You've probably solved a few pencil-and-paper logic puzzles like Sudoku, Slitherlink, Yajilin, etc. But did you know there's a lot of math hiding in these? We'll go over the rules of several puzzle types, and talk about some theorems related to them. These theorems provide tools to solve the puzzles, and let you solve puzzles which otherwise seem impossible. We'll pass out lots of puzzles for you to try, of a range of difficulty, including some to test your understanding of the theorems we discuss.

Learn how to play Hackenbush, a simple game that leads to interesting mathematics. After getting some practice playing, we'll see how the game inspires the surreal numbers, a system of numbers that allows us to to play with infinity in an unusual way.

What is information? How can we measure it? In this class, we'll introduce a way of quantitatively measuring information and use the tools we develop to discuss how redundant the English language is. We'll also see how to play Wordle strategically using information theory.

You've probably solved a few pencil-and-paper logic puzzles like Sudoku, Slitherlink, Yajilin, etc. But did you know there's a lot of math hiding in these? We'll go over the rules of several puzzle types, and talk about some theorems related to them. These theorems provide tools to solve the puzzles, and let you solve puzzles which otherwise seem impossible. We'll have a long list of puzzles for you to try, of a range of difficulty, including some to test your understanding of the theorems we discuss. Each week, we'll concentrate on one or two types of puzzles and corresponding mathematical techniques.

How does a quantum computer work and what does an algorithm for one look like? In this class, we'll talk about the fundamentals of quantum computing with the help of IBM's online circuit composer, which will allow you to build your own quantum circuits and see what they do!

Imagine you meet aliens with a different system of math, which doesn't use numbers or arithmetic in the ways we're used to. How could you explain numbers or arithmetic to them? How would you convince them of basic properties like x+y=y+x? In this class, we'll see one way to do this. Starting without any concept of numbers, we'll see how to successively build natural numbers, integers, rational numbers, and real numbers. For each type of number, we'll define addition and multiplication, and see how to prove some of the familiar properties they have.

You've probably solved pencil-and-paper logic puzzles like Sudoku, Slitherlink, Yajilin, and many others. But did you know there's a lot of math hiding in these? We'll go over the rules of several puzzle types, and talk about some theorems related to them. These theorems provide tools to solve the puzzles, and let you solve puzzles which otherwise seem impossible. We'll have a long list of puzzles for you to try, of a range of difficulty, including some to test your understanding of the theorems we discuss.

If you’ve ever been in a math class, you’ve probably seen the natural numbers - in fact, you’ve probably known about them since you were young. As you progressed, you discovered that there are many more numbers - the integers, the rational numbers, the real numbers, and the complex numbers. But can we go further? In this class, we'll learn about the Cayley-Dickson construction, a procedure that lets us builds new, weirder numbers from ones we already know. After reviewing the complex numbers, we'll construct and study the properties of the quaternions and see how they can be used to talk about geometry in 3D space and prove a cool theorem in number theory. We'll also go even further to build more obscure numbers with even weirder behavior!

If you count all the way to infinity, and then keep counting some more, you meet the beginning of an unfathomably large structure called the ordinal numbers. In this class, we'll get to know the ordinal numbers, and see ways they're useful even for solving finite problems.

What is information? How can we measure it? In this class, we'll introduce a way of quantitatively measuring information and use the tools we develop to discuss how redundant the English language is.

Come explore space and time with a relativity-based online game, and see how the main ideas of special relativity can be derived from simple principles and some basic algebra! We'll also talk about relativity "paradoxes" and how to resolve them.

A cellular automaton is a grid of cells that changes according to simple rules, but can have complicated behavior. The most famous one is Conway's Game of Life. We'll discuss 1- and 2- dimensional automata, look at cool patterns they can produce, and see just how powerful they can be.

