ESP Biography

ZANDRA VINEGAR, Lover of math and insanity -- Bay Area, CA

Major: Math+

College/Employer: MIT/MathCircle

Year of Graduation: 2013

Brief Biographical Sketch:

I love teaching, especially math, but anything crazy and beautiful will do. I majored in Math at MIT and graduated in January 2013. I was very active with MIT ESP while in college: I directed multiple programs, put a lot of thought and energy into teacher training and building student and teacher communities, and I've taught more than 1000 hours of ESP classes. I love allowing students to push classes in different directions, and I am constantly amazed by how many different ways mathematics can work and produce awesome experiences.

I studied both Math and Math Education at MIT, taking classes to complete a teaching certification and also following MIT’s research in educational reform through new technology. I currently hold a B.S. in Mathematics from MIT, and my areas of mathematical focus while in college included Abstract Algebra, Mathematical Economics, Computational Origami, and Theoretical Computer Science.

My most recent long-term position was as a full-time, Education Coordinator at the National Museum of Mathematics in Manhattan, NY. In that role, I helped to develop new outreach programs; I also managed the Museum’s Twitter and Facebook page, and taught 3-5 sessions every day for K-12 students. And over the 2014 summer, I was employed as a Core Class teacher for the Summer Program in Mathematical Problem Solving (SPMPS). SPMPS is a full-scholarship, residential program for underprivileged students with talent in mathematics.

Now in the Bay Area, I strive to teach for and and create new programs that exhibit amazing math in an appealing and practical way to the general public and especially to young students. I teach for many of the Bay Area Math Circle programs and I also do private tutoring in advanced and recreational mathematics.

Part of why I teach is for you, the students - I love when you have those 'AAAAH THAT MAKES SO MUCH SENSE NOW' moments, and I make sure that my classes are a lot of fun to simply be in. But another part of why I teach is for the fun of making a curriculum and projects that get to the heart of subjects.

I don't plant myself down in any one particular academic field, and the classes I teach for ESP are almost always multidisciplinary. As in, even if it's filed under math, it will probably have enough of either physics, computer science, natural science, and/or philosophy in it to be alternatively filed under at least a few other sections. But, in general, don't think too hard, just sign up and brace yourself.

Past Classes

(Clicking a class title will bring you to the course's section of the corresponding course catalog)

M8119: How to Cut a CAKE in Spark 2014 (Mar. 15 - 16, 2014)

If two people have to split a cake, is it "fair" if one cuts and the other gets to choose which piece they want? Does this still work for 3 people? What if 100 pirates need to split up their $1000 of loot? Or if you need to split a $20 weekly allowance between you and your younger sibling? How should ESP decide who gets into what classes? And, if we publish the lottery algorithm, what makes a system easy or difficult to 'game'? This class will explore the concepts of "fairness" and of "game theory" - using the intersection to discuss practical cases where people care about the result... LIKE WHEN THERE'S CAKE INVOLVED!!! (yes, there will be cake, and it will not be a lie)

C8120: Introduction to Programing a la Fractal Forgeries in Spark 2014 (Mar. 15 - 16, 2014)

Want to learn how to program a cloud? or a rough, and unpredictable mountain? or an infinitely precisely shaded fern? Then sign up for this class and I will BOTH introduce you to JavaScript, a powerful visual programming tool, and show you around the psychedelic world of Fractals! Check out some of these images and see if you can tell which are real and which are mathematically-generated forgeries: http://tinyurl.com/8erkfxy Those which are forgeries are made using Fractals: mathematical objects which are produced by repeating very simple instructions over and over again. You'd never want to draw these images by hand, but with the aid of computers, we can plot hundreds of thousands of points in seconds. This ability enables us to decode natural objects which the "smooth" curves and platonic solids you learn about in high school can never emulate.

M8121: Mad Hatter Mathematics in Spark 2014 (Mar. 15 - 16, 2014)

There is math. Like no math in school. And proofs full of wonder, mystery, and danger! Some say to survive them, you need to be as mad as a hatter!

M8123: How to Win $$$ in Spark 2014 (Mar. 15 - 16, 2014)

How to make the right choice… in order to win money, of course! A bit of math, and then some game show tricks and gambling card games in which most people are /very/ likely to slip up. And if you’re not into gambling yourself, at least come learn how to not get tricked!

S7463: Maxwell's Equations in Splash! 2013 (Nov. 23 - 24, 2013)

\begin{equation} \varepsilon \varoiint \mathbf E \cdot ds = \iiint \mathbf q_\mathbf v dv \end{equation} \begin{equation} \oint \mathbf B \cdot dl = \mathbf I + \varepsilon \frac{d}{dt} \iint \mathbf E \cdot ds \end{equation} \begin{equation} \oint \mathbf E \cdot dl = - \mu \frac{d}{dt} \iint \mathbf B \cdot ds \end{equation} \begin{equation} \mu \varoiint \mathbf B \cdot ds = 0 \end{equation} These four equations describe one of the most universal and elegant relations in physics. They are Maxwell’s equations, unifying all observations of relativity, electricity, and magnetism. Don’t let the notation scare you off – this class has no prerequisites (as in, just be able to graph a function), but we will rigorously derive Maxwell’s explanation of electromagnetic phenomena (including light, electricity, magnets, …). “Derive” with the catch that, as I don’t believe in writing long equations on the board, everything in this class will be presented as a series of intuitive /and/ rigorous deductions, preserving concepts rather than constants. We will begin with only two observations. First, the relativistic nature of light: you can’t catch up to a light beam – it will always move away from you at speed c. Second, our observations of the force between two charges. From these two observations, we will DERIVE the explanation of everything else. Aka, the world will unfold before you and it will be beautiful.

