2011 Talks
Here is the list of courses that were offered at cSplash 2011.
Link to Lecture Notes
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Teacher info: Mehryar Mohri (cs prof) Notes: csplash_2011.pdf" 

Let's play a prototype of a game in which we explore probability and statistics, interactively. How well do you know your theoretical probabilities? How well do you know the probability of events occurring in the world? How well do you know facts about the world that are based on statistics? Length: 1 Hour Prerequisites: Multiplication, division, addition, subtraction, fractions. Teacher info: Josephine Giaimo (josephinegiaimo [at] gmail [dot] com), Masters of Science 
Are you stuck in class doing calculations, and algebraic problems slowly? Or do you want to sharpen your algebraic skills to the point that multiplication and division of any two numbers is done mentally? Welcome to the wonderful world of Vedic Mathematics, a system far simpler and enjoyable than modern math. Vedic Mathematics is the ancient system of mathematics developed in India. According to the vedas, all of mathematics is based on sixteen sutras or formulae. These formulae describe the way the mind naturally works and are therefore a great help in directing the student to the appropriate method of solution. The simplicity of Vedic Mathematics means that calculations can be carried out mentally (though the methods can also be written down). This leads to more creative, interested and intelligent pupils. Even complex problems involving a good number of mathematical operations, the time taken by the Vedic method will be a third, a fourth, a tenth or even a much smaller fraction of the time required using modern methods. Come join us and get acquainted with the wonderful technique of doing complex math in your mind! Length: 1 Hour 15 minutes Prerequisites: Students should be acquainted with current methods of factorization, multiplication, division, solving equations simultaneously. Teacher info: Ankit Ashok Parekh (aparek01 [at] students.poly [dot] edu), NYUPoly Math, 1st Year, Masters Applied Math 
Feynman wasn't your typical physicist  renowned for his quirky sense of humor and remarkable discoveries in quantum electrodynamics, he's right up there with the likes of Maxwell and Newton. We'll discuss his Caltech years, ogle the sweet shuttlecraft named after him and look at a few of his published papers. An extensive knowledge in physics isn't required but you must have a good sense of humor! Length: 1 Hour 15 minutes Prerequisites: N/A Teacher info: Amber Bennoui (amberb [at] mit [dot] edu), Simmons College, Physics and Math, 2nd year undergrad 
It's easy enough to count like Count von Count from Sesame Street, but how about counting large? How long it would take to crack a safe by trying all combinations? Or how about the number of ways to arrange the books on your bookshelf or distribute candy to groups of kids? Seating arrangements at a dinner party? Now you too can learn some tricks for those times when you get so bored that you start counting sheep. Length: 1 Hour Prerequisites: None Teacher info: Evan Chou (chou [at] cims.nyu [dot] edu), Courant Math, 3rd Year PhD Course notes available here 
Combinatorial game theory studies games. Which games have winning strategies? Can we describe them? Do games like chess and checkers have optimal strategies? In this class, we will see how to *prove* that games have optimal strategies, and how to give explicit descriptions of optimal strategies for some very special games. Length: 1 Hour 15 minutes Prerequisites: no prerequisites. Teacher info: Wesley Pegden (pegden [at] math.nyu [dot] edu), Courant Math, NSF Postdoctoral Fellow 
Algebraic geometry is one of the oldest mathematical subjects, it has attracted research over thousands of years, and it is still very hot! We will do some time traveling; we will start off with curves in the plane, find out what polynomials give certain shapes (for example a cardioid) and end by constructing a space in which all lines intersect (even parallels). Length: 1 Hour 15 minutes Prerequisites: Geometric intuition is strongly required, everyone attending should have a good understanding of plane geometry (i.e. what are parallel lines, and how to check this property, how to compute the intersection of lines?). Some knowledge of algebra is useful, though not necessary. Teacher info: Lukas Koehler (lmk368 [at] nyu [dot] edu), NYU Courant, 2nd Year PhD 
Many phenomena in nature such as rainbows and blue skies come from scattering process: the interaction between waves and particles. Nobel Prize winners F. Crick, J. Watson, and M. Wilkins discovered DNA based on an Xray scattering pattern. Interestingly, recent advances in harmonic analysis connect this natural process to Nobel Prize winners D. Hubel, T. Wiesel's work to explain how information is processed in the brain. Length: 1 Hour Prerequisites: Curiosity Teacher info: Sixin Zhang (zsx [at] cs.courant.nyu [dot] edu) Course notes available here 
