2008 Talks

Here is the list of courses that were offered at cSplash 2008.

Icons




indicate difficulty rating, in ascending order.

Description of the icon system.

Colloquium Speaker

Teacher info: Leslie Greengard (math prof)

Period 1


Be A Scientist NOW (part 1)

"The whole of science is nothing more than a refinement of everyday thinking."
- Albert Einstein

Being a scientist requires little more than an eagerness to
discover. Million dollar equipment, a renowned university, or guidance
from someone called "Professor" is not always necessary to obtain
meaningful scientific results. During the first half of this course, we
will discuss what a "scientific result" means and will see that the
thought process that yields it is not very different from everyday
thinking. We will also talk about current scientific research that is
performed with resources that are readily available to most high school
students. During the second half, we will follow up by considering
remaining issues that prevent high school students from producing such
science and will discuss how to remedy these barriers. Finally, we will
end by formulating research questions that students can answer through
their own scientific inquiries, NOW.

Length: 150 minutes (2 periods)

Prerequisites: A desire to try being a scientist. Mathematical Sophistication Required: None

Teacher info: Will Findley (findley at nyu.edu), NYU Physiology and Neuroscience Departments, Grad student



Exploring Fractals with Maple

You may have seen fractals appear on tee-shirts, desktop
graphics or calendars, but those chaotic patterns appear in many
complex branches of science that are of importance to us, like weather
prediction, fluid dynamics, celestial mechanics, biological systems,
financial markets and many more. In this course, we will not do
anything that complicated, but we will learn what fractals are, how
they arise and how to calculate their dimensions. We will then use the
Maple computer software to generate a few nice fractal graphics. No
prior knowledge of Maple or programming is needed since we will work
through all the steps ourselves.

Length: 75 mins

Prerequisites: Not much. Just the will to learn new (and cool) things!

Teacher info: Enkeleida Lushi (lushi at cims.nyu.edu), NYU Math Department, 2nd year PhD student



Models of Human Learning

It's tempting to believe you are an expert in how you learn.
After all, you have been at it for over a decade. But have you asked
yourself what kinds of thought are most responsible for your
intellectual progress? If so, how do you know you are right? For
example, if you wanted to understand a new concept like a "standard
deviation," what would you do? Would you practice repeatedly plugging
in numbers into a formula? Would you try inventing your own formula?
Your approach will depend on your model of learning. While we all have
such models, many of us have never stated or questioned them. This
class will begin by helping you articulate your own model of learning.
We will then see what experimental predictions your model makes. At
this point, you may feel it needs some revision. We will then compare
your ideas to those of experts on human learning. After testing several
models through experiments in class, we will see what they say you can
do to improve your learning.

Length: 75 minutes

Prerequisites: A willingness to question how your own mind works.
Mathematical Sophistication Required: None!

Teacher info: Paul Hand (hand at math.nyu.edu), NYU Math Department, 4th year Grad student



Electrical Hearing

If you know someone who has lost their hearing due to an injury
or a degenerative disease (or if you have ever watched a medical drama
on TV), then you have probably heard of a cochlear implant. A cochlear
implant provides electrical hearing to someone whose ear no longer
functions by directly converting sound vibrations in the air into
electrical pulses that are delivered to the brain. Sound like science
fiction? The reason this works is because engineers can imitate the
natural function of the inner ear, which operates on some basic
principles of mathematics and physics - with a little biology mixed in.
We will learn about these principles, experience how the world sounds
to people with cochlear implants, and talk about some of the challenges
this technology still faces.

Length: 60 minutes (9:30-10:30am)

Prerequisites:
You should have some basic understanding of the physical nature of
sound and be familiar with the concepts of wave frequency, wavelength,
and amplitude.

Teacher info: Maria Ter-Mikaelian (maria at
cns.nyu.edu), NYU Center for Neural Science, graduate of the
Neuroscience Ph.D. program (January 2008)



Smart Bugs: Parasite-Host interactions

For all our intelligence and genetic complexity, humans are
still plagued by tiny bugs -- parasites! How do these smart bugs know
how fast to grow? How do they know that certain areas in their genome
will be detected by their host, and then change those areas quickly to
avoid identification and death? We will look at parasites including the
ones that cause malaria, learn about the math of population growth and
mutation rates, and see why these parasites seem to be so smart!

Length: 75 minutes

Prerequisites: Basic knowledge of probability and biology would be helpful.

Teacher info:
Shaila Musharoff (sm2734 at cs.nyu.edu), NYU Computer Science
Department, 2nd year Masters student. President of NYU's Women in
Computer Science organization.



Graph Theory and the Donut

Draw five dots on a page. Can you connect them without crossing any
lines? We'll (rigorously) solve this puzzle --and answer lots of other
questions about dots and lines-- in this investigation into Topological
Graph Theory. And the answers will not be limited to the plane: can you
connect the same five dots if they're sprinkled on a donut instead of
drawn on a piece of paper? Why would that be easier or harder?

Related to: An Introduction to Graph Algorithms and Complexity, The Euler characteristic

Length: 75 minutes

Prerequisites:
We'll introduce a lot of new vocabulary quickly and I'll ask you to
think a little on your feet. That said, you don't need any knowledge in
advance, just an already-awake brain!

