Droplet Spring 2009
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Computer Science Mathematics

Computer Science

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Digital Logic: How computers work!
Teachers: Aviv Ovadya

In this class we will start with the basics of digital logic and build up to a fully functional adding machine - and then a computer.


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Complex Numbers
Teachers: David Roe

You've learned how to take square roots: $\sqrt{4} = 2$. But what about $\sqrt{-4}$? You may have been taught that taking square roots of negative is impossible. This isn't quite true: you can enlarge your notion of what a number is in a way that allows one to compute with numbers including $\sqrt{-4}$. Such "complex numbers" are crucial all over mathematics, engineering and physics. Come and see why!

Number Theory
Teachers: David Roe

Number theory is the branch of mathematics that studies properties of the integers (..., -2, -1, 0, 1, 2,...). Despite being around for thousands of years, there are still many fundamental unsolved problems. Come learn about modular arithmetic, which helps explain quick methods for testing if a number is divisible by 11. Or Fermat's Little Theorem, which forms the basis for a powerful technique for quickly checking if a number is prime.

Number Tricks
Teachers: Daniel Zaharopol

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.

Fermat's Little Theorem
Teachers: Andrew Geng

Let's say two numbers are equivalent if they differ by a multiple of 11. That is, 11 ≡ 0, 12 ≡ 1, 13 ≡ 2, and so on. When we do arithmetic with these numbers, a trend emerges: any number raised to the 11th power is equivalent to its original self.

This turns out to be true if we use any other prime number in place of 11—so we'll prove it, and then we'll use it in a little magic trick.

Understanding Games
Teachers: Daniel Zaharopol

We'll play some simple games and then find the best strategies to win them. What happens if you take tic-tac-toe but each player can put down either X or O, and the first player to make three-in-a-row of either type wins? We'll explore this game and other games, and figure out what happens.


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Time and Frequency
Teachers: Michael Price

A signal is a function that conveys information, like sound or video. Get a head start on one of the most important concepts in engineering by seeing firsthand how we can interpret signals as functions of either time or frequency. We will use audio signals (artificial effects, music, and your voices) as examples.

Forensic Entomology!
Teachers: Melinda Dooley

How can a maggot tell you who committed a murder? Forensic entomology is using bugs to solve crimes. We'll talk about forensics in general, and bugs in specific, and we'll work a "crime scene" to see how it's done. You'll never watch CSI the same way again!
Warning: this class may get a little gross.

Teachers: Stephanie Bachar

When first discovered, prions were so novel and controversial that those who stood by the prion theory were shunned by much of the science community. Why? Because prions, the infectious proteins that cause Mad Cow Disease, break the fundamental genetic dogma of biology. How do prions work? Where are prions found? Why do prions exist? What do prions have to do with cannibalism? We'll attempt to answer all these questions and more during this class.

Seeing is believing... or is it?
Teachers: Abby Noyce

We trust our eyes to tell us the truth about the world. But, it turns out out that your eyes and brain take lots of shortcuts and guesses in order to make sense of visual information. In this class, we'll look at optical illusions and discuss how they reveal a "trick" of the brain.

Introduction to Civil Engineering
Teachers: Lucy Wu

Civil engineers design buildings, bridges, highways, tunnels, and other BIG things. In this class, we will explore major projects from ancient wonders to modern construction. We will talk about how construction materials like steel and concrete are used in buildings, bridges, and tunnels. I'll show you some famous projects and tell you why they are famous. If you want to know what civil engineers do and how they do it, come and find out.