So what is mathematics anyway? This may seem like quite an easy question to answer. You might go up to the chalkboard and write 2x + 1 = 3, solve the equation, and rightly say this is mathematics. Or maybe you will claim that the sum of the angles of a triangle equals to two right angles, and that this is mathematics. After all, mathematics is just mathematics. However, if we start asking more penetrating questions this apparently easy explanation seems to dissolve. Are mathematicians like geologists, surveying an already existing mathematical landscape? Or are they like artists, thinking up and creating mathematical theorems out of thin air? Would an alien race have the same mathematics as we do? What is the foundation of mathematics? Why is mathematics so useful? Why does nature conform to mathematical laws? This class will not give definitive answers to any of these questions (as they are still highly debated today), but we will instead raise them. Well talk about different philosophical views of mathematics like Platonism, empiricism, logicism and intuitionalism, and also discuss the historical development of mathematics foundations. The goal of this class is to get you thinking about mathematics in a different way, and give you an appreciation for its complexity. Length: 1 Hour 15 minutes Prerequisites: Familiarity with calculus and infinitesimals will be helpful but not required. However, we will be discussing some very abstract concepts, so an ability to think abstractly and outside the box will be crucial. Teacher info: Josh Fry (jpfry [at] uchicago [dot] edu), University of Chicago, Undergraduate 
The classic powerseries polynomial representation taught in Algebra hides wonderful geometric properties of polynomials. On the other hand, the Bernstein/Bezier representation, used frequently in drawing programs, was developed to design the surfaces of cars. We will see how the geometric properties of this representation suggest an iterative cornercutting procedure to carve the top of a triangular block of wood into a stylish polynomial curve. We will see how undesired artifacts of polynomial interpolation can be avoided by approximating using the Bezier representation. We will see how to generalize this representation to define surface patches, which can be tiled to create large, complex surfaces like those often used in computeranimated movies. Length: 1 Hour Prerequisites: Trigonometry (for the sake of exposure); Calculus is a plus. Teacher info: Ashish Myles (amyles [at] cs.nyu [dot] edu), Courant Computer Science, Postdoc Course notes available here 
An algorithm is the "how" of a computation. For example, one algorithm to multiply binomials is the "first, outside, inside, last" method. Algorithms tell a computer how to perform complicated operations (like factorization of an integer) in terms of simple functions (like division) that it already knows. Some algorithms take longer than others to execute. A number of fascinating and counterintuitive results pertain to the time that an algorithm takes to run. We will consider some of the most interesting algorithms used in modern computer science. Length: 1 Hour 15 minutes Prerequisites: Some programming experience would be helpful. Mathematically, you should be familiar with logarithms and other functions. Teacher info: David Lawrence (dlaw [at] mit [dot] edu), MIT computer science, First year undergraduate Course notes available here 

What on earth does juggling have to do with mathematics?! "Siteswap notation" is a means of expressing juggling patterns through strings of numbers. After introducing siteswap notation, we will use it to observe (and then prove!) some interesting and unexpected mathematical properties of juggling. Mathematically, we will reason using methods from combinatorics, and we will then draw connections to topics as seemingly unrelated as the limits of infinite series and the topology of braids. Even if they've never juggled in their lives, students will learn to visualize juggling patterns they've never seen before, and even invent new tricks. The teacher is himself a juggler, and he will juggle many of the patterns that are discussed. Length: 1 Hour Prerequisites: None. Teacher info: Jeremy Kuhn (jdk360 [at] nyu [dot] edu), Linguistics, 1st Year PhD 
Many live action and animated movies today use computer generated special effects to create more realistic animations of physical phenomena such as fire, water, explosions, fracture, and others. In this talk I'll describe some of the physics and mathematics used to create such special effects, giving a high level tour of some of the mathematics used in the movies. Length: 1 Hour Prerequisites: none Teacher info: Tamar Shinar (ttshinar [at] gmail [dot] com), NYU, postdoc 
