Sunday, 4 March 2012


Well sorry for not posting for a while anyway progress of sorts has been made on M338 I got my first TMA back and did reasonably well but lost a few marks for taking short cuts. Also there was some difficulty in notation hopefully the wrinkles will be ironed out in time for the exam. Have to admit some of this course seems like wading  through treacle and it's difficult to see the point of a lot of it. Still just keep carrying on I know a knowledge of topology is an essential pre-requisite if one wants to understand things like the singularity theorems of General Relativity proved by Penrose and Hawking so mustn't get too disheartened.

Also finished the first assignment for MS324 which was on the whole a joy to do I'm definitely an Applied mathematician. The questions were essentially a review of mathematical techniques one should be aware of with one or two wrinkles thrown in. The first question was a question on Partial Fractions and an integration based on taking the limit of the integral to infinity. This involved some tricky manipulations of Logartihms but I think I got there. The second question was a straightforward and pleasurable solution of an inhomogeneous second order differential equation. The third question was a straightforward but tedious question on multivariable calculus and finding the stationary points. What made this question a bit tedious was the fact that the nature of the points varied for a wide range of conditions and you had to be careful not to miss out any combinations. The final question was on the deformation of springs more of a modelling question than a mathematics question I think I got most of it correct but I admit the very last part seemed badly phrased so I'm not sure if I got it correct or not. Still it's only 3 marks so should be on target for a good stab at this.

Both courses haven't really got started yet I really hope I can penetrate the fog of definition and theorem that is plaguing the topology units but at the minute I really can't see the wood for the trees. Conversely I know that the first real block of MS324 is on one of my favourite topics namely the wave equation and it's solutions I and feel reasonably confident I can polish off the next TMA in the next two weeks. The problem is it would be like a kid who eats his dessert before his main course instead of leaving it to last but what the heck.

As a final point at the risk of overloading people I've found yet another book on mathematics as applied to physics.

Although quite old it covers all the branches of mathematics (apart from Topology) and their direct relevance to physics. It has quite an accessible introduction to the Hilbert space formulation of quantum mechanics stresses the key analogy between geometric and vector spaces which is so important to physics as well as having lots of concrete and challenging examples. I intend to try at least some of the questions which involve the separation of variables of pde's in spherical coordinate systems something not really covered in MS324 but which plays an important part in both classical and quantum physics. Anyway nice to see a book covering both classical and quantum physics in the same volume. A bit less abstract than say Szekres

but not just another recipe book, Szekres and Byron complement each other nicely in my honest opinion.


1 comment:

  1. Chris, thanks again for the stuff on Complex analysis, that you emailed across. It looks great.