2007 Talks

Here is the list of courses that were offered at cSplash 2007.

Icons




indicate difficulty rating, in ascending order.

Description of the icon system.

Colloquium Speaker

Teacher info: Leslie Greengard (math prof)

Period 1


The Art of Programming: Loops & Recursion

A fundamental concept in algorithms, recursion,
will be demonstrated via the lenses of three programming languages.



We will illustrate the complexity (in theory) and the simplicity (in
application) of recursion, by implementing the following three examples:
Towers of Hanoi, Binary Search and Factorial.


Topics covered: Algorithms (loops/recursion/complexity) & Programming
Languages (C#/Java/Perl).



loops

l      s & recursion.ecursion.cursion.ursion.rsion.sion.ion.on.n..

spool

Length: 75 minutes

Prerequisites: No background in programming is required. This is a basic introductory course and we will spend a little (emphasis on little) time reviewing basic coding practices.

Teacher info: Rajesh Vijayaraghavan (MS CS Alum 2006) & Asad Jawed (MS CS Alum 2005)



The Math of Fireflies

Some species of fireflies synchronize their flashes over the course of the night. Also, certain neurons in the human body are also known to synchronize. Here a couple of mathematical models of firefly/neuron synchronization will be introduced and analyzed, and on the way you'll learn a little about dynamical systems and the purpose of mathematical models. No fireflies will be harmed, and your own neurons might even profit from this mentally stimulating lecture.

Length: 75 Minutes

Prerequisites: Absolutely no knowledge of fireflies, neurons, or biology in general is needed. This course is best suited for someone who is currently taking calculus or has completed a calculus course, but requires nothing other than the most basic understanding of derivatives for complete understanding. Even with no understanding of calculus at all many things will make sense.

Teacher info: Tim Novikoff, tim.novikoff@gmail.com, graduated from NYU with a math major and currently teaching at Stuyvesant High School



Zero Knowledge Proofs

A Zero-Knowledge Proof is a two-player game. (Call the players "you" and
"me.") Let's say you know an Important Thing. In this game, you want to
convince me that the Important Thing is true, but you don't want to tell
me why. Can you prove it without revealing your information?



We'll discuss examples of Zero-Knowlege Proofs from philosophy, graph
theory, number theory, and cryptography. And we'll talk about what it
meana to "prove" something in the first place.

Length: 75 minutes

Prerequisites: Pre-calc would be helpful -- it'll be good to know what a logarithm is.

Teacher info: Marisa Debowsky, mad464@cims.nyu.edu, 2nd year graduate student in Math



Introduction to Arbitrage in Financial Math

The class will cover mathematical applications in finance involving arbitrage. Relationships between equivalent classes of financial instruments and the trading opportunities between them will be explored. This will pertain to some of the ways large institutions put their money to work.

Length: 75 Minutes

Prerequisites: Solid high school math background. Any calculus or precalculus will be helpful.

Teacher info: Scott Bernstein, masters in math finance student



Unsolved Problems

Have you ever wondered what makes some problems so difficult? In fact, many unsolved problems in math and computer science can be explained very simply. We'll talk a bit about recently solved problems like Fermat's Last Theorem and the four-color problem, and we may also go into Godel's Incompleteness Theorem to consider the idea that there can be true statements that will never be provable. Finally, we'll delve into the biggest problem that remains in computer science today: P != NP. Who knows, maybe someone in this session will end up with a million dollar prize one day!

Length: 75 Minutes

Prerequisites: Some interest in philosophy or logic would be helpful.

Teacher info: Marilyn Cole, first year CS Masters student



Cardinality and Infinity (part 1)

Two kids get into a competition to name the biggest number. They start
out 1, 2, 3, then they go through all the usual customers --- a hundred, a
million, a billion --- until one of them finally says "infinity." The
other one is silent for a minute, and then says "infinity plus one."

What is infinity, really? What does it mean to compare two "different"
infinities? It turns out that we can come up with a mathematically
rigorous way to compare two infinite sets, like the positive integers with
all integers, or the even integers; or all rational numbers, or even all
real numbers. This class will develop the mathematical intuition and
rigor behind the concept of "cardinality," a measure of the size of
infinite sets. It will be very challenging, but also very rewarding. It
may even finally answer some questions you've had since you were five
years old!

