The Four-Color Conjecture was a puzzle that fascinated and frustrated mathematicians for over 125 years. The question simply asks whether or not every map can be colored with a maximum of four colors in such a way that no two countries sharing a border share a color. This simple question, however, has a very difficult answer. In this talk, I will discuss the history and "proof" of the Four Color Theorem.
Many people take the basic physical facts of our universe for granted, especially those regarding our Solar System's heliocentric structure. But it was not always known that the Sun is the center of the Solar System; for many years people believed that everything in the universe revolved around the Earth. This talk will discuss the mathematics used to shift the widespread conception of the universe from being geocentric to heliocentric. I will specifically focus on the mathematical astronomy developed in Ancient Greece and during the Copernican Revolution, comparing some of the methods the astronomers and mathematicians of these eras used to arrive at their conclusions.
In this paper we will explore the use of elliptic curves in the area of public key cryptography. Before we can begin we must understand a few things about them and how they may be useful in this area. In doing so we will prove that the rational points on elliptic curves form a group and from that we see some other results. Then we can see how the rational points can be used in existing cryptosystems.
Andy Psak - Looking at Minimal and Maximal Profiles of Various k-Allowing Sets in the Boolean Lattice of Order n
The Boolean lattice is a collection of nodes arranged into levels where the objective is to form chains from the bottom level to the top level. Blocking nodes creates different situations where only a certain number of chains are possible. Profiles represent sets of nodes that are blocked. This project looks at previous research into minimal and maximal profiles of sets that allow various numbers of chains, adds new data, and attempts to arrange the information in a significant way for further research.
How is mathematics involved in stock market decisions? Can we model the seemingly random movements of stock prices? Mathematical finance seeks to answer these questions. This introductory talk about mathematical finance will introduce stochastic calculus and many of its interesting results. The talk will explore cases of stochastic processes that are discrete and continuous in space. We will touch on such fundamental topics such as Martingale Theory, Doob's Theorem, Markov Processes, and Brownian Motion. The discussion will provide the groundwork for understanding current research.
In preparing for the worst, mathematicians have modeled takeover by robot overlords. The focus of one such model (introduced by Soysal and Sahin in 2007) is probabilistic aggregation: specifically, the likelihood that we find robots in groups given that each individual in a ''swarm" follows a random path. This talk presents the model, and some results on the model obtained from linear algebra and probability.
Mathematics plays an important role in the study of epidemics. With our own outbreak of the flu on campus, it might not be apparent how the flu spreads through the student body. This is why epidemiologists use mathematical models to determine how a population is affected by a disease. In this talk, I will discuss how to generate a model of an epidemic with temporary immunity, such as the flu. I will also discuss how both the epidemic's behavior and the values at which the infected population becomes stable depend on the initial values of the model.
Suppose you are the owner of a firm and you are looking to hire a new secretary. You are being presented with n applicants one at a time; after each interview, you must make a choice that is final: to accept or reject. If you are satisfied with nothing but the very best, what is your strategy in order to obtain your ideal secretary? This selection process requires the decision maker to reject the first n/e applicants and then select the next person that is of a greater value relative to those skipped. We consider this and related problems.