I am a junior mathematics/philosophy double major looking to pursue mathematics into graduate school. Philosophy is a hobby which turned out to satisfy many degree requirements at first. Now, due to some unfortunate planning on my part, and the fact that the university schedules mathematics and philosophy courses almost exclusively in the same time, I'm in for a real crunch to finish the philosophy side of the program. In short, I'm considering taking a 9th semester of undergraduate, but I'm not sure it's worth it for me. I have a few reasons to consider this decision, but I'm not sure how bad that lost semester matters. I understand that it might implicitly translates into an extra year, since many first year graduate courses come in fall/spring sequences.
In order to graduate on time, I would have to take 18 and 19 credits in senior year, respectively, as well as write a thesis in mathematics (it need not be any new or groundbreaking work, but it must be at minimum an expository paper covering some highly non-trivial theorem and/or applications). However, since I have completed all of the mathematics courses for undergraduate necessary, I am free to take graduate level classes. Since I'm primarily interested in algebra and geometry, I'll be taking the core courses in those two subjects that year if possible. However, I could always nix these to work on philosophy, but since I'm really going to school for mathematics, that seems less than wise.
But in the event that it's too much to handle, I have only two choices. Drop the philosophy major and make it a minor when nearly finished, or take an extra semester of undergraduate.
How much does one extra semester hurt my application? There are quite a handful of benefits to the extra semester if I stay:
It takes stress off senior year proper, which is important to me because I struggle with moderate anxiety, and the high course load could impact my GPA. I could do 12 credits/semester taking 6 in graduate mathematics and 6 in philosophy quite comfortably, with room to meet with professor and work on my mathematics thesis.
It let's me spread the philosophy work sufficiently thin that I can take an advanced algebra course, and/or a graduate course in real analysis. This is particularly important because I didn't do so well in my undergraduate course because of that anxiety. In a lighter semester, I could do much better, since I do understand the material, in spite of underperforming on exams. At the very least I could retake the undergraduate course and do better in it.
I can be a TA, something I have not otherwise had time for and I understand to look good on an application.
I can continue to work as a peer tutor at my university. I am a certified tutor through the College Reading and Learning Association. I don't know if that's useful or not on a graduate application, but it can't hurt. The extra semester would get me another level of certification. I don't know how much graduate programs know about this organization, so I don't know if this means much or not.
Since I'm not graduating after "senior" year, I can possibly partake in a (second?) mathematics REU. Hopefully I will be admitted to one this summer.
So in short, the question is, should I try to get through in two semesters, and nix the philosophy program if I can't make it, or do I go for the ninth semester with all the tradeoffs?