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PROFESSOR: This idea of social practice is one that a lot of theorists and critics have talked about and tried to frame. I think of social practice as an engagement in art-making within a more recent contemporary moment, although there are historical antecedents perhaps many decades prior to now. We might think, in, relatively speaking, last 30 to 50 years, some of these pieces start to come together. But one person who I've looked at to help theorize this notion of social practice is educator and artist Pablo Helguera. Helguera says-- unlike social work that aims for betterment of humanity, defending human dignity, and strengthening human relationships, a socially engaged artist may subscribe to those same values but make work that ironizes, problematizes, and even enhances the tensions around those subjects in order to provoke reflection. So it's that end part of the phrase-- to provoke reflection-- that I bring into the classroom or that I try to center some of...

PROFESSOR: An elementary idea that gets you a long way in counting things is this idea of counting with bijections, which is counting one thing by counting another. And we can illustrate that by example. Let's begin with looking at some stuff that is easy to count using just the simple sum and product rules. So suppose that I'm trying to count passwords. This is a contrived, over-simplified example, but it gives you the idea. And this is what I mean by a password. A password is a sequence of characters that are either letters or digits subject to the constraints that they are supposed to be between six and eight characters long. They're supposed to start with a letter, and they're case sensitive. So you can tell the difference between uppercase and lowercase letters. So let's define the set L of all the letters-- uppercase and lowercase together. And let D be the set of digits from 0 through 9. Then we said that passwords are supposed to be between six...

So the idea is that if English is more of a creole than Haitian creole, then why is the term creole to only creole languages, right? That's a very valid question. And nowadays in Haiti and also in Mauritius-- I don't know whether you're aware of this debate in Mauritius. People ask, why do we call Mauritian creole, the creole? Why don't we just call it Mauritian? Why don't want we just call Haitian Creole Haitian? And so, as a linguist, might take, when I'm being asked that question is that-- well, the people who speak the language, most of them call it Creole. So who am I, as a linguist, to say, no, you won't call it Haitian. You see, because we have a basic principle in linguistics, at least in when you consider the sense of linguistics, it's supposed to be descriptive, not supposed to prescribe-- to tell people, no, this is what you say. You're supposed to report what we say. And I have a little anecdote when it comes to-- because pe...

PROFESSOR: The idea of congruence was introduced to the world by Gauss in the early 18th century. You've heard of him before, I think. He's responsible for some work on magnetism also. And it turns out that this idea, after several centuries, remains an active field of application and research. And in particular, in computer science it's used significantly in crypto, which is what we're going to be leading up to now in this unit. It's plays a role in hashing, which is a key method for managing data in memory. But we are not going to go into that application. Anyway, the definition of congruence is real simple. Congruence is a relation between two numbers, a and b. It's determined by another parameter n, where n is considered to be greater than one. All of these, as usual, are integers. And the definition is simply that a is congruent to b mod n if n divides a minus b or a minus b is a multiple of n. So that's a key definition to remember. There...