What does it mean for a voting method to be fair? Can we find a fair voting system? Is Democracy fair? We will look at what it means for an election to be fair and how the mathematics used to determine the winner affects the outcome. Length: 1 Hour 15 minutes Prerequisites: None Teacher info: Meredith Burr (mburr [at] ric [dot] edu), Rhode Island College, Math & Computer Science, Assistant Professor 
Have you ever wondered what a fourdimensional object would "look" like? In this session, we'll do more than tackle this question. It turns out that our common sense notions about what the word "dimension" means aren't enough to describe some things. These complex objects are called "fractals," and as the name suggests, they aren't at all like your garden variety lines or planes from geometry. As we'll see, it's disturbingly easy to construct something that has fractional, or noninteger, dimension. A recurring theme in this talk will be how complexity (even chaos) can arise from iterating simple processes. In addition to meaningful explanations for all the colorful images we shall encounter, we will discuss fractals in the real world. Rather than just telling you about them, I'll show you how to actually make one using some holiday decorations and light bulbs. (Live demonstration included.) Length: 1 Hour Prerequisites: Complex numbers and logarithms will make brief appearances, but familiarity with them is not at all essential. We won't use much aside from very basic algebra. Teacher info: Jarrett Lancaster (jll419 [at] nyu [dot] edu), NYU Physics, 4th year PhD 
We will be discussing interesting topics in number theory, algebra, and Length: 1 Hour 15 minutes Prerequisites: You should be enthusiastic about the study of mathematics, Teacher info: David Hankin (oana [at] nymathcircle [dot] org) 
The North American Computational Linguistics Olympiad (www.naclo.cs.cmu.edu) is in its fifth year now. It is a contest for high school students interested in languages, logic, and computation. http://en.wikipedia.org/wiki/North_American_Computational_Linguistics_Ol... The lecture will include several puzzles in linguistics and computational linguistics. Length: 1 Hour 15 minutes Prerequisites: nothing Teacher info: Dragomir R. Radev (radev [at] umich [dot] edu), CSE, U. Michigan, Professor Course notes available here 
Spock:"Really, Dr. McCoy. You must learn to govern your passions; they will be your undoing. Logic suggests..." (Star Trek VI: The undiscovered Country) Even outside Spock and the Star Trek universe, we often say, "So and So was not being very logical" or "This was the most logical choice". But what do we mean exactly when we say something is logical? What criteria should we use to make such an assertion? This class will explore these questions and develop a potential solution, Propositional Logic, from the ground up. We will cover rules of inferences and how to use these rules to prove logical statements. After discussing the completeness of our logical system, we will briefly consider the relationship between logic and mathematics. Embrace your inner Vulcan! Length: 1 Hour 15 minutes Prerequisites: There are no formal requirements, but a knack for abstraction and a good intuition of everyday logic will really help! Teacher info: Josh Fry (jpfry [at] uchicago [dot] edu), University of Chicago, Undergraduate 
What would happen if we bent geometry a little and instead of having only one parallel to a line through a given point you would have infinitely many? What does reflecting through a circle means? How are these two questions related at all? Find out when you learn about hyperbolic geometry: how it started, how you model it, and how you relate it to the geometry you normally see. Length: 1 Hour Prerequisites: A basic knowledge of Euclidean geometry, similarities and triangle geometry Teacher info: Andres Muñoz (munoz [at] cims.nyu [dot] edu), Courant Math, 1st year PhD 
In this talk, I will introduce the probability generating function (pgf) and I will discuss how to use pgf to compute the moments of probability distributions and tackle certain probability problems. Once the students are comfortable with the idea of pgf, I will apply it to study extinction problems in branching processes. Length: 1 Hour 15 minutes Prerequisites: Some knowledge of calculus and probability would be helpful. Teacher info: Ling Jiong Zhu (ling [at] cims.nyu [dot] edu), Courant Institute, NYU, 3rd Year PhD Course notes available here 
