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Planes, Trains and Quaternions

Posted in Biographical, History, mathematics, Maynooth with tags , , , , , , , , on January 4, 2018 by telescoper

Well, here I am in Maynooth for the first time in 2018. I flew over from Cardiff yesterday. The flight was rather bumpy owing to the strong winds following Storm Eleanor, and it was rather chilly waiting for the bus to Maynooth from Dublin Airport; nevertheless I got to my flat safely and on time and found everything in order after the Christmas break.

This morning I had to make a trip by train to Dublin city  to keep an appointment at the Intreo Centre in Parnell Street, which is about 15 minutes walk from Dublin Connolly train station. I bought an Adult Day Return which costs the princely sum of €8.80. Trains, stations and track in Ireland are maintained and operated by Irish Rail (Iarnród Éireann), which is publicly owned. Just saying.

The distance between Maynooth and Dublin about 25 km, which takes about 40 minutes on the local stopping train or about 25 minutes on the longer distance trains which run nonstop from Maynooth to Dublin. As it happens I took one of the fast trains this morning, which arrived on schedule, as did the return journey on a commuter train. My first experience of the Irish railway system was therefore rather positive.

I had thought of having a bit of a wander around the city on my way to Parnell Street but it was raining and very cold so I headed straight there. I arrived about 20 minutes ahead of my scheduled appointment, but was seen straight away.

The reason for the interview was to acquire a Personal Public Services Number (PPSN), which is the equivalent of the National Insurance Number we have in the United Kingdom. This number is needed to be registered properly on the tax and benefit system in Ireland and is the key to access a host of public services, the electoral roll, and so on. You have to present yourself in person to get a PPSN, presumably to reduce the opportunity for fraud, and I was told the interview would take 15 minutes. In fact, it only took about 5 minutes and at the end a photograph was taken to go on the ID card that is issued with the number on it.

So there I was, all finished before I was even due to start. The staff were very friendly and it all seems rather easy. Fingers crossed that the letter informing me of my number will arrive soon. It should take a week or so, so I’m told. After that I should be able to access as many personal services as I want whenever I want them. (Are you sure you have the right idea? Ed.)

For  the return trip  to Maynooth I got one of the slower commuter trains, stopping at intermediate stations and running right next to the Royal Canal, which runs from Dublin for 90 miles through  Counties Dublin, Kildare, Meath and Westmeath before entering County Longford, where it joins the River Shannon. One of the intermediate stations along the route next to the canal is Broombridge, the name of which stirred a distant memory.

A quick application of Google reminded me that the town of Broombridge is the site of the bridge (Broom Bridge) beside which William Rowan Hamilton first wrote down the fundamental result of quaternions (on 16th October 1843). Apparently he was walking from Dunsink Observatory into town when he had a sudden flash of inspiration  and wrote the result down on the spot, now marked by a plaque:

Picture Credit: Brian Dolan

 

This episode  is commemorated on 16th October each year by an annual Hamilton Walk. I look forward to reporting from the 2018 walk in due course!

P.S. Maynooth is home to the Hamilton Institute which promotes and facilitates research links between mathematics and other fields.

 

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Trees, Graphs and the Leaving Certificate

Posted in Biographical, mathematics, Maynooth, The Universe and Stuff with tags , , , , , , on December 15, 2017 by telescoper

I’m starting to get the hang of some of the differences between things here in Ireland and the United Kingdom, both domestically and in the world of work.

One of the most important points of variation that concerns academic life is the school system students go through before going to University. In the system operating in England and Wales the standard qualification for entry is the GCE A-level. Most students take A-levels in three subjects, which gives them a relatively narrow focus although the range of subjects to choose from is rather large. In Ireland the standard qualification is the Leaving Certificate, which comprises a minimum of six subjects, giving students a broader range of knowledge at the sacrifice (perhaps) of a certain amount of depth; it has been decreed for entry into this system that an Irish Leaving Certificate counts as about 2/3 of an A-level for admissions purposes, so Irish students do the equivalent of at least four A-levels, and many do more than this.

There’s a lot to be said for the increased breadth of subjects undertaken for the leaving certificate, but I have no direct experience of teaching first-year university students here yet so I can’t comment on their level of preparedness.

Coincidentally, though, one of the first emails I received this week referred to a consultation about proposed changes to the Leaving Certificate in Applied Mathematics. Not knowing much about the old syllabus, I didn’t feel there was much I could add but I had a look at the new one and was surprised to see a whole `Strand’, on Mathematical Modelling with netwworks and graphs.

