Can a school change their admission decision before April 15th? I have been accepted at a good school in the U.S. with full-funding. However, I am still waiting on the status of three very good U.S. schools as well. 

Can the school that already sent me an offer of acceptance change their mind before April 15th?

I want to wait until I receive all the schools letters and make a decision around the 1st week of April, but I'm worried that just in case nobody else accepts me; what if the first school that accepted me changes their mind? Is that a possible scenario?
I am very experienced with admissions in the U.S., in particular in math programs at my R1 university: unless you grossly falsified something in your application, it would be very unusual, and substantial professional misconduct, and would not be even contemplated as a dignified option, for a grad program to recant on an offer of admission and funding.

The only to-me-conceivable scenario would involve catastrophic budget problems at the university ... since, after all, grad student funding is a tiny bit of the whole.

So, at least approximately, I'd recommend thinking of the offer of grad admission and funding as a far more reliable contract than most others you'll encounter in life. (Car repair estimates? Real estate appraisal? Promises of eternal friendship :)

So, quite seriously, you should not worry about it (if the offer is from a reputable, long-established university (e.g.) in the U.S. that is not filing for bankruptcy etc.