M7464: Mad Hatter Mathematics in Splash! 2013 (Nov. 23 - 24, 2013)

There is math. Like no math in school. And proofs full of wonder, mystery, and danger! Some say to survive them, you need to be as mad as a hatter!

M7478: Uncanny Appearances of Sierpinski's Triangle in Splash! 2013 (Nov. 23 - 24, 2013)

The hairs on the back of your neck stand on end... It's there - you can see it - sometimes cloudy, as if in a fog, but no! It's a swarm! and the swarm forms... you cannot believe it. But wait, again, not one, but infinitely many overlayed in beautiful pattern... it rises from the predictable, and from randomness... it is: SIERPINSKI'S TRIANGLE. No, really, it's freaking ridiculous where you can find this infinitely-triangular-fractal, and the description above isn't exaggerating at all. Pascal's got nothing on this thing.

M7716: Re-Envisioning Games in Splash! 2013 (Nov. 23 - 24, 2013)

Have you ever wanted to remake Chutes and Ladders, War (the card game) or Candy Land so that they're fun again, even now that you understand how strategies work and why those three games don't have any? In this workshop, you might choose to do exactly this: to take a game that is entirely random, and give it mechanics so that there is some new kind of awesome strategy. Or you might choose to do the opposite: take a game that is entirely strategic, and add a bit of randomness to it to complicate both the strategy and the emotional thrill of the game. In either case, this will be an introduction to game design and game prototyping. And, of course, there will be plenty of game playing.

S7722: Developmental Psychology: Games and Play in Splash! 2013 (Nov. 23 - 24, 2013)

If you have a passion for teaching or tutoring younger students or peers, then you already know that "making it a game" is one of the best educational strategies out there. But why, and what kinds of play are most effective and most powerful? In this class, we'll explore why games and play make such an effective learning environment. The theoretical content of this class is inspired by the video game creator Scot Osterweil, who co-created the Zoombinis Logical Journey video games.

M6622: How to Cut a CAKE in Splash! 2012 (Nov. 17 - 18, 2012)

E6626: Structural Engineering Disasters in Splash! 2012 (Nov. 17 - 18, 2012)

In this class, we'll explore (and test!) how and who and what led to the destruction of several well known structures such as the Tacoma Narrows Bridge. The focus will be on structural engineering, and on the 'de-engineering' nature did to destroy these man-made projects. Come prepared to break things. The Tacoma Narrows Bridge Disaster: http://www.youtube.com/watch?v=gHgQALH9-7M&

C6628: Introduction to Programing a la Fractal Forgeries in Splash! 2012 (Nov. 17 - 18, 2012)

S6629: Maxwell's Equations in Splash! 2012 (Nov. 17 - 18, 2012)

These four equations describe one of the most universal and elegant relations in physics. They are Maxwell’s equations, unifying all observations of relativity, electricity, and magnetism. Don’t let the notation scare you off – this class has no prerequisites (as in, just be able to graph a function), but we will rigorously derive Maxwell’s explanation of electromagnetic phenomena (including light, electricity, magnets, …). “Derive” with the catch that, as I don’t believe in writing long equations on the board, everything in this class will be presented as a series of intuitive /and/ rigorous deductions, preserving concepts rather than constants. We will begin with only two observations. First, the relativistic nature of light: you can’t catch up to a light beam – it will always move away from you at speed c. Second, our observations of the force between two charges described by q_1*q_2/r^2: q_1 and q_2 being the magnitude of the two charges, and r being the distance between them. From these two observations, we will DERIVE the explanation of everything else. Aka, the world will unfold before you and it will be beautiful.

M6630: Mad Hatter Mathematics in Splash! 2012 (Nov. 17 - 18, 2012)

There is math. Like no math in school. And proofs full of wonder, mystery, and danger! Some say to survive them, you need to be as mad as a hatter!

S6631: Live-Action Vector Fields! in Splash! 2012 (Nov. 17 - 18, 2012)

Want to see yourself 30ft up on a giant screen? Want to be part of an MIT youtube broadcast? Come be part of the world's largest ever human vector field! (Actually, as far as I know, it will be the world's ONLY ever purposefully staged human vector field.) Vector fields are ubiquitous in physics, and we want to make an amazing video: 100 students together forming a massive human vector field! In the process, you'll also learn about and experience the science that governs electricity, magnetism, fluid, and heat. There will even be some calculus (slope-fields are vector fields!)

M5684: Fringes of Chaos in HSSP Spring 2012 (Feb. 18, 2012)

The common theme throughout this class is dynamic complexity, or, in a word, chaos – the chaos of the Mandelbrot fractal, the chaos of the universe that increases infinitely with time, the chaos that marks the edge of the set of patterns comprehensible to the human mind. This class will be like none other you have ever seen, and I may as well have filed it under physics or liberal arts instead of mathematics. There will be many days when we are extremely rigorous — assignments which ask for mathematically presented proofs — and days when we can't be rigorous simply because the questions we will discuss are still unanswered by science and mathematics at large. We will cover, in depth, the concepts surrounding and intertwining between Fractals, Entropy, and Universal Symmetries. We will discover the connections between these ideas through lectures and projects which range from online mathematical applets to discussions about required reading material. Every week will be intense and will require the full participation of all students. Come with an open and inquisitive mind and the work ethic to support it!

