What was our original problem that we started working with?

Look at this closely and notice that that is the same hopefully it's the same as our original problem.

NP hard and therefore a polynomial time solution for that problem solves everything in NP.

leading coefficients greater than one.

We can go from that cube to that cube.

And once we had the answer to that, we need to multiply that by 2 to get the answer to the original problem.

OK.

We basically have solved problem Y by bringing to to bear our solution to problem X, or to say it another way, problem Y has been reduced to problem X.

Family problems. She said so in her letter.

Where do we stand today in the field of computer vision in 2012? If you consider the area of recognition.

And we set the parameter theta zero to be only zero. In the next video.

Hometown security means creating wealth here at home, instead of destroying it overseas.

Well, it's going to give us what a minus 1 times b is, which is a times b minus b.

Catalan and Spanish.

So we just add the b back in and we should be done.

This problem is too much for me to handle.

This problem is a real challenge.

This problem baffles me.

12 7 is 5.

I understand there were some very strong objections to the lady.

I got a problem here.

I can't solve this problem.

Oh, we're doing fine. Yeah, we're doing great. Two little peas in a pod.

And that's choice B.

With that said, let me erase that and go back to our original problem.

When they're out of education, they do it on a computer.

So the inequality stays the same as in our original problem.

So it's choice B.

Listen, we've got a problem, a DEA problem.

Even though moving one over here and one over there would give a better solution.

So there were six ways to get to this cube right there, from that one.

The problem is beyond my power.

These problems are beyond me.

You're damn right. You're right in the middle.

And the answer is yes and no it's deeper than all of that.

We actually never even have to evaluate this integral.

Or do I have something wrong with the equipment?

That was a fine thing you did for Parker.

My next question pertains to the tracking problem that we talked about in class.

We can't get anybody to come.

that's a pretty big commitment. not if the mob has their way.

Hey, you know, if you have a problem, maybe I can help.

That bad spirit made biggest trouble of all.

So what did we do here?

But yes, it's also true that the Internet has problems, very serious problems, problems with security and problems with privacy.