Self-Learning Advice for Astrophysics & Physics Course

[fasterthanjoao]

Ok so I'm in a bit of a muddle- i'll give a bit of background just so you can better understand my questions. I've just received my exam results for my fourth year (i'm studying an undergraduate masters 5 year-degree, joint in astrophysics+physics) and whilst I'm pleased to be at the top end for the physics side of my course, I've hit way below what I expected for the astrophysics part. Now I still have about 3 months left until we go back and next year I will have two separate courses on general relativity: gravitation and dynamics to tackle so I'm basically hoping I can work through this part on my own and get a big chunk of next years work sorted.

So I've got a hold of the course notes from next year, worked my way through a few of the introductary lectures and I'm really not feeling like I'm progressing - the problem is neither myself nor the rest of the students on these courses have really been through any sort of mathematical rigor before and the professor taking it has started off with pages of jargon - I'm spending hours reading definitions and I'm just not confident I'll actually remember any of it..

I have lists of the course objectives that i'll be required to cover, but what I'm looking for from you guys is some guidance on how I should be approaching it - which things are going to be absolutely crucial and worth spending the most time on. Am I best to prepare for plenty of reading? With the amount of concepts there seems to be, I'm not sure to what extend problems are going to play a part in learning the basics. Just looking to set myself up with a proper foundation for the course rather than just hoping to remember everything covered in the lectures.

I've already asked for an appointment to meet with one of the professors teaching but he's away for the next 3 weeks and I figure I may as well start the books whilst I'm eager, hence my appearance here. I know I've been a bit vague and I'm not even sure I've actually asked a question, but thanks for any feedback and responses!

 

[jdstokes]

I just started learning GR at fourth year this week and my strategy has been to work my way through the GR problem book.

I think that the main conceptual hurdle with this subject is understanding the tensor algebra. This is made difficult by the fact that there are many isomorphic definitions in use throughout the literature so it depends on the style of your lecturer.

Although I started the opposite way, my suggestion would be to start learning the coordinate-based description of tensors as collections of functions obeying certain transformation properties, then soon after read about their coordinate free description as multilinear maps acting on the tangent space and its dual.

Whatever definition you use, you will inevitably end up working in local coordinates which means you should attempt lots of problems dealing with index gynmastics (raising/lowering, contractions etc.)