Length: 150 Minutes

Prerequisites: None

Teacher info: Daniel Zaharopol, University of Illinois Mathematics Department



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!

Length: 75 minutes

Prerequisites: A high level of enthusiasm and interest in the material. Some amount of knowledge of polar coordinates and some algebra/geometry/trigonometry might be useful.

Teacher info: Abhishek Kumar (Physics 3rd year PhD student)



Bits and Qbits

The coming revolution in Information Technology will be based on
harnessing the power of quantum computers. This class will initially
explain what can be done with bits: the fundamental unit of information
stored in a computer today. How information is quantified by
translating ideas into bits; how a Turing machine can be used for
arithmetic operations. Then will review probability theory and describe
the physical observations that justify quantum mechanics. Single and double slits,
atom decays will be mentioned to arrive to a rough description of
quantum reality. The Q-bit will be introduced and the promise of Quantum
information processes will be presented to the students. Quantum
information, quantum cryptography and quantum communication will be
described.

Length: 75 Minutes

Prerequisites: Elementary probability

Teacher info: Gabriel Chaves, Gdc229@nyu.edu, NYU Physics Graduate Student


Period 2


"SET" - a Multidimensional Card Game

The game "SET" gives rise to a number of interesting mathematical
questions. For those who don't know it:
The game consists of 81 cards showing symbols that differ with
respect to 4 different features. The goal is then to find Sets,
groups of three cards on display such that with respect to each of
the features, they either all agree or all disagree. It is not a set, if
with respect to one feature, two of the cards agree and the third one does
not.

One interesting question arises directly from the rules. If there is no
set, three more cards are added. But how long can that continue, how many
cards do we need to be certain to find a set? A multidimensional
geometrical representation of the game helps to answer this question.
Maybe also your personal Set-related questions? We will certainly have
some time for doing some set-research. If you own the game, it would be
great if you could bring it so that you can make your own examples. But
also if you never heard of SET, this is your chance to both get to know
a fun new game and learn something about the math background.

Length: 75 Minutes

Prerequisites: None

Teacher info: Felix Krahmer



Statistics for Psychological Science

People often say: "statistics can be used to prove anything." The goal
of this class is to explore basic statistics, so you can become better
critical thinkers and analyze when statistics are being used properly.
We'll cover some basic methods for using statistics in psychological
research.such as comparing means, correlation, and exploring
probabilities. And you.ll learn how certain high-profile studies in the
media just don't make the grade. As we explore how statistics are
applied to real data, you'll learn how research is done and how some
simple math principles are used in behavioral science. Problems for
researchers like the placebo effect, regression to the mean, and
correlation versus causation will be covered.

Length: 75 Minutes

Prerequisites: Some basic understanding of probability and how to read bar and line
graphs. Good critical thinking skills.

Teacher info: Kasey Soska, Kasey.soska@nyu.edu, 2nd year doctoral student in Psychology



"Math Gone Wrong!"

Why is it that we can rigorously prove that any triangle is an isosceles triangle? That any sum converges to Pi? That for any integer n, we have n = n+1? In this class, we'll want to try to get math to go wrong! We'll want to disturb our own reasoning! We'll want to get puzzled by our own thinking! We'll want to have fun!

To do so, we will work together on ten or so fun and seemingly easy problems, involving elementary geometry, elementary number theory, and elementary logic. We will try and solve them, and find out that either we are, or math is, completely.......wrong! Since it would not please many Courant grad students to be told that 0.9999999999999....= 1 (exactly!) and Pi = 3 (exactly too!), we will then carefully study the steps where we made our mistakes, and understand a lot about deep and fundamental properties of various essential fields of mathematics!

Length: 60 minutes

Prerequisites: No specific mathematical knowledge is required! Simply come with a large thirst for solving math puzzles! Being somewhat comfortable with mathematical reasoning, and with deductive and inductive proofs, will however surely help a bit.

