ESP Biography
ANDREW GENG, MIT alum studying math at UChicago
Major: Mathematics College/Employer: University of Chicago Year of Graduation: G 

Brief Biographical Sketch:
Andrew likes to teach math and science classes. From time to time he feels artsy and does drawing and music classes too. After graduating from MIT in 2011, he left for UChicago in search of math grad school and greener pastures—and soon found himself entangled in Splash at UChicago. His free time divides itself as it pleases among programming, music, art, and food—often where they intersect. Past Classes(Look at the class archive for more.)Idempotents: Forever Squared in Splash! 2013 (Nov. 23  24, 2013)
$$6^2 = 3\boxed{6}$$
$$76^2 = 57\boxed{76}$$
$$376^2 = 141\boxed{376}$$
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?)
Word Games! in Splash! 2013 (Nov. 23  24, 2013)
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).
The Magic of Wedge Products in Splash! 2010 (Nov. 20  21, 2010)
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!
The Magic of Wedge Products in Splash! 2009 (Nov. 21  22, 2009)
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 With Pictures in Splash! 2009 (Nov. 21  22, 2009)
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 halfangle rules, and a few more obscure identities if we have time!
Scheme in Splash! 2009 (Nov. 21  22, 2009)
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.
Fermat's Little Theorem in Droplet Spring 2009 (May. 01, 2009)
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.
Vectors And Beyond in HSSP Spring 2009 (Mar. 14, 2009)
So perhaps you've heard about vectorsyou 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 transformationsthings 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 righthand 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.
Relativity Without Light in Splash! 2008 (Nov. 22  23, 2008)
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 friendlylooking 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 11924.
* Singh S 1986 Lorentz transformations in Mermin's relativity without light Am. J. Phys. 54 1834.
Hyperbolic Functions in Splash! 2008 (Nov. 22  23, 2008)
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 splitcomplex numbers, hyperbolic rotations, and catenary curves.
The Dark Universe in Splash! 2008 (Nov. 22  23, 2008)
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.
Student Opinion Forum: The Future of ESP in Splash! 2008 (Nov. 22  23, 2008)
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 With Pictures in Splash! 2008 (Nov. 22  23, 2008)
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 halfangle rules, and a few more obscure identities!
Trigonometry With Pictures in Spark! Spring 2008 (Mar. 08, 2008)
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 Dark Universe in Spark! Spring 2008 (Mar. 08, 2008)
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" and the Complex Numbers in Spark! Spring 2008 (Mar. 08, 2008)
$$e^{i\pi} + 1 = 0$$
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" and the Complex Numbers in HSSP Spring 2008 (Mar. 15, 2008)
$$e^{i\pi} + 1 = 0$$
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 Dark Universe in SPLASHONWHEELS (2008)
The universe is full of darkness! You might have heard that there's this mysterious "dark matter" that holds galaxies together ...
Trigonometry With Pictures in SPLASHONWHEELS (2008)
Not satisfied with the confusing algebraic proofs of trigonometric identities in your textbook? Come see some terrific geometric proofs of ...
AP Music Theory in DELVE (2008)
Quotemined from the CollegeBoard website: "The ultimate goal of an AP Music Theory course is to develop a student's ability ...
How to Draw Shiny Things in SPLASH (2007)
Come learn some basics of drawing shiny things! After we talk about some ways to make things look shiny, you'll ...
How to Draw Shiny Things in SPLASH (2007)
Come learn some basics of drawing shiny things! After we talk about some ways to make things look shiny, you'll ...
How to Draw Shiny Things in SPLASH (2007)
Come learn some basics of drawing shiny things! After we talk about some ways to make things look shiny, you'll ...
How to Draw Shiny Things in SPLASH (2007)
Come learn some basics of drawing shiny things! After we talk about some ways to make things look shiny, you'll ...
Trigonometry With Pictures in SPLASH (2007)
Not satisfied with the confusing algebraic proofs of trigonometric identities in your textbook? Come see some terrific geometric proofs of ...
Trigonometry With Pictures in SPLASH (2007)
Not satisfied with the confusing algebraic proofs of trigonometric identities in your textbook? Come see some terrific geometric proofs of ...