S5830: Maxwell's Equations in Spark! 2012 (Mar. 10, 2012)

S5905: Maxwell's Equations... for Middle Schoolers in Spark! 2012 (Mar. 10, 2012)

I'm not really deviating from my normal, "tried and true" 2hr Maxwell's equations class. In spite of being for Middle School students, this class will still cover single and multivariable calculus, also special relativity, and will derive the integral form of Maxwell's equations. (full description below) I've just never tried teaching this class to a middle school audience: I want to see what happens! :-D Maxwell's Equations: These four equations describe one of the most universal and elegant relations in physics. They are Maxwell’s equations, unifying all observations of relativity, electricity, and magnetism. Don’t let the notation scare you off – this class has no prerequisites (as in, just be able to graph a function), but we will rigorously derive Maxwell’s explanation of electromagnetic phenomena (including light, electricity, magnets, …). “Derive” with the catch that, as I don’t believe in writing long equations on the board, everything in this class will be presented as a series of intuitive /and/ rigorous deductions, preserving concepts rather than constants. We will begin with only two observations. First, the relativistic nature of light: you can’t catch up to a light beam – it will always move away from you at speed c. Second, our observations of the force between two charges described by q_1*q_2/r^2: q_1 and q_2 being the magnitude of the two charges, and r being the distance between them. From these two observations, we will DERIVE the explanation of everything else. Aka, the world will unfold before you and it will be beautiful.

S5320: Your art teacher LIED to you! in Splash! 2011 (Nov. 19 - 20, 2011)

Somehow, art-instructors and primary school teachers (and sometimes quantum physicists... good story) are under the impression that Red, Yellow, and Blue are "primary" colors. *cough* this is COMPLETELY FALSE *cough* Are you interested in human vision? The physics and chemistry of the eye? This class will delve into the chemistry of the rod and cone cells which lead to our experiences of light and color. And then additionally cover some of the neurological components of vision. So if you want to know some ridiculous truths (EX: Magenta is a delusion shared by the entire human species!) and with enough context (chemistry, physics, and neurology) to understand exactly how your art teacher lied and what the truth really is, sign up for this class and brace yourself.

S5321: Your sailing instructor (or physics textbook) LIED to you! in Splash! 2011 (Nov. 19 - 20, 2011)

Somehow, sailors and most secondary school textbooks are under the impression that Bernoulli's Principle is a decent explanation of an airfoil (the wing shape that allows birds and planes to fly and sailboats to steer into the wind). You may have even seen a pretty diagram at some point of air flowing over a wing, horizontal before and after, moving faster above the wing... etc. *cough* this is COMPLETELY FALSE *cough* This class will basically be sailing 101 a la physics. Because the airfoil is what allows sailboats to sail "into" the wind (all directions except straight into the wind) and this class will cover the physics of how. So if you want to know some ridiculous truths (EX: Thousands of pounds of air are pushed down when airplanes fly by!) and with enough context (intro sailing and some physics) to understand exactly how your textbook lied to you and what the truth really is, sign up for this class and brace yourself.

S5322: Your chemistry and physics teachers LIED to you! in Splash! 2011 (Nov. 19 - 20, 2011)

Entropy. Is not. A state variable. And it's not a "measure of disorder" either (if it were maybe it would be a state variable). Entropy is also not "always increasing" in any fundamental-force-of-physics-sense. Why have you been LIED to so many times? Well, chemists have a good reason - they treat entropy like a state variable because in thermodynamics, you usually can because experimenters always lose information and are never patient enough to retrieve it. But, while you can work with the formulas in this light, the theory explained in textbooks makes no sense. It is *cough* COMPLETELY FALSE *cough* This class will be a rigorous explanation of entropy via the mathematics of information theory. We'll also need a rigorously defined notion of chaos and some high dimensional phase spaces... so, this class will be fast-paced and full of mathematical rigor.

S5551: Maxwell's Equations in Splash! 2011 (Nov. 19 - 20, 2011)

M5552: Uncanny Appearances of Sierpinski's Triangle in Splash! 2011 (Nov. 19 - 20, 2011)

M5554: Fractals and Fractal Dimension in Splash! 2011 (Nov. 19 - 20, 2011)

Math through a kaleidoscope: http://www.fractal-recursions.com/ Beautiful, no? This class will dive headfirst into the key concepts of Fractals including Symmetry, Expressible Infinity, and Chaos. Specifically, we will take an in depth look at the Sierpinski Triangle (briefly covering the difference between fractal dimension and topological dimension), the Lorenz Water Wheel (illustrating the ideas of the Butterfly Effect and Strange Attractors), and the well-known Mandelbrot Set. If you want to see mathematics from a completely alien perspective, this class is for you.

M5555: How to Win $$$ in Splash! 2011 (Nov. 19 - 20, 2011)

How to make the right choice… in order to win money, of course! A bit of math, and then some game shows tricks and gambling card games in which most people are /very/ likely to slip up. And if you’re not into gambling yourself, at least come learn how to not get tricked.

M5557: True but not Provable in Splash! 2011 (Nov. 19 - 20, 2011)

In mathematics there exist statements that are necessarily true, but that can never be proven. However, if you are willing to accept this claim without /proof! ‘you CANNOT say something like that without PROOF!’/ you probably can skip this class. But if that kind of claim shakes your world up a bit, come to this class and be shaken!!

X5558: Why Knot? in Splash! 2011 (Nov. 19 - 20, 2011)

Basically, we're going to hang out and play some games. These games may or may not be related to knot theory, but we're not going to look at too much of the math too closely. We're mainly just going to play the games. Why come to this class? I don't know, but why knot?

M5559: Graphiti in Splash! 2011 (Nov. 19 - 20, 2011)

MIT has far too much abstract art dotting our campus - what it needs is a little more color, a little more rigor... a little Graph Theory. This class will be an introduction to graph theory and to the beautification of MIT's concrete campus.

A5359: Chinese Brush Painting (sumi-e) - Bamboo Forrests and Pandas in SPICY Delve 2011 (Oct. 23, 2011)

This class will cover the basic techniques of painting layered bamboo forests and pandas in the traditional style of brush painting. There will be several brief periods of instruction and a lot of time to just relax and paint.

