Elliptic curves are easy to define, but lead to a vast amount of interesting math and important applications. In this class we'll talk about elliptic curves over the complex numbers and over finite fields, and in the second case we'll look into how they connect to cryptography.

This class is not actually about clocks, but actually about exploring a different number system that you might have seen under a different name. At some point, you've probably had to compute a remainder after dividing two numbers. This is what we will call clock arithmetic (and for a good reason!). You'll learn about the structure of this number system and some of its many amazing properties!

This class is about topology. We will be focusing on one particularly nice aspect called covering spaces. We will mostly talk about how to classify covering spaces of a given space $$X$$ by defining and understanding how the fundamental group $$\pi_1(X)$$ works.

Draw a shape on your piece of paper, and then draw a curve tightly around it, as close as you can. After you’ve completed the loop, do it again. And again. And again. Does the shape get more circular, and how? We'll answer this and then extend to more topics in geometry, topology, and much, much more! (This is a class based off a paper of the same name.)

Virtually everywhere in math and science, you will encounter the idea of a "linear map" at some point. One reason we care about these so much is that we can solve a lot of otherwise hard problems by making them linear, and linear things are easy to solve. In a lot of settings, linear algebra appears naturally and can be a powerful tool to have at your disposal. In this class we'll learn about linear maps and what linear algebra can tell us about them. We'll learn about linear algebra in a concrete and abstract setting, and also see some ideas from multilinear algebra. Even if you have already seen some linear algebra, this class should still be interesting for you.