Say you're hanging a picture from two nails. But, you want to hang it as trickily as possible, so you're looking for a way to hang the picture so that it doesn't fall, but so that if either of the nails falls out, the picture will fall. How do you do it? Or, say you take an empty soda can and twist it so that the top is rotated a full 360 degrees from the bottom. The top is in the same position relative to the bottom that it was originally. Is it possible to get the can back to its original position without rotating the top relative to the bottom? This class will address both of these concerns and more, while drawing many pictures and going through some of the basics of one of mathematics' most beautiful subfields; namely, algebraic topology!

We all know how to draw two-dimensional cubes (more commonly known as squares). Maybe you've also taken to doodling three-dimensional cubes in the margins of your notebooks. So we have two-dimensional and three-dimensional doodles. But what about higher dimensions? How would you go about visualizing, let alone drawing, a seven-dimensional cube, for example? What does that even mean? And what about triangles? Or octahedra? What shapes can you make in higher dimensions? All these questions and more will be answered in this class. We'll discuss what shapes exist in n dimensions, what they look like, and how to go about proving that they're the only ones. Spice up your doodle life!