Teacher info: Marisa Debowsky (mad464 at cims.nyu.edu), NYU Math Department, 3rd year grad student



Goedel, Euclid, Hilbert

In this class, we will try to understand why there still is such
a buzz around Goedel's two incompleteness theorems. In the first half
of the class, we will put these theorems in a historical perspective.
We will analyze the works of Euclid and Hilbert to understand the
problems with axiomizing mathematical theories, and study some famous
paradoxes which have led Hilbert to his search for an internal proof of
the consistency of the Peano axioms for arithmetic. (End of the 1st
half). We will then spend the second part of the class showing how
Goedel ruined Hilbert's hopes with his proof of the Incompleteness
theorem. To get there, we will need to introduce basic concepts of
first-order logic, and will give the proof of Goedel's completeness
theorem. Interested? (End of the 2nd half).

This class is rated blue/black.

Related to: Formal Deduction and Type Theory

Length: 75 minutes

Prerequisites:
No specific mathematical knowledge is required. The first half of the
class will be mostly descriptive, and pretty easy to follow. The second
part, however, will be much more technical and abstract!

Teacher info: Antoine Cerfon (antoine.cerfon at gmail.com), MIT Department of Physics, 3rd year PhD Student



On the Size of the Infinite

Infinity is big. No, really really big. You can count all your
life and never get there. Or halfway there. Or 1% there. Or really any
more than 0% of the way. Just as mathematics gives us a language for
dealing with large natural numbers, it gives us the language of
cardinality it to get a handle on the infinite.

In this class, we will ask (and answer!) whether there are more
rational numbers than integers, or more real numbers than rationals? Or
if infinity plus one is actually any larger than infinity? (Hint: one
of those three answers is yes.) What does it even mean for an infinite
set of numbers to be larger than another? Is there a smallest infinity?
A largest? You'll grapple with these concepts on an intuitive and a
formal level. Come prepared to think outside the box.

Length: 75 minutes

Prerequisites: None.

Teacher info: Michael Shaw (mshaw at mit.edu), Stanford University Physics Department, 1st year PhD student



Introduction to Computer Architecture

You use computers every day, but have you ever wondered how they
really work inside? Or why your new computers have names like "Core
Duo"? In this course we'll explore some of the basics of computer
architecture and programming. We'll start with an overview of computer
organization (things like what a CPU is and how memory in a computer is
structured). Next we'll briefly discuss how programming works and how
the code you write in a language like Java, PHP, or C gets translated
into something the computer can actually understand. We'll move fast,
so that we have time to finish with a brief overview of the frontier of
current architecture research: multicore systems and concurrent
programs. It's an exciting time to be a researcher in computer
architecture these days, as the shift to multicore systems
fundamentally changes how computers are designed. Thus there are lots
of interesting open problems to be solved - come find out what it's all
about.

Length: 75 minutes

Prerequisites: Prerequisites: Basic Algebra is helpful. Some programming experience in any
language recommended but not strictly necessary.

Teacher info: Eric Hielscher (hielscher at gmail.com), NYU Computer Science Department, 1st Year PhD student



Liar Games

Paul is trying to find a number from one to one hundred by
asking ten Yes/No questions of Carole. But, Carole can LIE, though she
may only lie at most one time. Can Paul win? Can Carole (playing what
is called an adversary strategy) win? If q is the number of questions
what is the largest n for which Paul can win? We will devise what is
called a weight function for a position. Using it we will to give
optimal strategies for both Paul and Carole.

BTW: Paul is Paul Erdos, the legendary questioning mathematician. Carole is an anagram -- for what?

Length: 60 minutes (9:45-10:45am)

Prerequisites: No calc, no trig. Only that elusive mathematical maturity.

Teacher info: Joel Spencer (spencer at cims.nyu.edu), NYU Math and Computer Science Departments, Professor


Period 2


Bioethics

We do not realize how we are all impacted by the controversial
issue of bioethics in our current world. Would you like to have your
doctor use a blood sample without your knowledge and consent with the
potential of making billions of dollars in the pharmaceutical industry
with your own very body specimens? Do you know that our bodies can
potentially hold unique chemicals or specimens that could lead to huge
scientific breakthroughs? This is among the many issues involving the
world of bioethics. In this class, we will go over the fundamentals of
bioethics, what has spurred controversy, and we will then have a group
discussion over our opinions over these issues.

Length: 60 minutes (11am - noon)

Prerequisites: A biology class will enhance your appreciation for this course.

Teacher info: Sharon Monassebian (srm309 at nyu.edu), NYU College of Arts and Sciences, Junior Undergrad



How to Solve a Problem without Knowing Anything (Almost)

When Ph.D. candidates in Physics at the University of Chicago
went before their committee in their final oral exam, they were
expecting to answer difficult questions on abstruse topics like quantum
field theory or general relativity. If Enrico Fermi was on the orals
committee, however, he would ask questions such as, "How many piano
tuners are there in Chicago?" The idea was to learn if the candidate
had learned to think like a physicist, which means facing unpredictable real world problems.

The
art of doing science involves figuring out what the answer to a problem
should look like before doing lengthy, complicated calculations or
experiments. Anyone can learn how to approach a problem that seems
forbidding, and to tease out the essentials of the answer using simple
reasoning and a few educated guesses. This class will introduce you,
through an example or two, to how this is done. But it requires your
participation and interaction.

This is not your parents'
physics class (if they took one). Be prepared to learn that your
everyday experiences contain a lot of quantitative information about
the physical world.