How can we talk about what computers can do mathematically? In this class, we'll talk about models of computation that attempt to capture the idea of algorithms, ranging from simple models to models that capture anything your favorite programming language can do. Using what we learn, we'll show that there are some things that you can't program, no matter how clever you are! Along the way, you'll get to play with models of computations by solving puzzles and designing algorithms.

This class will feel like solving a sequence of open-ended puzzles. You'll work with other students to solve these puzzles, and sometimes give mathematical arguments as to why they can't be solved. Imagine you're in a maze, but tunnels open and close based on your movement. For example, maybe there are two tunnels which can only be passed in one direction, and when you go across either one they both flip direction (we call this a "2-toggle"). Or maybe every time you go across a certain tunnel in either direction, another tunnel switches between open and closed (we call this "tripwire lock"). It's possible to put together several 2-toggles to construct something which behaves like a tripwire lock. It's also possible to use several tripwire locks to build a 2-toggle. In this class, we'll investigate which "gadgets" can simulate other gadgets. We'll play with lots of gadgets, including the 2-toggle and tripwire lock, and see what they can build. In some cases, we'll prove that certain gadgets can't simulate certain other gadgets. We might even find general-purpose simulations, showing that a particular gadget can simulate every possible gadget (or every gadget with some property). This will be a hands-on class, mostly focusing on you finding simulations for yourselves.

How many people do you need to put in a room to make sure four of them are either all friends or all strangers? Why does anyone care about numbers like Graham's Number, which way are too big to have any physical relevance? Ramsey theory is the study of how particular structures always emerge in sufficiently large clusters of randomness. Learn the answers to these questions and more!

This class will feel like solving a sequence of open-ended puzzles. You'll work with other students to solve these puzzles, and sometimes give mathematical arguments as to why they can't be solved. Imagine you're in a maze, but tunnels open and close based on your movement. For example, maybe there are two tunnels which can only be passed in one direction, and when you go across either one they both flip direction (we call this a "2-toggle"). Or maybe every time you go across a certain tunnel in either direction, another tunnel switches between open and closed (we call this "tripwire lock"). It's possible to put together several 2-toggles to construct something which behaves like a tripwire lock. It's also possible to use several tripwire locks to build a 2-toggle. In this class, we'll investigate which "gadgets" can simulate other gadgets. We'll play with lots of gadgets, including the 2-toggle and tripwire lock, and see what they can build. In some cases, we'll prove that certain gadgets can't simulate certain other gadgets. We might even find general-purpose simulations, showing that a particular gadget can simulate every possible gadget (or every gadget with some property). This will be a hands-on class, mostly focusing on you finding simulations for yourselves.

Computers can do a lot of things. If you've ever programmed, you might think you can theoretically write a program that does anything. But it turns out there are things you can't program, no matter how clever you are! In this class, we'll see examples of such things and proofs of why they can't be computed.

What happens when you keep counting past infinity, and never stop? You discover the ordinal numbers! We'll introduce this exciting tool and use it to understand some more finite problems.

Every hear about P vs. NP? Did you know that this fundamental mathematics question also relates to games and puzzles? This class will explore how the mathematics of computational complexity relates to games and puzzles.

Learn how to play Hackenbush, a simple game that leads to interesting mathematics. After getting some practice playing, we'll see how the game inspires the surreal numbers, a system of numbers that allows us to to play with infinity in an unusual way.

A cellular automaton is a grid of cells that changes according to simple rules, but can have complicated behavior. The most famous one is Conway's Game of Life. We'll discuss 1- and 2- dimensional automata, look at cool patterns they can produce, and see just how powerful they can be.

What happens when you start counting and don't stop? Can a hydra be beaten? What do hydras even have to do with math? Come to this class to find out!

Computers can do a lot of things. If you've ever programmed, you might think you can theoretically write a program that does anything. But it turns out there are things you can't program, no matter how clever you are! In this class, we'll see examples of such things and proofs of why they can't be computed.

How many people do you need to put in a room to make sure four of them are either all friends or all not friends? Why does anyone care about numbers like Graham's Number, which way are too big to have any physical relevance? Ramsey theory is the study of how particular structures always emerge in sufficiently large clusters of randomness. Learn the answers to these questions and more!

