Advice on how to start a Research (maths related)

The issue isn’t annual cost but available financial aid.
You can look up current (comprehensive) costs by typing “cost of attendance”+ name of any college. From that page you should see “net price calculator”. Or you can type the name of the college+ “NPC”.
The NPC will not be accurate - you have to run it as if you were a domestic applicant, which you’re not, so any federal aid wouldn’t apply - but it’ll help you understand the amounts+range involved and see net costs at a variety of universities.