Archive for Natural Sciences

Project Work

Posted in Biographical, Education, mathematics with tags , , , , , on April 23, 2018 by telescoper

I’m progressively clearing out stuff from my office prior to the big move to Ireland. This lunchtime I opened one old box file and found my undergraduate project. This was quite an unusual thing at the time as I did Theoretical Physics in Part II (my final year) of Natural Sciences at Cambridge, which normally meant no project but an extra examination paper called Paper 5. As a member of a small minority of Theoretical Physics students who wanted to do theory projects, I was allowed to submit this in place of half of Paper 5…

The problem was to write a computer program that could solve the equations describing the action of a laser, starting with the case of a single-mode laser as shown in the diagram below that I constructed using a sophisticated computer graphics package:

The above system is described by a set of six simultaneous first-order ordinary differential equations, which are of relatively simple form to look at but not so easy to solve numerically because the equations are stiff (i.e. they involve exponential decays or growths with very different time constants). I got around this by using a technique called Gear’s method. There wasn’t an internet in those days so I had to find out about the numerical approach by trawling through books in the library.

The code I wrote – in Fortran 77 – was run on a mainframe, and the terminal had no graphics capability so I had to check the results as a list of numbers before sending the results to a printer and wait for the output to be delivered some time later. Anyway, I got the code to work and ended up with a good mark that helped me get a place to do a PhD.

The sobering thought, though, is that I reckon a decent undergraduate physics student nowadays could probably do all the work I did for my project in a few hours using Python….

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In Praise of Natural Sciences

Posted in Biographical, Education with tags , , , , on April 24, 2016 by telescoper

The other day I was chatting with some students in the Department of Physics & Astronomy at the University of Sussex. One thing that came up was the fact that I’m basing the material for my Second Year Theoretical Physics module on the notes I took when I was a second-year undergraduate student at Cambridge over thirty years ago. I mentioned that to counter suggestions that are often made that the physics curriculum has been excessively “dumbed down” over the years. It may have been elsewhere, of course, but not on my watch. In fact, despite the misfortune of having me as a lecturer, many of the students in my class are picking up things far faster than I did when I was their age!

Anyway, that led to a general discussion of the changing nature of university education. One point was that in my day there weren’t any four-year “Integrated Masters” degrees, just plain three-year Bachelors. Teaching was therefore a bit more compressed than it is now, especially at Cambridge with its shorter teaching terms. We teach in two 12-week blocks here at Sussex. Week 11 of the Spring Term is about to start so we’re nearing the finishing line for this academic year and soon the examinations will be upon us.

The other thing that proved an interesting point of discussion was that the degree programme that I took was the Natural Sciences Tripos That meant that I did a very general first year comprising four different elements that could be chosen flexibly. I quickly settled on Physics, Chemistry and  Mathematics for Natural Sciences to reflect my A-level results but was struggling for the fourth. In the end I picked the one that seemed most like Physics, a course called Crystalline Materials. I didn’t like that at all, and wish I’d done some Biology instead – Biology of Cells and Biology of Organisms were both options – or even Geology, but I stuck with it for the first year.

Having to do such a wide range of subjects was very challenging. The timetable was densely packed and the pace was considerable. In the second year, however, I was able to focus on Mathematics and Physics and although it was still intense it was a bit more focussed. I ended up doing Theoretical Physics in my final year, including a theory project.

My best teacher at School, Dr Geoeff Swinden,  was a chemist (he had a doctorate in organic chemistry from Oxford University) and when I went to Cambridge I fully expected to specialise in Chemistry rather tha Physics. I loved the curly arrows and all that. But two things changed. One was that I found the Physics content of the first year far more interesting – and the lecturers and tutors far more inspiring – than Chemistry, and the other was that my considerable ineptitude at practical work made me doubt that I had a future in a chemistry laboratory. And so it came to pass that I switched allegiance to Physics, a decision I am very glad I made. It was only towards the end of my degree that I started to take Astrophysics seriously as a possible specialism, but that’s another story.

