MathML would be nice, but let's start with basic text first
If you want to help, a good first step would be to go through the code and replace all the MySQL-specific code in ARSC with equivalent calls using Moodle's database functions (lib/datalib.php). Also note that the returned variables will change from arrays to objects.
eg
$result = mysql_query("SELECT room, level from arsc_users WHERE user = '$userpassive'");
$a = mysql_fetch_array($result);
if ($a['room'] == $x) ..... etc
becomes (in the ancient Moodlish tongue)
$a = get_record("arsc_users", "user", $userpassive);
if ($a->room == $x) ..... etc
or to get multiple records:
$aa = get_records("arsc_users");
foreach ($aa as $a) { ...etc
Of course you'd also have to include moodle's "config.php" at the top of each file, just like all Moodle code.
If someone did that and sent me a modified copy of ARSC that works when stored as moodle/arsc, then it would be much easier for me to whip it into shape as a proper Moodle module.