Length: 60 minutes (11am - noon)

Prerequisites: 9th-grade algebra.

Teacher info: Daniel Stein (daniel.stein at nyu.edu), NYU Dean of Science, Professor of Physics and Mathematics.



Group Theory and its Applications

We will take a 75-minute journey through the world of group
theory, a somewhat mysterious generalization of concepts taught in high
school algebra. Starting with several rules like "multiplication," we
will build up a cohesive structure, and then study its properties
(associativity, commutativity, etc). Once we have a grasp on how this
thing works, we'll see some very interesting applications in
probability and number theory.

This class is rated green/blue.

Related to: Introduction to Number Theory and Cryptography

Length: 75 minutes

Prerequisites: High school algebra.

Teacher info: Karol Koziol (karolkoziol at nyu.edu), NYU Math Department, Junior Undergrad



Be A Scientist NOW (part 2)

See part 1 above for details.



A Quick Introduction to Visual Neuroscience

How do you understand what you see? You may remember that your
eyeball has a lens, which focuses the image in front of you onto your
retina --- a layer of cells which respond and send signals deeper into
your brain. But what happens then? What does our brain do with that
information? I won't be able to answer these questions, but I'll
describe some of the things that we do know, and present many interesting visual illusions which raise even more questions about the visual system.

Length: 60 minutes (11am - noon)

Prerequisites: Little to none.

Teacher info: Aaditya Rangan (rangan at math.nyu.edu), NYU Applied Math Department, Assistant Professor



Plague, Flu, AIDS, smallpox: using math to model the spread of disease

We will study the spreading of different diseases using a
mathematical model. We will begin by using a model developed by Kermack
and McKendrick in 1927 that can be used to explain many different
epidemics that have occurred in history, like the influenza epidemic of
1918-1919 or the spreading of the Great Plague. How can one model
represent so many different epidemics?

Most of the time in this class will be spent on developing the
model and looking at different solutions of the model. Most importantly
we will study how do we know when the epidemic spreads and when does it
die out. Depending on time, we will learn how to make the model more
specific, possibly for a specific disease, or how to include
vaccinations and so on.

Length: 60 minutes (11am - noon)

Prerequisites: None.

Teacher info: Shilpa Khatri (khatri at cims.nyu.edu), NYU Math Department, 5th year PhD student.



Introductory Survey of Computer Engineering Major

If you think you have interest in hardware, and software alike,
and you want to, or thinking about to major in computer engineering,
this talk is the one that you want to attend. We will talk about truth
tables, number representations, adders, flip-flop circuits, logic gates
and much more. If that scares you, don't worry! Everything from the
basics will be discussed! In addition, the future of computer
engineering major will be discussed with emphasis on research
opportunities in this field. Any questions related to selecting
computer science, electrical engineering, or computer engineering major
will also be answered.

Length: 60 minutes (11am - noon)

Prerequisites: none

Teacher info: Zeeshan Mughal (zeeshan.jp at gmail.com), Stony Brook Computer Engineering
Department, 1st year undergraduate student. cSplash alum!



Genetic Algorithms

It is all about survival of the fittest in problem-solving
techniques! Living organisms continue to perfect themselves through the
process of evolution. They exhibit versatility and ability to change
and adapt whenever necessary. If problem-solving techniques can follow
such a process, solutions may be more easily attainable than
traditional methods. Genetic algortihms are search procedures based on
the mechanics of natural genetics and natural selection. They are
increasingly being used to tackle difficult problems of engineering,
science, and commerce. In this course, you will take a close look at
what genetic algorithms are, where they come from, how they work, and
how and where they have been applied. You may be surprised at how well
these algorithms perform!

Length: 60 minutes (11am - noon)

Prerequisites: Basic mathematical knowledge in algebra and system of binary numbers will be required. Other concepts will be introduced in
class.

Teacher info: Preeti Parikh (preeti10583 at gmail.com), NYU Math Department, Graduated in Sept 2007 with Master's in Scientific Computing



Linkages

A linkage can be thought of a robotic arm in the plane - a graph
with a set of edges whose lengths will remain fixed. For some
configurations, we can move the vertices around (keeping the edge
lengths fixed) freely (think of a square or a rhombus), we call these
flexible. In other situations, this is impossible (think of the sss
test for triangles), we call these rigid. In this class, we will talk
about what makes certain configurations rigid and others flexible. We
will discuss what a robotic arm with a pencil on the end of some arm
could create using linkages (the answer is very surprising - almost
everything is possible!). Finally, we will see the weakest conditions
that are necessary to make a linkage rigid.

Related to: Graph Theory and the Donut

Length: 75 minutes

Prerequisites:
There are very few prerequisites, but this will be a fast moving class.
Good spatial orientation skills will be important, basic high school
geometry (geometric shapes, distance formulas, etc.) is necessary, and
knowledge of graph theory may be helpful.

Teacher info: Michael Burr (burr at cims.nyu.edu), NYU Math Department, 3rd year PhD student



The Euler characteristic: a way to understand surfaces

There are some two-dimensional surfaces that we all know about:
like beach balls or the inner tubes from your bicycle. There are also
some strange surfaces that we never see in ordinary life such as the
Klein bottle (which has no inside or outside). Well, what kinds of
surfaces really are there? The "Euler characteristic" is a concept that
helps us answer that. In this class you will learn to think about
surfaces like a topologist (that's someone who thinks their coffee mug
and doughnut have the same shape - think about it!).

