So I attend a small(top 20 ranked) liberal arts college. I want to pursue graduate school in Mathematics. I am currently a junior, so by the time I would be submitting my graduate applications next year, I would have completed only 1 course in real analysis, 1 course in abstract algebra, and 1 course in Complex Analysis. I am unable to take topology due to the very small number of math classes which my school offers Everything I hear suggests that this is not enough preparation for grad school.
Also, I will not have had any applied math courses beyond ODE at that point. In addition, looking at the sample GRE subject tests-I fear that it would be difficult for me to get a decent score if there are some questions about field theory, topology, etc. which I won't have the background to answer(although I understand the test is very difficult anyway). I also am unsure of which are of math I might most want to pursue at this point.
Anyway, would it be a good idea for me to start in master's program first? In that case, I would probably have to go somewhere in state. I live in New York, so that would might mean going to SUNY Albany, SUNY binghamton, etc., which are ranked in the 80s by US News. In a masters program, I would be able to obtain the desired preparation for grad school, explore applied math, and study for the GRE more, and try to go into grad school with more of an Idea of what I wanted to focus on. My other options for masters programs would be going to something at a Place Like Miami Ohio, North Dakota, University of Alaska Fairbanks which have funded terminal masters programs for people interested in strengthening their mathematics for graduate study.
There are also a few schools which offer post baccs in math, and I know Canadian universities do fund masters students, although their system is different in that they rarely admit students directly to PHD programs. Are these(and if any, which ones) masters programs a viable idea for trying to get into a better PHD program? Or would I need to get a masters program from a school which is ranked more highly?