Teacher info: Antoine Cerfon, antoine.cerfon@gmail.com, 2nd year PhD candidate at MIT, major in Plasma Physics



Wall St. AKA Mathematics Avenue

What's so cool about people's desire to work in finance? How come there is so much at stake? Why is mathematics so important in Finance? Stocks seem to be straight forward stuff, right? Well, maybe the fact that no one knows what the future will be has an impact on the way people react and want to pay/get paid to exchange these products. When there is little information, why does having a mathematical basis help a person make a better decision? Come learn about an atmosphere where billions of dollars are at stake. Learn about the financial problems that are so important that computer science, finance, and mathematics send some of their brightest to tackle these problems every year.

Length: 75 Minutes

Prerequisites: If you know how to count up to 100 and that it's better to buy cheap things and sell them high, you're all set up. Movies like Wall Street, Trader or Boiler Room would be a nice introduction.

Teacher info: Igor Schmertzler, igor@quantfs.com, senior, math and finance major



Web Design Exploration

Ever look at an amazing website and wonder "How do they do that?" Well, now is your chance to find out. We will look at some of the technologies that are being used at professional websites and learn some inside tricks on how to recreate them on your own. You will also learn the process of building websites from scratch and spicing it up with graphics, animation and sound. Join us in our exploration of the World Wide Web and soon your website will be the envy of the crowd.

Length: 75 Minutes

Prerequisites: basic computer knowledge

Teacher info: Triana Urraca, Tmu203@nyu.edu, 2nd year undergraduate Computer Science and Computer Applications minor



Introduction to Many-Body Simulations

Scientists often use large numbers of particles, planets, and objects to study and simulate how they interact in astrophysics, molecular dynamics, and fluid mechanics. We refer to these as "many-body" problems, and once the number of objects becomes large, we employ computers to help. Using gravitational forces from planets as an example, we'll show how easily this can be done as well as ways in which we can make computers do it more quickly. We will then show how this straightforward technique can be extended to simulating objects and particles in a fluid, not just in the scientific labratory, but also in movies and video games.

Length: 75 Minutes

Prerequisites: basic algebra (Pythagorean Theorem mainly for
computing distances) and familiarity with basic geometry is helpful.
Having learned some basic physics is also helpful but not necessarry.

Teacher info: Harper Langston, 4th year PhD Computer Science student



Geometric Measure Theory

In geometry and physics, we often want estimate the sizes of intersections
of shapes. For example, if two soap bubbles collide, and now overlap, we
suspect they intersect at a one-dimensional shape (a line), and we might
also want to say how long that line is.

From scratch, we will define a measure on an abstract space (a sheet of
paper, a box, flour, a snowflake), an essential
tool in geometry. Hausdorff measures, for example, are a family of
measures which give length (1-volume), area (2-volume) , usual volume
(3-volume), and "higher-dimensional volume", but there are also fractional
Hausdorff measures to measure shapes with "fractional" dimensional
volumes (fractals). We will discuss a few fractals and then ask, can two
soap bubbles collide with a fractal boundary instead of a line? We'll
combine our measure theory tools with some geometric facts to answer that
question.

Length: 75 Minutes

Prerequisites: Geometry, Trigonometry. Students should be very comfortable with notions of length, area and volume. Calculus is not necessary for this class, but familiarity with summation notation is recommended.

Teacher info: Hans Shmidheiser, Shmid@cims.nyu.edu, 3rd year Ph.D. student



Cardinality and Infinity (part 2)

See part 1 above for details.



Encryption: Hiding in the open

Up until 40 years ago, if you wanted to send a secret
message, you had to send it secretly. Encryption allows people to send
messages, completely out in the open, without anyone else being able to
read them. It is used everytime you check your email, go to a bank site,
and even everytime you shuffle your playlists (you.ll find out how). The
math is simple enough that anyone with a pencil and paper can do it, and
powerful enough that not even the biggest computers in the world can break
the codes.

Length: 75 minutes

Prerequisites: A knowledge of remainders, the ability to say what time it will be in, say, 31 hours, and you should know what a prime number is.

