Logically OLAP functions are calculated after GROUP BY/HAVING, so you can only access columns in GROUP BY or columns with an aggregate function. Following looks strange, but is Standard SQL:
SELECT employee_number,
MAX(MAX(course_completion_date))
OVER (PARTITION BY course_code) AS max_course_date,
MAX(course_completion_date) AS max_date
FROM employee_course_completion
WHERE course_code IN ('M910303', 'M91301R', 'M91301P')
GROUP BY employee_number, course_code
And as Teradata allows re-using an alias this also works:
SELECT employee_number,
MAX(max_date)
OVER (PARTITION BY course_code) AS max_course_date,
MAX(course_completion_date) AS max_date
FROM employee_course_completion
WHERE course_code IN ('M910303', 'M91301R', 'M91301P')
GROUP BY employee_number, course_code