated some of the touch features in DrawBoard PDF. I used to keep double-tapping accidentally and this was set by default to zoom in massively on that portion of the document. (I am happy to do zooming in and out using finger-pinching etc.)

Anyway, things are now going to be relatively quiet on the online live teaching front for the next few weeks.

Microsoft announce fix for problem with recording screensharing in Teams

The latest announcement (quoted/posted by Michel Bosch) showing on
looks promising!

Title: Some meeting recordings are not capturing screensharing

User Impact: Some meeting recordings were not capturing screensharing or other videos.

Final status: We’ve confirmed that the fix has been completely deployed the affected environment and our testing and telemetry indicated that the issue has been mitigated.

Scope of impact: Your organization was affected by this event, and any user may have experienced impact if they were viewing a meeting recording that has a screensharing session or other videos.

Start time: Monday, March 16, 2020, 7:00 PM (6:00 PM UTC)

End time: Saturday, March 28, 2020, 9:44 PM (8:44 PM UTC)

Root cause: A decoding issue within the video pipeline resulted in the record meetings feature to not work as expected.

Next steps: – We’re investigating why the increase in traffic degraded the video pipeline to find ways of preventing this issue from reoccurring.

This is the final update for the event.

So maybe it is now fixed! I’m going to test it out.

Teaching diary 26-27 March 2020

So I set up all my equipment ready for my tutorial at 11AM last Thursday. We started our Microsoft Teams meeting, I shared my Main Display (Display 1) with a blank DrawBoard PDF document open and copies (screenshots) of the tutorial questions open in a picture viewer. Then I attempted to start an Echo360 recording, and my tablet refused to cooperate!

[Note to self: make sure to restart the tablet in the morning. It sometimes helps!]

There was rather a lot running on my Windows Surface. I always make sure that it is running on mains power (which helps with the processing power), but it was still clearly struggling. The mouse pointer was starting to wander around randomly without me doing anything. When I did manage to get the mouse pointer over the Echo360 record button, it didn’t seem interested when I clicked. Eventually it did respond, and started a partially visible but fragmented visible countdown, before announcing that it was unable to start the recording. In fact I think it did start one recording, and also attempted to start a few other recordings unsuccessfully.

I started up Task Manager (which probably added a bit more to the tablet’s burden), and this confirmed that I had too much running. So I quit a few applications (Echo360, Adobe Acrobat and Chrome). One of my tutees then set a recording going in Microsoft Teams, and we got on with some maths.

I should probably have restarted the tablet, because it was still struggling. When I was writing or sketching curves/regions in the plane, I kept having to stop and wait for the inking to catch up with my pen. And additional random inking filaments were appearing. Nevertheless, we managed to cover some important stuff. And the recording uploaded to Microsoft Streams quickly and successfully at the end.

I should say that there are other reasons why my tablet sometimes has to stop and think about stuff. For example, if I right click and try to use “open with”, the tablet often hangs while it attempts to check all University of Nottingham applications in order to populate the list it (maybe) eventually offers. I am going to have to try to get out of the habit of right clicking.

I hit another problem when I installed PDF Annotator on the tablet. (This was because I wanted to be able to do a few things that the version of DrawBoard PDF I have can’t do. ) Suddenly I found that double-clicking on PDF files was having no effect! I tried quite a few documents. Their properties showed they were supposed to open with DrawBoard PDF. (I set that as my default on the tablet. That is also rather difficult to do at the moment, for similar reasons to the problems with “open with”!) I will admit that I probably overdid the double-clicking. I then uninstalled DrawBoard PDF and reinstalled it. This was almost certainly unnecessary. I had to find and re-enter the activation code DrawBoard had sent me, and then set up all my favourites again, etc..

At some point windows started to open up again and again (10 minutes or so after my spate of double-clicking) asking me whether I wanted to keep using DrawBoard PDF to open this file, or use a different app instead. (In fact the first few of these opened up during the time period when DrawBoard was still uninstalled!) That kept me busy for a while.

I think what happened was that, when I installed PDF Annotator, the tablet decided that I now had some new PDF software. So the next time I double-clicked on a PDF file, it thought it would be a good idea to ask me whether I wanted to continue using DrawBoard PDF to open the file, or another application. But it then had to try to populate the list of available applications, and this took several minutes at least. Anyway, maybe 20 minutes later the last of these windows had opened and closed and things were working again.

OK, so it looked as if recording meetings in Microsoft Teams was the way to go then! Admittedly my first attempt at recording a meeting on 11th March had not given me much confidence. But things appeared to have improved since then…

OK, so next was my 1PM online lecture for my Level 4 module. I set everything up the way I wanted, started the meeting, shared my main display, and started the recording in Teams. Everything seemed to work well, until I checked the recording later. See below!

