The short story:
So once upon a time I was really smart and went to Caltech on a full scholarship. Then I got horribly depressed and went on medical leave, so I went to this really shitty school ten minutes away from home. Should I transfer colleges, or wait another year and go to grad school?
Factors affecting my decision:
1) Whether I can get into a good college and/or grad school with my current credentials.
GPA: 3.8 Caltech/4.0 at current school
GRE: 1570/1600
Other: One paper from high school, two papers in the process of being published. None of them are related to math. I got top 500 at Putnam but that was frosh year so I might be able to take it again and do better. All in all I think my credentials are pretty good but I'm worried my courseload might be too light, and I'm worried graduate programs might hold my mental illness against me if they find out.
So far my courseload looks like this:
YEAR 1: frosh core at Caltech
-- Kicked out of school --
YEAR 2 SEMESTER 1: Intro Analysis 1, Mathematical Probability, Complex Analysis, Quantum Mechanics
YEAR 2 SEMESTER 2: nothing
YEAR 3 SEMESTER 1: Fractals in Psychology, Intro to Chaos, Intro to Abstract Algebra 1
YEAR 3 SEMESTER 2: Intro to Abstract Algebra 2, Algebraic Topology, LR-tableaux (1-credit independent study), General Psychology
YEAR 4 SEMESTER 1 and 2: stupid gen eds I need to take to graduate. Oh and I might do some research or independent study.
2) I have a weak background in analysis and linear algebra. I haven't taken any topology or geometry, in fact my university doesn't offer those courses except on a sporadic basis. The only math I am reasonably comfortable with is abstract algebra and I'm not even sure of that because our teachers really baby us. I'm worried that if I go to grad school right away I'll be underprepared compared to the rest of the students. (But of course if I went to college I'd take more math before moving on.)
3) If I go to grad school I'll be graduating in 4 years. If I go to college it'll be more like 6.
4) If I go to college I might suffer a horrible mental collapse. This could happen with grad school too, but then I'd have an extra year at home to "recover."
5) If I go to college I have to send out applications by March. This will be kind of hard because I'm about to go inpatient for a month.
6) For the past two years I've been taking "graduate level" classes with a bunch of 30-year-olds. I feel like if I went to grad school at age 20 I'd be missing out on the college experience. Despite trying to kill myself several times I loved my time at Caltech and I miss being a kid/hanging with people my age.
7) If I go to college I have to worry about losing my friends and starting again in a new place. I only have one friend here...but still. It's starting over.
8) Here I get put in really small classes and professors all treat me special because I'm one of the smartest ones here. Any professor here would take me on as a research student. If I went to a good college my letters of recommendation would not be as good. (I'd probably get to do cooler research though.)
9) I really don't want to go to college or grad school, I'd rather just lie in bed all day and go on the Internet. Maybe I should just say screw it and go to grad school here, hell I've already taken most of the master's curriculum anyway. Then I'll have a PhD in math and it'll be completely meaningless but at least I won't have to do anything for six years. I can be like the other smart kids who drink and play World of Warcraft all day.
So what should I do?
Thanks for any input or suggestions =)