Sunday, 12 February 2012

General Relativity and Neutron Stars

Hi I've been trying to consolidate some of my physics Notes that I wrote (over 10 years ago How frightening) on general relativity. I've put a couple on my dropbox public folder

A general review of General Relativity

And an application to Neutron Stars

This gives the background and then goes through the original calculation that Oppenheimer and Volkoff did just before the Start of the second world war. I wrote it as at the time there did not seem to be a clear account of the actual calculation in the public literature. I was also gratified to find a misprint in the original paper.

I wrote this stuff as at work I used to convene  a 'Failed physicists' society our work has lots of people who did PhD's and even post doctorates in physics or in my case a humble MSc but were brutally ejected from Academia. It arose out of a sense of frustration that the popular literature gave no hint of the actual maths and physics behind key caclulations or that people were doing calculations for themselves but had no means of sharing them with other people.   Anyway in the hope that other people find this useful I have posted the results here.

As for the maths courses I had my first tutorial on topology last week with Alan and it was good to meet up with Neil. Alan's tutorials are always useful in that they clear up ambiguities, for example when defining a set which covers all of the Real numbers should we include infinity. The answer is no so an interval R is the open set (-Infinity, Infinity) and not [-Infinity, Infinity]. Despite this procrastination has meant that I haven't yet tidied up the TMA for final send off. Still I'm not the only one in this position

http://learn.open.ac.uk/mod/oublog/view.php?user=108287

Must be something to do with the gloomy and rather oppressive winter in Edinburgh

Also have been racing ahead with the MS324 course jumping straight into one of my favourite topics of Applied maths namely solutions to partial differential equations by separation of variables. For this topic unlike Topology or pure maths I feel like I'm coming home, or to use a crude expression 'like a pig in shit'.
Topics like this remind me why I got interested in maths in the first place. I love going to the pub, notepad in hand doing such problems and I find they just flow. Guess that means I'll always be an Applied mathematician/theoretical physicist, rather than a Pure mathematician/ Mathematical physicsist. I'll put another post explaining the difference.

Finally last week I got my essay back that I did for the Edinburgh university course on Hume. It was essentially a synthesis of ideas that I explored on my posts about Hume. I was pleased to get 85% and my tutor seemed impressed. He said he didn't have much to add except some criticism of some stylistic features. I tend when laying out the points of a philosophical argument to list the points separately (see some of my earlier posts). Anyway thats another 10 points towards my philosophy education I have 100 so far, and I look forward to the Philosophy of Art course in the Summer given by the same tutor Dr John Gordan.

As far as further studies go,  It looks like I could have a unique opportunity to gain more than the usual 120 points for philosophy via the OU. The course I did A211 has been replaced with a more traditional course which is not an excluded combination with A211,

Also the current third level course AA308

is due to be replaced with one entitled 'Key  Questions in Philosophy' in October 2014 but given the way the OU works with replacement courses I suspect it wont be until 2015 till such a course appears on the horizon. So it looks like I could do the other second level philosophy course, AA308 and the new course by 2015 which would mean getting a total of 240 points in philosophy  before embarking on postgraduate work.
That would suit my other ambitions by then I would hope to be well into the Maths MSc and have finished my compositon courses.

So must stop procrastinating and write up the Topology TMA this week and do the first TMA for MS324.

1. It sounds like it's working out well for you, mate.
Congratulations on that 85% - I bet every mark was well-earned.
Keep going, Chris.

2. Sounds like you are doing brilliantly Chris.

And kudos on pursuing philosophy and maths at the same time. Do you find the rigour and logic involved in pure maths, helps with the clarity of thought and argument, when applied to your philosophy research?

Dan

3. I know what you mean about applied maths. I have just got to a question on vectors and it is a joy just to be able to apply pen to paper without hardly having to think about it. Also, well done in your Hume essay.

I tried looking at your pdf's but I couldn't read them as I had some error which maybe something to do with my software, I am not sure.

1. I'll send you the word versions as for Steve's question I don't know but I must be doing something correct. I focused on the question read the relevant sections (Section 4 and 12) a few times made my own paraphrase then wrote the essay. I'll put it on my public folder and you can judge whether or not my essay was worth the high marks.
As for Dan's I think yes having the help of maths helps you focus but also A211 introduced me to critical thinking whereby you convert an argument into premises and conclusions and you see whether or not the conclusion follows from the premise or whether the Author is making some unjustified leaps or assuming hidden premises and so forth.

4. I shall have to look at that chapter 4 for MS324 for separation of variables.

I hope it is as much fun as question 1 was.

Although I have to admit that this level 3 stuff is not quite the skim the pages stuff that level 2 work was. The MS324 book seems quite dense to me, and I have to work at it.

They also put some of the proof as exercises, which is mean, as now I have to do some exercises.

5. How do you get such high percentages in a humanities subject?

I know people who are delighted to get 56 percent.