Soon after my 1PM lecture finished (after grabbing a quick snack) I had an online dissertation supervision meeting with a 4th-year student. It isn’t obvious whether recording project/supervision meetings is necessary: after all, I never used to do that in my office! Still, the students agree that these recordings could be useful, so I’ll try to record them. I also generate PDF files with my annotations, and I make these available to the students too. For this particular meeting, somehow I forgot to start the recording until the middle, but it was still probably better than nothing.

OK, now I had some catching up to do! I distributed the various PDF files I had generated and made sure that the videos had processed on Microsoft Streams. The processing was pretty quick (a big contrast to the long delay I saw back on March 11th). I thought that the students might be more used to accessing videos on Echo360/Moodle, so I downloaded the videos from streams, uploaded them to, and shared them with the relevant students. (Or in the case of the Level 4 Module, I was able to make it available to the students via a link from the Module Moodle page.) However at some point I realised that there was something wrong with one of the recordings. The recordings of the tutorial and the (second half of the) dissertation meeting were both fine. But the recording of the Level 4 Module lecture had gone wrong. Instead of recording the audio and the shared screen where I was annotating a PDF file, Teams had recorded the audio and video of a static screen showing 4 discs containing the initials of the participants at the meeting. The audio may still be useful, in combination with the annotated slides. But the video/screencast showing the annotation happening would be much better!

I assumed that I had done something wrong, and that maybe I should attend a training session. But looking online I found that this was a known issue. See

The second page of that thread was unavailable (to me at least) yesterday, but it appears to be back today. See

I had another lecture at 12 noon yesterday (Friday March 27 2020). I thought it might help if a student started the recording instead of me, but unfortunately that made no difference.

This appears to be an ongoing issue (see continuing discussion and announcements in that thread). However, I have received advice locally that it is best to start the recording BEFORE you share your screen. I have examples showing that it sometimes works if you share the screen first, and some people in the thread above have had problems either way, but it could well be that your chances are improved if you do start the recording before the screen share.

It may also depend on your set-up. For example, I have dual displays: could that contribute to the problem? Does it help if you share a window rather than a display? (Because of my use of Pen Attention as a “digital pointer”, it is better for me to share the screen rather than just the DrawBoard window.)

Anyway, for now it isn’t obvious what I should do. If only everything worked smoothly, recording in Teams should be the way to go. But if the problem persists, I may have to try something else.

[Note added: fortunately Microsoft appear to have fixed this! See ]

More and more equipment

Well, my living room table is starting to fill up with more and more equipment. There is the surface pro on a stand, the Dock, the second monitor plugged into the Dock, external USB keyboard+mouse+webcam, some old computer speakers, earphones and an old Blue Snowball microphone. (I’ve ordered a new mouse mat …)

I am going to make some test recordings to see which microphone I should use for audio input, since I have quite a few options. I should probably listen to the results on something decent before I decide.

When the audio doesn’t fail completely (as it did for the lecture yesterday), the audio recording can still be distorted if the tablet can’t cope with the demands placed on it. I think that it may be at its limits when I’m recording audio and video with Echo360 at the same time as running a Microsoft Teams meeting, annotating a PDF file using DrawBoard PDF, keeping an eye on Student Confidence using my Google Form (and having lots of equipment attached!). I think I’d better keep an eye on this using Task Manager. It is probably just as well that I’m not recording two simultaneous video streams (for now!).

Perhaps if I allow Microsoft Teams to record the meeting, instead of Echo360, that will help. I had some problems with this before, but maybe I should give it another try.

Failed audio in one of my recordings today

I recorded two sessions/live meetings today: an undergraduate project supervision meeting, and a lecture. I remembered today that I wanted to use the webcam for audio input, and set that up successfully.

The first meeting and recording were fine, but I hit problems with the second meeting and recording. The students said that they couldn’t hear me. So I switched the audio input on Microsoft Teams back to my tablet microphone, and then they could hear me. But I was using Echo360 for the recording, and I didn’t switch the audio input there. That was a mistake! I think from now on I’ll make sure that Teams and Echo360 are sharing the same audio input, so the students can warn me if there is an issue. The audio on that recording is very strange: just a lot of squeaking and other weird noises.

There was also a problem with connectivity. Teams flashed up some messages to say that my internet connection was slow and so the call would be low quality. Of course the whole family is sharing the broadband connection, and we have some significant backup-to-cloud uploads running on various machines (perhaps I should try to make sure these are paused when I am teaching). I’m not sure whether there was any connection with the other problem though.

