Spring 2011 Talks

February 8: Hang Wang
Title: Chaos and Fractals
Abstract: Fractals are shapes exhibiting a high level of similarity. Many objects in nature, such as snowflakes, crystals, ferns or lighting, have the characteristic, that is, part of its shape looks like the whole. The work on fractals brings in the idea of Chaos, sometimes called the butterfly effect, defined as the behavior of certain systems that are highly sensitive to initial data. Besides the idea of chaos and fractals, a new concept of dimension measuring the self-similarity levels in fractals will be introduced.

February 15: Tara Davis
Title: To infinity and beyond!
Abstract: Infinity is a universal idea that has captured man’s imagination for centuries. It is ubiquitous in mathematics, art, philosophy and science. But what is infinity? We will discuss this question through the framework of history, anthropology, and mathematics, and along the way will meet some challenging questions which will illuminate just how mystical infinity really is. Click here to see a review of Tara’s seminar talk from the Vanderbilt admissions site: Inside ‘Dores.

February 22: Nick Boatman
Title: Sticking Pigeons in Holes
Abstract: In this talk, we’ll discuss the pigeonhole principle, the simple observation that placing some number of objects into a smaller number of boxes requires at least two of the objects to share a box. Amazingly, clever applications of this principle enable us to discover surprising and interesting truths. We will discuss a few of those.

March 1: Ayla Gafni
Title: Counting to 21: How to make money in Las Vegas
Abstract: Blackjack is one of the most popular casino games worldwide. For a player who knows some basic strategy, the odds in favor of the casino are less than 1%. By keeping track of which cards have already been played, the player can actually gain the advantage. We will discuss the rules of blackjack and the basic strategy. Then we will look at some card-counting techniques that give the player a considerable edge over the casino. We will see how some simple math can in fact be very profitable.

March 15: Kristina Cernekova of the University of Minnesota
Title: The Origin of Integration Techniques in Ancient Greece
Abstract: Although calculus was invented in the seventeenth century, ancient Greeks had a technique to calculate areas of curved figures already few centuries BC. This so called “method of exhaustion” is an elaborate rigorous technique of integration which enabled them to determine lengths, areas, and volumes. In this talk, we will explore how this method works and how proper or applicable it is. Also, while trying to determine who invented this method, we will trace the work of historians to see how they establish historical facts.

March 22: Emily Marshall
Title: The Mathematics of Gerrymandering
Abstract: The American Heritage Dictionary defines gerrymandering as the act of “dividing a geographic area into voting districts so as to give unfair advantage to one party.” The problem of gerrymandering has led to the development of several mathematical measures of shape compactness, some of which have been used in court cases to argue for or against the legality of congressional redistricting plans. In this talk, we will show how the notion of convexity can be used to detect irregularly shaped districts. We will explore both theoretical and empirical aspects of this convexity-based measure of shape compactness.

March 29: Jacque Davis
Title: Geometry of Complex Numbers
Abstract: Complex numbers have powerful geometric properties. Although the study of complex numbers most often begins in algebra as the study of roots of polynomials, we will study a geometric motivation for the introduction of the imaginary number i into our number system. Through viewing two short films, we will discover the geometric meanings of multiplication and addition of complex numbers and how these lead to the complicated mathematical structure of fractals.

April 5: Justin Fitzpatrick
Title: Bi-Winning via the Use of Power Series
Abstract: You might know that e^{i*pi} = -1, but do you know where this classic formula comes from? You might know that the infinite sum of 1/n^2 converges, but do you know what it converges to? In this talk we introduce power series not only to answer these questions but also several other questions that are much more easily solved using power series than by the standard techniques taught to first- and second-semester calculus students.