Digital computers are fast, powerful machines that are used to predict the weather, display 3D scenes, and play movies and music. But how do programmers instruct these machines to perform such complicated tasks, when most processors only understand simple commands, such as adding two numbers and checking whether a number is zero? We will learn how programming languages bridge human expression and the machine. We will program together in a computer lab an arithmetic expression evaluator that can calculate the result of expressions such as (8+8/2)*(2*84). Arithmetic expressions are natural to humans, but computers cannot understand them without our help. Length: 1 Hour 15 minutes Prerequisites: Students must have programmed before. Python and Ruby templates will be provided for the expression evaluator, but students are free to use any language available on the provided workstations (perl, java, etc). Feel free to email the teacher to find out which. Teacher info: Paul Gazzillo (pcg234 [at] nyu [dot] edu), Courant Computer Science, 1st Year PhD 
Through a series of examples in various fields of mathematics we are going to look at: Length: 1 Hour 15 minutes Prerequisites: No prerequisites are necessary but it would be good to read (wiki is enough) on axiomatic systems, ZermeloFraenkel axioms, Gödel's incompleteness. Teacher info: Dmytro Karabash (karabash [at] cims.nyu [dot] edu), Courant Math, 3rd Year PhD Course notes available here 

We will discuss the Vigenère cipher, cryptanalysis through statistical techniques, and how the one time pad overcomes the weaknesses in the Vigenère Cipher. Afterwards, students should be able to encrypt, decrypt, and crack the Vigenère Cipher, as well as see how mathematics is used in cryptography. Length: 1 Hour 15 minutes Prerequisites: Understadning of modular arithmetic and some basic statistics will be preferable. Teacher info: Harold Metz (Ham298 [at] nyu [dot] edu), Courant Math, 1st year masters 
In the year 1905 Albert Einstein published a paper that revolutionized our understanding of space and time. The theory he proposed, nowadays known as Special Relativity, shows us that when traveling very fast, the world looks very different from what our intuition leads us to expect. Space and time, although different in nature, are put on an equal footing. This class will teach us how a few simple but deep modifications of our picture of the world naturally lead to consequences which may seem outlandish: time dilates, space contracts and not everyone agrees on whether or not two events took place simultaneously. Length: 1 Hour 15 minutes Prerequisites: Basic Newtonian kinematics and trigonometry Teacher info: Klaus Widmayer (klaus.widmayer [at] cims.nyu [dot] edu), ETH Zurich, Courant / Math, M.S. Mathematics 
Game theory seeks to mathematically model people's behavior in strategic situations, or games, where the players' outcomes depend on the decisions of the other players. This class will be an informal introduction to the subject, where you will be introduced to the basic concepts, such as Nash equilibrium and extensive and normal form representation. We will then use these concepts to analyze some famous mindbending game theory problems! Additionally, this class will explore the many reallife situations where game theory comes into play, such as decisionmaking, auctions, and popular games of strategy. By the end of class, you will have learned some new strategies to help you make decisions and obtain the best outcomes for yourself. We will also play some games during the class to gain insight on how people think strategically! Length: 1 Hour Prerequisites: Basic algebra and probability, and an inclination to think rationally! Teacher info: Victoria Gregory (vg559 [at] nyu [dot] edu), Mathematics and Economics, Undergraduate Junior Course notes available here 
We will be discussing interesting topics in number theory, algebra, and Length: 1 Hour Prerequisites: You should be enthusiastic about the study of mathematics, and able to do the first few questions on AIME contest. Teacher info: David Hankin (oana [at] nymathcircle [dot] org), New York Math Circle, Mathematics Teacher 
Since the times of ancient civilizations, making and breaking codes has been of paramount importance. Throughout history, the balance between the two has won wars, saved or doomed lives, helped unravel ancient scriptures, and ultimately allowed communication and business in this Information Age. These dual disciplines have both required a great deal of art, craft and science, including the study of linguistics, mathematics and computing. You will have a chance to take a peek into the history of making and breaking codes, and you will learn the basic methods to encrypt and decrypt messages. Who knows, maybe you will come up with a new one! Length: 1 Hour 15 minutes Prerequisites: No math prerequisites. Some knowledge of permutations or modular arithmetic might help, but is not necessary. Teacher info: Eduardo Corona (corona [at] cims.nyu [dot] edu), Courant Math, 3rd Year PhD Course notes available here 