The introductory blurb reads:

In this strand students learn about networks or graphs as mathematical models which can be used to investigate a wide range of real-world problems. They learn about graphs and adjacency matrices and how useful these are in solving problems. They are given further opportunity to consolidate their understanding that mathematical ideas can be represented in multiple ways. They are introduced to dynamic programming as a quantitative analysis technique used to solve large, complex problems that involve the need to make a sequence of decisions. As they progress in their understanding they will explore and appreciate the use of algorithms in problem solving as well as considering some of the wider issues involved with the use of such techniques.

 

Among the specific topics listed you will find:

  • Minimal Spanning trees applied to problems involving optimising networks and algorithms associated with finding these (Kruskal, Prim);  
  • Bellman’s Optimality Principal to find the shortest paths in a weighted directed network, and to be able to formulate the process algebraically;
  •  Dijkstra’s algorithm to find shortest paths in a weighted directed network; etc.

 

For the record I should say that I’ve actually used Minimal Spanning Trees in a research context (see, e.g., this paper) and have read (and still have) a number of books on graph theory, which I find a truly fascinating subject. It seems to me that the topics all listed above  are all interesting and they’re all useful in a range of contexts, but they do seem rather advanced topics to me for a pre-university student and will be unfamiliar to a great many potential teachers of Applied Mathematics too. It may turn out, therefore, that the students will end up getting a very superficial knowledge of this very trendy subject, when they would actually be better off getting a more solid basis in more traditional mathematical methods  so I wonder what the reaction will be to this proposal!

 

 

 

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Historical References

Posted in Biographical, History, Maynooth with tags , , , , , , , on December 2, 2017 by telescoper

This morning, having a few hours free after breakfast before some househunting activities, I took a stroll to buy a newspaper and decided to take a few snaps.

First, here are a couple of pictures of St Patrick’s College, where I am staying. My room is on the top floor, to the left in the wing that juts forward from the main building. The chapel (with the spire) is on the other side.

The building I’m in forms the most impressive side of a quadrangle, one other part of which you can see in the second photograph.

St Patrick’s College was founded in 1795, and its style could best be described as Gothic Revival. It was in fact built as a theological college with funds supplied by King George III. There was a political reason for his largesse. Roman Catholicism was brutally suppressed in Ireland during and after the Eleven Years War in the mid-17th Century, culminating in the vicious subjugation of Ireland by Oliver Cromwell. In effect, the Catholic Church in Ireland was outlawed. Starting from about 1766 some of the restrictions on Catholics began to be removed, but there were no institutions in Ireland capable of training priests so all of those wishing to join the priesthood had to study abroad, primarily in France. George was worried that this would lead to an influx of priests whose heads were filled with revolutionary ideas from the continent, so he decided to fund a place where they could be taught in Ireland, where at least there could be some control over their education.

The old theological college of St Patrick (the `Pontifical University’) forms the core of what is now the South Campus of Maynooth University. Some of the old buildings here seem to take their names from the components of the old Liberal Arts degree: there is a Music House, Logic House, Rhetoric House and so on.

Next the entrance to the South Campus you can see this:

These are the remains of Maynooth Castle (or Geraldine Castle, after the Fitzgerald family), built around 1200. It was a huge and imposing fortress but now only the gatehouse and solar tower remain. It has violent history: heavily damaged in 1535 by siege cannons, its garrison surrendered only to be summarily executed. Rebuilt in the 1630s, it was destroyed completely in the 1640s during – you guessed it – the Eleven Years War. It has been a ruin ever since, but provides an intriguing entrance to the campus!

I’m by no means an architectural expert but I had a hunch that the Church (above) that stands opposite the Castle on the other side of the road leading into campus might also be quite old. Indeed it is. It was built in 1248 as the chapel to Geraldine Castle. It is now an Anglican Church, still used for regular worship.

The South Campus is separated from the North Campus (where the Science Building and other modern facilities are) by a main road. The North Campus is very new, most of the buildings are less than 20 years old. Here’s a picture showing the splendid library, with the spire of the chapel of St Patrick’s College in the background.  This is one of the few newer buildings on the South Campus: the pedestrian path you see leads to the main road that splits North and South Campuses.

 

 

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The Veggiana Monologues

Posted in Biographical, Cardiff, Maynooth with tags , on October 19, 2008 by telescoper

I’m not a vegetarian, but I do like vegetables.

