Undergraduate Student Paper Session
Friday Afternoon
Session I – UC 104
5:00-5:12 Oral Communication Skills
Mary Servatius, Worcester Polytechnic Institute
Abstract: Students need to learn how to communicate, especially in their major field of study. An oral presentation requires written communication skills, technical expertise as well as oral communication skills. We are surveying if and how oral communication skills are taught and we will investigate the educational value of student presentations, in particular in the mathematical sciences.
5:15-5:27 REU Experience
Allah Shved, UMass Boston
Abstract: Brief description of REU programs in mathematics is given. The benefits of the program are presented. The personal experience during 2006 REU in industrial mathematics at WPI is described. We worked on mathematically modeling the self-tapping screw process in order that engineers may set appropriate assembly torques for their automated manufacturing processes. The main results of this research are stated. The skills learnt during the program are listed. Important dates and information sources for REU programs are provided
5:30-5:42 Asymmetrical Binary Branching Fractal Trees
Kinneret Suberri, University of Hartford
Abstract: I would like to discuss asymmetrical binary branching fractal trees, specifically a line that is constructed by connecting two points on any fractal tree. These points are referred to by their addresses, (LR) and (RL) , L is the left branch and R is the right branch. This line, which exists on all fractal trees, contains infinitely many points of the tree. This research was conducted while I was participating in a Research Experience for Undergraduates (REU) program at Ithaca College.
5:45-5:57 Chaos Theory
Tariq Lescouflair, Sacred Heart University
Abstract: Chaos theory has applications in many different aspects of math and science. Some of these areas include biology, engineering, and fractal geometry. In this presentation three main areas of chaos theory will be explored: population growth, a mechanical system, and fractals. An iterative equation used for population growth with discrete time intervals will be derived and plotted. The mechanical example will concern a mass suspended at the end of a rod that is swinging back and forth. The fractal example will concern the Koch curve. It will be shown that chaos theory has certain overarching characteristics that are evident in each example.
Session II – UC 105
5:00-5:12 The Impact of the Sleeper Effect and Relapse on the Dynamics of Cigarette Smoking Among Adolescents.
Pamela Reitsma, University of Maine
Abstract: We model the dynamics of cigarette smoking among children ages 11 to 18 as a socially transmitted disease, and explore possible mechanisms of a "sleeper effect". The model fits the number of smokers for the past 16 years as reported by the CDC. The feasibility of the CDC's goal for 2010 is evaluated. The significance of relapse is highlighted by a simple bifurcation analysis. The effects of education on this group are explored and recommendations for effective approaches are made.
5:15-5:27 Determinism in Text
Adam Callahan, UMass Dartmouth
Abstract: Our proposition is that literary works contain a significant amount of determinism. Words are not chosen entirely at random by any author when writing. We stripped punctuation and replaced words in Darwin’s “On the Origin of Species” by their relative frequencies to obtain a discrete numerical time series. We applied various techniques of non-linear time series analysis, including false nearest neighbors, higher-order autocorrelations, and noise reduction, to test this hypothesis. We provide evidence for weak determinism in embedding dimension ten.
5:30-5:42 Numerical Instability of Loop Quantum Cosmology II
Jessica Rosen, UMass Dartmouth
Abstract: Loop quantum cosmology is based on discretization of space and time. Consequently, difference equations are obtained to describe the evolution of the universe. One of the goals of loop quantum cosmology formulation is to avoid singularity. In our previous work, however, we showed that there exists some numerical instability in equations used to represent Bianchi Type I model. Currently, we attempt to modify the difference equation in order to eliminate instability. We will explain concept of the modified equations.
Session III – UC 106
5:00-5:12 Ehrenreucht-Fraisse Games on Linear Orderings
Tom Kern, Dartmouth College
Abstract: A linear ordering consists of a way of placing points on a number line. I will explain how to play Ehrenreucht-Fraisse games on linear orderings, and how these fun exercises help us discover important facts about the underlying logic of linear orderings. For instance, given only a certain quantifier depth, we may only exactly specify a finite number of linear orderings. If time permits, I will discuss my current research into what these numbers are.
5:15-5:27 A Generating Function Description of the Sieve Method
Yangyang Liu, Dartmouth College
Abstract: The sieve method establishes a relation between the number of objects that have exactly the properties in a set S of properties and the number of objects with at least the properties in S. We give a generating function description of the sieve method making use of its definition only. This elegant result has applications to the two classical examples of the sieve method: computing the fixed points of permutations (in particular, derangements) and rook polynomials (rooks-on-chessboards).
5:30-5:42 Vertex-Magic Total Labelings
John Walthour and Matt Burger
Abstract: In this paper, we discuss techniques for labeling graphs by associating a number with each vertex and each edge. Our techniques create vertex-magic total labelings - labelings where the sum of a vertex label and the incident edge labels is the same for each vertex in the graph. These techniques are based on expanding smaller labelings using a Kotzig Array, to create two-regular labelings, or trimming larger labelings using logic, to create bipartite labelings.