Come ask all the math questions you've been dying to have answered to a panel of MIT math majors! We'll answer anything from conceptual questions (what are Lagrange multipliers?) to computational questions (how do I compute this integral?) to philosophical questions (what is math?)! We'll have teachers studying all areas of math, so hopefully we can answer any (reasonable) questions you throw at us.

Here are three questions that look like they're pretty similar. (1) I have exactly two children. One of them is a boy. What's the probability that I have two boys? (2) I have exactly two children. John is a boy. What's the probability that I have two boys? (3) I have exactly two children. One of them is a boy born on Tuesday. What's the probability that I have two boys? The answers: 1/3, 1/2, and, you guessed it, 7/27. Huh? Another problem - I give you a circle, with an equilateral triangle inscribed. Then, you choose a random chord in the circle. What's the probability that the length of the chord is longer than the side length of the triangle? Seems pretty innocuous, but as is turns out, this problem isn't well-formed enough to admit a correct answer. Why not? In this class we'll investigate these questions and some other seemingly paradoxical problems in probability.

You may have learned to multiply matrices at some point. Adding matrices of the same size is pretty straightforward (as is subtracting), but let's face it: multiplication is pretty weird. Where does it come from? Why does it make sense? Take this class to find out what matrix multiplication is all about and why it really does make sense. And what it has to do with the formula $$\sin(a+b)=\sin(a)\cos(b)+\cos(a)\sin(b)$$.

Johann Sebastian Bach. Jo-ho-ho-ho-ho-hann. Se-he-bastian Bach. Jo-ho-hann Seba-ha-ha-ha-ha-ha-hastian Bach. Let us Ba(s)ch in his glory.

You and your 14 of your prisoner friends are being given a chance to be freed. Each of you is randomly given either a red or a black hat to wear, which you can't see, but everyone else can. At the count of three, each person must simultaneously guess the color of his or her hat, or pass. If at least one person guesses correctly and no one guesses incorrectly, everyone is freed; otherwise, you are all sent back to your cells for a lifetime of misery. It turns out, it's (probably) your lucky day: you and your friends can win this game with probability $$15/16$$! In this class we'll learn how, and learn a bit about error-correction in computer science along the way.

Do you dream of picking up big ladies in the blind? Do you dare to pick on red death? Do you have nightmares schmearing to the partner, only to find yourself failing to make schneider, or even worse, getting schwartzed? Come play Schafkopf, a German trick-tacking card game of epic proportions — and even more epic words. We pity the mauers

You can do a lot of things with compass and straightedge. So many things, in fact, that Euclid wrote a whole series of books about things you can do with compass and straightedge. Yet, there were a few things he wanted to do, but they just seemed to hard. So hard, in fact, that many centuries later, using techniques of modern algebra, it was proven that they were impossible. Specifically, you've probably heard that it's impossible to trisect an arbitrary angle using compass and straightedge. You may also have heard that it's also impossible to square the circle, or to double the cube. While these facts are relatively easy to digest, and our set-up seems simple (all we're doing, after all, is drawing lines and circles), it turns out that getting a handle on \textit{why} these tasks are impossible is very hard. In this class, we'll define a field, an abstraction notion of a set in which we can add, subtract, multiply, and divide (except by zero!) to our heart's content, and think about field extensions, what arise after we throw in extra elements and somehow get a bigger field. Then, we'll be able to relate our new notions of abstract algebra back to our original geometric problem, and eventually be able to prove that, no matter how hard he tried, Euclid just couldn't have done certain things with a compass and straightedge.

The Sylow Theorems are a set of three important theorems in finite group theory that describe a certain class of subgroups of finite groups. I will state and, using the magic of group actions, prove these theorems, and if there's time, we'll look at examples of how the Sylow Theorems are used in understanding certain finite groups.

Do you dream of picking up big ladies in the blind? Do you dare to pick on red death? Do you have nightmares schmearing to the partner, only to find yourself failing to make schneider, or even worse, getting schwartzed? Come play Schafkopf, a German trick-tacking card game of epic proportions -- and even more epic words. We pity the mauers.