Teacher info: Seth Cottrell, the_eipi@hotmail.com, Math PhD Student


Period 3


Math Potluck or BYOM

Have a math problem you are absolutely obsessed with? Have come across a
mathematical conundrum/fact that stole your heart and you think about day and night? No matter how strange or random, we want you to share! During this "course" come speak your mind through math that has catches your breath, problems that fascinate you, or just listen to come things the instructor feels are neat/super-cool in the field of mathematics.

P.S. anyone who comes up with a math freestyle/song will get a prize! MUST BE ORIGINAL

Length: 75 Minutes

Prerequisites: None

Teacher info: Arina Chesnokova, math major undergrad, aec333@nyu.edu



Functional Programming: Functions as Data?

In the worlds of Math and Computer Science, you're usually taking
some data (an equation, a number, a text file), and applying a
function to that data ("simplify the equation", "square the number",
"print the text file"). In functional programming, you can take
functions and apply operations to them, so that you can change the
functions themselves in really cool ways!

We'll be taking a computer science prospective; we'll be looking at
treating functions as variables, and at "decorators", functions that
operate on other functions. We'll be digging into how "memoization",
a common trick in Algorithms to make functions remember their own
past solutions, can actually be written.

We'll be using the Python programming language in class, though
though the ideas we'll discuss apply to other languages too.

Length: 75 Minutes

Prerequisites: Some programming experience (in any language) is recommended. We'll review basic programming concepts as we go, but it'll be very fast-paced if you've never seen them before.

Teacher info: Adam Seering, aseering@mit.edu, second year undergraduate in Computer Science at MIT



An Introduction to Mathematical Finance

Consider a share of stock worth $100 today. If you can choose in a month whether or not to buy the same stock for $90, how much would you pay for that choice? This is one of many questions that mathematical finance seeks to answer. The class will review some basic topics in math that have applications in finance and economics. This is a great opportunity to see how a fusion of math and finance is being used on Wall Street. Mathematics has become a highly desired skill set in the financial markets. As the financial center of the world, New York offers excellent opportunities for those mathematically minded people who are interested in a career in finance. Come and see how to approach some financial problems from a mathematical perspective.

Length: 75 Minutes

Prerequisites: If I flip a coin, can you tell me what the probability of it landing heads up is? If I flip it twice, what is the probability it lands heads up both times? Have you ever seen a quadratic equation? Can you find its vertex? Basic ideas of probability/statistics and good algebra skills required. The class is supposed to be a little advanced but will not require calculus, trigonometry or matrices.

Teacher info: Max Nissman & Alex Shvartser



Finite Automata (part 1)

This class will teach you how to model computation in a mathematical way.
We'll work with what are called "Deterministic Finite Automata," simple
machines that can solve some computational problems. You'll design some
of these and test out what they can do; then you'll get a chance to prove
results about the limits of their abilities. This functions as a first
introduction to a field called "theoretical computer science," and I'll
talk a little bit at the end of the class about a model of computation
called a Turing machine, which is just as powerful as any computer you
might use --- then I'll mention some problems that Turing machines, and
your own computer, can't solve at all.

Length: 150 Minutes

Prerequisites: None

Teacher info: Daniel Zaharopol, University of Illinois Mathematics Department



Einstein's Relativity

Einstein's theory of relativity changes our usual views of space and time. As an example, suppose you built a 10-foot-long rocket, launched it, and watched it fly past you. Einstein's theory says that your rocket, while flying through space, will appear to be *shorter* than 10 feet long! And if you stuck a clock to the rocket and watched the clock tick as it flies by, the flying clock will appear to tick *slower* than your wristwatch! In this class, we'll see how Einstein made these discoveries from two simple assumptions, and we'll see why Einstein's theory is important for science. If there is time, we will also see how these assumptions lead to the famous equation E=mc^2.

Length: 75 minutes

Prerequisites: Pythagorean Theorem: a^2 + b^2 = c^2

Teacher info: Sam Stechmann, stechman@cims.nyu.edu, 4th year PhD student in math and atmospheric science



Looking at waves from the shore

Waves breaking at the beach tell us a lot about the world we live in, and about the mathematical models used to describe it. Looking at waves near the shore, we'll infer when, where and by what kind of storms they were created, and learn about the sea-swell. More generally, we'll learn about dispersive waves, phase and group veocity, even Quantum mechanics!

