You can skip the first paragraph.
I’m an anomalous student in both good and bad ways. I’ve taken the most advanced math classes (e.g. Senior Seminars, rep theory, and etc.) from my freshman year and gotten 40-ish points in Putnam and the maximum score in GRE math subject test, and also I’m doing pretty well on research so far. But the problem is that my GPA is catastrophic (3.1 in math and 3.3 overall). That’s mainly because I perform pretty poorly in some classes. For example, I got A, A-, F, and A- on Complex Analysis, Senior Seminar, Rep Theory, and Abstract Algebra, respectively in my Freshman year, although Rep Theory was considered as a relatively easy class among them (I performed totally fine on class and assignments but tests on Rep Theory class). This is because I sometimes can’t concentrate well when I get so strained during test due to my learning disability. I have such a crucial defect for a math major student, but I strongly hope to become a mathematician, since I do pretty fine on anything (esp. research) other than several tests (which are pretty important, though). With this GPA, it’s quite likely that I will end up in a PhD program ranked around 100 in the nation, but I want to somehow stand out when my grades on tests will no longer be an important factor for me.
So, among the relatively non-competitive programs which accept students with even 3.1 GPA in math, which ones do you think I should apply to? If I had decent GPA, I could apply to programs which has profs by whom I wanted to be taught. But I clearly can’t do that in this situation, so I think I should instead look for programs which have high acceptance rate in order to be accepted by at least one program.
Can you retake Representation Theory, get an A, and fix your GPA? Maybe another class you did poorly in too? To get your GPA up to 3.4-3.5 or so. Seriously, it’s impressive to take Representation Theory as a freshman. I never learned about it until taking a grad algebra class as a senior, and it was only a short module (ha) in that class. 40 on the Putnam is really impressive too. With research and great LORs/SOP, you may be able to get in to a good program. Probably not top 10, maybe not even 20, but top 50 might not be out of question.
I’m assuming you’re a junior? Or are you a senior and taking a year off before applying?
Anyway, if you don’t believe you’ll get into a strong enough program that you could actually become a professor, consider where you want to live long term and apply to some programs in the area. For example, if you hate the south, don’t go to Auburn (picked a random school near #100 on US News). You’d be unlikely to get a good professor job from there and you’d likely get stuck in the local job market after finishing your Ph.D. because no one’s going to hire you from across the country when they’ve got plenty of local un/underemployed Ph.D.'s.
By max subject score, what do you mean? I think the max is officially 990, but in reality it’s more like 900 or something even if you get every question right? Honestly getting 800+ will give you a shot at some really good schools.
I’m glad to know that I may have shot on top 50! Since I like California and want to visit other UC schools nearby, I will probably apply to UC Riverside, which I previously considered as out of reach. I’m currently a junior. Unfortunately, I can’t retake rep theory, since it’s a special course offered only in that year. It’s also hard to pull up my grade drastically at this moment. I got 900 (about 97 percentile) and thought it was the maximum score in these days. I like coastal areas, so I will probably not apply to universities in southern areas. I really appreciate your comment!
Well I’d recommend focusing on your research and LORs and SOP. See if you can take a couple grad classes and do well. Some adcoms might interpret your record as “can do well in the undergrad stuff, can’t do well in harder grad material.” Some people say programs care more about your junior/senior year grades, but considering you won’t have your senior grades when you apply (even your fall grades won’t be known until after many deadlines), I’m not sure how realistic that is.
Keep in mind you’ll have to take exams in grad school. Finals, quals, etc.
OK. I will focus on my research and try to make myself look better for the prof I’m working with on research.