Is there a factory near your home or school that's polluting your air or water? How would you find out? What can you do about it? In this class, we'll dig into a couple of the major federal environmental statutes (especially the Clean Water Act). We'll learn how to look up companies and check to see if they are following the law, and we'll discuss the kinds of things lawyers can do when they find illegal pollution. Best of all, we'll talk about things you can do right now (even without a law degree) to make a difference in your community.

You're the Supreme Court! Have you ever wondered how legal precedents are made? Now you get to participate. We'll divide the class into "judges" and "attorneys," with half of the students presenting mock oral arguments, while the other half asks tough questions and decides the case. This is your opportunity to decide what the law should be, to figure out how to weigh the perspectives of different sides, and to practice arguing persuasively for one viewpoint while being forced to grapple with the other side's arguments. Law students practice oral arguments as a way to improve their analytic skills and understanding of the law -- now you can too!

$$6^2 = 3\boxed{6}$$ $$76^2 = 57\boxed{76}$$ $$376^2 = 141\boxed{376}$$ Can you find more numbers like this? Is there a limit to how long they can get? Can you find any which end in 5 instead? Can you do this in base 2? Base 12? In our quest to answer these questions, we’ll get a little glimpse of a kind of math known as "ring theory". (What does this silliness have to do with rings anyway?)

I'll bring Deluxe Scrabble, Bananagrams, Boggle, (and of course the Official Scrabble Dictionary)...you bring your wits (and if you want, your favorite word game).

Did you ever find it suspicious that the cross product only works in three dimensions? Does it disturb you that physics makes such heavy use of cross products? What about matrix determinants? How come it’s possible to compute a cross product using a determinant? What sort of quantity do you need to describe angular momentum in 4 dimensions anyway? This is why we have the wedge product (try looking it up on MathWorld or Wikipedia)! You can compute it using two easy rules, and it can be used to find both cross products and determinants! We’ll warm up with a quick review of cross products, and then we’ll define the wedge product and see how far we can go!

Did you ever find it suspicious that the cross product only works in three dimensions? Does it disturb you that physics makes such heavy use of cross products? What about matrix determinants? How come it's possible to compute a cross product using a determinant? This is why we have the wedge product (try looking it up on MathWorld or Wikipedia)! You can compute it using two easy rules, and it can be used to find both cross products and determinants! We'll warm up with a quick review of cross products, and then we'll define the wedge product and see how far we can go!

Trigonometry can be intimidating, especially if you're trying to understand it intuitively. Formulas like the law of cosines look pretty scary, but since they're supposed to address questions from geometry, geometry might give us some insight into why they work! So, armed with the techniques of high school geometry, we'll draw some pretty pictures and derive the law of sines, the law of cosines, the angle addition formulas, the half-angle rules, and a few more obscure identities if we have time!

Ever wanted to learn Scheme? Have you heard of functional programming, but never learned any functional languages? Come to our class, and we’ll teach you the basics of Scheme, and how to learn more.

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.

So perhaps you've heard about vectors--you know, these things that have a magnitude and direction and stuff. Of course, that understates how awesome they are. We'll take a look into the world of vectors, starting from what it means for something to be a vector. We'll introduce matrices as descriptions of linear transformations--things that turn vectors into other vectors in certain predictable ways. (Oh hey, matrices are useful after all!) As we explore the uses of vectors and matrices, we'll try to answer the questions that arise, such as: Why do we need a right-hand rule for cross products? What can we say about things that turn matrices into other matrices? And what happens to a coconut when you stretch it? Planned topics include: vector spaces, matrices and matrix groups, dot and cross products, covariance and contravariance, tensors, and applications to physics.

Light plays a pivotal role in relativity because its speed (in a vacuum) is invariant. Yet to have relativity we need not assume a priori that there is an invariant speed! Instead, all we really need are some friendly-looking assumptions about space being pretty much the same everywhere. From there we will show that the formula for adding velocities has one invariant speed (which may be infinite) and discuss how this speed could be determined by experiment. This class is essentially a walkthrough of two papers from back in the day: * Mermin N D 1984 Relativity without light Am. J. Phys. 52 119-24. * Singh S 1986 Lorentz transformations in Mermin's relativity without light Am. J. Phys. 54 183-4.

