I'm completely clueless on the process, but on track to graduate in two years, so I have a few questions about what I should do.
1) What's the difference between a Master's degree in Mathematics and a Ph.D in Mathematics? I have always wanted to teach mathematics at the college level, and so my family has always joked that I'd be in school forever to get a Ph.D. What is the difference between the two, and how do I go about choosing which is right for me? I don't really know the difference between undergraduate and graduate school, except that the latter is supposed to be much more difficult, much deeper, and is the starting point for research for many people.
2) What do I need to go to graduate school? At the moment, I have a 3.6 GPA, which I guess is alright, but I don't know if it's good enough or if there's anything else I need. I have awful test anxiety, and so my GPA in mathematics specifically is probably a lot worse than my overall GPA boosted by my minor and general electives. I am working on getting an undergraduate research opportunity to help put weight behind those numbers. Is this an appropriate things to do in undergraduate, and is it going to help me go further?
3) I have to come to realize just how expansive mathematics is through my time on MSE. There are tons and tons of fields of mathematics with all kinds of interesting problems. At the moment I'm really fascinated with differential equations because that's what Stony Brook researches at the graduate level, so their undergraduate course is like an introduction. If I decide I want to do that, how can I find other schools with similar focuses? If not, how can I figure out what I do want to study? It seems I'll never experience even the surface of some of these fields that are particularly deep.
Sorry for the long post, but thanks for any insight any of you can offer.