Are undergraduate math courses required to do well on the GRE subject test? I'm in the process of selecting courses for my third year, and I wasn't planning on taking certain mathematics courses (in particular, "pure" courses, such as Algebra). However, upon speaking to come colleagues, I've found that I might want to substitute Advanced ODEs for Algebra, given that I could probably learn the former on my own, and the latter weighs more on the GRE Subject Test, so I should have a good handle on it. 

This has made me ask two things: 

1) Is the Subject Test even required for all Grad Schools? I'll be doing the GRE, and the schools I'm planning on applying to fall into sort of an "Applied/Computational" category, so I don't know how much of the Subject Test they'd be interested in. 

2) Do courses (and their subsequent grades) matter more than scores on the subject test, or is it vice versa, or are they both pretty equal? 

I'd love to hear any and all advice. I'm doing a combined honours in general sciences and mathematics, if that makes any difference. I'm close to course selection, and I'd like to have a good idea of what would be useful to take. 

Thanks!
It's difficult to answer this question because a lot depends on the programs that you're applying to and on the undergraduate program that you're currently in (because not all undergraduate programs are equal.)  The GRE subject test in mathematics covers a broad range of undergraduate mathematics that anyone going on to graduate study in mathematics should have mastered.  Your grades in undergraduate math courses should provide similar information to an admissions committee.

However, the graduate admissions committee might not be able to interpret your undergraduate grades (e.g. because they have no experience with students from your institution.) At some places grades are now so inflated that even a 4.0 GPA in math courses with the appropriate GPA says little about what you actually have learned.  A good score on the GRE subject test in mathematics will help to confirm your good grades.  Highly ranked graduate programs will want to see both good grades and a good score on the GRE subject test and for the very best programs this is simply a bare minimum- they'll want to see something beyond this in your admissions packet.    

The subject test is really written from the point of view of traditional programs in mathematics.  For programs in computational applied mathematics, the test content isn't as relevant and the subject test is not always required.   

To answer your specific question about taking an advanced ODE course vs. a course in Abstract Algebra, you'd probably be better off taking the advanced ODE's course.    In the other direction, if you were applying to a mainstream PhD program in mathematics, than you would almost certainly want to have an undergraduate abstract algebra course on your transcript.  Certainly if you were applying to my graduate program I'd rather see a second course in ODE's than a course in Abstract Algebra (although both would be even better.)