Length: 75 Minutes

Prerequisites: If you have learned some calculus, bring it along! Else we'll introduce the necessary ideas in class.

Teacher info: Esteban Tabak, Tabak@cims.nyu.edu, Professor



Introduction to Group Theory

We will undertake a 75 minute journey through the subject of group theory, a mysterious voyage abstracted from high school algebra, exploring the very properties that make multiplication what it is. Abstracting from the numbers to the properties of multiplication, we will delve into the concept of an abstract group. From there, we will explore a few elementary properties of this new object: subgroups, isomorphisms, homomorphisms, etc. In exploring these properties, we will draw our examples from cyclic groups and permutation groups. We will only touch the surface of this marvelous field, but your appetite will be whet for the future.

Length: 75 Minutes

Prerequisites: High school algebra required.

Teacher info: Michael Shaw, MShaw@MIT.edu, 4th year undergraduate at MIT, dual degree candidate in Physics and Mathematics



2D 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.

Length: 75 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

Teacher info: Lyubov (Luba) Chumakova, lyubov@cims.nyu.edu, 3d year math PhD student



3D Computer Graphics

How does Pixar make the graphics which make their movies? What is
the math and science behind it? Turns out it's simpler than you
might think! In this course we'll take a look at some fundamental
equations and algorithms used to produce photorealistic 3D computer
graphics. In particular we will focus on ray-tracing, a very popular
technique which simulates the paths that light travels and how it
interacts with objects in a scene. We'll see how with just a few
equations, we can produce some pretty sophisticated images that
include shading, shadows, and even reflections. We'll also touch on
some more advanced techniques such as Monte-Carlo ray-tracing and
photon mapping.

Length: 75 Minutes

Prerequisites: Familiarity with geometry (e.g., equations for lines, planes, and spheres) is enough for most of the talk. Integral calculus is helpful for the more advanced topics.

Teacher info: Jason Reisman, 1st year Computer Science PhD student


Period 4


Teaching Robots to See

This is 2007! Why doesn't my car drive itself? Building a mobile robot
that can see and drive autonomously is still an incredibly hard
problem. Many scientists believe that the key to success is to let the robot learn to drive itself using machine learning techniques. We'll look at various mobile robot platforms, including the DARPA Grand Challenge entrants, consider what strategies they use to see and drive, and discuss what the future holds.

Length: 75 Minutes

Prerequisites: None

Teacher info: Raia Hadsell, Raia@cs.nyu.edu, 4th year PhD in computer science



Making Webpages Two-Way Streets

Do you already know how to use HTML, and how to program? Have you been wondering how to collect information from users who visit your webpage, or have you wondered how other websites from simple search front-ends like Google, to complex front-ends like Blogspot and MySpace, do this?

Cool! Then making webpages that collect and display information from users will be fun and easy. In this class we'll learn how to create a form, collect information, and display the results in a webpage. We'll also learn how to use cookies to track who is visiting the site and determine if someone is properly logged in. The goal for this class is to familiarize students with the basic techniques for collecting user information and provide hands-on experience making simple web forms. We will be using PHP and HTML, but PHP is easy if you already know another programming language.

Length: 75 Minutes

Prerequisites: Knowledge of HTML a must, and some programming language (e.g. Javascript, Java, C++, Pascal, Unix Shell, all would work.) If you're already fluent in PHP and have been running your own Social Networking Website, you probably won't get much from my class. If you've been wondering how to start your own social networking site, this is a useful first step.

Teacher info: Murphy Stein, mms479 at cims.nyu.edu, 1st Year Masters Student in Math/CS



Finite Automata (part 2)

See part 1 above for details.



An Introduction to Randomized Algorithms

Many of approaches in our living life, in problem solving, are
through randomized algorithms. With the presence of tolerance in the
actual solution we meet as a consequence, we can enjoy meaningful
ones given from ""deterministic"" randomized algorithm. What's this?
Any of you familiar with coin tossing is welcome! We investigate the
efficiency and accuracy of an algorithm.

