Should i take differential geometry?

[ia_]

Should I take a semester-long differential geometry course (in lieu of a thermo/stat mech course, which while not terribly challenging would prepare me for qualifiers, etc), or should I just jump into GR and maybe pick up a mathematical methods in physics course later? I first learned partial dif eqs in an advanced e&m course, will differential geometry and general relativity be a similar deal, or do I really need a solid foundation in it before starting?

To be more clear: I'm a grad student, differential geometry and thermo/stat mech are both mixed undergrad/grad courses. Thermo/stat mech is probably similar in content to a mixed undergrad/grad course I took a few years ago as an undergrad. I'm sure taking it again as a grad student would improve my stat mech, but I'm also a little hesitant to go through it with undergrads forcing us to cover everything I've already done before. On the other hand, I'm somewhat worried that either 1. differential geometry could turn into a time consuming exercise in mathematics that won't really be used ever again or 2. I will end up kind of screwed by not taking it. I will sit in on differential geometry tomorrow and see what I think of it.

 

[dmoravec]

I'd recommend taking the differential geometry class. It was by far the best math class i took as part of my mathematics degree. The way it was tought made me really know linear algebra, topology as well as some analysis. As for jumping into GR it could be done, but the math is difficult and taking differential geometry would make it easier and give you a better understanding of where a lot of the math comes from.

 

[Meir Achuz]

i took as part of my mathematics degree.

I think the answer to the original question is whether you want to go on in the math or the physics of GR.

 

[Daverz]

I'm not clear whether you're an undergrad or a grad student. I wouldn't take an elective math course in lieu of a core physics course like thermal physics, unless you mean you can pick it up another semester before graduating.

A GR course will introduce the necessary Riemannian geometry, but usually makes a beeline to the Riemann tensor, and doesn't have much time to develop geometric intuition. The usual undergraduate differential geometry course covers local and global theory of curves and surfaces in 3 dimensions, and maybe generalizes that to manifolds in n-dimensions if there's time. That will give you a lot of insight and intuition you might not get otherwise, but it's not absolutely necessary for doing well in GR. Maybe you can audit the course.

 

[geenious]

Should I take a semester-long differential geometry course (in lieu of a thermo/stat mech course, which while not terribly challenging would prepare me for qualifiers, etc), or should I just jump into GR and maybe pick up a mathematical methods in physics course later? I first learned partial dif eqs in an advanced e&m course, will differential geometry and general relativity be a similar deal, or do I really need a solid foundation in it before starting?

i think that if the geometry course (in lieu) will prepare you for the qualifiers and that is what you need then i think you should take it.