Related to: Graph Theory and the Donut

Length: 75 minutes

Prerequisites: If you can figure out how many edges appear in an icosahedron (or maybe
just a cube) and if you can draw a real-looking doughnut (the kind with a
hole) then you'll probably be fine.

Teacher info: Carl Gladish (gladish at cims.nyu.edu), NYU Math Department, 1st year PhD student


Period 3


The Joy of Programming

In this class, you will learn about the fundamentals of computer
programming with a very cool high-level programming language called
Python. In an hour, you should be able to grasp the basics of
programming and the rest is up to you: curiosity will lead you to
bigger, better and more fascinating things! Keep learning on your own
and you can do all sorts of cool stuff: build dynamic web sites that
talk to databases, find matching DNA sequences in the Human Genome
project, pretend to be a human being in a chat room, filter spam from
legitimate emails, do some basic spell-checking like Google does...who
knows what, it's up to your imagination! (I will also introduce you to
other languages you can play with, so you can choose whatever helps you
to think better.) But wait...are there things that a computer can
never, ever do, no matter how hard you try? Yes, as shocking as it is,
there are! Time permitting, I will guide you on how to find some of
these mind-blowing impossible things by yourself!

Length: 75 minutes (Block 3a: 12:30 - 1:45pm)

Prerequisites:
Math? What math? You will learn about the basic building blocks of
mathematics itself, so don't worry, come without any fear! But bring a
laptop if you have one, because I might give away free Ubuntu GNU/Linux
CDs or at least tell you how to get it for free.

Teacher info: Trishank Karthik (trishank.karthik at nyu.edu), NYU Computer Science Department, 1st year MS student



The CPU, Revealed

This course reveals the inner workings of the CPU, the heart of
every computer. We will design a simple CPU, down to the (zero or
one-carrying) wires. Then we'll trace the execution of a computer
program, leaving no mysteries unrevealed. Time permitting, we'll also
talk about high-level programming languages. This course is for
everyone unsatisfied by explanations that don't reach to the very
bottom.

Length: 75 minutes (Block 3a: 12:30 - 1:45pm)

Prerequisites: You need to know what binary (base 2) numbers are and have some basic boolean logic (and, or, not).

Teacher info: Yotam Gingold (gingold at cs.nyu.edu), NYU Computer Science Department, 5th year PhD student



Girls in Math

Are you interested in studying mathematics, but shy about being
coined as "girl in math"? If you have ever felt alienated as a female
interested in mathematics, you are not alone! Come join us as for a
panel discussion on women in mathematics. We know what it's like, and
we want to encourage you to pursue mathematics in college and beyond.
We will talk about the history of women in mathematics, resources that
are available to women in the field, and any questions or experiences
you might like to discuss. Boys are welcome to attend!

Length: 75 minutes (Block 3a: 12:30 - 1:45pm)

Prerequisites: Interest in Mathematics!

Teacher info: Jessica Lin (jessicalin at nyu.edu), NYU Math and Physics Departments, Junior Undergrad



Programming Art (part 1)

In this class you will be learning the basics of Processing, an
object oriented computer language used to program images, animation,
and interactive environments. We will overview the basics of the code,
and learn to create our own images, and touch on animating the images
we create. You will leave this class with enough knowledge to create
your own images, and understand the basics of animating these images.
You may be astounded by the small amount of code needed to create a
beautiful, individual, animated, environment with the ability interact
with a user.

Length: 150 (two 75-minute blocks: 3b and 4)

Prerequisites: None.

Teacher info: Samantha Richman (scr259 at nyu.edu), NYU, Gallatin, computer programming, and art concentration.



A Random Walk to Diffusion Town

So you think you can beat the house? Even if the game is fair...
in the long run you are toast! We will explore the simplest random
behavior, the random walk, in which a particle (or body, or stock
price) bounces around on a "predictably unpredictable" path. The random
walk is used to model systems in a wide variety of fields. We will
learn about the Gambler's Ruin problem, and see how none of your fancy
betting schemes are going to help you avoid long term disaster. As a
second application of the random walk, we will learn about bacterial
chemotaxis, where microorganisms propel themselves towards food and
away from danger in an erratic way.

If instead of a single body we set many bodies out for random
walks, we will find that the individual random behavior can give rise
to a coherent group behavior, which in this case amounts to something
called diffusion. We will look at the properties of diffusion, and we
will learn about some applications. For example, we will discuss the
diffusion of a gas in a liquid, and diffusion as a (frequently
incorrect!) model of stock price behavior.

Length: 75 minutes (Block 3b: 1:15 - 2:30pm)

Prerequisites:
You should know about logarithmic and exponential functions. It would
help to know a thing or two about probability, but we'll cover
everything we need.

Teacher info: Saverio Spagnolie (saverio at cims.nyu.edu), NYU Math Department, 6th year PhD Student



Einstein's Special Theory of Relativity

According to Einstein, if you watched a 100 ft. long train car
pass you at a very high speed, it would appear to be shorter than 100
ft.long. If, as the train was passing you, you looked at a clock on the
train and compared it with your own watch, it would be ticking slower
than your own watch. Einstein's special theory of relativity not only
predicts this but dramatically changes the way we perceive events in
time and space. It also puts a universal speed limit on everything: the
speed of light. In this class, we'll investigate how Einstein came to
these conclusions and explore some of the seeming "paradoxes" that
arise as a result of it.