S3469: Maxwell's Equations in Junction Summer 2010 (Jul. 01 - Aug. 11, 2010)

M3470: Fractals and Fractal Dimension (FC part 1) in Junction Summer 2010 (Jul. 01 - Aug. 11, 2010)

A3474: Chinese Brush Painting (sumi-e) - Bamboo Forrests and Pandas in Junction Summer 2010 (Jul. 01 - Aug. 11, 2010)

Beginning with a very short introduction to the culture and tradition behind the art of Chinese brush painting, this class will be an hour of learning the basic techniques of painting layered bamboo forests.

A3475: Chinese Brush Painting (sumi-e) - Plum Trees and Sparrows in Junction Summer 2010 (Jul. 01 - Aug. 11, 2010)

This class will cover the basic techniques of painting plum trees and blossoms in the traditional style of brush painting. There will be several brief periods of instruction and a lot of time to just relax and paint.

M3476: Beyond Computation (TCS part 1) in Junction Summer 2010 (Jul. 01 - Aug. 11, 2010)

This class is on the mathematical treatment of ALL machines, ALL languages, ALL algorithms. Exactly what abilities – finitely many states? finite memory? infinite memory? non-determinism? – are necessary to solve problems? What sets of abilities are equivalent? And are there problems that are simply impossible to solve, although they clearly must have an answer - YES! and in this class, I will prove why!

M3477: Pvs.NP, NP complete, and the Turing test: Literacy in TCS research (TCS part 2) in Junction Summer 2010 (Jul. 01 - Aug. 11, 2010)

In this class, I will introduce enough of the modern concepts and terminology to cover current TCS research topics like Pvs.NP and Building a “Turing Complete” Computer or AI Why should you care? -- If P=NP almost all forms of computational security are a joke and any computational pattern can be modeled quickly to arbitrary precision. In other words, science, math, and physics are SOLVED.

M3110: Fractals and Fractal Dimension in Splash! 2009 (Nov. 21 - 22, 2009)

M3111: How to Win $$$ in Splash! 2009 (Nov. 21 - 22, 2009)

M3112: The Mathematics of Monsters and Machines in Splash! 2009 (Nov. 21 - 22, 2009)

Can you add by dropping marbles through a maze of switches? http://www.youtube.com/watch?v=GcDshWmhF4A (watch with the volume off and figure out how it works - /very/ simple, but elegant, no?) That machine clearly only works as directed for some range of numbers. How about if you want to add arbitrarily large numbers with one, finite machine? Can you build such a machine and then tell someone how to drop marbles into it to add their numbers? – NO!! STOP!! I did not ask, ‘how would you’ – I asked CAN you? Sure, you could prove the affirmative by construction, by making a machine which does so (if one can exist) but can you more succinctly, more elegantly, simply prove that such a machine exists? What if one could not exist? How would you go about proving this? If you like looking at machines and figuring out what they do, or constructing machines to solve problems, then you will probably like this class. On the other hand, what this class is /really/ about is the mathematical treatment of ALL machines, ALL languages, ALL algorithms. Exactly what abilities – finitely many states? finite memory? infinite memory? non-determinism? – are necessary to solve problems? What sets of abilities are equivalent? How long does it take to solve problems of sufficient complexity? Are there problems that are simply impossible to solve, although they clearly must have an answer? To answer the last question, YES! However, if you are willing to accept this claim without /proof! ‘you CANNOT say something like that without PROOF!’/ you probably can skip this class. But if that kind of claim shakes your world up a bit, come to this class and be shaken!!

S3113: Maxwell’s Equations in Splash! 2009 (Nov. 21 - 22, 2009)

S3114: Keeping the Earth From Going ‘Foom’ in Splash! 2009 (Nov. 21 - 22, 2009)

Every second, the sun radiates, in addition to light, more than a million tons of protons and elections. If the earth didn’t have some protection, we might look a lot like Mars. However, the earth has a magnetic field (a force field!) that protects us from this ‘solar wind.’ This field exists because of four beautiful relations called Maxwell’s equations. In this class, we will discuss how Maxwell’s Equations explain these phenomena. We will also make magnets out of electricity, nails, wire, and math.

S3115: Human Vision in Splash! 2009 (Nov. 21 - 22, 2009)

From the physics of parallax, to the bio-chemistry of rods and cones, to theories of human visual cognition, this class will explore, in depth, the mechanisms of human vision. Three lecture segments will be broken by two blocks of hands-on lab. The first lecture will be an introduction to the eye biologically. The first lab will be on the mathematics of how parallax gives you depth perception. The second lecture will delve into the chemistry of the rods and cones which lead to our experiences of light and color. The second lab will be a series of experiments on the associated phenomena of “primary colors.” (Magenta is a lie! A delusion of the human state!) And the final lecture will introduce some of the neurological components of sight, specifically those which lead to our experience of optical illusions.

A3116: Introduction to Chinese Brush Painting in Splash! 2009 (Nov. 21 - 22, 2009)

This class will cover the basic techniques of painting layered bamboo forests in the traditional style of brush painting. There will be several brief periods of instruction and a lot of time to just relax and paint.

A2047: East Asian Art: Sumi-e and Origami in HSSP Spring 2009 (Mar. 14, 2009)

In this course we will cover japanese brush painting (sumi-e) and paper folding (origami). For origami, we will start with basic folds like the waterbomb and move onto more complicated folds like the lily and the crane. We will also briefly investigate the wonderful world of modular origami and make kusudama (flower balls). For brush painting, we will introduce traditional sumi-e methods and themes beginning with bamboo forests and plum blossoms and including many animals and other natural objects. Classes will have brief instructive segments and a lot of time to enjoy the art on your own.

