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.

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.

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 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!

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.

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.

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.

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.

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 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.

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.

Curious what the hype around quantum computing is all about? Want to know what quantum computing actually is? In this class, we'll discuss the key quantum mechanics that quantum computing is based on and how it differs from classical computing. Then, we'll see a few examples of simple quantum algorithms. Note that this isn't a class on how a quantum computer can physically be built. Instead, we'll be discussing the theory of quantum computing.

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.

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.

Come explore relativity, where space and time mix and the laws of physics are not the same as what you've learned in school! In this class, we'll see how special relativity is a consequence of a few simple postulates. We'll analyze so-called paradoxes of relativity and see that they aren't so paradoxical after all.

The new Star Wars movies tell the story of classic and new characters years after the original movies. But did you know that books, games, and comics were telling a very different story of the events after Return of the Jedi for over 30 years before the new movies? In this class, we'll talk about how the old Star Wars media, known as the "Expanded Universe (EU)", told the stories of Luke, Leia, and Han after Return of the Jedi. We'll also talk about how the Expanded Universe explored other times in the Star Wars timeline. If you're already an EU fan, come to meet other fans and share your favorite EU moments. If you're new to the EU, come explore this expansive set of Star Wars stories for the first time!

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.

I need to send you some important information! How should I do it if I want to minimize the number of bits I send you? How should I do it if we're communicating over a noisy channel that might mess up my message? We'll talk about what information is mathematically and some clever ways to encode data!

You are given http://web.mit.edu.ezproxy.canberra.edu.au/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.

Temperature seems like a pretty natural everyday quantity - you choose the temperature to heat baked goods to, look at the weather predictions for the temperature, and more. But what is that number? In this class, we'll use physics to give a mathematical, precise definition of temperature. Along the way, we'll talk about entropy and its role in statistical mechanics.

How many ways can you break up the number 19 into a sum of positive integers (for example, 18+1 or 10+5+1+1+1+1)? What does the number of ways to break up a number into odd parts have to do with the number of ways to break up a number into distinct parts? In this class, we'll study these ways of breaking up positive integers, called integer partitions. But rather than just listening to a lecture, you'll be making the discoveries for yourself! You'll work with other students to find patterns, make conjectures, and prove things about integer partitions. I'll introduce a few important concepts and help you along the way.

So you went into your chemistry or physics class and the teacher said something about not being able to know both the position and momentum of a particle at the same time due to something called the Heisenberg Uncertainty Principle. Honestly, the whole thing was just vague and confusing, and you just want to understand what this mysterious principle really is. In this class, we'll actually explain where the Heisenberg Uncertainty Principle comes from and what it is saying, making it less mysterious. If we have time, we'll also explore a more general uncertainty principle.

You are given http://web.mit.edu.ezproxy.canberra.edu.au/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)!

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 Turing machine is a simple machine that can do everything that your favorite programming language can! Come learn about what Turing machines are, things they can do, and things they can't do!

Wondering what quantum mechanics is all about? Wondering what makes people say that it's strange (and why it actually isn't)? We'll learn about quantum mechanics through Mach-Zehnder interferometers and see that some of the things people think are strange and mysterious about quantum physics can actually be explained very simply! Along the way, we'll talk about how you could test if a bomb is functional without detonating it!

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.

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. Using what we learn, we'll show that there are some things that you can't program, no matter how clever you are!

Permutations are nice, but how could we make them better? With pictures, of course! In this class we'll talk about Young tableaux, simple diagrams with numbers, and prove find a correspondence between permutations and pairs of standard Young tableaux. If we have time, we'll also touch on where these funny little diagrams show up in mathematics. Be prepared for some fun combinatorics!

In 2020, NASA will be launching a new Mars rover with exciting new scientific devices! One of them is being developed right here at MIT! In this class, I'll tell you about our plan to make oxygen on mars using the carbon dioxide in the Mars atmosphere involving solid oxide fuel cells. We'll talk about the science behind the device going to Mars, called MOXIE, and some of the current work on related topics.

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!

Let's play a game! I have a very large chess board and I place a rook somewhere on it. On your turn, you must move the rook one or more squares to the left or one or more squares up. The first player who is unable to make a move loses! How do you win? Can you win? In this class, we'll play games like this one and develop the math that will allow us to learn how to win them.

You've heard of the natural numbers, integers, rationals, reals, and complex numbers. These number systems are nice, but don't all of those nice properties get boring after a while? In this class, we'll construct and play around with number systems that behave differently than the number systems you're used to: ones where multiplication isn't commutative (or associative), ones where something like $$\dots 121012102$$ makes sense, and more! Along the way we'll encounter multiple branches of mathematics. Come see how many strange examples we can get through!

Today's biotechnology makes crime investigation a simple procedure. Come learn how to use a few small pieces of DNA to identify a person! If we have time, we'll talk about how this technology can be applied to other problems in biology.

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!