Linear Algebra

3 Credits · Level: Undergraduate

We often think of a space as a collection of points. But strictly speaking, points are one dimensional, and they can't be added together. Points occupy a location, but they take up no space, so they can't be scaled bigger or smaller, and they can't be added together (putting two points in the same spot doesn't make a bigger point). But here's a thought experiment. What if the "points" of a space were things that could be scaled up and down, and added together? Amazingly, these strange sorts of spaces do exist, and they pop up incredibly often, in many different disciplines ranging from economics, to physics, to artificial intelligence. Mathematicians call these kinds of spaces "vector spaces," and linear algebra is the branch of mathematics that studies them. In this course, we introduce ourselves to the basic concepts and techniques of modern linear algebra. No prior mathematical training is required. Our perspective will be that of the curious philosopher: we will aim to understand why these ideas work the way they do. To help make our quest more concrete, we will learn about game theory as we go, and we will utilize linear algebra to learn efficient ways to analyze strategies that would otherwise be too complex to understand.