Open course ware

PROFESSOR: OK. Here's an example that's more or less for fun. Because you'll see me try to do it. You can do it better. I call the problem the tumbling blocks. Only in this example, in my demonstration, it's going to be a tumbling book. I'm going to take a book, the sacred book, and throw it in the air. And I'll throw it three different ways. And the question is, is the spinning book stable or not? And let me tell you the three ways and then give you the three equations that came from Euler. So those are the three equations. You see that they're not linear. And those are for the angular momentum. So there's a little physics behind the equations. But for us, those are the three equations. So the first throw will spin around the very short axis, just the thickness of the book, maybe an inch. So when I toss that, as I'll do now, you will see if I can toss it not too nervously I hope. It came-- it was stable. The book came back to me withou...

Let's consider another example of continuous mass transfer. Suppose we have a truck, and that truck has some type of plow. And it's plowing snow. And there's some type of external force acting on this truck, friction, pushing the truck forward, so let's just assume we have some type of force, F, on the truck. And this is our snow. And what's happening in this problem is that the truck connects-- picks up the snow. And then, which is at rest initially, gets the snow up to the speed of the truck. And then the snow falls off the plow. So how do we model this problem? Well, let's look at our situation at time t. And what we're going to do is, we're going to consider a certain mass of snow, delta ms, that's at rest. And our truck, it's a fixed mass truck, is moving with a velocity vt at time t, the truck. So now, what happens at time t plus delta t? Well, the truck has picked up the mass of the snow. And the truck has now changed its spe...

PROFESSOR: So in this example, we want to hit an apple hanging from a tree with a projectile. And the main point of the problem is to figure out at what angle to the ground should we aim our projectile when we fire it off in order to hit the apple. And in this example, we're assuming that the apple drops from the tree at the same instant that we fire the projectile. So in this drawing, let's just put some dimensions in here, we'll assume that the apple starts out at a height, h, above the ground. That the horizontal distance from where the projectile starts to the apple is a distance, d. That the projectile starts at a distance, s, above the ground. And that we fire the projectile off with an initial velocity, v0, at an angle theta, sorry, theta not, with respect to the horizontal. And let's define our origin to be right here on the ground, directly below where the projectile begins. We need to define our coordinate system, so the i-hat direction will be h...

PROFESSOR: The example of scheduling courses in terms is really a special case of a general problem that you can probably see of scheduling a bunch of tasks or jobs under constraints of which ones have to be done before other ones, which is a topic that comes up actually in lots of applications. But you can see applications in computer science where you might have a complex calculation, pieces of which could be done in parallel and other parts had to be done in order because later results depended on the results of an earlier computation. It leads us to the general discussion of parallel scheduling. And we've already worked out some theory of that really just from the example. Namely, if we look at the minimum number of terms to graduate, this corresponds to the minimum amount of number of stages or the minimum amount of time that it takes to process a bunch of tasks, assuming that you can do tasks in parallel and as many in parallel as you need to-- that there's ...

Our first example today is a story of IBM Watson. IBM research, a distinguished industrial laboratory, strives to push the limits of science. In the mid-1990s it created Deep Blue, a computer that beat Garry Kasparov, the world champion in Chess at the time, showing to the world that machines can beat humans in tasks that people thought were restricted to human intelligence. In the 1990s-- in the late 1990s-- it created Blue Gene, a computer to map the human genome. In 2005 IBM decided to create a computer that would compete at Jeopardy, a popular game show. From the T.J. Watson Research Center in Yorktown Heights, New York, this is Jeopardy-- The IBM Challenge. Please welcome back our contestants. He has never been defeated. And his winnings of more than $3.2 million make him Jeopardy's all time biggest money winner. From Los Angeles, California, here's Brad Rutter. An IBM computer system able to rapidly understand and analyze natural language, including puns, ri...