Ever wondered if you could travel in time? The short answer is yes. According to known laws of physics (Einsteins theory of relativity) its not only possible to travel into the future, its been done already. How about traveling to the past? We cannot say decisively no. There are respectable scientists with theories that make it look as a possibility, but there is no evidence of it being done yet. If you come to this lecture, youll gain a basic understanding of relativity and the nature of time, speed and the universe we live in; this could be your first step to building yourself a time machine. This topic, being much used in Science fiction, may soon become as scientific and as doable as traveling to the moon. Length: 1 Hour 15 minutes Prerequisites: Basic arithmetics including square root and exponents Teacher info: Jack Shutzman (js3104 [at] nyu [dot] edu), Courant CS, 2010 Alumnus M.S. Course notes available here 
Many of the properties of the integers  specifically, the existence of a unique additive identity (zero), the existence of unique additive inverses, and the associativity of addition  can be generalized so that they apply to objects other than numbers. Any collection of objects that satisfies these properties is called a "group". Group theory is an extraordinarily rich and beautiful branch of mathematics concerned with the study of groups. We'll examine some of the most interesting and surprising parts of group theory! Length: 1 Hour Prerequisites: Experince doing algebra with variables. Teacher info: David Lawrence (dlaw [at] mit [dot] edu), MIT computer science, First year undergraduate 
Fifteen years ago, the content of this class would have been considered science fiction. Cameras that detect and recognize human faces. Selfdriving robots finding their way in a forest. Telephones that seem to understand spoken language. How was that made possible? Well, one uses intelligent algorithms that can learn from examples, and of course, lots of data. From Google search to washing machines, machine learning is now all the rage. By the way, did you know that information about who you are friends with on a social network could be used for advertising? We will learn about features, linear classifiers, neural networks, and applications of the Bayes Theorem. We will see how it all works on a relatively simple problem: spam filtering. Then, we will take a peek at more difficult problems like computer vision (e.g. avoiding obstacles using a Kinect sensor). Length: 1 Hour 15 minutes Prerequisites: vectors, equations and basic probabilities Teacher info: Piotr Mirowski (mirowski [at] cs.nyu [dot] edu), Courant CS alumnus, Courant alumnus, research scientist at Bell Labs Course notes available here 
We will start by describing simple games that students can relate to (e.g. rock, paper, scissors) and gradually explain the abstract formal definition of a game in strategic normal form. We will explore notions such as the Nash Equilibrium and the Price of Anarchy of a Game. We will also be playing some fun games in class that will help students understand how players think and which strategies are good. Putting yourself into other people's shoes is the first thing that you want to do here before you choose your course of action. Length: 1 Hour 15 minutes Prerequisites: Capability of grasping abstract notions and some basic discrete math (sets and functions). Teacher info: Vasilis Gkatzelis (gkatz [at] cims.nyu [dot] edu), Courant Computer Science, 3rd Year PhD 
Take addition and multiplication. Figure out the properties they observe. What things that aren't numbers might you be able to add and multiply? Well, there are lots of things: matrices, polynomials, functions, and much more. When you take these properties you get what mathematicians call a "ring", a collection of elements with rules for addition and multiplication. Find out how to dramatically generalize things you've known since elementary school. Length: 1 Hour 15 minutes Prerequisites: You should enjoy a very abstract conversation! Teacher info: Daniel Zaharopol (dan [at] learningu [dot] org), CEO, Learning Unlimited 
Machine learning is the branch of artificial intelligence which concerns itself with getting computers to learn automatically from data. Since 1985, this field went from having few commercial applications, to having literally thousands. I'll cover a few of the big ideas from the field, as well as some interesting applications. Length: 1 Hour Prerequisites: Some simple calculus (especially taking derivatives), and a basic understanding of matrices (e.g. operations like matrix multiplication) would be useful, though these are not essential to understand most of the material. Teacher info: Spencer Greenberg (willfind [at] gmail [dot] com), Courant Math, 5th year PhD 

