I still remember the initial thrill of realizing that — contrary to what classes in school may lead you to think — math is not about mindlessly memorizing equations and moving around numbers. Instead, it's chock full of interesting, weird, confusing ideas, some of which I hope to share with you in this class. We'll aim for breadth over depth, bouncing to a new topic each week and covering approximately what would be taught in the first day of an introductory class on {number theory, combinatorics, set theory, proof writing, etc.}. In particular, we'll examine the following questions: What's so interesting about numbers? How do we count things that are not numbers? Are there things we can't count? Is any of this true? (Caveat: specific topics may change depending on time and interest.)

In this class, we'll learn about the fascinating world of vector spaces via a little something mathematicians like to call "linear algebra." We'll play around with matrices, dabble in some real world applications, and also prove a few theorems along the way.

The First Amendment of the U.S. Constitution prohibits, among other things, laws "abridging the freedom of speech." This right manifests itself in some pretty wonderful ways (we can publicly criticize our leaders, for example), but where do we draw the line? Should hate speech be protected? Or obscenity? Have you ever heard the phrase, "fire in a crowded theater"? ...Besides, what is speech, anyway? Does flag burning count? Does money? We will explore and discuss this issue by examining a series of Supreme Court cases, both historic and recent, and determine where we stand on what is free speech, and what isn't.