 As we begin our discussion of the role of mathematics and data science, we'll, of course, begin with the foundational elements, and in data science, nothing is more foundational than elementary algebra. Now, I'd like to begin this with really just a little bit of history. In case you're not aware, the first book on algebra was written in 820 by Muhammad ibn Musa al-Khwarizmi, and it was called The Compendious Book on Calculation by Completion and Balancing. Actually, it was called this, which if you transliterate that comes out to this. But look at this word right here. That's the algebra, which means restoration. In any case, that's where it comes from. And for our concerns, there are several kinds of algebra that we're going to talk about. There's elementary algebra, there's linear algebra, and there are systems of linear equations. We'll talk about each of those in different videos. But to put it into context, let's take an example here of salaries. Now, this is actually based on real data from a survey of the salary of people employed in data science. And to give a simple version of it, the salary was equal to a constant. That's sort of an average value that everybody started with. And to that you added years and then you added some measure of bargaining skills and how many hours they worked per week. And that gave you a prediction, but because it wasn't exact, there's also some error to throw into it to get to the precise value that each person has. Now, if you want to abbreviate this, you can write it kind of like this, S plus C plus Y plus B plus H plus E. Although it's more common to write it and although it's more common to write it symbolically like this. And let's go through this equation very quickly. The first thing we have is outcome, we call that Y, the variable Y, for person I, I stands for each case in our observations. So here's outcome Y for person I. This letter right here is a Greek beta. And it represents the intercept or the average, that's why it has a zero because we don't multiply it times anything. But right next to it, we have the coefficient for variable one. So beta, which means a coefficient sub one for the first variable. And then we have variable one and then X one means variable one and then the I means it's the score on that variable for person I, whoever we're talking about. Then we do the same thing for variables two and three. And then at the end, we have a little epsilon here with an I for the error term for person I, which says how far off the prediction was from their actual score. Now I'm going to run through some of these procedures and we'll see how they can be applied to data science. But for right now, let's just say this in some first off, algebra is vital to data science. It allows you to combine multiple scores, get a single outcome, do a lot of other manipulations. And really, the calculations are easy for one case at a time, especially when you're doing it by hand.