Find out how a search engine goes through all the billions of pages on the web to give an answer to your query in a second or two. Length: 1 Hour 15 minutes Prerequisites: None Teacher info: Ernest Davis (davise [at] cs.nyu [dot] edu), Courant Computer Science, Professor Course notes available here 
And who wouldn't want to know the answer to these tough questions! But sometimes we can model simple scenarios when two objects interact and use Math to gauge the final state. For example foxes hunt rabbits, but if they outhunt them, they may run out of their food source and die out themselves. If rabbits and sheep compete for the same amount of grass, which species will survive a drought? Romeo is in love with Juliet, and he believes she likes him, but she runs away and hides every time he tries to ask her out. Do they have a chance of living happily ever after? You will learn how to introduce two variables, write the dynamics of the scenarios above in terms of simple equations, and determine the final state of a system through math analysis (with the help of the computer software "pplane"). Length: 1 Hour 15 minutes Prerequisites: None, but the class will be much more enjoyable if you know how to solve a quadratic equation and know what a vector is. Teacher info: Enkeleida Lushi (lushi [at] cims.nyu [dot] edu), Courant Math, PhD student 
Did you know that the 60 foot mural across the front of the Courant Institute contains dozens of hidden clues? In this class, we will unravel the Courant Code and take a journey through the secret history of Mathematics itself. Length: 1 Hour Prerequisites: None! Teacher info: Shane Keating (skeating [at] cims.nyu [dot] edu), Center for AtmosphereOcean Science, Postdoctoral Researcher 
Will Lebron win a championship with the Heat? Is Michael Phelps an aquatic anomaly or would some other lucky person have won his collection of gold medals? Even the most exciting and complicated real life situations can be modeled using basic concepts in probability. This talk will discuss some of those possible models. Length: 1 Hour Prerequisites: The class will include basic probability, so no prior knowledge is necessary. Teacher info: Ima Narvell Abia (ina216 [at] nyu [dot] edu), Courant Math, 1st Year Masters 
In this talk we explore the nature of numbers and the eluding concept of infinity. On the journey we will visit the merchants of Babylonia, Arkimedes in Greece, Dedekin in Germany and spend a few nights at Hilbert's Hotel. Length: 1 Hour 15 minutes Prerequisites: The talk presumes little more than familiarity with rational numbers except for mathematical courage to dive into problems that will set your head spinning. Teacher info: Jens (jcbjorgensen [at] gmail [dot] com), Courant Math, 3rd year 
Did you know knots are also mathematical objects?? How do you know if 2 knots are the same or not? I'll try to answer these questions and introduce you to a special class of "tangles," the rational ones, and then play an interesting game with them. Length: 1 Hour Prerequisites: 9th grade math should be enough Teacher info: Domingos Lopes (domingos [at] cims.nyu [dot] edu), Courant Math, 2nd year PhD 
Geometry has been a wellspring of profound ideas in every Length: 1 Hour 15 minutes Prerequisites: High School Geometry. Nice to have some programming experience. Teacher info: Chee Yap (yap [at] cs.nyu [dot] edu), Computer Science, Courant, Professor 
Ever wondered how altruistic behaviors can exist in a world of competition for food, space, and resources? Or why there are about as many males as females in (most) animal species? Surprisingly some relatively simple mathematics, combined with clever and subtle arguments from game theory, can shed a great deal of light on these dilemmas from biology. This course will give a very short introduction to game theory, a field which you may have heard of through such "artificial games" as Prisoner's Dilemma and their Nash Equilibria. We will then discuss how biological scientists found examples of situations in their field work that closely matched these seemingly simplistic models. Finally, we will explain how these game theoretic models lead to a solution to some puzzles in the biological and social sciences, and survey some big questions that still remain. Length: 1 Hour Prerequisites: Only high school algebra is required for most of the talk, though some familiarity with calculus will be helpful for understanding certain derivations. Teacher info: Eliot Brenner (epb254 [at] cs.nyu [dot] edu), Courant Scientific Computing 
