IIRC the situation is that it is possible that Obama went to Columbia via the wide-open “friend-of-the-school” General Studies program, but we don’t have the direct evidence to confirm that hypothesis.
Some info from a Columbia alumnus:
If he were in the COLLEGE, he would have had to have taken Columbia COLLEGE's required and extensive Core Curriculum, that consists of 4 seminars of Literature Humanities, Contemporary Civilization, Art Humanities, and Music Humanities. Columbia is pretty strict on this and all transfers must take these, as did all the transfers I knew while attending.
The other required courses in the Core Curriculum are writing, foreign language, and foreign culture courses that he may have been able to avoid through earlier coursework at Occidental.
Columbia COLLEGE has had this Core Curriculum since 1919, and all 4 seminars were required when Barack attended, especially of transfers.
Also, these COLLEGE-required seminars are not large lecture classes. The seminars have a maximum of 12 to 14 students. They are strictly regulated, e.g., missing more than 4 classes results in automatically failing the class.
The School of General Studies doesn't require the Core Curriculum, so Barack would've been more under the radar there. It also explains why no one knew him.
The School of General Studies also awards the B.A. degree. The School of General Studies is for non-traditional students, who are usually older, have unfinished degrees, etc. It is similar to Harvard's Extension School.
second link is particularly good.