I have now rearranged things a bit so that the less demanding USB devices are plugged into the USB ports in my Dock (for my Surface Pro), while the USB webcam is now plugged directly into the USB port on the Surface Pro itself. I would still prefer to use the audio input from the external webcam if possible, to avoid the issue of recording/broadcasting loud tapping and scratching of the tablet pen. I’ll make a couple of test recordings to see how the equipment is behaving.

I now have a USB keyboard plugged into the Dock, rather than using the standard Surface Pro keyboard. This gives me more options when it comes to the physical setup I use for annotating PDF files on my Surface Pro using DrawBoard PDF. My table is getting a bit crowded now though!

Using multiple screens with Teams and Echo360

Amazingly, after all this time, before today I had never used multiple screens to have an extended monitor!

I got a few things wrong at first, which I don’t fully understand yet. For a while I couldn’t get the mouse pointer from one display to the other! This was, I think, a combination of the display arrangement and the choice of “main display” in the display settings. Once it is all working, it is fine! Currently I have the external monitor (Display 2) to the left of the tablet screen (main screen, Display 1), and I have the screens aligned vertically in the middle, so I can’t get from one screen to the other if I am too high or low on the “taller” display. I may rearrange this to fit more closely with the actual physical relationship between the two screens.

OK, so that’s all working. My next task was to see how this plays with Teams and Echo360. I’m rather pleased to see that Echo360 is happy to record both displays as separate streams. That could possibly be quite useful, though it isn’t currently my top priority.

In Teams, I can now share Display 1, where I will annotate the PDF files, while having separate Teams windows etc. open on Display 2. This should allow me to see my students’ faces during the class, without recording their faces in the video. I can also have the chat window open on Display 2. But I probably need a different keyboard, because I can’t annotate properly on my Windows Surface while the standard keyboard is attached to it. (Of course I could continue to use a second computer and/or my mobile phone.)

I am not sure whether my Student Confidence Google Form is still necessary, but I’ll keep it going for now.

Using a Google form to measure student confidence levels

At the moment I haven’t found a way to see my students’ faces while I am sharing my screen with them in Microsoft Teams. So I thought I should look for a simple app that would allow students to indicate, in real time, how confident/confused they were feeling about the material currently under discussion. I would see the summary, and should be able to tell if something needs further explanation, even if no-one says anything aloud or in the text chat window.

Well, I haven’t yet found the right app, so I’ve gone back to Google Forms. You can see a copy of the form I am using at

It’s just a very simple scale 1-10 question, with 1 being very confused and 10 meaning very confident. When students submit a response they are invited to go back and edit their response (rather than submit a new response).

This does appear to work in my small Level 4 class, and I was pleased to see confidence levels rise when I provided additional explanation! (On the other hand, students in that class are anyway willing to speak when they have a question.)

I’d still like to be able to see their faces though! So either I have to get better at using Teams, or I should maybe use some other software.

In my recent online classes I have been using (simultaneously) a Windows Surface with an external USB webcam attached, another computer, and my mobile phone. This does at least allow me to see the chat window on one computer while annotating full screen on the Windows Surface (and sharing the screen in Teams and recording a screencast using Echo360) and keeping an eye on the students’ confidence levels on my phone. But so far I haven’t managed to combine this with seeing my students’ faces.

I’m going to see if attaching an extra monitor to my Windows surface provides some more options.

DrawBoard PDF and the Microsoft Store

As I mentioned in a previous post, in my teaching I am currently using DrawBoard PDF on a Windows surface to annotate PDF slides with gaps .

My first Windows Surface had DrawBoard PDF included with it. But later generations of Surfaces don’t, and the free trial only lasts 3 days.

The School of Mathematical Sciences (University of Nottingham) purchased a batch of DrawBoard licenses for various members of the School, using their work Microsoft Store accounts, but there were a few issues getting these licenses to work. By the time I started trying to install it (on my new Surface), there was a local troubleshooting guide (thanks Dave!), a link to DrawBoard’s guidance, and a suggestion to contact DrawBoard support if all else fails. Apparently some colleagues had succeeded, but others had given up and purchased the app using a personal Microsoft Store account. (It isn’t very expensive, and there isn’t any hassle that way.)

One of the first steps in the troubleshooting guide is to make sure that you log in to the Microsoft Store using your Work account (given that the license was purchased for your Work account) and not a Personal account. Now I don’t know if it is just me, but I simply could not work out how to log in using my Work account for ages! The instructions I found online all said (when in the Microsoft Store) to click the user icon (top right) and select “Sign in”. When I tried this, it said that there was no account associated with my (work) email address, and would I like to create one? So I tried to create one, and it told me I couldn’t create an account with that email address, because it was a work email address.