Related to: General Relativity and Black Holes.

Length: 75 minutes (Block 3a: 12:30 - 1:45)

Prerequisites:
High school algebra and trig. A high school physics class (basic
kinematics, momentum, energy) would also be good, but you could get by
without.

Teacher info: John Thompson (jdt257 at nyu.edu), NYU Physics Department, 3rd Year Undergraduate



Introduction to Number Theory and Cryptography

Have you ever wondered how websites keep your credit card number
secure when you buy something online, or how you can send a secret
message over the internet? It's simple, public key cryptography, or
RSA. In this class we will learn the math behind keeping your identity
safe. We will start by learning some basic properties of the integers
and prime numbers and apply them to learn how the RSA algorithm works.
We will then explore why RSA is so safe and possibly talk about some of
the weaknesses of public key cryptography.

Related to: Group Theory and its Applications

Length: 75 minutes (Block 3b: 1:15 - 2:30pm)

Prerequisites: Basic algebra, quick elementary school long division; you should also know what a prime number is.

Teacher info: Dan Mitchell (dam444 at cims.nyu.edu), NYU Math Department, 1st Year MS student



Generating Functions

Suppose you have an infinite sequence of numbers. Maybe it's a
boring one like 1 1 1 1 1 1... Maybe it's a bit more interesting, like
1 1 2 1 3 1 4 1 5 1... And there is no limit to how challenging we can
make these things. How about 1 1 3 2 6 0 10 3 15 4 21 0... (can you see
the pattern on this one?). You want a way to describe the terms of the
sequence. Of course there are many ways, but I want to show you how to
write down a function (for example, it's f(x)=1/(1-x) for the boring
example) that, while having nothing to do with the sequence at first
glace, actually encodes all the terms of the sequence in a clever way.
We won't be concerned with applications in this class, you should think
of this as a "find the function" game.

Length: 75 minutes (Block 3b: 1:15 - 2:30pm)

Prerequisites: No previous knowledge will be assumed, but we'll see a lot of material in a short time.

Teacher info: Juliana Freire (jufreire at gmail.com), NYU Math Department, 3rd year PhD student



Fourier Analysis and "the most frequently cited mathematics paper ever written".

What is Fourier Analysis and why is this subject so profoundly
important in the study of probability, differential equations, heat
flow, music, X-Ray diffraction and DNA (among other things)? I will
outline the basics of this subject and try to explain why it is so
remarkably useful while shallowly immersing you in a few applications.
I will then discuss how Fourier techniques can be implemented on a
computer, and perhaps touch on the theory of 'distributions', those
sinister and beautiful 'functions' that aren't really functions at all
(and which are so important to the subject).

Related to: Formal Deduction and Type Theory

Length: 75 minutes (Block 3b: 1:15 - 2:30pm)

Prerequisites:
Familiarity with the sine, cosine, exponential and logarithm functions,
as well as a basic understanding of derivatives and integrals will all
come in very handy.

Teacher info: Spencer Greenberg (willfind at gmail.com), NYU Math Department, 2nd year PhD student



Formal Deduction and Type Theory

To begin with, we introduce relatively standard Laws of Logic,
and a Type System for a Programming Language. Immediately an element of
surprise may appear, as though we just have done the same thing twice.
This is called the Curry-Howard correspondence. We shall strictly
distinguish between classical and non classical Logics (which will be
defined), and see another spectacular manifestation of this distinction
in computing, by considering the infamous Laws of Double Negation and
Excluded Middle. Using all this material we are going to look at the
famous principle of Mathematical Induction, and in particular, at the
question of its (non) derivability from other logical Laws. We then
shift gears and prove the Tarski Theorem, saying informally that any
consistent Logic can't fully "understand" itself. The conclusion will
consist of a very short and easy proof of Goedel's Incompleteness
Theorem for Curry-Howard style deductive systems.

Related to: Goedel, Euclid, Hilbert

Length: 75 minutes (Block 3a: 12:30 - 1:45pm)

Prerequisites: Familiarity with Lambda Calculus or Formal Logic will be helpful, but not required. I will introduce them as we go.

Teacher info: Igor Shikanyan (igor at cs.nyu.edu), NYU Computer Science Department, 7th year PhD student


Period 4


Programming Art (part 2)

See part 1 above for details.



The Nature of Invention in Computer Science -- a collaborative reflection

This talk takes excerpts from a book of biographies (Out of
their Minds: the lives and discoveries of 15 great computer scientists)
in order to explore:

  1. the source of their discoveries in their life experiences;
  2. the nature of their discoveries and the common threads that link them together;
  3. lessons that we can all learn from the style of these creative individuals.

Length: 60 minutes (3-4pm)

Prerequisites: Junior high school math.

Teacher info: Dennis Shasha (shasha at cs.nyu.edu), NYU Computer Science Department, Professor



Flash Animation using ActionScript 3.0

Flash, the seemingly ever-present Web multi-media and
programming platform, is powered by the increasingly sophisticated
scripting language ActionScript. In this brief introduction, we will
first explore the Adobe Flash drawing tools, stage, timeline, and
library to create some interesting animations. We will then delve into
some of the basics of ActionScript 3.0 to control these movies.
Although it is fun to use, ActionScript is far from being a toy. In
fact, it has become a powerful programming language, and in just a few
steps we will be able in a to create a simple interactive program that
could serve as the basis for a video game. While creating these
cartoons, animations and games, we will demonstrate several computer
programming concepts which are also used in many other languages
ranging from C and Pascal to more modern languages like Java.