Meet the hyperbolic trig functions cosh and sinh! Maybe they aren't as famous as their cousins cos and sin, but they have their niche. We'll try to understand the motivation for having these functions at all, and then we'll look at some of their applications. Among the possible topics are the split-complex numbers, hyperbolic rotations, and catenary curves.

The universe is full of darkness! You might have heard that there’s this mysterious "dark matter" that holds galaxies together and an even weirder "dark energy" that’s accelerating the expansion of space. It's no joke! Come see the evidence that this stuff actually exists and some predictions about what it’s going to do to our universe. We might even talk about a few guesses at what some of it actually is.

We'll have an informal discussion and feedback session about ESP in general. Here's a chance to tell us what you like and dislike about the way we do things and to toss around some ideas about the future of our programs. Bring breakfast and we'll make it a breakfast forum!

Trigonometry can be intimidating at first, especially if you're trying to understand it on an intuitive level. Formulas such as the law of cosines look pretty scary, but since they were designed to address questions from geometry, we might expect geometry to give us some insight into why they work! So, armed with the techniques of high school geometry, we'll draw some pretty pictures and derive the law of sines, the law of cosines, the angle addition formulas, the half-angle rules, and a few more obscure identities!

Not satisfied with the confusing algebraic proofs of trigonometric identities in your textbook? Come see some terrific geometric proofs of your favorite formulas from trig!

The universe is full of darkness! You might have heard that there's this mysterious “dark matter” that holds galaxies together and an even weirder “dark energy” that's accelerating the expansion of space. It's no joke! Come see the evidence that this stuff actually exists and some predictions about what it's going to do to our universe. We might even talk about a few guesses at what some of it actually is.

$$e^{i\pi} + 1 = 0$$ So said Euler in 1748. This equation, considered by many as the most amazing equation ever, is known as "Euler's Identity". Doesn't it disturb you a bit? Like, what does it even mean to raise something to an imaginary power? And what's so special about e anyway? It's not like 2.718 measures some elementary geometric ratio the way $$\pi$$ does, though the appearance of $$\pi$$ in there is spooky too. We'll take a little trip into the wonderful world of complex analysis in an attempt to reach an understanding of this equation.

$$e^{i\pi} + 1 = 0$$ So said Euler in 1748. This equation, considered by many as the most amazing equation ever, is known as "Euler's Identity". Doesn't it disturb you a bit? Like, what does it even mean to raise something to an imaginary power? And what's so special about e anyway? It's not like 2.718 measures some elementary geometric ratio the way $$\pi$$ does, though the appearance of $$\pi$$ in there is spooky too. We'll take a little trip into the wonderful world of complex analysis in an attempt to reach an understanding of this equation.

The universe is full of darkness! You might have heard that there's this mysterious "dark matter" that holds galaxies together ...

Not satisfied with the confusing algebraic proofs of trigonometric identities in your textbook? Come see some terrific geometric proofs of ...

Quotemined from the CollegeBoard website: "The ultimate goal of an AP Music Theory course is to develop a student's ability ...

Come learn some basics of drawing shiny things! After we talk about some ways to make things look shiny, you'll ...

Come learn some basics of drawing shiny things! After we talk about some ways to make things look shiny, you'll ...

Come learn some basics of drawing shiny things! After we talk about some ways to make things look shiny, you'll ...

Come learn some basics of drawing shiny things! After we talk about some ways to make things look shiny, you'll ...

Not satisfied with the confusing algebraic proofs of trigonometric identities in your textbook? Come see some terrific geometric proofs of ...

Not satisfied with the confusing algebraic proofs of trigonometric identities in your textbook? Come see some terrific geometric proofs of ...