I tried this several times, because I couldn’t see what else to do. I began to think that I didn’t and/or couldn’t have a Microsoft Store account associated with my work email. But, by chance, one time when I clicked on the user icon, I spotted that underneath “Sign in” it offered “Add work or school account”. I clicked that, and suddenly I was able to sign in using my work email! (If you start off signed in to a work account, then under “Sign in” it offers “Add personal account” instead.)

I thought that I was home and dry now! I downloaded DrawBoard PDF using my Work Microsoft Store account … but all I got was the three-day free trial, and when this expired I was stuck again.

I followed all the online troubleshooting advice available, but nothing worked. So I finally contacted DrawBoard support, telling them when my license was purchased and for which (work email) Microsoft Store account. They were very helpful. They knew that the usual troubleshooting steps wouldn’t solve the problem (“Unfortunately the steps you took will not fix this, as it is a Microsoft Business Store issue …”), and sent me an activation key to use. 

All is now well! But if I consider the amount of time I spent on this and the price I would have paid to purchase the app myself using a personal account, I don’t think it was the best use of my resources. Unless, of course, this post helps others who have similar problems?

Online teaching diary: March 17 2020

I have a very small Level 4 class, Further Topics in Analysis (FTA), with just 5 students registered. As with all my modules these days, I have been teaching the module using a Windows Surface and DrawBoard PDF to annotate PDF slides with gaps.

I decided that today would be my first attempt at remote, online, live teaching of this module.

Earlier in the day, I had a short test meeting on Microsoft Teams with David Hodge. This gave me a chance to practise sharing my screen or my DrawBoard PDF window during a meeting. There were some problems with my webcam video stream: it was permanently on, but didn’t say so. (The button always said “Turn video on”, but David could see me whatever I did. Be warned!)

I also recorded about four minutes of the meeting using the Teams record meeting button. After the meeting it took a VERY long time before this recording became available on Microsoft Streams. So I decided that this was not the way to go.

Meanwhile, I had set up a team with the five FTA students in it. I contacted the students to say that I would have a test meeting in the hour before the real lecture. That gave me a chance to iron out a few more wrinkles. Then we started the “real” lecture at 3PM. Four of the five registered students joined the meeting.

I was able to use DrawBoard PDF in the usual way to annotate a PDF file which they could see. I had to choose whether to share my whole screen, or just the DrawBoard window. Because I use a digital pointer (PenAttention), in order for the mouse pointer highlighting (red blob) to be visible to the students, I decided to share my whole screen.

I used Echo360 Universal Capture – Personal to record the class.

Now, when I am annotating slides on a tablet, I don’t like to use the tablet’s camera and microphone. The microphone records loud tapping etc. from the tablet pen, and the video from the camera is quite scary! So I needed to attach a USB webcam. I also have a USB mouse attached because it makes a few things easier. But these surfaces only have one USB port. Fortunately I have a Dock for my surface, and that provides a couple of extra USB ports. Otherwise I suppose I would have needed to plug in a USB hub.

Teams and Echo360 were happy to share the audio stream from the USB webcam. But they couldn’t share the video stream. I decided to let Teams have the video stream, and not to bother recording a separate stream dedicated to showing footage of myself today. (In theory I could probably plug in a second USB webcam? But that seems over the top!)

Everything went relatively smoothly, but I found it felt rather strange not to be able to make eye contact with the students. They could see and hear me, and see me annotating my PDF file and using my digital pointer. I could hear them, and we also had a chat window for text chatting (though my windows tended to get in the way of each other a bit). But I couldn’t see them. In theory I could, if they turned their cameras on, but even then when I was annotating my PDF file I wouldn’t have been able to see them. Maybe what I need is a second screen (I don’t know how that fits with Echo360), or perhaps I could log in a second time on my desktop PC and see the students there.

Usually with such a small class, there are lots of easy ways to get some idea of how well they are engaging with and following the material. Today I felt cut off from a lot of the things I would usually be able to do.

I could try different software. What have other people been using? Can you get a more interactive experience?

With a bigger class, I would be using mobile phone voting on multiple choice questions, so I could interact that way. Perhaps I should set something up so that students could keep me informed of their levels of puzzlement as we go. (David Hodge showed me Jitsi Meet, and I could maybe try that.)

Anyway, the class seemed to go OK, and the recording worked fine. (I must remember to turn off Windows Mail notifications before the next class!) But I still think that some things could be better. Next class will be Thursday afternoon. I also have a first-year Group Tutorial (6 students) on Thursday morning. Tomorrow I’ll have a play with various bits of software/mobile apps.

Oh yes, the Surface did struggle to cope with all the software that was open. I can tell when this happens, because you suddenly get unexpected straight lines appearing between two recent places the pen was on the screen. In the past this problem only happened if I wasn’t plugged into mains power. But today the surface was plugged in, and the machine was still struggling. It may be just as well that I didn’t try to record another video stream!