 The next step in our discussion of data science methods is mathematics, and I'm going to give a very brief overview of the math involved in data science. Now, the important thing to remember is that math really forms the foundation of what we're going to do if you go back to the data science Venn diagram. We've got stats up here in the right corner, but really it's math and stats, or quantitative ability in general. But we'll focus on the math part right here. And probably the most important question is how much math is enough to do what you need to do? Or to put it another way, why do you need math at all? Because you've got a computer to do it. Well, I can think of three reasons you don't want to rely on just the computer, but it's helpful to have some sound mathematical understanding. Here they are. Number one, you need to know which procedures to use and why. So you have your question, you have your data, you need to have enough of an understanding to make an informed choice. That's not terribly difficult. Two, you need to know what to do when things don't work right. Sometimes you get impossible results. I know in statistics, you can get a negative adjusted R squared, that's not supposed to happen. And it's good to know the mathematics that go into calculating that so you can understand how something apparently impossible can work. Or you're trying to do a factor analysis or principal component to get a rotation that won't converge. It helps to understand what it is about the algorithm that's happening and why that won't work in that situation. And number three, interestingly, some procedures, some math is easier and quicker to do by hand than by firing up the computer. And I'll show you a couple of examples in later videos where that can be the case. Now, fundamentally, there's a nice sort of analogy here. Math is to data science, as for instance, chemistry is to cooking, kinesiology is to dancing, and grammar is to writing. The idea here is that you can be a wonderful cook without knowing any chemistry. But if you know some chemistry, it's going to help. You can be a wonderful dancer without knowing kinesiology, but it's going to help. And you can probably be a good writer without having an explicit knowledge of grammar, but it's going to make a big difference. The same thing is true of data science, you will do it better if you have some of the foundational information. So the next question is, what kinds of math do you need for data science? Well, there's a few answers to that. Number one is algebra. You need some elementary algebra. That's the basically simple stuff. You can have to do some linear or matrix algebra because that's the foundation of a lot of the calculations. And you can also have systems of linear equations where you're trying to solve several equations all at once. It's a tricky thing to do in theory, but this is one of the things that's actually easier to do by hand sometimes. Now, there's more math. You can get some calculus, you can get some big O, which has to do with the order of a function, which has to do with sort of how fast it works. Probability theory can be important. And then Bayes theorem, which is a way of getting what's called a posterior probability can also be a really helpful tool for answering some fundamental questions in data science. So in sum, a little bit of math can help you make informed choices when planning your analyses. Very significantly, it can help you find the problems and fix them when things aren't going right. It's the ability to look under the hood that makes a difference. And then truthfully, some mathematical procedures like systems of linear equations that can even be done by hand, sometimes faster than you can do with a computer. So you can save yourself some time and some effort and move ahead more quickly towards your goal of insight.