This is an informal discussion of several problems we have begun to notice in our graduate degree program. As the birthplace of the ENIAC, the University of Pennsylvania has long been a source of computer related courses in its graduate curriculum. With the growth of the undergraduate computer science curriculum, however, several significant problems have developed. In the first place, many of the courses in our graduate program are being overtaken by courses which are now recognized as part of the undergraduate curriculum. As a consequence, we are now faced with a “mixed bag” of backgrounds in our graduate student body, ranging from those with no background in computers at all, much like our earliest graduate students, to those who have had a full undergraduate computer science program and seek further education.