I've seen similar questions here, and I wish there was a narrower tag than the broad soft-question and career-development.
I am currently a freshman/sophomore-to-be at a top ten math program in US. My major GPA is around 3.5-3.6, and so is my overall GPA. Due to fast progress in my courses (skipped all lower divs) I will be ready to graduate in a year or year and a half. The question is whether I should do that.
I do not see myself outside of academia, and dead-set on pursuing PhD in math. With my GPA far from being stellar, I was going to take more grad courses to improve the situation. The college is quite pricey, with me being an out-of-state, and so I am not really sure whether I should just graduate and take those courses back home (or apply for masters).
Recap: is it better to graduate early, with an average GPA and no hooks (e.g., research, high Putnam grade, no grad courses), apply for Masters program and save money, or graduate later and improve my record as an undergrad?
Too long to be a comment, and originally written for Math.SE -
Firstly, if you're set on a math PhD, then you will probably never apply for a Master's program. Most math PhDs apply straight to PhD, and these are generally funded (this is all under the assumption that you stay in the US).
The typical accepted candidate to a good math PhD program has a good background in the following:
- Math knowledge
- GRE/Math GRE
One doesn't need to be perfect at everything, and everyone has their strengths and weaknesses. The exception to this rule is that you must have great recs - there is a certain recommendation inflation right now, and it seems to me that recommendations are judged just as harshly by what is not said. I say this only because without grad courses/research/high gpa, it might be challenging for one of your professors to speak highly on your behalf. Or maybe not - it's case by case, right?
I cannot speak as to how strong your exact application would be, as I don't know the specifics. Your best feedback would probably come from a mentor or advisor from your department, or one of the professors whom you would ask for a recommendation.
Without knowing specifics, I might also ask: what is the rush for? (rhetorically)
As a final note, I should mention that it might be possible, depending on your school's policy, to apply for grad programs and decide to actually graduate only if you get accepted/have positive feedback. But this is not ideal, as it's sort of a punt. Were you to not get accepted, you wouldn't have set up summer plans and your last year would be somewhat hodge-podge. Yet these are the exact things that would improve your application for the next year.
Food for thought.