 Welcome to Mathematics and Data Science. I'm Barton Polson, and we're going to talk about how mathematics matters for data science. Now, you may be saying to yourself, why math? And computers can do it. I don't need to do it. And really fundamentally, I don't need math. I'm just here to do my work. Well, I'm here to tell you, no, you need math. That is, if you want to be a data scientist, and I assume that you do. So we're going to talk about some of the basic elements of mathematics really at a conceptual level and how they apply to data science. There are a few ways that math really matters to data science. Number one, it allows you to know which procedures to use and why so you can answer your questions in a way that's the most informative and most useful. Two, if you have a good understanding of math, then you know what to do when things don't work right, that you get impossible values or things won't compute. And that makes a huge difference. And then three, an interesting thing is that some mathematical procedures are easier and quicker to do by hand than by actually firing up the computer. And so for all three of these reasons, it's helpful to have at least a grounding in mathematics, if you're going to do work in data science. Now, probably the most important thing to start with is algebra. And there are three kinds of algebra that we want to mention. The first is elementary algebra, that's the regular x plus y. Then there's linear or matrix algebra, which looks more complex, but is conceptually simple and is used by computers to actually do the calculations. And then finally, I'm going to mention systems of linear equations where you have multiple equations simultaneously that you're trying to solve. Now there's more math than just algebra, a few other things that I'm going to cover in this course, a little bit of calculus, a little bit of big O or order, which has to do with the speed or the complexity of operations, a little bit of probability theory, and a little bit of Bayes or Bayes theorem, which is used for getting posterior probabilities and changes the way that you interpret the results of an analysis. And for the purposes of this course, I'm going to demonstrate the procedures by hand. Of course, you would use software to do this in the real world. But we're dealing with simple problems at conceptual levels. And really the most important thing to remember is, even though a lot of people get put off by math, really, you can do it. And so in some, let's say these three things about math, first off, you do need some math to do good data science, it helps you diagnose problems, it helps you choose the right procedures. And interestingly, you can do a lot of it by hand or you can use software computers to do the calculations as well.