Neurons, the excitable cells of the nervous system, are often called the brain's basic computational units. Each neuron communicates with many others via electrical and chemical signals, allowing animals to create an internal representation of their surroundings. To understand how brains work, we often build simplified mathematical models and implement them on a computer, stringing together individual neurons into networks that perform rudimentary brainlike functions. As a first step, it makes sense to design an individual neuron. This already raises a whole series of questions. What does it mean to mathematically "model" a neuron, anyway? What assumptions can we make? How many annoying biological details can we throw away before we lose touch with reality? Length: 1 Hour 15 minutes Prerequisites: The concepts will be quite basic and we will aim for an intuitive approach. However, we will touch on a rather diverse range of subjects: animal biology, simple electrical circuits, differential equations, numerical approximation, and computer programming. Familiarity with any of the foregoing, then, would be helpful but is not assumed. Teacher info: Robert Levy (rbl2 [at] nyu [dot] edu), NYU Center for Neural Science, postdoctoral fellow Course notes available here 
Consider the following thought experiment. Suppose you have an ocean that is at rest, and then you perturb it just a little (imagine putting your foot in and stirring it up a bit). What happens? Do the ripples you just created die off, or do they persist forever? If you don't kick too hard, does the surface of the ocean remain smooth, or does it create waves that overturn? The answer to these questions is, moreorless, that we don't know. This is strange. The modern theory of fluids dates back to the mid18th century, and water has always been a subject of intense interest. Certainly it's reasonable to expect that we know all there is to know about water. Unfortunately, that's not even remotely true. While we understand a lot, many, many fundamental questions about how water behaves (like the one above) remain unanswered. Starting from the absolute basics, in this course we will look at the equations that govern water waves, and try to get a sense of what types of problems contemporary mathematicians and physicist are trying to answer. Length: 1 Hour Prerequisites: Students should be familiar with differential calculus and basic physics Teacher info: Samuel Walsh (walsh [at] cims.nyu [dot] edu), Courant Math, Courant Instructor 
In this handson class, you'll have a chance to learn about a subject that mixes mathematics and computer science. Together, we'll look at a few problems dealing with points, triangles, and polygons and try to come up with algorithms to solve them on our own. Computational geometry is a subject which is studied with both mathematics and computer science. It can be thought of as teaching a computer how to work with simple geometric objects. One place where computational geometry shows up is in computer graphics, because graphics require keeping track of many different polygons so that objects look right (we won't talk about these applications in class though). Length: 1 Hour 15 minutes Prerequisites: High school geometry including triangle and circle theorems. Teacher info: Michael Burr (mburr1 [at] fordham [dot] edu), Fordham University, Mathematics, Postdoc 

Suppose one wants to prove a statement involving a parameter that is Length: 1 hour Prerequisites: None Teacher info: Sean Li (seanli [at] cims.nyu [dot] edu), NYU/Math, 3rd Year, Math PhD 
Are you interested in vases? Are you interested in figuring out how much water a vase can hold? Are you interested in interesting 3D Shapes (Like a 3D Parabola) and how you can actually describe these shapes with MATH??? Well if this sounds like you on a Saturday night, sign up and learn!! Length: 1 Hour Prerequisites: Basic idea of Calculus I & Geometry should be more than sufficient. Teacher info: Xiaowei Wang (xw379 [at] nyu [dot] edu), Stern, 2014 Undergraduate 
Most of you have probably heard about the Fibonacci numbers (1, 1, 2, 3, 5, 8, 13, ...) and how they are found practically everywhere in nature. But has anyone ever given you a convincing reason why? In this class, we will go through the history of the Fibonacci numbers and see for ourselves their allure through the ages, point out common misconceptions regarding their ubiquity, and finish up by giving a very "rational" reason for their emergence in the context of flower patterns and plant growth. No background necessary!if you can reason about numbers, then you, too, can learn how nature "knows" math. Length: 1 Hour Prerequisites: Numbers. Maybe fractions? Teacher info: Ken Ho (ho [at] courant.nyu [dot] edu), Courant, Computational Biology, 4th year PhD student Course notes available here 
When you fire up your web browser and visit a website, a staggering number of computers have to work in concert to get you the page you wanted. This talk will introduce you to what really happens when you browse the Internet, give you some historical context, and touch on some design issues that the Internet is currently facing. Length: 1 Hour 15 minutes Prerequisites: Helpful if students are already familiar with some general computing principles such as binary counting. Teacher info: Guy Dickinson (guy [at] gdickinson.co [dot] uk), Courant CS, NYU ITS Technology Security Services, 2nd Year MS Student, also Network Security Analyst 
