Aiming for Ph.D. in math -- am I screwed? I just finished my first year of college this May, declared a double major in mathematics and philosophy, and after a lot of thought, I'm pretty sure that I want to go to a Ph.D. program in pure mathematics. Not aiming for the ridiculously top schools like Harvard/Princeton/MIT, but perhaps something along the lines of NYU/UPenn/Hopkins. I have a good number of strengths. 3.93 overall my first year (will try to maintain ~3.90); became very familiar with the math department faculty, won two schoolwide math-related awards; doing research with a physics professor this summer and presenting at a few conferences; just asked by a math professor to do research with him in the upcoming academic year. I'm very confident that I can finish my 4 years with a stellar GPA, superb recommendations, and extensive research experience under my belt. Problem: I go to a small, obscure liberal arts college. Due to the small size of the department, few advanced courses can be offered. Most Ph.D. programs recommend two semesters of both real analysis and abstract algebra, but only one semester of each is offered here. Other than that, I'll only have one semester of complex analysis plus some stuff like probability, graph theory, and geometry. There is an advanced "Topics in Pure Mathematics" course that's offered once every 4 semesters, and if I'm lucky, the chosen topic will be something like number theory or topology when I get to take it. My math professors have expressed their optimism about my chances, but I'm seriously wondering how much the limited course offerings here will hurt me when it comes to grad school admissions. Can anyone give some insight?