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Suppose you get a text message. Your friend tells you to go to Lobby 7 at MIT to find the gift they left you 7 meters from the center of the lobby. Is that enough information to find the gift right away? As you can see, there are many locations 7 meters from the center of the room. Don't forget that we live in 3 dimensions, so there are actually even more points 7 meters away from the center of the room. Fortunately, in this problem, you can ignore most of them since we don't expect our gift to be hanging in mid air. Distance alone wasn't enough information. It would have been helpful to have both the distance and the direction. This video is part of the Representations video series. Information can be represented in words, through mathematical symbols, graphically, or in 3-D models. Representations are used to develop a deeper and more flexible understanding of objects, systems, and processes. Hi, my name is Dan Hastings and I am Dean of Undergraduate Educati...

SRINI DEVADAS: Let's get started. So today, we're going to look at one of my favorite puzzles. I'll say right at the beginning, that the coding associated with the puzzle is fairly straightforward. But the analysis associated with this puzzle is quite intricate. And in particular, we're going to have to do worst-case analysis, which is really a good thing for you to learn about, because asymptotic analysis in algorithms is all about worst case. All right. So keep that in mind. When you try to come up with the answers to my questions, always keep in mind that I'm going to be asking for what happens in the worst case. In the context of our puzzle-- which is called the crystal ball puzzle, and it's fairly popular in literature, though I've generalized it a little bit-- you have a situation where you're supposed to figure out the hardness coefficient of a crystal ball. And in the generalized version, you have a set of identical crystal balls. S...

PROFESSOR: OK. Before we get started, I'd like to deal with a small matter of some unpleasantness. The class is sort of like a football game. When there's two minutes to go, you shoot off a pistol. But when there are two meetings to go until we have the quiz, we shoot off a pistol to wake you up. We're scheduled to have a quiz on October 6. And even though October seems far away when you're still in September, that is going to be a week from this coming Thursday. So if you have problems that you're working on, try to get them to me on Thursday, or just come slide them under my office door, if I'm not in. And I'll have them back for you on this coming Tuesday. The way the material has played out is that we're really at a nice, convenient juncture between one chunk of interconnected material moving on to another. So I think the first quiz we'll confine to two-dimensional symmetry. And beginning in about two minutes flat, we'll begin t...

PROFESSOR: Why don't we get started. Good afternoon-- to stretch the literal meaning of the word considerably. What a miserable day out there. I get to and from the boonies via the commuter rail. And this morning, we sat there for an hour part way in because a tree had fallen across the railroad track. I don't know who went out to do it, but somebody had to get a saw and saw the tree up and take it off the tracks before we could proceed into Boston. Even with that, I was sort of reluctant to get off the train. I saw how it was pouring outside. So I am highly flattered that you decided to trudge through the puddles and show up this afternoon. All right, this is a momentous occasion because we are exactly at this point, halfway through the term. And this is when we are about to change gears from our discussion of symmetry theory and switch over to physical properties of crystals and the way in which symmetry impacts on those properties. What I wanted to do primarily...