Length: 75 Minutes

Prerequisites: probability and statistics at high school level

Teacher info: Pilhwa Lee (email: leep at cims.nyu.edu) Courant Institute, New York Univerisity



Mathematics for the iPod generation

Ever wondered why mp3 CDs can hold far more songs than the ordinary CDs? How is music stored in a computer file anyway? And what about pictures and videos? Is the megapixel craze ever to end, or does it matter? Whether you are taking advantage of or suffering from data compression in your daily multimedia routine, perhaps you didn't know that it is mathematics that is behind the scenes. Come and learn some of the math that goes into your iPod.

Length: 75 Minutes

Prerequisites: Precalculus (basic functions such as sine and cosine), elementary probability and some exposure to linear algebra. Owning an iPod is not a prerequisite.

Teacher info: Sinan Gunturk, Gunturk@cims.nyu.edu, Mathematics Professor



Rigid Origami

When scientists launch a satellite into orbit, the solar panels must fit inside the shuttle or the rocket. To make the panels fit, they must be folded up and must unfold in space. However, solar panels cannot bend, except at hinges - the solar panels must unfold in a "rigid way." This class will discuss the problem of deciding if a folding or unfolding is rigid using curvature and spherical geometry (which will be introduced in the class).

Length: 75 Minutes

Prerequisites: Know how to multiply 3x3 matrices. Good spacial orientation skills prefered (otherwise you'll get lost easily). Some experience with origami would be helpful - but not necessary.

Teacher info: Michael Burr, 2nd year PhD student at NYU



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@MIT.edu, 4th year undergraduate at MIT, dual degree candidate in Physics and Mathematics



From secured emails to elliptic curves in an hour

The number (129 digits): 114 381 625 757 888 867 669 235 779 976 146 612 010 218 296 721 242 362 562 561 842 935 706 935 245 733 897 830 597 132 563 958 705 058 989 075 147 599 290 026 879 535 541 is the product of two prime numbers, which are they? The robustness of the RSA cryptographic protocol, which is used in particular to secure our emails, is based on this type of questions. Let's see if we can find a clever way to solve this math problem, and thus break this famous and widely used protocol!

To do so, we will have a fast and beautiful journey through many very important fields of mathematics: from a quick introduction to the principles of public key cryptography (and a quick touch on the P versus NP issue), we'll jump to the basics of number theory on which it is mainly based, and come across some fundamentals of group theory on the way. We'll then use what we just learned about groups to launch our assault on the final topic, elliptic curves, with which we'll hopefully be able to solve our question!

Length: 75 Minutes

Prerequisites: No specific mathematical knowledge is required, you'll be introduced in class to all the concepts presented. But it's a black diamond class, we'll go pretty fast! The goal will be to learn about and get interested in many new fields to you, and it'll be okay if you do not understand everything. Just try and keep up!:) Students having already heard about algebra and binary relations on different fields than simply Q, R or C, will probably feel a bit more comfortable in this class.

Teacher info: Antoine Cerfon, 2nd year PhD candidate at MIT, major in Plasma Physics


Period 5


Elementary Java

Java is a high level programming language frequently used in the computer industry. Most programming languages are designed using similar logic, so understanding the basics of Java will help you to learn any other language. You will be surprised how much sense the
programs you use every day will make after learning the core concepts of programming. In this class you'll learn how to write simple programs in Java, and we'll review many over arching programming concepts; such as, primitive data types, selection statements, and loops.

Length: 60 Minutes

Prerequisites: None

Teacher info: Sam Richman, Scr259@nyu.edu, 3rd year undergraduate at NYU, Computer Science/Philosophy double major, Art minor.



Want to Sound Like a Mathematician?

