Short version: Graduate prelims include lots of topics which are only distantly related to your particular research area. How does one motivate oneself to learn and do this stuff?
Long version with personal background: I'm a 3rd year undergrad who's planning on applying to graduate schools in the US next year (in mathematics). I'm taking a graduate course (Galois theory) which, in the graduate programs I'm looking at, typically amounts to less than 1/3 of the material on the algebra prelim, which is one of the usually 3 topical prelims. For me, the concrete consequences for failing this class are academic probation with possible loss of funding/scholarships; if I were in the graduate school here, this would be possibly ejection from the program.
Unfortunately, I find this topic to be horribly uninteresting. I did very well in the first half of the class because it was essentially a very fast-paced redux of group and field theory, but I can't find a single drop of inspiration or interest in my mind for these classic Galois theory results that we're developing. I've done some undergraduate research in algebra (factorization theory) and, if I were to go into that as a professional, I feel confident that I will never touch Galois theory ever again. So for me, Galois theory being mandated to be learned by me for only this one purpose, a prelim exam. Therefore, I'm having trouble finding motivation to learn it.
The lectures are in the usual "lemma: proof, theorem: proof, corollary: proof" style (occasionally throwing in a sentence or two of motivation, why we study this topic), with weekly homeworks which heavily supplement the lectures (only a small percentage of grade), and 2 tests (midterm and fnial). These homeworks are pretty in-depth and are expected to take upwards of 5 hours to properly complete. (Usually 1-2 pages of proofs for each problem, and 3-5 problems per week.) Nobody is holding my hand any more and walking me through the class like in undergrad classes. (E.g., the homework problems aren't even close to self-explanatory and often cover topics not even mentioned in lecture.) Even though I'm showing up to lecture and taking detailed notes, I haven't even started the last 3 homeworks. The final is still 3 weeks away so it's not impossible for me to catch up, but it's going to take a lot of hours to get this material learned so that I don't fail the class.
As far as I can tell, this class structure is more or less standard in graduate mathematics, so if I'm serious about wanting to continue in academia I'm going to need to find out how to manage this problem (lack of interest). How do others handle this? Where does the motivation come from? (other than Adderall.)