For colleges and universities within the United States and its territories, you can obtain this information by clicking on the related links section (College Board) indicated at the bottom of this answer section and using the College Board site College MatchMaker search engine. You can research colleges and universities by name, or by programs of study, or by geographical location, size, or combinations of part or all of them. The site will provide you with a list of institutions based on your request. It will give you the schools background, accreditation, degree offerings, programs of study (majors), entrance requirements, tuition and fees, financial assistance, room and board, athletic programs, school activities, etc., and a link to each institutions official web page. Practice navigating this site. It will be well worth the time and effort.
WARNING!!!
When choosing a college or university within the United States, make sure the institution has a regional accreditation. With a regional accreditation you can be assured the coursework and degree you complete will be recognized by all other colleges and universities as well as employers. Below I have listed the six regional accrediting agencies and their geographical areas of responsibility. I am disclosing the below so you do not become a victim of educational scams, institutions that are nothing more than diploma mills, or that do not have the best accreditation, and are eager to take your money for a degree that is worthless. Make sure the institution is accredited by one of following responsible agencies.
Regional Accreditation Agencies
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Depends on which "big east" you're talking about
In the 2013 Big East: (Butler, DePaul, Georgetown, Marquette, Providence, St. John's, Seton Hall, Villanova, and Xavier)
In the 2013 America 12 or whatever it will be called: (Cincinnati, UConn, Houston, Louisville, Memphis, Rutgers, SMU, USF, Temple, UCF, East Carolina, Tulane, and Navy (football only))
College Basketball teams have many more conferences than football conferences. Even small colleges can field quality national Basketball teams. A group of so-called "Catholic colleges" have taken the old Big East conference name and it now is for basketball teams. Butler, however, is not affiliated with Catholic Universities, it is a private non religious university.
Villanova, Seton Hal,l Butler, Providence, DePaul, St. Johns, Creighton, Xavier, Georgetown, and Marquette