Yes. All departments will assign faculty advisors to every student committing to either a major or concentration in that department.
How large are Columbia's classes?
80% of undergraduate classes taught at Columbia have fewer than 20 students. Since Columbia’s Core classes are small seminar classes and since more advanced courses are meant to allow direct connection with faculty, few courses at Columbia are larger than 20 students. Those classes generally are either popular introductory lectures or upper-level classes in especially great demand.