math – Explaining mathematics

Latest posts on my Blogger blog 5/2/25

Joel — Wed, 05 Feb 2025 18:55:29 +0000

For more of these summaries, you can search this blog for “Latest posts on my Blogger blog”, or click this search link

Here are some links to my most recent posts on my Blogger blog, where I am able to use MathJax.

I’ll periodically post updates on this blog, with links and brief descriptions.

Date	Title and link	Description
5/2/25	The Extreme Value Theorem: a bootstrap approach	An approach to the Extreme Value Theorem where you can deduce all of the rest of the theorem from the first part where you show that every continuous function on a closed and bounded interval must be bounded above.
2/2/25	Set of real numbers, bounds and sequences II	In this part we (try to) tie together everything we know about infimum, supremum, epsilons and sequences
1/2/25	Set of real numbers, bounds and sequences I	Discussion of lower and upper bounds for sets, including the definitions of infimum and supremum
29/1/25	Injective continuous real-valued functions on an interval must be monotone	Some discussion of this very useful theorem of Real Analysis, and how to get around a minor obstacle in the usual proof by contradiction
11/12/24	A rule of thumb for when to use the Ratio Test	A discussion of when it might be a good idea to try the Ratio Test, and when you should definitely not try the Ratio Test (for sequences and/or series)

Mathematics News from the University of Nottingham, Volume 1, Number 1

Joel — Tue, 14 Dec 2021 17:56:18 +0000

See all posts about the UoN maths newsletter

The first issue of our new maths e-newsletter for teachers and students, Mathematics News from the University of Nottingham, is now available from https://tinyurl.com/uonmathsnews-Volume-1-Number-1

This issue includes information on the careers of University of Nottingham maths graduates, a puzzle about prime numbers, a short article about Edmund Landau and Landau’s problems, and some links to useful resouIf you would like to receive a link to each newsletter as soon as it is available, you can fill in the form at https://tinyurl.com/uonmathsnewsform

Taster Sessions Update 11

Joel — Mon, 06 Dec 2021 06:34:13 +0000

For other messages in this series, see https://explainingmaths.wordpress.com/?s=Taster+Sessions

(This post to our Maths Taster Sessions Mailing List was dated November 30th 2021)

Our final pre-Christmas Taster Session will be on Wed Dec 8^th 2021.

To join these events, you don’t need to register. Just visit our Taster Sessions page at https://tinyurl.com/uonmathstaster on the day and click on the relevant ‘Join event on the day’ button.
Wed 8th December 2021, 5PM
Speaker: Alan Barker
Taster Lecture on Fermi Estimates
This talk will introduce the concept of Fermi estimates, which are a way of making surprisingly good approximations given very limited data and some general knowledge and common sense. These are widely used by engineers and scientists, and are also very useful in other situations which might be met in day to day life. The ability to make such estimates is an important skill looked for by many employers.

Study with us: https://tinyurl.com/mathscourseuon
Open Day maths talk videos: https://tinyurl.com/uonmathsvod
Maths taster sessions: https://tinyurl.com/uonmathstaster
Sign up for our new maths e-Newsletter: https://tinyurl.com/uonmathsnewsform

Taster Sessions Update June 6 2021

Joel — Thu, 10 Jun 2021 11:55:58 +0000

Hi everyone,

Slides from all 6 of our recent Maths Taster Sessions are now available from the Taster Sessions web page, https://tinyurl.com/uonmathstaster
Meanwhile, we are continuing to post videos from these sessions on that page and on the School of Mathematical Sciences YouTube channel, https://tinyurl.com/uonmathsyt
(It takes me a while to correct the auto-generated captions!)

The latest video available is from Peter Neal’s Taster Lecture (11/05/21) on Probability. This video is available on YouTube at https://tinyurl.com/uonmaths110521

I am currently correcting the captions for Tom Wicks’s Taster Lecture on Problem Solving, so that should be ready soon.

University of Nottingham Maths Taster Sessions: two announcements

Joel — Thu, 27 May 2021 21:38:45 +0000

This post has two parts:

1. Our next event

2. Slides and video on demand

Tags: #mathematics #maths #math #appliedmaths #university #nottingham #calculus #covid

1. Our next event

Our next event, which will be the last in our current series of Taster Sessions, will be a Taster Lecture on Applied Mathematics by Stephen Creagh, at 5PM on Thursday 3^rd June 2021.

Applied mathematics is all about constructing models of the world around us, in contexts as diverse as mechanics, pandemic modelling or weather prediction, and then solving the resulting equations. Calculus is the central language of this modelling cycle. Typically, our mathematical models take the form of differential equations, in which the governing equations tell us about the rates of change (derivatives) of the quantities we are interested in.

In this taster lecture we will explore qualitative and graphical approaches to understanding the solutions of these models. These qualitative approaches often give really good insight into the problem while demanding much less effort than would be needed for complete solutions in the form of explicit formulas. For example, in modelling a pandemic, we might be much more interested in answering questions such as whether infection numbers will rise or fall, whether they will approach an equilibrium or keep changing steadily, and if rising, what parameters might be changed to make infections fall etc.

For full details of our Taster Sessions, see the page

https://tinyurl.com/uonmathstaster

To join one of our Teams Live events, simply visit that page at the right time and use the session’s Join Teams Live Event button.

2. Slides and video on demand

Slides from the first five Taster Sessions in the current series are now available (in PDF format) from the page https://tinyurl.com/uonmathstaster. Videos from our sessions will be available on demand from the same page once the captions are ready. So far you can watch videos from the first two sessions, which are the Taster Lecture on Calculus by Anna Kalogirou from 29th April 2021, and the popular maths talk Using maths in the fight against Covid-19 by Katie Severn from 6^th May 2021. You can also find these videos on our YouTube channel, available at https://tinyurl.com/uonmathsyt