How many ways are there to write down $$n$$ pairs of correctly nested parentheses? How many rooted planar trees are there with $$n+1$$ vertices? How many ways are there to divide a convex $$n+2$$-gon into triangles? In this course, you'll learn why all of these questions have the same answer: the Catalan numbers $$C_n$$. You'll learn multiple ways to prove the surprising formula $$C_n = \frac{1}{n+1} {2n \choose n}$$ (one of which involves the quadratic formula!). You'll get a glimpse of how deep the rabbit hole goes. (It goes pretty deep.)

What's the product of zero numbers? What's the determinant of a zero-by-zero matrix? What's the degree of the zero polynomial? These may seem like silly questions. I'd like to convince you that they're actually extremely important, and I'd also like to convince you that I have the right answers. If time permits, we'll discuss related questions. There's a lot to say about nothing.