I'm considering graduating a year early and I'm having a bit of a hard time making the decision. I'm going to be as specific as possible so that I can get the best advice possible, so sorry if this becomes a bit lengthy.
I'm going into my third year as an undergraduate, majoring in mathematics. Here is a list of courses I have taken:
Calculus III, Intro to Linear Algebra, Differential Equations, Modern Algebra I, Advanced Linear Algebra, Modern Algebra II, Discrete Math, General Topology, Real Analysis I, Real Analysis II, Algebraic Topology, Complex Variables, Abstract Algebra I (a graduate course in Group Theory).
I am currently participating in an REU, and I am attending Math in Moscow in the Fall, where I will (most likely) be taking Algebraic Number Theory, Commutative & Homological Algebra, Riemann Surfaces, and possibly one other course.
I've done a fair bit of reading outside my courses as well: Group Representation Theory, some classical Algebraic Geometry (Fulton's Algebraic Curves, so I haven't been exposed to schemes yet), and Category Theory just to name a few.
Here are the upsides I see to graduating early:
- opportunity to take more advanced coursework earlier (my university doesn't have an overly active graduate department, and it's likely that most of my learning would come from independent reading courses if I were to stay)
- being in an environment with stronger students will probably force me to develop better as a student
and here are upsides I see to taking a fourth year:
- more time to figure out what subject I want to pursue research in
- opportunity to have more coursework under my belt before I apply
- it might be difficult to apply from Moscow, so I wouldn't have to worry about that
I'd like to hear other people's opinions. I've of course asked my professors first. One is adamant that I should graduate early, he's actually the one who suggested it to me. Another says he thinks I'll be fine either way, it's just a matter of if I want that extra year to prepare.
So according to them, I should be okay. But I can't get the idea out of my mind that I might not get into as good of a graduate program if I graduate early, so I wanted to hear other opinions. Am I just being paranoid?