Update Doesn't Work - 1064 Error

The code:

update course_series_assignments as c, users as u
set c.user=u.UsersID
where c.user=u.User;

...returns an error "1064-You have an error in your SQL syntax near 'as c, users as u set c.user=u.UsersID where c.user=u.User;' at line 1".

The c.user column currently contains varchar data like "John Smith", as does u.User. The u.UsersID column contains an auto-incremented unsigned integer. I want the integers to replace the full names in the c table where they match the User column in the u table.