The first thing is to change your query:

select
    course_id,course_name,course_sitting_id,course_sitting_date
from courses
order by course_id, course_name, course_sitting_id
[download]

Then, you just need to realize that whenever the course_name changes, you want to begin a new entry in your results.

...
my %courses;
for my $row (@results) {
    my $course_id = $row->[0];
    $courses{ $course_id } ||= {
        ...
        desc => $row->[1],
        sittings => {},
        ...
    };
    $courses{ $course_id }->{ sittings }->{ $row->[2] } = $row->[3];
};
[download]

Also see perldsc and Data::Dumper.