M2226: The Mathematics of Monsters and Machines in HSSP Spring 2009 (Mar. 14, 2009)

Can you add by dropping marbles through a maze of switches? http://www.youtube.com/watch?v=GcDshWmhF4A (watch with the volume off and figure out how it works - /very/ simple, but elegant, no?) That machine clearly only works as directed for some range of numbers. How about if you want to add arbitrarily large numbers with one, finite machine? Can you build such a machine and then tell someone how to drop marbles into it to add their numbers? – NO!! STOP!! I did not ask, ‘how would you’ – I asked CAN you? Sure, you could prove the affirmative by construction, by making a machine which does so (if one can exist) but can you more succinctly, more elegantly, simply prove that such a machine exists? What if one could not exist? How would you go about proving this? If you like looking at machines and figuring out what they do, or constructing machines to solve problems, then you will probably like this class. On the other hand, what this class is /really/ about is the mathematical treatment of ALL machines, ALL languages, ALL algorithms. Exactly what abilities – finitely many states? finite memory? infinite memory? non-determinism? – are necessary to solve problems? What sets of abilities are equivalent? How long does it take to solve problems of sufficient complexity? Are there problems that are simply impossible to solve, although they clearly must have an answer? To answer the last question, YES! However, f you are willing to accept this claim without /proof! ‘you CANNOT say something like that without PROOF!’/ you probably can skip this class. But if that kind of claim shakes your world up a bit, come to this class and be shaken!!

S2306: Discovering Astrophysics in HSSP Spring 2009 (Mar. 14, 2009)

Pinpricks of light. That's all we can see in the sky, yet somehow astronomers can still understand phenomena like galaxies and supernovae and quasars. Even more basic than that, how can we tell how far away a star is? How do we know what stars are made of, or their temperature, or their age? How can we understand black holes, or come up with the big bang theory for the formation of the universe? In this class, you'll be directing experiments and interpreting the results. We'll give you data, but you'll come up with new ways to collect it, you'll find the patterns, and you'll make conclusions about just what's going on out there in the universe. Meanwhile, we'll present material that will help you in your investigations or explain more of the background behind what you're seeing, from the physics of black holes to general relativity to the formation of the universe.

S2322: Electricity and Magnetism by Experiment in HSSP Spring 2009 (Mar. 14, 2009)

The first reference to electrical effects, such as static electricity and lightning, were recorded over 2500 years ago. Ancient man believed electricity to be a form of magic; Greek philosophers noticed that when a piece of amber was rubbed with cloth, it would attract pieces of straw; Indian priests used electromagnets to impress religious followers. Far from demystifying the mechanics of Electricity and Magnetism, this class aims to introduce students to the full beauty and elegance of this field of physics by theoretical discussion and by experimentation. In 1861 James C. Maxwell summarized almost everything we know about Electricity and Magnetism in four equations: $$ \epsilon_0 \displaystyle \bigcirc \hspace{-1.42em} \int \hspace{-.8em} \int E \cdot ds = \int\!\!\!\!\int\!\!\!\!\int\! q_v\;dV \\ \mu_0 \displaystyle \bigcirc \hspace{-1.42em} \int \hspace{-.8em} \int B \cdot ds = 0 \\ \oint\! E \cdot dl = -\mu_0\frac{d}{dt}\int\!\!\!\!\int\! B \cdot ds \\ \oint\! B \cdot dl = I + \epsilon_0 \frac{d}{dt}\int\!\!\!\!\int\! E \cdot ds $$ These four equations describe one of the most universal and elegant relations in physics. Don't let the notation scare you off -- this class has no prerequisites (that is, all you have to be able to do is graph a function), but we will rigorously derive Maxwell's explanation of electromagnetic phenomena including light, electricity, magnets, motors and generators, batteries, and the circuitry of your home computer. (See syllabus.) Labs will include a Van de Graaff generator, making solenoids, making an electric motor, and playing with bread board circuitry.

S2217: Human Vision in Spark! Spring 2009 (Mar. 07, 2009)

From the physics of optical lenses, to parallax, to the bio-chemistry of rods and cones, this class will explore, in depth, the mechanisms of human vision. Three lecture segments will be broken by two blocks of hands-on lab. The first lecture will be an introduction to the eye biologically and to the physics of the eye’s lens. The first lab will be on the mathematics of how parallax gives you depth perception. The second lecture will dive into the chemistry of the rods and cones which lead to our experiences of light and color. The second lab will be a series of experiments on the associated phenomena of “primary colors.” And the final lecture will introduce some of the neurological components of sight, specifically those which lead to our experience of optical illusions.

M2218: How to Win Money Off Your Friends in Spark! Spring 2009 (Mar. 07, 2009)

First section of the class: How to be very very likely to Win Money off your friends How to make the right choice… in order to win money, of course. A bit of intro math, and then some situations in which the right setup makes most people /very/ likely to slip up. Second section of the class: How to definitely Win Money off your friends Not a gambler? – this isn’t cheating per se, it’s simply leading your opponent to assume that they have a chance…

S2220: Maxwell's Equations in Spark! Spring 2009 (Mar. 07, 2009)

These four equations describe one of the most universal and elegant relations in physics. They are Maxwell’s equations, unifying all observations of relativity, electricity, and magnetism. Don’t let the notation scare you off – this class has no prerequisites (as in, just be able to graph a function), but we will rigorously derive Maxwell’s explanation of electromagnetic phenomena (including light, electricity, magnets, …). “Derive” with the catch that, as I don’t believe in writing long equations on the board, everything in this class will be presented as a series of intuitive /and/ rigorous deductions, preserving concepts rather than constants. We will begin with only two observations. First, the relativistic nature of light: you can’t catch up to a light beam – it will always move away from you at speed c. Second, our observations of the force between two charges described by $$ \frac{q_1 q_2}{r^2} $$: $$ q_1 $$ and $$ q_2 $$ being the magnitude of the two charges, and r being the distance between them. From these two observations, we will DERIVE the explanation of everything else. Aka, the world will unfold before you and it will be beautiful.

