I could rewrite the code this way...
SELECT personID
FROM #gradPerson AS g
WHERE NOT EXISTS (SELECT TC.PersonID
FROM TranscriptCourse AS tc
WHERE tc.PersonID = g.PersonID
Are you saying you don't understand what an alias is? I'm creating aliases to #gradPerson and TranscriptCourse so that I can join them in the correlated subquery... you just set the PersonID of the subquery (tc.PersonID) equal to the same field in the outer query (g.PersonID).