[For the sake of preserving anonymity, I'm going to be vague about some specifics (e.g.; school names, specialty subjects of interest) of my case. I don't think this makes the question itself vague, but please let me know if it does.]
I think this is what they refer to as a "good problem":
I just finished the grad school application process, and I'm getting my first letters of acceptance. I've received letters from some of my safer bets, but I also received one from one of my dream schools. I put out three dream school applications out of the ten+ applications that I submitted. I expected rejections from all of my dream schools, given my somewhat shaky undergrad work (ranging from C's to A's, even for in-major classes). I figured I'd probably get at least one letter from one of my lowest three choices, at best.
I got one letter from one of my bottom three schools, one from a "middle of the pack" school, and one from a dream school. And, at the risk of humble bragging, this is a great school with a great reputation and true luminaries in my specific research interest amongst its faculty. I literally screamed when I got the letter. This is a school that's a US New & World Report (all of the schools I applied to are in the USA) ranked top-30 math school, and top-10 in my specialty (actually, both of my specialties, which have considerable overlap in the context of my specific research interests). It's arguably top-3 in my specific research interest within that specialty, and has a high concentration of top researchers in my specific research interest in the department. And to top it all off, they sent me the letter of acceptance only three weeks after I submitted my application. As I understand it, that's a very quick turn-around time, especially for a prominent research institution. I assume that's a very positive thing.
You might ask, "So where's the problem?"
As I said, this is a "good problem".
I'm not sure whether to just accept the offer right away, or wait to see if some of the other dream schools respond. At least one of the other dream schools will have funding for me from the get-go if I'm accepted. I know "non-funded for any amount of time" is a big red-flag, but I feel the pedigree of the school that I got accepted to trumps that. Having good recommendations from any of the professors I would work under would be worth more than gold. I feel like, in this situation, you just bite the bullet and go for it. But I also feel that if you might have basically the exact same opportunity, except WITH funding, at another institution or two, it might be worth waiting/holding out a bit to see how things play out.
I feel left with a few questions:
Is it stupid of me to hold out at all, given the high level of the institution I received the letter of acceptance from? I worry my ego might have got too inflated, and it's wrong to hope that another dream school (with or without available funding) will come knocking at my door.
If I do accept the offer, but then receive an offer from another dream institution that could offer me funding, would it be bad form to pull out of my agreement of acceptance? (Like I said, the school that has already sent me a letter has a lot of researchers I admire, a few of whom I've even met and talked with. I wouldn't want bad blood.
How long is too long to wait on accepting the offer? Will they fill the open position if I take too long to respond? I don't want to miss out on what could be the opportunity of a lifetime because I sat on my hands.
Thanks for reading, and advance thanks for any answers/advice given.
