Computers these days are doing some crazy things: driving cars, speaking English, and even making artwork. We couldn't have taught them all that, of course. They had to figure some of it out for themselves. In this class, we'll take a mathematical perspective to show that the ideas behind these achievements are not very hard to understand. I'll explain the basic ideas of machine learning and dive deeper into some of the algorithms, starting with logistic regression, and (time permitting) build up to neural networks and Google's Deep Dream. I'll try to strike a balance between rigid mathematics, hand-wavy philosophizing, and cool-looking pictures.