Archive for the mathematics Category

Calculations, Calculations…

Posted in Biographical, mathematics, Politics on November 6, 2020 by telescoper

So it’s past 1pm GMT on Friday 6th November and the USA is still trying to work out who will be its next President after the elections that took place on Tuesday. The process is taking so long I wonder if Americans might be starting to appreciate the nature of Test Match cricket?

In the meantime I’ve been occupying myself with some simpler calculations for my second-year vector calculus module:

Standing Up for Online Lectures

Posted in Covid-19, Education, mathematics, Maynooth with tags , , , , on November 3, 2020 by telescoper

I have a break of an hour between my last lecture on Vector Calculus (during which I introduced and did some applications of Green’s Theorem) and my next one on Mechanics & Special Relativity (during which I’m doing projectile motion), so I thought I’d share a couple of thoughts about online teaching.

I started the term by doing my lectures in the form of webcasts live from lecture theatres but since we returned from the Study Break on Monday I’ve been doing them remotely from the comfort of my office at home, which is equipped with a blackboard (installed, I might add, at my own expense….)

I still do these teaching sessions “live”, though, rather than recording them all offline. I toyed with the idea of doing the latter but decided that the former works better for me. Not surprisingly I don’t get full attendance at the live sessions, but I do get around half the registered students. The others can watch the recordings at their own convenience. Perhaps those who do take the live webcasts appreciate the structure that a regular time gives to their study. Even if that’s not the reason for them, I certainly prefer working around a stable framework of teaching sessions.

“Why am I still using a blackboard?” I hear you ask. It’s not just because I’m an old fogey (although I am that). It’s because I’m used to pacing myself that way, using the physical effort of writing on the blackboard to slow myself down. I know some lecturers are delivering material on slides using, e.g., Powerpoint, but I have never felt comfortable using that medium for mathematical work. Aside from the temptation to go too fast, I think it encourages students to see the subject as a finished thing to be memorized rather than a process happening in front of them.

I did acquire some drawing tablets for staff to enable them to write mathematical work out, which is useful for short things like tutorial questions, but frankly they aren’t very good and I wouldn’t want to use them to give an hour long lecture.

In addition to these considerations, my decision to record videos in front of a blackboard was informed by something I’ve learnt about myself, namely that I find I am much more comfortable talking in this way when I’m standing up than sitting down. In particular, I find it far easier to communicate enthusiasm, make gestures, and generally produce a reasonable performance if I’m standing up. I know several colleagues who do theirs sitting down talking to a laptop camera, but I find that very difficult. Maybe I’m just weird. Who else prefers to do it standing up?

Thought for the Day

Posted in mathematics, Maynooth on October 15, 2020 by telescoper

Littlewood on `the real point’ of lectures

Posted in Education, mathematics, The Universe and Stuff with tags , , , on September 3, 2020 by telescoper

We’re often challenged these days to defend the educational value of the lecture as opposed to other forms of delivery, especially with the restrictions on large lectures imposed by Covid-19. But this is not a new debate. The mathematician J.E. Littlewood felt necessary to defend the lecture as a medium of instruction (in the context of advanced mathematics) way back in 1926 in the Introduction to his book The Elements of the Theory of Real Functions.

(as quoted by G. Temple in his Inaugural Lecture as Sedleian Professor of Natural Philosophy at the University of Oxford in 1954 “The Classic and Romantic in Natural Philosophy”.)

Temple concluded his lecture with:

Classic perfection should be reserved for the monograph: the successful lecture is almost inevitably a romantic adventure. It is at once the grandeur and misery of a scientific classic that it says the last word: it is the charm of a scientific romance that it utters the first word, and thus opens the windows on a new world.

Modern textbooks do try to be more user-friendly than perhaps they were in Littlewood’s day, and they aren’t always “complete and accurate” either, but I think Littlewood is right in pointing out that they do often hide `the real point’ so students sometimes can’t see the wood for the trees. The value of lectures is not in trying to deliver masses of detail but to point out the important bits.

It seems apt to mention that the things I remember best from my undergraduate lectures at Cambridge are not what’s in my lecture notes – most of which I still have, incidentally – but some of the asides made by the lectures. In particular I remember Peter Scheuer who taught Electrodynamics & Relativity talking about his first experience of radio astronomy. He didn’t like electronics at all and wasn’t sure radio astronomy was for him, but someone – possibly Martin Ryle – reassured him by saying “All you need to know in order to do this is Ohm’s Law. But you need to know it bloody well.”

