I'm trying to decide whether to stay where I'm at (a big public state school) or transfer to Rice next semester (I just got accepted). I'm a pure mathematics major, and my ambitions for graduate school are high. I spoke with my advisor today for nearly an hour about my schedule next semester and for the next 2.5 years (this is my third semester), and he suggested that if I stay here I may be able to set up some reading courses in differential geometry and geometric and algebraic topology (these are areas for which good courses do not exist at my university). Now, at Rice there is a great selection of ordinary courses in these topics at the advanced undergraduate and beginning graduate level (i.e., just perfect for me). Now here is where it starts getting complicated. These courses at Rice are not actually offered next semester, but I may be able to get a reading course in one of them here next semester. Also, I think I've made a really, really good impression on the math department here so far, so I think I stand a good chance at getting departmental scholarships and awards, whereas this would probably not happen at Rice since the only award given there is for juniors and I don't think I'd have time to establish any sufficient reputation by then. Rice is a much more prestigious school (although it is, of course, not at the Harvard or MIT level) than the one I'm currently at and the students there will be of a much higher caliber (so I could learn from them more than I would learn from my peers here). On the other hand, I'm currently roommates with one of the best math majors at my school; I also went to high school with him. We both learn much from one another. I'd have 2.5 years there, which would be enough to do well and get good recommendations, but here it seems like I'm already nearly guaranteed great recommendations (and I already got some--hence my acceptance to Rice), and it's only my third semester. Because I stand out so much more here than I presumably would at Rice, it seems like my professors here (although some more than others) are really willing to help me out (e.g., the reading courses weren't even my idea; my advisor suggested them to me, even though he or whoever supervises such a course wouldn't get paid). Rice has the VIGRE grant for undergraduate research in math, but my advisor also point-blank suggested that I could work out a way to do research with one of the professors here during the semester, which seems like it could have just as much value as participating in VIGRE. However, courses at Rice would generally be harder and at a higher level than courses here and thus good performance there would mean more than good performance here. To me, a reading course almost sounds ideal, as I'd almost undoubtedly want to use a more difficult textbook and move at a faster pace than would be possible in an ordinary course (unless it were a graduate course). I feel I could probably learn more from such a course than from an ordinary course because I'd be the kid who spends all his spare time reading and doing problems for fun. I'm concerned, though, that they may appear unfavorably to graduate schools since they aren't official courses. Also, I'd probably want to study material at very upper undergraduate or beginning graduate level, but I'm pretty sure it would be written as 2000 level credit on my transcript; this could be explained away in my personal statement to graduate schools I suspect, though. I was wondering if anybody could give me some advice here. I'm deep in thought about whether I should transfer or stay where I'm at. There are clear advantages and disadvantages to both moves, and I can't seem to figure out what the right move is.