Suppose I give you a set of elements and some operation, and I tell you six very basic facts about this set. Can you tell me what the set is? With a topic as well-studied and foundational as group theory, the simplest of facts can develop into some incredibly powerful results. Group theory is one of the most central studies in math; in fact, most everything you've dealt in with math belongs to a group. The integers form a group; so are the symmetries of a square. Because of its ubiquity, group theory both generalizes our already familiar knowledge and provides various tools to tackle problems in other areas of math, some of which we'll see near the end of the class. This class will hopefully make large parts of basic group theory much more accessible to facilitate future, more advanced studies!

and why Frozen was so immensely popular. You'll never see Disney the same way after this class.

A brief guide to some famous paradoxes, and why they might actually become relevant in our real world soon.

Come play high school Science Bowl and try to win for bragging rights and learn some awesome things about science! Know lots of science trivia, love hitting buzzers, or just want to try to answer questions ridiculously fast? This is the walk-in for you! You do not need to have familiarity/experience with this game to participate!

Come play Mastermind, but with words!

we have icebreakers that aren't corny and team-building exercises that don't suck. authentic relating games is the fancy phrase, but we just like to think of it as games. stare into each others eyes! talk about your feelings! experience deeper connections! play some games with us and get to know your classmates.

There is a Polish village that hasn't had a male baby in nearly 10 years. Okay sure, they've only had 12 babies total in the past decade ... but still, doesn't something seem off? Is this some biological anomaly? Does Poland just have weird environmental factors? Using probability, we'll explain why this Polish village, as well as other weird phenomena, is not so abnormal after all. Come for a good time!

In less than an hour, we will try to convey to you that classical music is important, you should listen to classical music, and classical music is for you, if you are willing enough to open your heart and embrace it. Come join us to understand what the "universal language" is all about.

There are infinitely many primes of the form $$4k+3$$. There exists irrational numbers $$x$$ and $$y$$ such that $$x^y$$ is rational. What do these statements have in common? Nothing much, besides they're 1) both related to math, and 2) they're both true. We'll be proving statements like these, and much more, in one cute, chaotic hour!

Lambda calculus: it's like "calculus" - except with more programming, and no calculus! You can think of it as a super low-level functional programming language; all data is composed of functions (written with the letter λ), and by combining functions in various clever ways, we can actually perform any computation. Learn about Alonzo Church's famous invention that rocked the foundations of computer science, and try your hand at solving programming puzzles in the language itself!

"Oh, crypto? I know a lot about bitcoin!" You've heard about crypto everywhere in the news, but behind all the bait, there's actually some very beautiful, clever mathematics that goes into engineering the systems that keep our world running securely. We'll start with a brief discussion of classical cryptography (2000 BC-1950 AD), where we talk about various ciphers and puzzle about how to crack them. In the second half, we'll talk about the modern model of cryptographic systems in the computer era, including secure hash functions and pseudorandom number generators, and we'll culminate in a discussion of the RSA cryptosystem.