M2222: Fractals and Fractal Dimension in Spark! Spring 2009 (Mar. 07, 2009)

Math through a kaleidoscope: http://www.fractal-recursions.com/ Beautiful, no? This class will dive headfirst into the key concepts of Fractals including symmetry, expressible infinity, and chaos. Specifically, we will take an in depth look at the Sierpinski Triangle (briefly covering the difference between fractal dimension and topological dimension), the Lorenz Water Wheel (illustrating the ideas of the Butterfly Effect and Strange Attractors), and the well-known Mandelbrot Set. If you want to see mathematics from a completely alien perspective, this class is for you.

S1603: Human Vision in Splash! 2008 (Nov. 22 - 23, 2008)

S1855: Maxwell's Equations... Derived in Splash! 2008 (Nov. 22 - 23, 2008)

$$\oint_S \mathbf{E} \cdot \mathrm{d}\mathbf{A} = \frac {Q_S}{\varepsilon_0}$$ $$\oint_S \mathbf{B} \cdot \mathrm{d}\mathbf{A} = 0$$ $$\oint_{\partial S} \mathbf{E} \cdot \mathrm{d}\mathbf{l} = - \frac {\partial \Phi_{B,S}}{\partial t}$$ $$\oint_{\partial S} \mathbf{B} \cdot \mathrm{d}\mathbf{l} = \mu_0 I_S + \mu_0 \varepsilon_0 \frac {\partial \Phi_{E,S}}{\partial t}$$ These four equations describe one of the most universal and elegant relations in physics. They are Maxwell’s equations, unifying all observations of relativity, electricity, and magnetism. Don’t let the notation scare you off – this class has no prerequisites (as in, just be able to graph a function), but we will rigorously derive Maxwell’s explanation of electromagnetic phenomena (including light, electricity, magnets, …). “Derive” with the catch that, as I don’t believe in writing long equations on the board, everything in this class will be presented as a series of intuitive /and/ rigorous deductions, preserving concepts rather than constants. We will begin with only two observations. First, the relativistic nature of light: you can’t catch up to a light beam – it will always move away from you at speed c. Second, our observations of the force between two charges described by $$\frac{q_1*q_2}{r^2}$$: $$q_1$$ and $$q_2$$ being the magnitude of the two charges, and r being the distance between them. From these two observations, we will DERIVE the explanation of everything else. Aka, the world will unfold before you and it will be beautiful.

M1997: Theoretical Computation in Splash! 2008 (Nov. 22 - 23, 2008)

Can you add by dropping marbles through a maze of switches? http://www.youtube.com/watch?v=GcDshWmhF4A (watch with the volume off and figure out how it works - /very/ simple, but elegant, no?) That machine clearly only works as directed for some range of numbers. How about if you want to add arbitrarily large numbers with one, finite machine? Can you build such a machine and then tell someone how to drop marbles into it to add their numbers? – NO!! STOP!! I did not ask, ‘how would you’ – I asked CAN you? Sure, you could prove the affirmative by construction, by making a machine which does so (if one can exist) but can you more succinctly, more elegantly, simply prove that such a machine exists? What if one could not exist? How would you go about proving this? If you like looking at machines and figuring out what they do, or constructing machines to solve problems, then you may be a bit disappointed, because examples in this class will be few (if awesome) and far between. Rather, this class is on the mathematical treatment of ALL machines, ALL languages, ALL algorithms. Exactly what abilities – finitely many states? finite memory? infinite memory? non-determinism? – are necessary to solve problems? What sets of abilities are equivalent? And are there problems that are simply impossible to solve, although they clearly must have an answer?

H1998: Introduction to Chinese Brush Painting in Splash! 2008 (Nov. 22 - 23, 2008)

If you've never heard of Chinese brush painting: http://studioboone.com/art/index.html a beautiful art, no? Beginning with a very short introduction to the culture and tradition behind the art of Chinese brush painting, this class will be an hour of learning the basic techniques of painting layered bamboo forests.

H1999: More Chinese Brush Painting in Splash! 2008 (Nov. 22 - 23, 2008)

This class will cover techniques for painting several forms of colored flowers, trees, and animals in the traditional style of brush painting. There will be several brief periods of instruction during the hour and a lot of time to just relax and paint.

C2001: Beyond Computation in Splash! 2008 (Nov. 22 - 23, 2008)

There exists a finite set of domino pieces with words on each side, for which it is impossible to deduce whether or not a domino chain of copies of those pieces can be set up so that the top, altogether, reads exactly the same as the bottom. The problem is simply not solvable, by computer, by a mind, by any reason. If you are willing to accept the previous sentence without /proof! ‘you cannot say something like that without proof!’/ you probably can skip this class, but if that kind of claim shakes your world up a bit, come to this class and be shaken… because it turns out that we can prove that there are problems, /with answers/ that we simply will never be able to find – clearly every set of dominoes either can be or cannot be used to make a chain as described above, but for many, many sets, we can never calculate the answer.

M2002: How to be very very likely to Win Money off your friends in Splash! 2008 (Nov. 22 - 23, 2008)

How to make the right choice… in order to win money, of course. A bit of intro math, and then some situations in which the right setup makes most people /very/ likely to slip up. If you're not the kind of person who would trick others, at least learn how not to be tricked yourself!

M2003: How to definitely Win Money off your friends in Splash! 2008 (Nov. 22 - 23, 2008)

Not a gambler? – this isn’t cheating per se, it’s simply leading your opponent to assume that they have a chance…

M2005: Fractals and the Fringes of Chaos in Splash! 2008 (Nov. 22 - 23, 2008)

Math through a kaleidoscope: http://www.fractal-recursions.com/ Beautiful, no? This class will dive headfirst into the the key concepts of Fractals including Symmetry, Expressible Infinity, and Chaos. Specifically, we will take an in depth look at the Sierpinski Triangle (briefly covering the difference between fractal dimension and topological dimension), the Lorenz Water Wheel (illustrating the ideas of the Butterfly Effect and Strange Attractors), and the well-known Mandelbrot Set. If you want to see mathematics from a completely alien perspective, this class is for you.