As we are now approaching examination season I’ve been dealing with some matters in my role as External Examiner for Natural Sciences (Physics) at Cambridge, a position I have held since last year. It’s certaintly extremely interesting to see things from the other side of the fence, thirty years on since my finals. In particular I was struck last year by how many senior physicists there are at Cambridge who actually came as undergraduates expecting, like I did, to do Chemistry but also then switched. No doubt some moved in the opposite direction too, but the point is that the system not only allowed this but positively encouraged it.

Looking back, I think  there were great educational advantages in delaying  the choice of speciality the way a Natural Sciences degree did. New students usually have very little idea how different the subject is at university compared to A-level, so it seems unfair to lock them into a programme from Year 1. Moreover – and this struck me particularly talking to current students last week – a Natural Sciences programme might well prove a way of addressing the gender imbalance in physics by allowing female students (who might have been put off Physics at school) to gravitate towards it. Only 20% of the students who take Physics A-level are female, and that’s roughly the same mix that we find in the undergraduate population. How many more might opt for Physics after taking a general first year?

Another advantage of this kind of degree is that it gives scientists a good grounding in  a range of subjects. In the long run this could encourage greater levels of interdisciplinary thinking. This is important, since some of the most exciting areas of physics research lie at the interfaces with, e.g. chemistry and biology. Unfortunately, adminstrative structures often create barriers that deter such cross-disciplinary activities.

 

 

One Fine Conformal Transformation

Posted in Brighton, Cute Problems with tags , , , , , on March 25, 2015 by telescoper

It’s been a while since I posted a cute physics problem, so try this one for size. It is taken from a book of examples I was given in 1984 to illustrate a course on Physical Applications of Complex Variables I took during the a 4-week course I took in Long Vacation immediately prior to my third year as an undergraduate at Cambridge.  Students intending to specialise in Theoretical Physics in Part II of the Natural Sciences Tripos (as I was) had to do this course, which lasted about 10 days and was followed by a pretty tough test. Those who failed the test had to switch to Experimental Physics, and spend the rest of the summer programme doing laboratory work, while those who passed it carried on with further theoretical courses for the rest of the Long Vacation programme. I managed to get through, to find that what followed wasn’t anywhere near as tough as the first bit. I inferred that Physical Applications of Complex Variables was primarily there in order to separate the wheat from the chaff. It’s always been an issue with Theoretical Physics courses that they attract two sorts of student: one that likes mathematical work and really wants to do theory, and another that hates experimental physics slightly more than he/she hates everything else. This course, and especially the test after it, was intended to minimize the number of the second type getting into Part II Theoretical Physics.

Another piece of information that readers might find interesting is that the lecturer for Physical Applications of Complex Variables was a young Mark Birkinshaw, now William P. Coldrick Professor of Cosmology and Astrophysics at the University of Bristol.

As it happens, this term I have been teaching a module on Theoretical Physics to second-year undergraduates at the University of Sussex. This covers many of the topics I studied at Cambridge in the second year, including the calculus of variations, relativistic electrodynamics, Green’s functions and, of course, complex functions. In fact I’ve used some of the notes I took as an undergraduate, and have kept all these years, to prepare material for my own lectures. I am pretty adamant therefore that the academic level at which we’re teaching this material now is no lower than it was thirty years ago.

Anyway, here’s a typically eccentric problem from the workbook, from a set of problems chosen to illustrate applications of conformal transformations (which I’ve just finished teaching this term). See how you get on with it. The first correct answer submitted through the comments box gets a round of applaud.

conformal transformation

 

Cambridge Entrance Examination – Physics (1981)

Posted in Biographical, Education with tags , , , on February 27, 2012 by telescoper

In response to a request to a while ago when I posted the Mathematics paper, here is the Physics paper I took as part of the Cambridge Entrance  Examinations way back in 1981.