Length: 75 minutes

Prerequisites: Basic understanding of simple computer skills. A background in beginning programming will be helpful, but not necessary.

Teacher info: Nathan Hull (hull at cs.nyu.edu), NYU Computer Science Department, Clinical Associate Professor



The Math of Bits and Bytes

To store or transmit images, music or videos using computer
technology, one needs to represent them in digital form - as a sequence
of bits, i.e. zeros or ones. In order to minimize transmission times,
one is looking for a representation that uses as few bits as possible.
Images for example are far from random. The more of that regularity you
can use, the more efficient your encoding will be. You will experience
that yourself, when you design your own digital representation method
for images. You will see that knowing how likely different color
combinations are, can already improve your efficiency tremendously.

Length: 75 minutes

Prerequisites: Some elementary probability.

Teacher info: Felix Krahmer (krahmer at courant.nyu.edu), NYU Math Department, grad student.



Math of Music I: The Physics of Sound and Musical Instruments

Ever wonder how the piano works? or why the violin sounds
different than the clarinet? or how computers can imitate different
instruments? The answer to all of the above questions lies in the
interesting and intimate relationship between mathematics and music. We
will look at the physics and math behind musical instruments and what
physical principles are at work when you play an instrument. We will
start with basic properties of sound waves, like superposition,
interference, and standing waves. Then we will look at how each type of
instrument produces sound, starting from string instruments and onto
winds and brass instruments. Finally we will look at digital media and
how computers can generate sounds of different instruments. It should
be a very interesting class, especially if you enjoy music or play a
musical instrument!

This class will be followed by Math of Music II: Tuning
Systems. The classes are related, but independent, and you can take
one, the other, or both!

Length: 75 minutes

Prerequisites:
High-school algebra and trigonometry. Students should be familiar with
sine and cosine as functions of real variables and their graphs. Some
experience with high-school physics is recommended, but not required.
Most importantly, a strong interest in math and/or music.

Teacher info: Arthur Yu (xy244 at nyu.edu), NYU Math and Physics Deparments, Senior undergrad, music enthusiast.



How do brain cells think?

Neurons are, loosely speaking, the cells in the brain that do
the thinking. In this class we explore what it means to build a
computational model of a neuron. Why do it at all? What assumptions do
we make? How many annoying biological details can we throw away before
we lose touch with reality?

We'll start with a discussion of how
real brain cells communicate and what features we might want to build
into a model cell. Then we'll implement those features, using physical
analogy, simple mathematical expressions, and computer code. Finally,
if time permits, we'll see whether networks of these abstract neurons
can perform like (very) simple brains.

Length: 75 minutes

Prerequisites:
The class involves simple electrical circuits, a little biology,
rudimentary programming, and a whiff of calculus. Some familiarity with
any or all of those would be helpful, but is not assumed. We'll aim for
an intuitive presentation, utterly lacking in mathematical rigor.

Teacher info: Robert Levy (rlevy at cns.nyu.edu), NYU Center for Neural Science, Postdoctoral Fellow



Introduction to Machine Learning

We live in an age of smart machines. Netflix knows your movie
tastes better than you do. Gmail filters out unwanted emails with a
remarkable degree of accuracy. More worryingly, self-piloting airplanes
regularly fly combat missions in modern wars. How did all these
machines get so smart?

In this class, we will formalize the task of learning and
explore some common machine learning algorithms. We will discuss
feature extraction, supervised learning, and the difference between
discriminative and generative models.

Related to: Will Computers Ever Understand Language?

Length: 75 minutes

Prerequisites: Familiarity with vectors. Knowledge of probability and statistics helpful, but not necessary.

Teacher info: Alex Rubinsteyn (ar1738 at nyu.edu), NYU Computer Science Department, 1st year Masters student



Analysis and Compact Spaces

Real Analysis. Compact metric space. Finite subcover of an open
cover. By the end of the hour, these words will resonate with deep
mathematical meaning. You will learn why the open interval (0,1) is
much bigger than the closed interval [0,1], even though it is a proper
subset. We will study the mathematical concept of a compact metric
space, one fundamental to the study of analysis and topology. You will
stretch your minds in directions you never thought they could stretch,
and see the beauty of mathematics.

Length: 75 minutes

Prerequisites: Algebra I. Understanding of distance between two points on a plane.

Teacher info: Michael Shaw (mshaw at mit.edu), Stanford University Physics Department, 1st year PhD student



What is the Numerical Halting Problem?

The famous Halting Problem is the "representative
problem" for what any conceivable physical computer can compute. We
give a brief introduction to Computability Theory by using the simple
and elegant formulation of Turing Machines (from Alan Turing, 1937).

Turing
computability addresses computation over discrete objects (like natural
numbers). But many computational problems in Mathematics involve real
numer. The set of real numbers is very much larger than the set of
natural numbers, and this causes a real strain on Turing Machines! In
fact, there is no fully satisfactory theory of computation for real
numbers (we will briefly discuss two competing theories). One of the
sources of this mystery is what we call the "numerical halting
problem". Come hear why this problem is so central.