On Grinds

Posted in Literature, mathematics with tags , , , , on July 24, 2020 by telescoper

When I moved to Ireland a couple of years ago, one of the words I discovered had a usage with which I was unfamiliar was grind. My first encounter with this word was after a lecture on vector calculus when a student asked if I knew of anyone who could offer him grinds. I didn’t know what he meant but was sure it wasn’t the meaning that sprang first into my mind so I just said no, I had just arrived in Ireland so didn’t know of anyone. I resisted the temptation to suggest he try finding an appropriate person via Grindr.

I only found out later that grinds are a form of private tuition and they are quite a big industry in Ireland, particularly at secondary school level. School students whose parents can afford it often take grinds in particular subjects to improve their performance on the Leaving Certificate. It seems to be less common for third level students to pay for grinds, but it does happen. More frequently university students actually offer grinds to local schoolkids as a kind of part-time employment to help them through college.

The word grind can also refer to a private tutor, i.e. you can have a maths grind. It can also be used as a verb, in which sense it means `to instil or teach by persistent repetition’.

This sense of the word grind may be in use in the United Kingdom but I have never come across it before, and it seems to me to be specific to Ireland.

All of which brings me back to vector calculus, via Charles Dickens.

In Hard Times by Charles Dickens there is a character by the name of Mr Thomas Gradgrind, a grimly utilitarain school superintendent who insisted on teaching only facts.

Thomas Gradgrind (engraving by Sol Eytinge, 1867).

If there is a Mr Gradgrind, why is there neither a Mr Divgrind nor a Mr Curlgrind?

Straight from Ireland

Posted in mathematics with tags on June 15, 2020 by telescoper

I came across this the other day. I think it’s fun because it’s a bit counterintuitive and it has generated quite a lot of discussion so I thought I would share it here. Two things are worth amplifying:

  1. By “in a straight line” I assume it means “along a great circle“.
  2. As it states in the small print on the diagram all lines originate at the geographical centre of Ireland which apparently lies at a place called Carnagh East, close to the border between County Roscommon and County Westmeath.

The main bone of contention is why the USA looks so small, in the matter of which I direct you to this reddit thread. The answer is clear when you look at what a great circle from Ireland to the USA looks like: most great circles from Ireland to the Eastern seaboard pass over Canada:

Math versus Maths

Posted in mathematics, Pedantry with tags , on June 8, 2020 by telescoper

I was amused by this discussion on Dictionary.Com of the different abbreviations of mathematics..

I’d like to think that ending is deliberate!

Job Alert!

Posted in mathematics, Maynooth on May 21, 2020 by telescoper

It occurred to me that there might be among the readers of this blog people interested in a job opportunity just announced at the Hamilton Institute at Maynooth University, which exists to promote interdisciplinary research spanning applied mathematics, computer science, engineering, and statistics. Applicants from any of those areas are welcome.

There is a lot more detail including instructions on how to apply here. The deadline is at the end of September 2020.

Calculating the UK COVID Alert Level

Posted in Covid-19, mathematics, Politics with tags , , , on May 11, 2020 by telescoper

I didn’t watch yesterday’s broadcast by the UK’s Clown-in-Chief Bozo Johnson but I gather that he delivered an address that was every bit as coherent and lucid as one might have expected.

I for one am delighted that at last there is some clarity in the UK Government’s position and that they have applied the necessary level of mathematical rigour to their treatment of the Covid-19 Pandemic.

Catching up on these pronouncements via Twitter I was impressed to see, for example, to see this precise formulation of the calculation required to establish the COVID Alert Level.

Let me take you through a detailed calculation using this important formula.

As far as I know the best estimate of the basic reproduction number R in the UK is around 0.8.

As of this morning (11th May) the number of confirmed Covid-19 infections in the UK is 219,183.

Applying the formula I obtain a value

COVID Alert Level = 219183.8

That seems a big number. I thought it should only go up to 11. Have I slipped up somewhere?

Testing YouTube

Posted in Biographical, mathematics, YouTube with tags , , on May 3, 2020 by telescoper

To do something a bit different during this Covid-19 lockdown I decided to set up my very own YouTube channel to which you may (or may not) wish to subscribe.

I’m new to this so I posted a short video to test how it works. It’s a little video explainer about Cramer’s Rule in linear algebra I made using Screencast-o-matic. I’ve done a lot of these over the past few weeks but they’re not what the channel is about: I posted this example is just to try out the system (mainly to see how long the upload would take).

I put this up yesterday and I’ve already amassed five subscribers so I’m well on the way to becoming a YouTube sensation. I may even become viral so please ensure that you practice social distancing while watching the videos.