What's the biggest number you know? 6? A million? A googolplex? In this class, we'll talk about ways to describe way bigger numbers.

Every hear about P vs. NP? Did you know that this fundamental mathematics question also relates to games and puzzles? This class will explore how the mathematics of computational complexity relates to games and puzzles.

Want to learn more about math you've learned in school? Noticed a pattern you're interested in finding more about? One of your Splash teachers mentioned something that sounds cool? Come with your questions, and I'll try to answer them! If nobody has any questions, I'll probably just talk about set theory or something for an hour.

Have you ever wondered exactly how hard puzzles like Sudoku or Rush Hour are? In a certain sense, most puzzles like these are "as hard as they can possibly be": Sudoku is "NP-complete" and Rush Hour is "PSPACE-complete." In this class, we'll talk about what it means for something to be hard (including defining the terms above), and build a toolkit that lets us prove problems hard. At the end of the class you should know how to look at a new kind of puzzle and determine how hard it is. This is related to the P vs NP problem, which you might have heard of, but we won't talk a lot about that in this class.

Ever wondered why people are so excited about quantum computers? In this class, we'll learn how to use quantum mechanics to perform computational tasks. We'll see examples of algorithms that solve problems faster than any known classical algorithm, such as Shor's factoring algorithm. We'll also see provably-secure quantum cryptography.

We'll start by introducing sets and basic operations on them, and quickly move on to topics such as the ZF axioms, ordinal numbers, and the axiom of choice. This class will be hard and go fast, with each week relying heavily on previous weeks. Expect to participate in class and work on hard problems that require genuine creativity to solve.

Come explore space and time, and see how the main ideas of special relativity can be derived from simple principles and some basic algebra! If we have time, we'll also talk about relativity "paradoxes" and how to resolve them.

You are given http://web.mit.edu/puzzle/www/2015/puzzle/rectangles/. You need to get an answer that is a word or phrase. What do you do? (Try it, and check the solution linked on the page.) Puzzles can be almost anything - you're given strange data and very few instructions, and you find a way to extract an answer from it. Come try puzzles from various puzzle hunts! Whether you're an expert puzzler or have never done a puzzle hunt, we'll have puzzles for you (and help if you get stuck)!

Learn how to play Hackenbush, a simple game that leads to interesting mathematics. After getting some practice playing, we'll see how the game inspires the surreal numbers, a system of numbers that allows us to to play with infinity in an unusual way.

A cellular automaton is a grid of cells that changes according to simple rules, but can have complicated behavior. The most famous one is Conway's Game of Life. We'll discuss 1- and 2- dimensional automata, look at cool patterns they can produce, and see just how powerful they can be.

Computers can do a lot of things. If you've ever programmed, you might think you can theoretically write a program that does anything. But it turns out there are things you can't program, no matter how clever you are! You'll see some examples of these functions and learn more about what computers are actually capable of.

You are given http://web.mit.edu/puzzle/www/2015/puzzle/rectangles/. You need to get an answer that is a word or phrase. What do you do? (Try it, and check the solution linked on the page.) Puzzles can be almost anything - you're given strange data and very few instructions, and you find a way to extract an answer from it. Come try puzzles from MIT Mystery Hunt, the largest puzzle hunt in existence! Whether you're an expert puzzler or have never done a puzzle hunt, we'll have puzzles for you (and help if you get stuck)!

λf.(λx.f(x x))(λx.f(x x)) What does that mean? Come to this class to find out! Lambda calculus is a minimal, inefficient, and hard-to-read, but still interesting and useful, programming language.

How many people do you need to put in a room to make sure four of them are either all friends or all not friends? Why does anyone care about numbers like Graham's Number, which way are too big to have any physical relevance? Ramsey theory is the study of how particular structures always emerge in sufficiently large clusters of randomness. Learn the answers to these questions and more!

