A little about me:
-I'm a math major.
-I'm going to be starting my senior year this fall.
-I have the credits to graduate early, at the end of the fall semester.
-I have taken a few graduate level math classes, computer science and statistics classes, and science classes (psychology, biology, chem, physics).
-I'm leaning towards applied math.
-I go to my state school, which isn't very selective or prestigious.
-I have a 3.9 GPA.
I haven't had any advising beyond getting me to fulfill my graduation requirements and now it's my senior year and I still don't know what I want to do career-wise. I think I want to go to graduate school because I really enjoy the school environment and learning, but I'm not 100% certain.
Assuming I do choose the grad school path, I feel that my application would be weak at this point. I would like to stand a chance at getting into a more prestigious program than my state school.
-I have not taken the GRE General or GRE Math test. These seem to be the most important factors in admission. I don't know that it's possible to get a good score on both between now and the application deadlines around December.
-I have no research experience yet. I plan to assist a professor with research in the fall, but I wish I would have more prior to applying.
-I have little work experience so my resume isn't impressive.
-I still don't know what program/research area I'd want to go into. I think this would show in my personal statement and recommendation letters.
Do I have time to improve all this before the application deadline? Should I take a gap year to see if I can get some research/work experience, make sure I want to go/figure out what I want to research, and do well on the GRE? Does a gap year weaken an application?