Now, we take the three gallon jug, fill it a third of the way up. Now we pour that three gallons into the five gallon jugs, giving us exactly 3 gallons in the five gallon jug, right? We fill the three gallon jug exactly to the top, right? Obviously, we can't fill the three gallon jug will four gallons of water, right?
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If you're still alive in five minutes, we'll speak again. One ounce or lower less will result in demolition. Fill on of the jugs with exactly four gallons of water and place it on the scale, and the timer will stop. Do you see them? A give gallon, and a three gallon. It has a proximity circuit, so please don't run. Simon said you're supposed to be helping with this. To save New York City in the Die Hard number 3, I believe. So number theory is something, you'll be very surprised, that can be used to save- oops. And number theory actually will help us with this. So this art of hiding information is extremely important, especially nowadays. We do not want others who are not allowed to see my private information to see it. Do we really want that? We actually want to hide our information. We have like medical data that we need to store outside in the cloud. So you can imagine how important that is. Now cryptography is the study and practice of hiding numbers. But we'll be talking about one of them to show you how useful this actually is. There are many application in cryptography. And at the end of the second lecture, we will be talking about this application into cryptography. So number theory got used actually in cryptography only about 40 years ago. So number theory got- Oh, there's some more over here. And what are the integers? Well, these are the numbers 0, 1, 2 3, and so on. So what this number theory- it's actually the study of the integers. And only recently it actually got to have some more practical applications. One of the oldest mathematical disciplines. Well, first of all, it's a very old science. But we will use the same concepts as you have learned before, like induction, and invariance, stuff like that, to prove whole theorems. And this is a really different way of thinking, actually.
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So today we're going to talk about number theory. And we will be using these throughout the lecture. Please raise you hand if you don't have any, then one of us can actually come over and hand you out this sheet, which contain some facts about the visibility. Actually, before I forget, there are some handouts at the very back. We are going to talk about number theory. To make a donation, or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. The following content is provided under a Creative Commons license.