Undergraduate Student Presentations
Friday 5:00
– 5:50
Session I
5:00-5:12 Nathan
MacKay,
Title: Introduction to Vensim
Abstract: The presentation will be an
introduction to the mathematical modeling program known as Vensim.
It will introduce the basics of Vensim and briefly
show how it operates. The introduction will also include a step by step
demonstration of the creation of a model of a group of people hiking
5:15-5:27 William
Eller,
Title: Simulation of Pigs for the
Ancestors
Abstract: In Pigs for the Ancestors, Roy Rappaport
proposed that a ritual cycle of the Tsembaga
tribesman, living in the highlands of
5:30-5:42 Chris Bresten, UMass Dartmouth
Title: Numerical Convergence of the Discreet
Logistic Map
Abstract: The discrete logistic map is a simple population dynamics model in quadratic form. This model has been well studied for a long time and it is well known that the model, albeit extremely simple, yields rich dynamical complexities such as bifurcation, fractality and chaos. In this work, we revisited the logistic map and investigated a region where no particular complexity has been studied. By numerically gauging the speed of convergence, we found an interesting structure displaying some fractal properties.
5:45-5:57 Michael Gagnon, UMass Dartmouth
Title: Stochastic modeling of Amur tiger population
dynamics and viability
Abstract: The Amur tiger faced near extinction during the 1940s and has recently began to return from the brink of extinction. In my research, I analyze the dynamics and risk of extinction of the Amur tiger found in a Russian natural reserve. I illustrate the differences between stochastic and deterministic modeling by analyzing both the discrete logistic equation and a linear birth and death process. I demonstrate how sensitive the models are to the parameters; carrying capacity, birth and death rates.
Session II
5:00-5:12 Ron Colaianni and Adam Gilbert,
Title: Candy, Cones, and Chaos
Abstract: We took the Merrimack College Math Club to a local candy and ice cream store where we presented a project for our Combinatorics class. The presentation will consist of three parts, each relating to the name of the store. The first introduces counting techniques from combinatorics to solve simple problems about candy. Next are the results from an experiment in which we measured and modeled the temperature of ice cream being made. Last, we will introduce chaos theory.
5:15-5:27 Jennifer Carvalhal,
Title: Bungee jumping
Abstract: When jumping off a cliff with a bungee cord attached to your ankle, having the correct length cord is essential. This fun mathematical project uses Differential Equations to determine the correct length of cord for bungee jumping. This interesting problem incorporates two of the standard mathematical models covered in undergraduate differential equations: free fall and spring-mass motion. Using basic techniques, we examine various cord lengths and determine how to get the maximum thrill while staying alive.
5:30-5:42 Mark McGettrick,
Title: What's so special about Kevin Bacon? Using Graph Theory to investigate the properties of Social Networks
Abstract: A discussion of co-occurrence and "small-world" networks from a graph theory perspective. Particular focus is placed on the properties of the Film/Actor co-occurrence network. We look at the structure of this network and learn why "six degrees of separation" games work. This talk introduces most of the fundamental concepts of graph theory via entertaining subject matter!
5:45-5:57 Mark Tokarz and Marc Pereira,
Title: Lost in space
Abstract: This very accessible talk will examine unexpected connections between the torus, continued fractions, and space-filling curves. We will introduce the torus and continued fractions by presenting them in a very vivid and engaging style. Some background in elementary topology would be helpful, but not necessary.