Length: 75 minutes

Prerequisites: It would be nice if you know the difference between countable and uncountable sets, but if not, I plan to tell you.

Teacher info: Chee Yap (yap at cs.nyu.edu), NYU Department of Computer Science, Professor



An Introduction to Graph Algorithms and Complexity

We describe some of the foundational computer science algorithms
from the 20th century, and also look at what kinds of problems we
cannot solve.

One of the first success stories of modern computer science was
in the area of graph algorithms. We introduce the idea of a "flow
network" on a graph, and describe an algorithm to find the best
possible network. Surprisingly, the maximum flow turns out to be
related to the minimum cut, or partition of the graph into two sides.
From this, we get a solution to the problem.

Then, we look at the case where we are looking for the
*maximum* cut. It seems like a minor difference, but this problem
happens to be provably difficult -- "NP-complete". We introduce the
central question of complexity theory, that of proving whether "P = NP"
or not, which remains unsolved, and give examples of "difficult"
(NP-complete) problems.

Related to: Graph Theory and the Donut

Length: 75 minutes

Prerequisites: You should be familiar with the concept of a graph. Mathematical maturity is useful.

Teacher info: Carl Bosley (bosley at cs.nyu.edu), Computer Science, 5th year PhD student.


Period 5


Math of Music II: Tuning Systems

Play a major scale. C-D-E-F-G-A-B-C.
Simple, right? But what made you play the 'D' exactly that way? How do
you know how high 'E' should be? What would happen if you played the
'F' a little higher and the 'G' a little lower? What makes us choose
the frequencies that we use today?

In fact, there is no right answer for how this scale should be
played. In this class, we will look at the problem of constructing a
scale, or a sequence of notes, that sounds good to our ears. We will
examine different tuning systems that musicians have used over the
centuries, and show, using mathematics, why it's impossible to
construct a "perfect" scale. We will be able to understand why Mozart's
music sounds different today than it did to him, why some cultures use
5-note, or 24-note scales, why not every 5th is perfect, and why
choosing how you play your major scale comes down to a compromise
between sounding good, and being able to make interesting music. And
after we have looked at all of this, we will listen to it to!

This class will be preceded by Math of Music I: The Physics of
Sound and Musical Instruments . The classes are related in that we will
use some of the ideas about frequency introduced in the first class,
but you don't have to take part I in order to take part II.

Length: 60 minutes

Prerequisites:
Fractions, exponents, and an ear for music. Knowing a little bit about
music theory would help too - if you know what an octave is and you can
find the note a 5th above middle C, you should be fine.

Teacher info: Miranda Holmes (holmes at cims.nyu.edu), NYU Applied Mathematics and Atmosphere-Ocean Sciences, 3rd year PhD student



The Mathematics of Juggling

Do you find yourself juggling your schedule around, trying to
keep all the balls in the air? The original version of juggling was
practiced by magicians, circuses, and entertainers, but there is
actually mathematics lurking there as well.

We illuminate the connections between mathematics and juggling, and develop a theory of juggling patterns.

This class is rated green/blue.

Length: 60 minutes

Prerequisites: None. This is combinatorics, which is just a fancy word for "counting".

Teacher info: Carl Bosley (bosley at cs.nyu.edu), NYU Computer Science Department, 5th year PhD student



Cloud Physics

How do clouds form? Why do some clouds rain and some don't? Why
does it hail in the summer? In this class we will answer questions like
these. We will illustrate the life cycle of clouds, from the formation
of cloud droplets to the falling of rain and snow. If there is time, we
will discuss other topics such as weather modification ("cloud
seeding") and the effect of pollution on clouds.

Length: 60 minutes

Prerequisites: None

Teacher info: Sam Stechmann (stechman at cims.nyu.edu), NYU Math Department and Center for Atmosphere-Ocean Science, 5th year PhD student



Molecules and Magnetism (Spectroscopy)

Things are small in the molecular world! If we can't see these
individual molecules, how do we know what they look like and what
they're made of? Analytical chemistry has come a long way over the
decades and many advancements in the field have allowed us to determine
the structure of more complex molecules. Mass spectrometry, Infrared
spectroscopy, and Nuclear Magnetic Resonance Spectroscopy have made
invaluable contributions to our understanding of chemistry. The magic
of these tools rests in magnetic fields and vibrations of molecules,
and ultimately, physics! This class will introduce the concepts behind
analytical spectroscopy and how to deduce simple molecular structures
from MS, NMR, and IR data. These problems can be fun puzzles to work
out and a new way to use your math and logic skills! Math and physics
apply to chemistry, too!

Length: 60 minutes

Prerequisites: No special math background is required; basic chemistry knowledge would help, and a little familiarity with physics.

Teacher info: Jennifer Quinn (jkq202 at nyu.edu), NYU Biology Department, Junior Undergrad



LaTeX, a introduction to Mathematical Typesetting

LaTeX is the most popular document preparation tool in the
mathematical and scientific world. Knowledge and execution of LaTeX as
an alternative to Microsoft Word or like programs become a powerful and
useful tool to mathematicians at any level. This class will illustrate
the basics of creating a PDF file using LaTeX. Also, learn some helpful
tricks and useful codes to produce sharp and clear articles and
homeworks. LaTeX and accessory packages make it incredibly easy to
typeset any mathematical equation from matrices to analytical proofs to
more complicated figures and diagrams. LaTeX has environments quickly
organizing sections, chapter, table of contents with way less work than
WYSIWIG programs can provided.

