I'm an undergrad student at a fairly well known math program (top 20). I have taken several upper level undergraduate courses (real/complex analysis, honors abstract algebra) and graduate level courses (commutative algebra, topology) and I also did some independent learning with one of the professor here in homological algebra, and I did very well in my math courses (All A and A+). However, some of my geneds are not very good (I don't feel like I'm interested in learning them because I think they are useless and I would rather spend time learning math by myself rather than study for the exam). My question here is: How bad will it be? Will those general education courses hurt my chance of admission for grad school? Thanks
I'm not in your discipline, so I'm not sure how much this is similar...When we evaluate doctoral and master-level students for admission, we first check if their GPA meets the minimum criteria. If it does, then we look to see how well they did in courses that would help them succeed in our graduate programs. If your GPA hasn't suffered too badly because of the non-math courses, they might not hurt you. However, I would caution not to mention to admissions personnel/reviewers that you believe the non-math courses were "useless" so you blew them off. That doesn't sound very professional- if asked, I would say that you focused more on the math courses to prepare for your graduate studies, which took time away from your other coursework.
My answer is based on limited experience with being on graduate admissions committee at an R1 university in the US. My sense is that it won't make much of a difference, though the effect can be lumpy. Most people will probably barely notice, but probably there are people who will think that this reflects a worrying lack of discipline, as this can be a big problem in graduate programs. Most professors have had bad experiences with students who think that requirements shouldn't apply for them, and that they can blow off ones they don't feel like doing; giving that impression will not help you. So, it could be a problem if you are right on the edge between admit and not, but it's a little late to worry about it now.