I've posted a few questions here in the past couple of days regarding grad school decisions; apologies for asking so many! It's a big decision and I want to do it right, but I don't want to bombard this forum with too many nitpicky questions. This should be the last one! The previous two are here and here, if you want additional context for this.
The gist of it is: I did my undergrad major in math and linguistics, and I'm looking to pursue research at the intersection of the two fields. For various reasons, it seems the optimal path is to come at this largely from the math side rather than the linguistics side. So I applied to grad programs in both fields, hoping to get into a math PhD. Instead, I got in to a few math Masters programs (at respectable, though not top-ranked, schools) and a linguistics PhD program at a top school. The PhD program also seems like it will offer me the chance to take some math classes along the way, and to pursue some generally math-heavy research topics. This, along with the fact that the degree is fully funded, made it very attractive, and I ended up selecting this school on the April 15 deadline.
However, now I am having some regrets. I feel like choose a math program would have given me much greater flexibility, and perhaps afforded me the chance to research other math topics that I really like (e.g. knot theory) that don't have much to do with linguistics. I am fearful that, by choosing this linguistics degree, I may have locked myself out of ever touching certain areas of math, whereas choosing a math school would given me the option to work on applied problems in linguistics and pure math problems, eventually in my career. I also heard something to this effect directly from a former professor of mine, and with this in mind I am having some serious regrets.
However, I see one option (though I'm not sure I really want to take it, but I at least want to consider it): perhaps, since it is still the weekend, I can contact one of the math programs whose offer I declined and let them know I have changed my mind, and see if they still have a spot for me. I am not sure if this would be the right decision, and even if it was it feels like a long-shot, but perhaps it's the right gamble to take. Apparently, others here have considered similar questions before, but their situation seems different enough from mine that I think posting my own question is probably warranted.
My main concern is that, because I've already accepted the offer to the linguistics program, contacting one of the math programs in this way would be against the rules (I am not totally sure?) and could get me rejected from both for some kind of ethics violation. I would really not want this to happen, so I want to double- and triple-check before I even consider this. It is worth noting that both of these programs are part of the same state university system (this is in the U.S.), and so I fear that contacting one would quickly get back to the other and possible hurt my reputation there.
Does anyone have any advice on what to do?