Need advice on which math classes to take

[HeLiXe]

This is a direct spinoff to the thread I started about which class general relativity is offered in. That question was answered and now I would like to align my math classes to prepare for tensor calculus. Here are the classes I am thinking of taking

Linear Algebra
Abstract Algebra I and II
Vector Analysis
Number Theory
Numerical Analysis
Probability and Statistics

I have already taken Calc I-III and Differential Equations. Because of the scheduling of courses at my school, I will probably have to take the most of these after I graduate. My question is, which classes are most essential for tensor analysis, and which of these would you recommend for self study (as they probably would not be a prerequisite for graduate courses)? I plan to go to graduate school for astrophysics and am currently majoring in physics and chemistry. Thanks!

 

[WannabeNewton]

One usually encounters tensor analysis either in a GR course or a riemannian / smooth manifolds class. Typically you need to know your calc 3 and your LA very well if you want to get started on an introduction that isn't heavy on theory but is more bent towards computation (I'm not sure what your vector analysis class entails but for example at my uni there's an undergrad class called vector and tensor analysis so is it a tensor analysis class for you as well?).

 

[HeLiXe]

I don't think so...from what I have read in the catalog, it covers vector fields, divergence theorem, Greene's theorem, and stokes theorem. There is no clear tensor analysis course at my school. The only course description that even mentions "tensor" is a graduate course on continuum mechanics.

 

[WannabeNewton]

Yeah tensor analysis is big in fluid dynamics. Well if the majority if the stuff in the vector analysis class are things you haven't already learned in calc 3 then it would probably help to take it (I'm not sure how theoretical that class gets but if you know the textbook you can probably gauge it from that - the one at my uni uses Geometry of Physics - Frankel). Anyways, if you are right now looking to get used to the computational / classical aspects of it all (basically what you would see in a first GR course) then you need to have calc 3 and LA under your belt but not much else really. Note that if your goal is to eventually get to a good learning of GR then tensor calculus isn't really the major thing to focus on as its own separate entity because most GR books will teach that along the way. It is really differential geometry that forms the core of GR. So yeah put your efforts on LA and, if needed, vector analysis. If you have the time and interest then take Abstract Algebra 1 but for a first GR course you won't see the stuff in that show up much at all in terms of tensor calculus.