In response to a request on Piazza, I gave a detailed proof that the uniform really is a norm, including some comments and warnings on possible pitfalls along the way. Here (essentially) is what I said.
This post is available from my Blogger blog at
https://explaining-maths.blogspot.com/2023/10/discussion-of-proof-that-uniform-norm.html
Alternatively, a PDF of that post is available for viewing or downloading below.
One of our first-year students asked (on Piazza) whether converse and negation were the same thing. One of my colleagues explained the differences in terms of propositional logic. I added some comments afterward to see if some specific examples might help. I don’t know whether this helped or not! See below for what I said.
This post is available from my Blogger blog at
https://explaining-maths.blogspot.com/2023/10/converses-and-negations.html
Alternatively, a PDF of that post is available for viewing or downloading below.
My recent series of posts about Fatou’s Lemma for sums was aimed primarily at mathematics students at 3rd-year undergraduate level or above. So I think I should write a post more suitable for first-year undergraduate students. So I’m going to have another look at the topic of 
This post is available from my Blogger blog at
https://explaining-maths.blogspot.com/2023/08/revisiting-liminf-and-limsup.html
Alternatively, a PDF of that post is available for viewing or downloading below.
See also my earlier post
An application of absorption to teaching lim inf and lim sup (sequences)
For other posts in this series, see
https://explaining-maths.blogspot.com/search?q=Sums+and+integration+against+counting+measure
This post (Appendix 5 to this series) is available from my Blogger blog at
https://explaining-maths.blogspot.com/2023/08/sums-and-integration-against-counting_30.html
Alternatively, a PDF of that post is available for viewing or downloading below.
Continue readingFor other posts in this series, see
https://explaining-maths.blogspot.com/search?q=Sums+and+integration+against+counting+measure
This post (Appendix 4 to this series) is available from my Blogger blog at
https://explaining-maths.blogspot.com/2023/08/sums-and-integration-against-counting_81.html
Alternatively, a PDF of that post is available for viewing or downloading below.
Continue readingFor other posts in this series, see
https://explaining-maths.blogspot.com/search?q=Sums+and+integration+against+counting+measure
This post (Appendix 3 to this series) is available from my Blogger blog at
https://explaining-maths.blogspot.com/2023/08/sums-and-integration-against-counting_29.html
Alternatively, a PDF of that post is available for viewing or downloading below.
Continue readingFor other posts in this series, see
https://explaining-maths.blogspot.com/search?q=Sums+and+integration+against+counting+measure
This post (Appendix 2 to this series) is available from my Blogger blog at
https://explaining-maths.blogspot.com/2023/08/sums-and-integration-against-counting_79.html
Alternatively, a PDF of that post is available for viewing or downloading below.
Continue readingFor other posts in this series, see
https://explaining-maths.blogspot.com/search?q=Sums+and+integration+against+counting+measure
This post (Appendix 1 to this series) is available from my Blogger blog at
https://explaining-maths.blogspot.com/2023/08/sums-and-integration-against-counting_28.html
Alternatively, a PDF of that post is available for viewing or downloading below.
Continue readingFor other posts in this series, see
https://explaining-maths.blogspot.com/search?q=Sums+and+integration+against+counting+measure
This post (part IV in this series) is available from my Blogger blog at
https://explaining-maths.blogspot.com/2023/08/sums-and-integration-against-counting_27.html
Alternatively, a PDF of that post is available for viewing or downloading below.
Continue readingFor other posts in this series, see
https://explaining-maths.blogspot.com/search?q=Sums+and+integration+against+counting+measure
This post (IIIb in the series) is available from my Blogger blog at https://explaining-maths.blogspot.com/2023/08/sums-and-integration-against-counting_26.html
Alternatively, a PDF of that post is available for viewing or downloading below.
Continue readingFor other posts in this series, see
https://explaining-maths.blogspot.com/search?q=Sums+and+integration+against+counting+measure
This post (IIIa in the series) is available from my Blogger blog at
https://explaining-maths.blogspot.com/2023/08/sums-and-integration-against-counting_25.html
Alternatively, a PDF of that post is available for viewing or downloading below.
Continue readingFor other posts in this series, see
https://explaining-maths.blogspot.com/search?q=Sums+and+integration+against+counting+measure
This second post in the series is now available from my Blogger blog at
https://explaining-maths.blogspot.com/2023/08/sums-and-integration-against-counting_24.html
Alternatively, a PDF of that post is available for viewing or downloading below.
Continue reading[Note: I really prefer the way the maths looks using MathJax, which I use on Blogger (at no cost). Unfortunately I am unable to use MathJax on this WordPress Blog. In future I will write my mathematical posts on Blogger, and link to them from a short post here, perhaps with an image of the introduction. The MathJax version of this post is available at
https://explaining-maths.blogspot.com/2023/08/sums-and-integration-against-counting.html
For all of my Blogger posts on this topic, see
https://explaining-maths.blogspot.com/search?q=Sums+and+integration+against+counting+measure]
Note added 30/8/23: I’m not quite sure when I started to say “integration against a measure”. I’m not alone, but I think that “integration with respect to a measure” is a lot more common! However, I don’t want to change the titles of my latest 10 blog posts, so I’ll leave it as it is. I’ll probably change back to “integration with respect to a measure” in future though!
A PDF version of the Blogger version of the post, for viewing or download. Below that is the version typed on WordPress, where I think that the maths doesn’t look as clear.
Continue readingFor more posts about our maths taster sessions (https://tinyurl.com/uonmathstaster), see https://tinyurl.com/uonmathstasterposts
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
Our quarterly maths e-Newsletter: https://tinyurl.com/uonmathsnews
Maths Taster Sessions: https://tinyurl.com/uonmathstaster
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?
Explaining mathematics 