My issue is avoid Wordpress's WPDB class, however with the MySQL syntax. I am trying result in the following sequence work:

  • Get a range of all Posts IDs
  • Remove posts from the specific Category
  • Remove replicates, revisions, drafts etc. Only show Released content.

Help? Thanks.

Use query_posts function for your http://codex.wordpress.org/Template_Tags/query_posts by passing the course id or even the category title into it. It's all regulated described around the link.

Edit after your comments:

You should use get_posts http://codex.wordpress.org/Template_Tags/get_posts, too, AFAIK both of them return arrays.

$posts = get_posts('category=1');
foreach($posts as $post) {
    echo $post->ID; // or whatever you want to do with it...
}