Graduating a year early? 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 &amp; 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?
You are obviously in a good position either way, but as you suggested, graduating early appears to be your "practical" decision.

If you are considering a doctorate or masters (it sounds as though you are), graduating will allow you to get a head start on it.

However, if you you truly don't know what what graduate degree to pick, and don't decide to go with that, consider doing an independent study with a favored professor or doing some tutoring at your local university, as it would not only contribute to your resume when applying for a masters program, but also give you opportunities to dabble in subjects you find interesting, and ultimately help you decide which field you'd like to master in.