In the graduate schools across the US, the teaching of graduate courses continues to constitute a significant component of graduate education. In general, graduate courses are organized into introductory and advanced levels. The introductory courses are designed primarily to bring the knowledge level of the incoming graduate students from different institutions and disciplines such as mathematics and electrical engineering, to a. common standard that is set by the individual institution concerned. Thus, the nature of such a course is similar to a traditional undergraduate course in that it prescribes a textbook, follows a well defined syllabus, utilizes conventional homeworks and examinations, and resorts to the usual grading mechanisms. In contrast, the primary goal of the advanced graduate courses is to prepare full-time graduate students to undertake highest-quality Ph.D. dissertation research and to impart advanced knowledge to the students coming from industry to enable them to engage in frontier research projects at work. In essence, the objective is to create first-rate, original thinkers of the future. In many universities in the US, including ASU, the quality of the graduate courses, designed and taught by a faculty member, plays a vital role in defining the quality of the graduate program and in promotion and tenure considerations. Since research, by definition, implies unknown knowledge, a priori, and as knowledge in the CSE discipline is continuing to experience rapid advancement, the design of advanced graduate courses and the metrics for assessing them must clearly be different. This paper presents a philosophy that underlies the design of a few advanced graduate courses at ASU in the sub-disciplines of hardware description languages, communications networks, computer-aided design of digital systems, distributed systems, distributed algorithms, and modeling and simulation. From the philosophy, a new metric emerges - the extent and significance of the knowledge "discovered" by the students, towards evaluating the quality of such courses. Discovery refers to the knowledge that is brought out into the open, through logical reasoning from the first principles, by the student for himself/herself. It is significant in that it becomes an integral part of the individual who not only gains invaluable insight and confidence in the subject matter but can improvise, reason, and apply it to other areas in creative ways. The choice of the metric is influenced by the author's experience as a doctoral student at Stanford and as a faculty, first at Brown and currently at ASU, as well as the candid comments and feedback from full-time graduate students and graduate students coming from industry. The paper illustrates the application of the metric through a number of actual cases encountered during teaching at ASU. It also presents a list of the desirable attributes of the underlying educational environment to ensure success in the design and delivery of such courses.