Just one of those times when I just can't see the problem. It appears to be the opening brace at the end of the if statement.
$('#title_number').change(function () {
if ($('#title_number').val() == 73) or ($('#title_number').val() == 74) {
$('#ProfessorDiv').show();
}
});
orkeyword in JavaScript, and the entire expression used by theifmust be in().