I am going to talk about some basic principles I am currently learning about in a math elective I'm taking called "Chaos and Dynamical Systems." I'm going to relate these math principles that explain a complex dynamical system to what we know as the "Butterfly Effect," which takes its root in chaos theory. This effect will then explain some real world phenomena such as weather. I will include simulations of the butterfly effect and talk about the 3D evolution of trajectories. Length: 1 Hour Prerequisites: calculus Teacher info: Serena Sian Yuan (ssy248 [at] nyu [dot] edu), College of Arts and Science, Physics, Undergraduate, 2nd year Course notes available here 
Ruby: Are you a CS major? Let the Geek give you an insight as to what are the important concepts you learn as a computer science engineer. You will learn to solve puzzles in a really cool way, that you would have never thought of before. Also you will learn what computer science is really about. Basic Algorithms and data structures which are the foundations of computer science engineering will be taught in this class. Length: 1 Hour 15 minutes Prerequisites: Basic Teacher info: Apoorva Vadi (av893 [at] nyu [dot] edu), Courant Computer Science Dept, 2nd year Masters student Course notes available here 
Understanding the spread of diseases such as Flu, AIDS, Plague and Length: 1 Hour 15 minutes Prerequisites: Teacher info: Enkeleida Lushi (lushi [at] cims.nyu [dot] edu), 5th year, Courant PhD student 
Whether you are whistling a tune, singing a song or jamming on your Length: 1 Hour 15 minutes Prerequisites: If you can graph the sine, cosine, exp, and log functions, you should be fine. Some interest in music is a plus, but knowledge of musical theory is not necessary. Teacher info: Jim Portegies (jim [at] cims.nyu [dot] edu), Courant Math, 2nd Year PhD 
Have you ever wondered what a traveling salesmen, Mapquest, and internet service providers have in common? They all want to move things (like cars or data) around quickly in some network of paths (like roads or cables), and graph theory, which concerns itself precisely with the properties of networks with pairwise relations, can tell them how to do it the quickest. In this talk we'll discuss the traveling salesman and shortest path problems, giving plenty of examples along the way. We'll also learn interesting properties of graphs, such as why it's impossible to do a tour of Königsberg, Germany crossing each bridge only once (due to Euler), and how results from graph theory can be applied to making maps. Length: 1 Hour 15 minutes Prerequisites: No previous knowledge is assumed, only an eagerness to learn! Teacher info: Thomas Fai (tfai [at] cims.nyu [dot] edu), Courant Math, 3rd Year Ph.D. 
There is a simple and elegant yet powerful idea known as convergence that allows virtually all of calculus to be done. In fact, a good proportion of higherlevel mathematics makes use of this idea in some form. If you decide to major in Mathematics in college, you will see it quite often. In essence, the idea of convergence is that we might or might not be able to get to a value, but we can still get as close to that value as we want. I will illustrate this concept by detailing the convergence of sequences. I will then explain how that idea is used to conceptualize limits, derivatives, and integrals. I will also show how to calculate the exact value of certain simple infinite series. Length: 1 Hour 15 minutes Prerequisites: Good knowledge of elementary algebra, including inequalities and absolute value required. Some knowledge of sequences, series, derivatives, and integrals is helpful but not required. The class might be somewhat fast paced, hence the difficulty. Teacher info: Zachary DeStefano (zrd202 [at] nyu [dot] edu), Courant Math, 4th Year Undergraduate 
What are numbers, really? I mean, what are they? As children, we were taught how to count, as if numbers had always been there and were obvious. When you got to fractions, well, those were supposed to be clear too. And then real numbers? pi? It was always brushed under the rug... it's just some weird decimal that goes on forever, right? Well, you can't prove anything about numbers if you don't know what they really are. We're going to give you a taste for how you go about defining a mathematical object and start proving things about how they work. Length: 1 Hour 15 minutes Prerequisites: A willingness for extreme abstraction Teacher info: Daniel Zaharopol (dan [at] learningu [dot] org), CEO, Learning unlimited 
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 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!
Table of Course Notes: