mathematics - Can auditing students attend consultation hours?

Assume a university allows students to audit classes informally, so they're not enrolled and don't pay, but they attend classes anyway. Obviously, no one has obligation to allow these students to attend anything and therefore doesn't even have the obligation to check their exams and such.

In case this is relevant, my intention is for math classes.

(12 hours ago, I was rejected for a math PhD program, and the professor told me I could audit. I told the professor that 6 months ago I asked the math department if I could, but it said no. The professor told me "Don't ask; just go!" The professor suggested I audit some classes and try to do some of the classwork. I didn't think of many questions about this, but I think I won't go since the commute is 4 hours by train or 70 us dollars by taxi, and I can ask all my questions on stackexchange anyway. Thank God for the Internet)

I don't think students really learn from just attending the classes even if they ask questions in class. Exams of course are great ways to learn, but what I had in mind is asking further questions either during the professor's consultation hours or in further auditing the teaching assistant's tutorial classes.

It sounds like the questions of auditing students in class, tutorial or consultations is taking up time that could instead be used for the registered students, but I think anyone who speaks up is making a contribution by asking something anyone could wonder. Therefore, the professor or teaching assistant could clarify to the rest of the class before anyone else would ask, which actually saves time.

(I don't want to first ask the professor because it might be disrespectful if the answer is a definite no anywhere in the world. If the answer here is maybe/yes/double check with the university/go ahead and ask the professor/"Don't go; just ask", then I will be inclined to ask the professor)

Answer

Since it hasn't yet been mentioned in an official answer, let me note here that, in the US, at least, auditing is a formal relationship between a student and the university. You need to pay for the privilege of sitting in on a course as if you were a regular student. You get a line in your transcript marking the course as audited and receive no grade. Whether you are allowed to take exams (for no grade) or not depends on things, perhaps just on the professors willingness to grade them. If the course is a large lecture, with break-out sections, you are probably permitted to attend these as well and ask questions as any other student would. Among other things, formal registration allows the professor to get an official list of who should be present in the classroom.

Actually, a professor could get in some trouble for letting you sit in with no registration of any kind. Not only are you taking up resources that others are paying for, there are liability issues. If you are hurt in some way, or have a grievance, or if you harm another student when the university doesn't know about your presence, the situation can be quite dire.

I think it is a mistake for a professor (in the US) to permit this. But if they permit it, they will probably also permit you to come to smaller sections, though you will be consuming even more time that should be devoted to others. But, I think, an individual professor permitting this without the knowledge of the university is a poor, possibly dangerous, practice.

However, the question of "taking up resources" is a delicate and subtle issue. If such a student asks a question in such a situation are they "consuming resources" or are they "contributing to the class"? Normally, my view is the latter. Questions from students contribute to the learning of everyone, provided they are properly thought out. This is true independent of the official status of the student.

I'll also note that in the past (maybe in the present) in at least a few graduate schools, a math student would never consider taking an advanced course unless they had (officially) audited it first - possibly more than once. In such places, such courses can be extremely rigorous, so you want a heads up (and practice on exercises) before you take the course "at risk" (i.e. for a grade). Part of that was just student paranoia and obsession over grades, but the courses were very rigorous requiring a lot of self-learning.