Splash Biography

Think you're perfectly logical? Think that you see everything around you? That you remember things just how they happened? Turns out, you don't. We'll see just how your brain doesn't work the way you think it does. It misleads you. It takes shortcuts, and tells you things that aren't true. Be aware of where your brain goes wrong, and you'll be smarter, better able to avoid being misled, and more aware of what's around you.

In school, how often do you get to solve deep math problems? Problems that require thinking, not just doing the same thing over and over again? They're a lot more interesting, and a lot more fun. This is your chance to play around with problems that will actually make you think. You'll get a chance to work individually and stretch your mind in new ways.

Want to be able to tell in your head if 48302853453 is divisible by 9? What about 3? What about 11? We’ll learn some tricks to tell quickly which numbers are divisible by 2, 3, 5, 9, and 11. But I’m not just going to tell you a rule: I’ll also show you *why* that rule is true. We’ll learn a little bit of modular arithmetic and understand something really interesting about numbers – all while you learn some quick tricks in math.

Here's a game. We have two piles of pennies. Two of us alternate turns. On our turn, we can remove as many pennies as we want but from one pile only. The last person who can remove pennies wins. It's a simple game, but the strategy is not so easy to come up with. (Can you?) We'll play some games like this one and understand how to always win them. Not just will you be able to beat your friends, but you'll also see some really beautiful patterns.

What are numbers, really? I mean, what *are* they? As children, we were taught how to count, as if numbers had always been there and were obvious. When you got to fractions, well, those were supposed to be clear too. And then real numbers? $$\pi$$? It was always brushed under the rug... it’s just some weird decimal that goes on forever, right? Well, you can’t prove anything about numbers if you don’t know what they really are. How do we know that mathematical constructions actually work? What basis tells us that even something as simple as addition makes sense – how do you even define it? What could it possibly mean to take something like $$\pi^{\sqrt{2}}$$? Well, the numbers can be built out of something much, much simpler. You can work your way right up from almost nothing to the full complexity of the real numbers. Come and find out how a mathematician thinks about a concept you might have thought was simple. This will be a very challenging course, but not like the mathematics you see in school: it won’t be about memorizing formulas or lots of calculations. This class is for people who like and are good at dealing with abstract concepts and logical deduction.

How do computers "think?" If you ever want to understand that, you need to come up with a good way to model them: to say exactly what they can do, and how. In this class, you'll get to work with a model of computers called "finite automata." You'll design some of them yourself and test out what they can do; then you'll get a chance to prove results about the limits of their abilities. This functions as a first introduction to a field called "theoretical computer science," and I'll talk a little bit at the end of the class about a model of computation called a Turing machine, which is just as powerful as any computer you might use --- then I'll mention some problems that Turing machines, and your own computer, can't solve at all.

The organization running this conference, Splash! Chicago, is one of several similar organizations around the country running programs based on ...

Most students come out of school without an appreciation for real mathematics. They have never paused to think about the ...