Welcome to this second course in this specialization on math for machine learning and data science. In this second course, you learn about calculus. So derivatives, what does that mean? How does it work? How is this used in machine learning? And you also learn about some advanced techniques like Newton's method. I'm thrilled that once again, we have as our instructor for this course, Luis Serrano. Thank you very much. Yes, I'm very excited about this course. Machine learning is a lot of minimizing and maximizing functions. And that's the main application of this course. And for that, we use derivatives. In fact, almost everything we do in machine learning. So the large fraction of what we do in machine learning is create a cost function and then minimize it. And that's calculus. Exactly. When you want to train a machine learning model, you calculate how bad it is with the error and try to minimize that. And so for that, we use derivatives, we use gradients, and we teach a lot of techniques. So often those few lines of code implementing gradient descent or some other algorithm, that is actually using calculus that someone had derived a derivative and then implementing that in code. So understanding that seems central to having good intuitions about how the algorithms are doing. Absolutely. Yeah. If you want to understand how these optimizers work, that they normally look at black box, if you want to understand them, it's good to know the calculus behind. And at the end of the day, you're just doing something step by step, because gradient descent is just taking small steps to get lower and lower and lower values. And in what direction do you take that step? Well, the gradient tells you exactly the direction. So one thing that sometimes seems mysterious to people learning this for the first time is when you think about derivatives in one dimension or two dimensions, that's like the slope. But in machine learning, we often take derivatives in very, very high dimensions, like 10,000 or a million dimensional space is really hard to visualize. So in this course, you also give people intuitions about what's going on in these very high dimensional spaces. And when you do calculus in these very high dimensional spaces. Absolutely. So just like you saw in course one, data can be very high dimensional. And when you talk about the derivative, it could be in many directions. And these are captured by long vectors and long matrices. So we even go for like second derivative. A second derivative would tell you what the curvature of the space is based on the matrix that comes out of the second derivative. And the derivative of the derivative, that also leads into the Newton's method. Yeah, Newton's method is a really cool method to minimize functions. So gradient descent actually works well. But many times gradient descent could take hundreds of steps, and Newton's method could take just a few steps to get the same results. Yeah, doesn't work for all applications. You have many ones with not too many parameters, but when it works, it can be blazingly fast. Yes. And the idea is for you to have a toolkit of different techniques. And if this one works, that's fantastic. But if not, you try this one or that one or that one. And that's how we do it in machine learning, right? And in fact, in terms of toolkits, one of the cool things about this specialization is also all the notebooks, all the labs. Absolutely. So just like in the previous course, you'll be able to have a lot of code labs where you can see this concept working in real time. So in this course, you learn the concepts, run code labs, and hopefully even come away with code snippets that you can use in your own projects. So I'm excited to have you dive into this second course and start learning these important concepts of calculus. So with that, please go on to the next video.