"Is it my imagination or is it true, every time I read about Columbia University, some embedded socialist, communist, or Islamic terrorist makes the news. Who is sending their kids to this dump? How is this bastion of terror funded?"
Well, it's not such a dump. Even though the campus is in Harlem, it is quite nice, actually. You probably read about Columbia more than elsewhere, because Columbia's the Ivy League school in New York, so the media outlets all have the most immediate direct access to Columbia professors as compared to other schools outside of the City. Columbia ends up being cited more often in media sources than any other school for that very reason.
It's a private university, funded by tuition (about $25,000 a year and rising) and by a massive endowment fund.
Students from all over the world attend, so of course there is a broad diversity of opinion.
And yes, the social studies department and law school is liberal indeed. The business school and engineering school are not. But there is no suppression of speech at Columbia. This is New York. People are free to have any crazy damned idea they want, and to express it too. And those who disagree are free to call them psycopaths, or worse. If you're going to live in New York, you've gotta learn to grow a thick skin, and going to college in New York teaches you that in addition to other things.
So you needn't worry your head about your tax dollars going to fund the place. They don't, much, except for research the government wants done there, and the standard educational institution tax exemption that all such institutions get.
When I attended the law school (1981-1984) I didn't see any evidence that it was unusually liberal, and I have seen none since. There were traditionally liberal professors and visiting professors, and lots of New Deal style Democrats, who revered the Franklin Roosevelt administration as the golden age of professionalized administration and quality government. Certainly, many people can disagree with that analysis. However, there was no radical element there that I ever encountered.
Most graduates get jobs at large NY law firms and in the various administrative agencies of the federal government in Washington, D.C. (the SEC, the DOJ, etc.), and I don't believe that Columbia's law school is any more or less liberal than those two pillars of the US establishment.
What evidence do you have that the law school has become "liberal indeed"?
The Columbia College class of 2004 commencement speaker spent probably 2/3 of his time trashing the Bush administration, in typical Jackass Party fashion. It was obviously assumed that the parents and students would be delighted. Not? The tuition is now up to about $31,000 per year, and total expenses about $40,000 per year for the college. Parents should start voting with their feet and send their kids to colleges where the faculty realize that the terrorists are the enemy, not President Bush.