AUDITING: The requirements for auditing depend on the professor and the school at which the class is being held.
At the Journalism School, auditors pay nothing, may do no work, and receive no mention on their transcripts of having attended. Students simply contact the professor to make a request to sit in.
A professor in any other department is permitted to offer that same arrangement. You may contact any professor directly to see if he/she is amenable.
Some professors in outside departments may ask that you register for “R ” credit. In this case, you will pay for the course, do any work the professor requires, and it will appear on your transcript ( see the “R” section at http://registrar.columbia.edu/content/grade-options for full details).
Please note that taking a class for “R” credit does not count in your accumulation of credits/requirements for graduation.