A few years ago when I lived in Nottingham I decided on a plan to increase the quantity and quality of the vegetables I was eating by ordering a weekly box of from an organic supplier. The one I picked there was River Nene who provided very good stuff all year around. When I moved I had to cancel the arrangement, and I remained predominantly inorganic while I was renting a flat here. When I finally managed to buy a new house and move in, though, I looked to reestablish the regular deliveries. I was pleased to find a company called River Ford, which is kind of affiliated to River Nene, and which undertakes deliveries of organic produce in the Cardiff area. I’ve been getting a box from them regularly for a few months now, and I’m very happy with the quality.

There are several reasons why I get my vegetables this way.

First and foremost, organically grown vegetables definitely taste far nicer than the bland varieties carried by most mainstream suppliers, including both supermarkets and local greengrocers. Once you’ve tasted how carrotty a carrot should be you’ll never want to eat one of those supermarket ones that look too orange to be true and have no flavour at all.  This applies not just to carrots but to most vegetables; fresh organic ones are so much better. Although, strictly speaking, they are not vegetables, organic mushrooms are particularly good. I often get the huge flat portobello variety which are absolutely delicious and are very easy to include in all kinds of dishes.

Some supermarkets do carry organic ranges but the prices are astronomical, and they are often shipped in from all around the world. That brings me to the second point which is that all (or virtually all) the vegetables I get in my weekly box are grown locally. They’re correspondingly fresh and the environmental impact of bulk transportation is also lessened.

Third, the nature of the scheme is that all the vegetables are seasonal. I think it’s quite sad that people have largely forgotten about the passing of the seasons by virtue of the fact that you can get strawberries all year around in Sainsbury’s. I think it’s have a bit more respect for the passage of time and enjoy the correct food when it happens to be ready. You wouldn’t want to have Xmas dinner every day, so why not be prepared to wait until October to eat fresh sweetcorn?  To every thing there is a season. There’s always something yummy to eat if you’re prepared to be imaginative with your cooking.

And that’s the final point. I have a standing order for a small box of vegetables every week costing about £10. The composition varies from week to week and with the time of year. The company does email and post on its website the contents of the following week’s boxes, but I generally don’t look at it. When the box arrives, it’s usually a mixture of staples (potatoes, carrots, onions, etc) plus things that are not so familiar, and that I’ve often never cooked before.  If it hadn’t been for the veggie box, I would probably never have found out about how to cook chard, romanesco, jerusalem artichokes and celeriac. I look forward to these surprises. Not knowing exactly what’s coming forces me to cook new things, and if I don’t know how to cook them there’s always google.

Of course, the summer salads and lighter things have now finished and, with winter coming on, there will be more root vegetables. I think the heavier vegetables tend to put some people off a bit, but there’s enough variety to keep it fun. Last week’s box contained a nice swede and leeks (of course, I’m in Wales) among other things, but I’m really looking forward to cauliflower and parsnips which should be ready soon.

Each box looks like a lot of food, but I always manage to eat most of it. I have to admit that not all my culinary experiments are successful, but more often than not I am pleasantly surprised. I tried curried beetroot a few weeks ago, with more than a little trepidation. It turned out to be absolutely delicious, even if I did have to ad-lib a bit with some of the ingredients. The only drawback was an unexpectedly colourful trip to the lavatory the next morning…

Anyway, if anyone is thinking of taking the plunge I’d thoroughly recommend them. You don’t have to buy vegetables the way I do it. You can do one-off orders or you can order specific things rather than set boxes.  They do meat and poultry too, but you have to buy a relatively large amount and I don’t eat enough meat to make it worthwhile. I also have a splendid butcher around the corner from me and tend to buy enough there to satisfy my carnivorous side.

I thought I’d break my own tradition and have a peep at what Tuesday’s box has in store. Here we go:cosmos potatoes, red onions, carrots, cauliflower, bunched beetroot, sweetcorn, butternut squash, cavolo nero

Hang on a minute. Cavolo Nero? For a moment I thought it was a black horse from Italy, but  a quick google and I learn that it is Black Kale. Sounds nice. The carrots are always tasty and as I’d hoped the cauliflower is coming through now. I thought the sweetcorn might be finished, but there’s more on the way apparently. Butternut squash is quite trendy these days.

And more beetroot. Ah well. At least this time I won’t think I’m suffering from internal bleeding.

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