S2006: Chaos and Strange Attractors in Splash! 2008 (Nov. 22 - 23, 2008)

Banned to the backs of math textbooks as the “monsters” of mathematics, chaotic dynamics has become a frontier of physics. This class will rigorously cover the nature of chaotic dynamics and strange attractors including the well know logistic growth orbit diagram and the Lorenz attractor. “People were talking about the end of physics. Relativity and quantum looked as if they were going to clear out the whole problem between them. A theory of everything. But they only explained the very big and the very small. The universe, the elementary particles. The ordinary-sized stuff which is our lives, the things people write poetry about – clouds – daffodils – waterfalls – and what happens in a cup of coffee when the cream goes in – these things are full of mystery, as mysterious to us as the heavens were to the Greeks…" - Arcadia by Tom Stoppard

H2007: Skills that Could Save Your Life #74 in Splash! 2008 (Nov. 22 - 23, 2008)

Wait!? Do I know that person? We're going to pass each other - do I stop, do I wave, do I smile, how long should I maintain eye contact?! ... How to survive... dun dun dun Social Navigation of Public Transportation (Subways, Busses, Elevators, Escalators, and Hallways -- note: we are well aware of the current contentions concerning moving sidewalks, but, so as not to prematurely discourage and confuse introductory-level students, this material will not be covered in class)

M2008: Mathematical Analysis of the Psychology behind Noise and Music in Splash! 2008 (Nov. 22 - 23, 2008)

Gregorian chants are boring, Post-modern noise is insane, Pop music is incredibly repetitive, and Improve Jazz is recognizable as music, but is certainly not predictable. From a psychological perspective – WHAT?! However, mathematically, our enjoyment of music over noise and scales is a recognizable and, yes, computer-reproducible phenomena. Come listen to funny noises and bizarre music for an hour and learn what computations make your mind happy.

S2009: Information Theory and Entropy in Splash! 2008 (Nov. 22 - 23, 2008)

What is information? And how does physics manage to loose it? Will the universe die as a result? When I was in high school, I was slammed face first into an enormous paradox in how our physics was taught: Given completely reversible equations describing all of mechanics, somehow, by probability, the universe was irreversibly tending towards disorder – towards heat death (the warm kind, not the hot kind). Teachers tried to explain how ‘disordered’ states were simply more likely, however, given infinite time, shouldn’t even the most unlikely result occur? Beginning with an introduction to binary, this course will rigorously derive what your teachers should mean by entropy. By rigorous, I mean derived from the mathematics of Claude Shannon’s information theory.

S2010: Defining Life (A science/math class, NOT a philosophy discussion) in Splash! 2008 (Nov. 22 - 23, 2008)

What is fire? Is it alive? How about a growing crystal? Or a virus? Or Clouds? Or a computer? But what definition can include these, include grass and frogs, but not rocks? Surly the phenomena of life are interesting and distinct enough to warrant a definition answering the above questions, but can you think of one? I find textbooks and Wikipedia even lacking in this regard – as, at the least, ‘life’ seems to have little to do with ‘having cells.’ But what else is completely unique to everything that we think of as alive? Please play around with this before class: http://www.bitstorm.org/gameoflife/ and this: http://psych.hanover.edu/JavaTest/Play/Life.html for the rules and theory: http://en.wikipedia.org/wiki/Conways_Game_of_Life - and we’ll discuss this more in class

M1472: The Fringes of Chaos in HSSP Fall 2008 (Sep. 13, 2008)

S1473: Biology and Astrobiology in HSSP Fall 2008 (Sep. 13, 2008)

Starting from the basic chemistry of cellular biology and the astronomy of stellar and planetary formation, I will, in class, build up the structure of life on Earth and the history of how it evolved. In parallel, I will introduce our best hypothesizes concerning the blueprints for life on planets with different properties than earth: more or less gravity, different atmospheric conditions, and/or exposure to different spectra or amounts of radiation.This research is know as Astrobiology: the interdisciplinary study of life in the universe, combining aspects of astronomy, biology and geology. Lecture topics will range from an introduction pf chemical biology (good for people preparing for AP bio) to the definition of life to types and life cycles of stars to the ecosystems found in high methane high heat undersea vents to the evolutionary history of whales to NASA's current predictions for life on undiscovered planets and the currently observed signs for past and present life on Mars.

H1448: Cultural Secrets in the Arts in HSSP Summer 2008 (Jun. 29, 2008)

What hides behind the masks of El Día de los Muertos? in the webs of Native American Dream Catchers? under the Henna of Indian tatoos? What lurks in wait between the cracks of South African Batik, among the brush strokes of Chinese Brush Painting? tied away by the knots of English crochet? Spooky, eh? And only one way to find out. Most of the class will be doing art, but we will focus on the culture behind the techniques.

S1467: Biology and Astrobiology in HSSP Summer 2008 (Jun. 29, 2008)

Starting from the basic chemistry of cellular biology and the astronomy of planetary formation, I will, in class, build up the structure of life on Earth and the history of how it evolved. In parallel, I will introduce our best hypothesizes concerning the blueprints for life on planets with different properties than earth: more or less gravity, different atmospheric conditions, and/or exposure to different spectra or amounts of radiation.This research is know as Astrobiology: the interdisciplinary study of life in the universe, combining aspects of astronomy, biology and geology. Lecture topics will range from an introduction for chemical biology (good for people preparing for AP bio) to the definition of life to types and life cycles of stars to the ecosystems found in high methane high heat undersea vents to the evolutionary history of whales to NASA's current predictions for life on undiscovered planets and the currently observed signs for past and present life on Mars. This class has no prerequisites: introductary chemistry, biology, and physics will be covered as needed.

