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?

I'm in chemistry, and I also went to a small, top-20 liberal arts school that did not offer much additional, higher-level coursework.

I experienced two main challenges:

  1. Transitioning into graduate-level courses. This was difficult, because of not having experienced similar class-work before. However, the fundamentals you learn at liberal arts colleges are solid, and you've learned how to learn.
  2. Transitioning to the difference in teaching quality. At most graduate programs, the course instructors are research faculty and their priority is research. It can take some time to adjust to how to learn in a class that was not well-constructed for learning.

That said, unless the masters programs are very different than the phd programs in mathematics,I think you'll encounter the same challenges in either the masters or the doctoral program. In chemistry and physics, masters students take the same coursework. Additionally, usually you have to write a thesis for a masters, so during your coursework there is more pressure to do successful research, since you only have ~2 years (instead of ~5-6, as in a PhD program). Also in my experience graduate schools only rarely grant course exemptions for masters work.

You have several options:

  1. Apply directly to PhD program. If you do this, I highly recommend studying some of the advanced coursework over the summer before you start. MIT Open Courseware has some great materials for this.
  2. Apply to a masters program at a less selective school, then apply to more selective PhD programs. In a less-selective school, the classes might start at a lower level, there might be more support for students, and you might be able to take advanced undergraduate coursework not offered at your undergraduate institution, if you need it.
  3. Get a job or internship and take a few courses. You could take a gap-year in which you get a job or internship in your field. You'll grow your skills and content knowledge via that position, and you may also have time to take ~1 class at a time at a local university, online (through a university or a free service like coursera), or via independent study (like MIT OCW). This way you'll also earn money, if that's a concern. (Masters students may or may not be stipended.)
  • @bounder34, in your particular case I would not advise you to go with NMJD's option 1. Option 2 sounds best. As you get some more coursework under your belt, you'll gain self-confidence. // If you can get funding, fantastic. // The problem with Option 1 is that you'd be on a conveyor belt to the basic PhD exams. You might get that feeling of being on a treadmill that's set to too fast a pace. Doing more coursework before the PhD would prevent that. – aparente001 Dec 24 '16 at 8:49

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