It seems like the $in
operator would serve your purposes just fine.
You could do something like this (pseudo-query):
if (db.courses.find({"students" : {"$in" : [studentId]}, "course" : courseId }).count() > 0) {
// student is enrolled in class
}
Alternatively, you could remove the "course" : courseId
clause and get back a set of all classes the student is enrolled in.