It is possible to earn a prestigious degree from Columbia University without completing a residency. Check out this blurb from Columbia's Video Network website:

"CVN enables students globally to pursue residency-free, fully accredited engineering courses and degree programs completely via the Internet, allowing students to view their lectures anytime and anywhere."

Students can earn online master's degrees in dozens of majors including applied mathematics, civil engineering, computer science, electrical engineering, and more. There are also several online doctorate and certificate programs available. Find out more: Columbia Video Network Degree Programs.