 Alright, let's talk a little bit about learning in an online environment. So if I wanted to learn how to skydive, here's the traditional method that we would do this. We might sign up and pay for a few classes. We'd go to class, sit through a few lectures, maybe do some reading, practice some of our skills with an instructor in the class, and at some point they decide we're ready so we get in a plane and jump out. And the advantage to this method of learning how to skydive is there's someone there to make sure that you're ready. On the other hand, because the class is run by an instructor, it goes at the pace that the instructor sets. You can't pause, rewind, or replay. And if you don't feel like going to class, the class is at a particular time and a particular place. Which means that if you decide to say, oh, I don't know, three o'clock in the morning that you really want to learn something, you have to wait until class starts. The internet's come along and made some possibilities for education, so we could learn to skydive on the internet. We can watch a few YouTube videos. We can buy a parachute through Amazon, then go on Craigslist and hire a pilot and a plane, and have them take us up and get in the plane and jump out. And the nice thing about this is that because we're watching the YouTube videos, we can watch those whenever we have a couple of minutes, and so we can work the class at our own pace. On the other hand, there's nobody there who's helping us along the way, and at some point we have to step out of the plane. So the natural question is, can we do something that'll combine the best of both worlds? Well, let's take a look at that. We might watch some YouTube videos because these are kind of nice. They're permanent. They are online. We can watch them anytime, anywhere, any place, under any circumstances. And if you only have five minutes, you can watch five minutes. But then it's also nice being able to go to class and have somebody who knows what's going on to work you through the process of what you're doing. And again, no matter how you do it, at some point you have to get in the plane and jump out. And so the advantages to these, again the videos, you can watch them anytime, anywhere, any place, anytime you have a couple of minutes. And the videos are also useful because you can pause, rewind, and re-watch any of these videos. And then when you're in class, there's somebody there to help you out to make sure that you're heading in the right direction. Now this is all good. There is one important disadvantage. You have to be prepared for the class. You have to watch the videos beforehand because otherwise you don't get any of the benefits from being able to work anytime, anywhere, from being able to pause, rewind, and re-watch, and having someone there to help you in class because you're spending class time trying to figure out what you should have seen, what you should have seen again. So just a quick note, here's how to watch an instructional video. Technology allows us to do things we've never done before, but it's at the cost of requiring us to do things we've never done before. A good lecture runs at the pace that you learn the material at. However, if there's more than one person in the audience, the lecture in general will run a little bit too quickly for others because some speakers tend to talk quickly and some people tend to process information a little bit more slowly. On the other hand, you'll also have lecturers who slowly talk their way through points, and perhaps for some people this rate will be too slow for them. What I think about technology is it allows you to run the lecture at your pace using the pause and rewind buttons. These are two of the three most important buttons on your video controller. These two buttons are especially important in mathematics because there may be many unstated steps between one mathematical statement, for example solve x squared minus 8x equals 10, and the next step in the problem. Here's the solution. And in a real-time class, the instructor may write down something like this and then immediately go to what that next step is going to be. And at best, they might pause and say, don't forget, here's how you obtained it. You use the quadratic formula and then they'll proceed on to the next thing. Now, if you're watching a video and that happens, if you don't see how to go from this line to the next, hit pause and think about where that is coming from. Have you hit pause yet? If you've hit pause and actually thought about what it is, you might look up and remember what the quadratic formula is and remember that if you have an equation like that, well there's a bunch of steps we can fill in. We have to put the equation in standard form, apply the quadratic formula and that's where that comes from. And potentially this may require going offline or searching for other sources. You might look for course notes from previous classes you've taken or YouTube is pretty good about recommending suggested videos whenever you're watching something, and maybe you follow that and it'll tell you how to apply the quadratic formula to equations like that. The important thing is that you need to take those pauses to fill in whatever gaps that there may be. A good rule of thumb is that if you're watching a video and you don't hit pause at least 10 times during the course of the video, it's either a very, very simple video or you're missing something very important. The third thing that you should always be doing with any instructional videos is, in addition to using pause and rewind, you also want to replay it several times to make sure that you really understand what's going on. And on those rare occasions when you are in a place that doesn't have internet service, the other possibilities, you can also download the video so you can watch them when you don't have internet connectivity. This is particularly useful if you want to do a little bit of studying on the subway into school, for example, where you don't have internet underground, but you still have your iPod or video player. Legal disclaimer, this is ordinarily illegal. You cannot freely download something. However, in this case, for the educational videos for this course, I'm the producer and copyright holder, so you have permission to download and distribute the course videos for non-commercial use, as long as you maintain the attribution. That's the title page.