I attended the University of Texas and got my degree in Computer Science there. I graduated in 1999. I had the privelege of taking a class from Dijkstra. The name of it escapes me, but it hardly matters, because it should have been named "Listen To Dijkstra's Views On Everything".
One class he spent the entire time discussing the importance of publicly funded radio stations. Seems he loved classical music, and some local Austin station was publicly funded and having financial difficulties, so he spent that class period talking to us about it.
On another occasion he devoted most of the class period praising brevity. He hated it when people wrote or spoke more than was necessary. Get to the point, say what you need to say, but don't talk just to talk. (As you can see from my writing, I wasn't able to fully integrate that lesson into my life).
Another crusade of his was that counting should begin at zero. Let's say you see a collection of items you wish to count. When you see the first object, you say 0. When you see the second, you say 1. And so on. When you reach the last one, you just add one to the last number you spoke, and that would be the number of items in the collection. He argued this had the advantage that you could count empty collections. That is, if you wanted to count a group that had nothing in it, you would say nothing, then you'd be done. You'd know the next number you would have spoken would have been 0, so that's the number of things in the group.
The closest we got to discussing computers was working on proofs. An example from the class -- suppose you have an 8 by 8 grid. Clearly the area is 64 square units. If you were given 31 pieces of material that were 2 units long and 1 unit wide, could you cover all of the grid other than the upper left and lower right corners? We had to answer and prove our answer. A hint -- it helps if you think of it as a checkerboard, remember that the squares are colored, and remember that any 2x1 pieces will cover one red and one black square.
The goal in these proofs was not to know the right answer. Or even, necessarily, to prove it. The goal was elegance. He firmly believed that there always existed an elegant proof of any assertion. If your proof wasn't elegant, you should find one that was. He hated proofs where you just showed every possible case (as would be possible in the proof I listed, although it would be laborious). He accepted that they were valid, but who cares? They weren't elegant.
The class was not graded in a normal sense. He gave assignments which you had to turn in (such as formally written proofs), but they were not returned with a grade. Your grade in the class was determined by your grade on the final exam. The final exam was a two hour oral exam with him in his office. What did that consist of? Just him talking to you about various propositions, how you would approach proving them, and then maybe trying to prove them right then and there, on his blackboard. I don't think I really knew what it meant to be under pressure until I was standing at a blackboard, thinking about a proof, with Edsger Dijkstra's gaze burning into my back. I managed to get an A in the class, but I had the advantage of having taken a lot of mathematics courses, so I had a good background in proofs. By the way, I do NOT recall a computer being in his office. He did make a point when he was teaching the class that he didn't use computers.
I was truly saddened to hear of Dijkstra's passing. I won't say he taught me more than anyone else ever did, but he was a man who had definite convictions. And he appreciated the beauty and elegance of math, which I respect and relate to. Rest In Peace, Edsger. You are missed.