2007 Talks
Here is the list of courses that were offered at cSplash 2007.
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Teacher info: Leslie Greengard (math prof) 

A fundamental concept in algorithms, recursion, Topics covered: Algorithms (loops/recursion/complexity) & Programming 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) 
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 
A ZeroKnowledge Proof is a twoplayer game. (Call the players "you" and Length: 75 minutes Prerequisites: Precalc 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 
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 
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 fourcolor 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 
Two kids get into a competition to name the biggest number. They start What is infinity, really? What does it mean to compare two "different" Length: 150 Minutes Prerequisites: None Teacher info: Daniel Zaharopol, University of Illinois Mathematics Department 
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 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) 
The coming revolution in Information Technology will be based on Length: 75 Minutes Prerequisites: Elementary probability Teacher info: Gabriel Chaves, Gdc229@nyu.edu, NYU Physics Graduate Student 

The game "SET" gives rise to a number of interesting mathematical One interesting question arises directly from the rules. If there is no Length: 75 Minutes Prerequisites: None Teacher info: Felix Krahmer 
People often say: "statistics can be used to prove anything." The goal Length: 75 Minutes Prerequisites: Some basic understanding of probability and how to read bar and line Teacher info: Kasey Soska, Kasey.soska@nyu.edu, 2nd year doctoral student in Psychology 
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 
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 
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 
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 "manybody" 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 Teacher info: Harper Langston, 4th year PhD Computer Science student 
In geometry and physics, we often want estimate the sizes of intersections From scratch, we will define a measure on an abstract space (a sheet of 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 
See part 1 above for details. 
Up until 40 years ago, if you wanted to send a secret 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 

Have a math problem you are absolutely obsessed with? Have come across a Length: 75 Minutes Prerequisites: None Teacher info: Arina Chesnokova, math major undergrad, aec333@nyu.edu 
In the worlds of Math and Computer Science, you're usually taking We'll be taking a computer science prospective; we'll be looking at We'll be using the Python programming language in class, though 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 fastpaced if you've never seen them before. Teacher info: Adam Seering, aseering@mit.edu, second year undergraduate in Computer Science at MIT 
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 
This class will teach you how to model computation in a mathematical way. Length: 150 Minutes Prerequisites: None Teacher info: Daniel Zaharopol, University of Illinois Mathematics Department 
Einstein's theory of relativity changes our usual views of space and time. As an example, suppose you built a 10footlong 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 
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 seaswell. 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 
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 
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:
Teacher info: Lyubov (Luba) Chumakova, lyubov@cims.nyu.edu, 3d year math PhD student 
How does Pixar make the graphics which make their movies? What is 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 

This is 2007! Why doesn't my car drive itself? Building a mobile robot Length: 75 Minutes Prerequisites: None Teacher info: Raia Hadsell, Raia@cs.nyu.edu, 4th year PhD in computer science 
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 frontends like Google, to complex frontends 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 handson 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 
See part 1 above for details. 
Many of approaches in our living life, in problem solving, are 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 
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 
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 
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 
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 

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 Length: 60 Minutes Prerequisites: None Teacher info: Sam Richman, Scr259@nyu.edu, 3rd year undergraduate at NYU, Computer Science/Philosophy double major, Art minor. 
Proofs form the basis for mathematical literature. However, sometimes the language that is used to compose a proof intimidates us. Hearing "Deltaepsilon 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 
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 (cofounder 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 
Ever wonder how Mathematics can aid in processing and modifying sounds The students will practice with a computer demo/applet that illustates 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 
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 
Take a string, without cutting it, tangle it up, and glue Length: 60 minutes Prerequisites: Good spatial abilities preferred. Teacher info: Tatyana Kobylyatskaya, tk552@nyu.edu, undergraduate senior at NYU, majoring in math. 
If you've ever played on the swings in a playground, you've used resonance In this class, we'll use a mathematical model to see why you can make 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 
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 highschool mathematics background should be able to follow. A black icon indicates that the talk will be fastpaced, and that students without extracurriculuar exposure to more advanced mathematicsthrough math camps, college courses, competition preparations, and so onare 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!