Want to learn more about math you've learned in school? Noticed a pattern you're interested in finding more about? One of your Splash teachers mentioned something that sounds cool? Come with your questions, and I'll try to answer them! If nobody has any questions, I'll probably just talk about set theory or something for an hour.

What happens when you start counting and don't stop? Can a hydra be beaten? What do hydras even have to do with math? Come to this class to find out!

A cellular automaton is a grid of cells that changes according to simple rules, but can have complicated behavior. The most famous one is Conway's Game of Life. We'll discuss 1- and 2- dimensional automata, look at cool patterns they can produce, and see just how powerful they can be.

How many people do you need to put in a room to make sure four of them are either all friends or all not friends? Why does anyone care about numbers like Graham's Number, which way are too big to have any physical relevance? Ramsey theory is the study of how particular structures always emerge in sufficiently large clusters of randomness. Learn the answers to these questions and more!

If you've looked at Minecraft builds on the internet, you've probably seen some pretty impressive contraptions people have made with redstone, ranging from piston doors to fully functional computers. We'll learn how to make these sorts of things, start from the basic blocks you can build with and combining them to make useful components. We'll talk about how redstone relates to the inner workings of real-life computers. You don't need a Minecraft account or any experience with the game, though having played Minecraft might help give some context to what we talk about.

Topology is a way to talk about points being close together and sequences converging. You probably have some idea of what this means in, say, the real numbers, but what can we say about closeness in other sets? This class will be very hard. I'm not going to stand at the board and lecture; instead, I'll provide you with some definitions and you'll solve problems and prove theorems, and then present them to each other. I'll be there to guide you along the way. If that sounds fun to you, great! If not, this probably isn't the best class for you to take.

Learn about the inner workings of your computer! We'll look at bits and logic gates, and see how to perform computations using simple building blocks.

Computers can do a lot of things. If you've ever programmed, you might think you can theoretically write a program that does anything. But it turns out there are things you can't program, no matter how clever you are! You'll see some examples of these functions and learn more about what computers are actually capable of.

Come learn food tongue, a language in which every word is a food, by immersion!

What if you started counting and never stopped? In this class, we'll talk about ordinals, the numbers you get by doing this. We'll see many types of infinity and do strange and exciting things with them!

We play a game, starting with 100 berries. On your turn, you eat between 1 and 5 berries, and the person who eats the last person wins. What's the best strategy? We'll talk about a large class of games like this (called impartial games), and learn how to win all of them. If there's time at the end we'll talk briefly about partisan games, where the legal moves are different for different players.

There's so much awesome math to do that we couldn't pick just one thing to teach. Join us for a class of small snippets of cool math! Bring your own questions or be ready to choose your favorite topics from our list, and we'll see how much cool math we can show you in 50 minutes!

A cellular automaton is a grid of cells that changes according to simple rules, but can have complicated behavior. The most famous one is Conway's Game of Life. We'll discuss 1- and 2- dimensional automata, look at cool patterns they can produce, and see just how powerful they can be.

Suppose you have N men and N women, and each of them submits preference rankings for the other set of people. It's your job to pair them up to go to a dance, but you need to make sure that nobody wants to cheat: make sure no pair of people likes each other better than their partners. Can you always make it work? What if the women bribe you to care more about their preferences? What if the situation isn't so ridiculously heteronormative? Aah! Matching is hard!

Mint-apple sauce food tongue. Pear spinach sauce food tongue. Pear wonton pasta-peach-sauce food tongue? Pear shrimp kumquat plantain mint-apple clam peach-sauce pear!

What's a good anagram for Banach-Tarski? Banach-Tarski Banach-Tarski. Come learn how to cut a ball into 5 pieces and reassemble them into two balls of the same size! All you need is an infinitely sharp knife, an infinitely divisible ball, and the Axiom of Choice. Disclaimer: the Banach-Tarski Theorem, despite popular belief, is not actually a paradox.