Proofs form the basis for mathematical literature. However, sometimes the language that is used to compose a proof intimidates us. Hearing "Delta-epsilon language, Cauchy sequences, the IVT, the MVT." thrown around comfortably in a proof makes math seem too complex to understand. However, in this class, we will explore these basic ideas of real analysis from an intuitive point of view, only to find that these .fancy terms. are quite simple! From there, we will compare our intuition to rigorous definitions, and we will construct proofs of famous theorems that are widely used by all mathematicians. By the end of the hour, you will be able to impress your friends with your expanded mathematical vocabulary!

Length: 60 Minutes

Prerequisites: None

Teacher info: Jessica Lin, jessicalin@nyu.edu, Second Year Undergraduate Math/Physics major



The math behind Google

Ever wonder how Google knows which web sites are better than others? Well, part of the recipe is a company secret, but a very important aspect of Google search is the idea of PageRank, named after Larry Page (co-founder of the company). We start by introducing elementary graph theory, which is a very useful way to model the internet. One way to think about PageRank is as a random walk on a graph (it's ok if you don't know what that means yet). Next we will see how to combine this idea with standard matrix multiplication. The result is a huge system of simultaneous equations, but we can't solve it in the usual way! This is because the variables to solve for are on both sides of the equation -- so how can we solve it? We'll see a very clever algorithm which might surprise you with its simplicity and effectiveness. And in the end, the solution to this daunting equation gives us our ranking of all the net's web pages!

Length: 60 Minutes

Prerequisites: what a matrix is (even better if you know how to multiply them)

Teacher info: Tyler Neylon, neylon at cims.nyu.edu, recent math PhD graduate



Modifying images and sounds using mathematical tools

Ever wonder how Mathematics can aid in processing and modifying sounds
images? In this class we will introduce the Fourier Transform, one of
the most powerful Mathematical tools that is used to solve problems in
Physics, Engineering and even Image Processing of figures and sounds.

The students will practice with a computer demo/applet that illustates
the points made in class and can themselves use this tool to modify images.

Length: 60 Minutes

Prerequisites: Basic knowledge of mathematics and computers. It is helpful, but not necessary, to know sine and cosine functions. The course will introduce you to all the notions you need for it. A willingness to learn something new (and cool) is more important!

Teacher info: Enkeleida Lushi, 1st Year Applied Math PhD Student @ Courant



Muddle Mania

How long do you think it would take you to sort 1,000 random numbers by hand? How about 10,000? Probably a very long time. So how does a computer do it so quickly? In this class we will take a look at some of the most interesting ways to sort data. We will look at the different algorithms and rate them from least efficient to most efficient. Sorting data seems like such a simple thing to do, but it's complexity comes from the many ways to do it. Newer and better sorting algorithms are constantly being invented; perhaps now it's your turn!

Length: 60 Minutes

Prerequisites: TBD

Teacher info: Alina Shah, alina.shah@nyu.edu, NYU alumni, Chemistry Major, Math and Computer Science minors



Introduction to Knot Theory

Take a string, without cutting it, tangle it up, and glue
the two loose ends together, you have just obtained a knot! Since the
two ends are glued, you cannot untie the string anymore without cutting
it. What if you were to take another string and repeat the process?
Would you get the same knot or a different one? How would you define
which knots are the same and which are not? Knot theory is all about
answering these questions. During this talk, we will look at many
examples of knots, ways of distinguishing different knots from one
another, and a method for classifying them.

Length: 60 minutes

Prerequisites: Good spatial abilities preferred.

Teacher info: Tatyana Kobylyatskaya, tk552@nyu.edu, undergraduate senior at NYU, majoring in math.



Resonance

If you've ever played on the swings in a playground, you've used resonance
(whether you knew it or not!). You've also seen resonance at work if
you've ever seen somebody break a wine glass or a window by using sound.

In this class, we'll use a mathematical model to see why you can make
yourself swing on a swing. The same ideas apply to other amazing results
in science, and we'll watch a short video of using sound to shatter a wine
glass! The mathematical model will be an example of a differential
equation, which is a common application of calculus to physics.

Length: 60 Minutes

Prerequisites: Some calculus. Students need to be able to take derivatives and integrals, especially of sines and cosines.

Teacher info: Sam Stechmann, Stechman@cims.nyu.edu, 4th year PhD student in math and atmospheric science


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!