Length: 60 minutes

Prerequisites: Programming experience will help but is not necessary. No advanced math or science knowledge needed.

Teacher info: Alec Jacobson (alecjacobson at nyu.edu), NYU Math and Computer Science Departments, Junior Undergraduate



Will Computers Ever Understand Language?

There are many different aspects of computational linguistics.
Qb lbh rawbl pelcgbtenzf? Have you ever met Eliza? Do you think
spelling correction software would work better if we could take context
into account as well as dictionary look-ups? Do you believe that the Turing test
could serve as a sufficient proof of intelligence? Even if you think it
does not, the Turing test still stands as a symbol of the deep and
elegant nature of language, and a cornerstone for understanding the
complexity of how we, as humans, think.

Related to: Introduction to Machine Learning

Length: 60 minutes

Prerequisites:
We may approach the math behind some machine learning techniques in CL,
but I'll try to introduce everything clearly for those who've never
calculated n-grams.

Teacher info: Marilyn Cole (mcole at nyu.edu), NYU Computer Science Department, graduating MS student



Floating Points: Interpreting Sensor Data for Robotics

Machines "see" the world through a variety of sensors ranging
from buttons to LIDAR. Machines are also far more limited than humans
in terms of the amounts of data they can process in real-time,
especially in the world of modern minicomputers called
'microcontrollers.' That data (as well as whatever else may have been
preprogramed) is the only way they can interpret and interact with the
environment around them.

In this class, I will discuss some strategies (in software as
well as in hardware) which can be used to interpret sensory information
in a simple and robust way. This mostly includes identifying obstacles
and targets, getting rid of noise, and creating maps. These strategies
can be used in things as simple as robotic vacuum cleaners and as
complex as full-sized humanoid robots.

Length: 60 minutes

Prerequisites: Will appreciate best with some trigonometry. Geometry OK, too.

Teacher info: Rob Lockhart (bobbylox at gmail.com), 4th year NYU Undergraduate Film Student and Professional Robotics Teacher



Upstart Puzzles

The writer of puzzles often invents puzzles to illustrate a principle.
The puzzles, however, sometimes have other ideas.
They speak up and say that they would be so
much prettier as slight variants of their original selves.

The dilemma is that the puzzle inventor sometimes can't solve those variants.
Sometimes he finds out that his colleagues can't solve them either,
because there is no existing theory for solving them.
At that point, these sassy variants deserve to be called upstarts.

We discuss a few upstarts inspired originally
from the Falklands/Malvinas Wars, zero-knowledge proofs,
and hikers in Colorado, and city planning.
They have given a good deal of trouble to a certain
mathematical detective whom I know well.

Length: 60 minutes

Prerequisites: Junior high school algebra.

Teacher info: Dennis Shasha (shasha at cs.nyu.edu), NYU Computer Science Department Professor



Love Dynamics

Would your life be easier if you could predict the future? You
will learn how to do just that in some simple cases -- when only two
types of objects interact. For example, Romeo and Juliet are in love.
Will they live happily ever after? If sheep and rabbits compete for
food during a 10 month drought, which species will survive? You will
learn how to introduce two variables, write the dynamics in terms of
equations, and determine the final state of a system through math
analysis. Notice: no rabbits will die during this course.

This class is rated blue/purple.

Length: 60 minutes

Prerequisites:

  • be able to solve a quadratic equation in 30 seconds,
  • what is a vector in 2D (we will deal with vector-fields),
  • what is a rate of change (think of what is velocity)
  • what is a graph of a function, how to plot it
  • bring crayons
  • knowing about matrices would help, but is not necessary.

Teacher info: Lyuba Chumakova (lyubov at cims.nyu.edu), NYU Math Department, 4th year PhD student



General Relativity and Black Holes

General Relativity is the most beautiful and elegant physical
theory to date. We will review the fundamentals of GR and the
intriguing nature of Black Holes. Starting with the notion of
spacetime, both flat and curved, we will try to understand physics in
curved spacetime. Eventually, we will plunge into the depths of a black
hole and understand the meaning of a classical singularity. If there is
time, we might even be able to watch the black holes evaporate!

This class is rated purple/black.

Related to: Einstein's Special Theory of Relativity.

Length: 60 minutes

Prerequisites:
A high level of enthusiasm and interest in the material. Some amount of
knowledge of polar coordinates and some linear
algebra/geometry/trigonometry will be useful. If you are
interested/familiar with the words metrics, light cones, geodesics,
black holes, singularities, curvature, event horizon, then you should
come!

Teacher info: Abhishek Kumar (abhishek at nyu.edu), NYU Physics Department, 4th year PhD student


About the difficulty icons:

We have delopved a color grading system in an attempt to indicate the overall difficulty of each talk. A green icon indicates that
anyone with a standard high-school mathematics background should be able to follow. A black icon indicates that the talk will be fast-paced, and that students without extra-curriculuar exposure to more advanced mathematics---through math camps, college courses, competition preparations, and so on---are likely to find the talk challenging. These are the two extremes, and blue and purple icons indicate the midpoints of the difficulty spectrum. It is, of course, impossible to determine the objective difficulty of a talk, and the icons should only be taken as a crude approximation. The best way to figure out whether the talk is at the right level for you is to talk to the lecturer. Instructors' emails are listed on this page, so ask away!