J1439: Magrathea: A Natural Science Class with a Science Fiction Twist in Junction Summer 2008 (Jun. 30, 2008)

"Magrathea?" -- Watch This: http://www.youtube.com/watch?v=MbNtlS69HhU Starting from the basic chemistry of cellular biology and the astronomy of planetary formation, I will, in class, build up the structure of life on Earth and the history of how it evolved. In parallel, your projects (which you will be expected to work on mostly outside of class) will be to hypothesize and create the blueprints for life on planets with different properties than earth: more or less gravity, different atmospheric conditions, and/or exposure to different spectra or amounts of radiation. In non-fictional science, this research is know as Astrobiology: the interdisciplinary study of life in the universe, combining aspects of astronomy, biology and geology. Lecture topics will range from the types and life cycles of stars to the ecosystems found in high methane high heat undersea vents to the evolutionary history of whales to NASA's current predictions for life on undiscovered planets and the currently observed signs for past and present life on Mars. This class has no prerequisites: introductary chemistry, biology, and physics will be quickly covered as needed, but be prepared for fast paced classes and assignments that require significant research and creative reasoning. Every day will be intense and will require the full participation of all students. Come with an open and inquisitive mind and the work ethic to support it!

M1119: The Fringes of Chaos in Spark! Spring 2008 (Mar. 08, 2008)

This small discussion course will dive headfirst into the the key concepts of Fractals including Symmetry, Expressible Infinity, and Chaos. Specifically, we will take an in depth look at the Sierpinski Triangle (briefly covering the difference between fractal dimension and topological dimension), the Lorenz Water Wheel (illustrating the ideas of the Butterfly Effect and Strange Attractors), and the well-known Mandelbrot Set. If you want to see mathematics from a completely alien perspective, this class is for you. This class is the first session of a ten session HSSP class. The full description is available in the HSSP catalog, however, here's an excerpt: The common theme throughout this class is dynamic complexity, or, in a word, chaos --- the chaos of the Mandelbrot fractal, the chaos of the universe that increases infinitely with time, the chaos that marks the edge of the set of patterns comprehensible to the human mind. We will cover, in depth, the concepts surrounding and intertwining between Fractals, Entropy, and Universal Symmetries. Come with an open and inquisitive mind and the work ethic to support it!

S1124: Human Vision in Spark! Spring 2008 (Mar. 08, 2008)

From the physics of optical lenses, to parallax, to the chemistry of rods and cones, this class will explore, in depth, the mechanisms of human vision. Three lecture segments will be broken by two blocks of hands-on lab. The first lecture will be an introduction to the eye biologically and to the physics of the eye's lens . The first lab will be on the mathematics of how parallax gives you depth perception. The second lecture will dive into the chemistry of the rods and cones which lead to our experiences of light and color. The second lab will be a series of experiments on the associated phenomena of “primary colors.” And the final lecture will introduce some of the neurological components of sight, specifically those which lead to our experience of optical illusions.

H1137: Skills that Could Save Your Life #158 in Spark! Spring 2008 (Mar. 08, 2008)

What the heck? That napkin's shaped like a swan... And it's holding silverware! How to survive... dun dun dun Formal Dinner Boredom (including the top 5 napkin creations I've figured out, even that silverware-holding swan.)

M1118: The Fringes of Chaos in HSSP Spring 2008 (Mar. 15, 2008)

The common theme throughout this class is dynamic complexity, or, in a word, chaos --- the chaos of the Mandelbrot fractal, the chaos of the universe that increases infinitely with time, the chaos that marks the edge of the set of patterns comprehensible to the human mind. This class will be like none other you have ever seen, and I may as well have filed it under physics or liberal arts instead of mathematics. There will be many days when we are extremely rigorous -- assignments which ask for mathematically presented proofs -- and days when we can't be rigorous simply because the questions we will discuss are still unanswered by science and mathematics at large. We will cover, in depth, the concepts surrounding and intertwining between Fractals, Entropy, and Universal Symmetries. We will discover the connections between these ideas through lectures and projects which range from online mathematical applets to discussions about required reading material. Every week will be intense and will require the full participation of all students. Come with an open and inquisitive mind and the work ethic to support it!

We're Knot Doing any Math in DELVE (2011)

Basically, we're going to hang out and play some games. These games may or may not be related to knot ...

Chaos and Strange attractors (FC part 3) in JUNCTION (2010)

Banned to the backs of math textbooks as the “monsters” of mathematics, chaotic dynamics has become a frontier of physics. ...

Chaos + Information Theory -> Entropy (not the stupid version) (FC part 4) in JUNCTION (2010)

In school, you may have been taught the stupid definition of Entopy: "an increase in the 'disorder' of a system." ...

Fractals and Fractal Dimension (FC part 2) in JUNCTION (2010)

This class is a continuation of the material in Fractals and Fractal Dimension.

Keeping the Earth From Going ‘Foom’ in JUNCTION (2010)

Every second, the sun radiates, in addition to light, more than a million tons of protons and elections. If the ...

Test Class in JUNCTION (2009)

hmm, I'd usually make this section a joke about niki... but, for some reason, I'm feeling nice and genteel today... ...

Human Vision in SPLASHONWHEELS (2008)

From the physics of optical lenses, to parallax, to the chemistry of rods and cones, this class will explore, in ...

Math through a Kaleidoscope in SPLASHONWHEELS (2008)

This small discussion course will dive headfirst into the the key concepts of Fractals including Symmetry, Expressible Infinity, and Chaos. ...

The Optimal Strategy in SPLASHONWHEELS (2008)

Will two prisoners separately offered deals to betray their parters remain loyal to minimize total loss of liberty, or will ...