I’ve decided to try out Qu. 13 on my third-year students doing Nuclear and Particle Physics this year just for fun. Other comments on the content and/or difficulty are welcome through the box below!

Cambridge Entrance Examination – Mathematics for Natural Sciences (1981)

Posted in Biographical, Education with tags , , , on February 7, 2012 by telescoper

I thought I’d take 5 minutes this lunchtime to add another item to the collection of old examination papers I’ve been posting, as someone asked me about this type of examination via a comment recently. This is the Mathematics paper I took way back in November 1981 for entry the following October to do Natural Sciences. I also took papers in Physics and Chemistry, as well as a General paper. Looking at this after a gap of over 30 years it looks pretty tough. One thing I should point out, though, is that the timing of the paper required us to come back after A-levels for an extra term (“the seventh term”)  at my school, the Royal Grammar School in Newcastle,  to form the “Third Year Sixth” who were all Oxbridge candidates. We were then intensively coached for the entrance examination. You will notice, for example, a couple of questions on this paper relating to group theory, which wasn’t on the A-level syllabus but which we were taught specifically for this examination. Some schools couldn’t offer this specialist teaching so pupils from them were significantly disadvantaged by this form of selection. As it happens, I answered both the (relatively easy) questions on group theory and got in to Cambridge…

Comments on the content and/or difficulty are welcome through the box below!

Life, the Universe, and Coloured Pencils

Posted in Biographical, The Universe and Stuff with tags , , on April 18, 2010 by telescoper

Yesterday’s post got me thinking about what it is that makes scientists decide on their own speciality. It’s got to have something to do with the intersection between interest and aptitude, in that I think we learn gradually through our time at School that there are some things we can do well and others that we can’t but the things we can do well aren’t always things we find sufficiently interesting to make a career doing.

I suspect luck also plays a big part, in that the choices one gets to make must be taken from the options at a very particular time. I ended up doing research in cosmology after my first degree, but it wasn’t any kind of a grand plan that got me to Sussex in 1985 to do that but it just seemed the best choice to me out of all the half-a-dozen other places I visited.

Before I meander off the point again I’ll just pass on something that one of my teachers at school told me, and which probably had a big effect on an impressionable teenager. It was my chemistry teacher, Geoff (“Doc”) Swinden, that probably had more influence than anyone in making me decide to become a physicist.

By the way he was called “Doc” because he had a PhD (or perhaps a DPhil, as I think  he got his doctorate, in organic chemistry, from Oxford University). I didn’t go into Organic Chemistry, of course, but that was mainly because I hated the practical aspects of chemistry and pose a considerable threat to the safety of others when placed in any kind of laboratory environment.

Anyway, I remember very well a comment of Doc Swinden’s to the effect that anyone wanting to be called a proper scientist should avoid any subject that required the use of coloured pencils. That ruled out biology, geology and a host of others and left me firmly in the domain of physical science. I ended up going to Cambridge to do a degree in Natural Sciences, which allowed me to do chemistry and physics for a year and then decide which to continue. Obviously I went the way of physics.

I don’t regret going into physics at all, but I don’t think this bit of advice was all good. When I went to Cambridge to study Natural Sciences, I had to pick an extra subject to do in the first year to do alongside my main choices, chemistry, physics and mathematics. Among the options were geology, biology of organisms, and biology of cells but, mindful of the possibility that all of these might require the dreaded coloured pencil, I went for a course called Crystalline Materials. It’s true that I didn’t have to colour anything in, but it was the most mind-numbingly awful course I’ve ever taken. I very nearly failed it at the end of the first year, in fact, but still managed to get  a First-class mark overall.

Going back to yesterday’s post, I realise that one of the reasons I’m less gung ho for Mars exploration than some of my colleagues might be that it’s a bit too much like geology or even biology. It seems the ghost of the coloured pencil is still haunting me.