my $dbh = DBI->connect("DBI:mysql:database=proyecto;host=localhost", "root", "xyz123", {'RaiseError' => 1});

# Pre-prepare using placeholders
my $sth_a = $dbh->prepare("SELECT dept, course FROM final WHERE pat=?");

my $sth = $dbh->prepare("SELECT DISTINCT PAT FROM patentes");  $sth->execute();
while (my ($pat) = $sth->fetchrow_array()) {  # You don't need an array here
	$sth_a->execute($pat);
	while (my ($dept,$course) = $sth_a->fetchrow_array()) { 
		print "$pat, $dept, $course\n";

		# Here you can create and populate your new tables as needed 

	}
}
$sth->finish()
$sth_a-finish();