I'm attempting to write a sub query that wold accomplish the same results as the join query shown below.
INNER JOIN Course
ON Department_to_major.Dcode = Course.OFFERING_DEPT
WHERE Course.COURSE_NAME LIKE '%INTRO%'
GROUP BY Department_to_major.DNAME
Try the below query. I am assuming that you have used "GROUP BY" clause to make DNAME field unique.
SELECT DISTINCT(DNAME) FROM Department_to_major WHERE Dcode IN (SELECT OFFERING_DEPT FROM Course WHERE COURSE_NAME LIKE '%INTRO%');