Other Statistics and Probability Commons^™

Entropic Dynamics Of Networks, Felipe Xavier Costa, Pedro Pessoa

Northeast Journal of Complex Systems (NEJCS)

Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into account the natural information geometry of probability distributions. We apply this framework to the Gibbs distribution of random graphs obtained with constraints on the node connectivity. The information geometry for this graph ensemble is calculated and the dynamical process is obtained as a diffusion equation. We compare the steady state of this dynamics to degree distributions found on real-world networks.

Harmony Amid Chaos, Drew Schaffner

Pence-Boyce STEM Student Scholarship

We provide a brief but intuitive study on the subjects from which Galois Fields have emerged and split our study up into two categories: harmony and chaos. Specifically, we study finite fields with elements where is prime. Such a finite field can be defined through a logarithm table. The Harmony Section is where we provide three proofs about the overall symmetry and structure of the Galois Field as well as several observations about the order within a given table. In the Chaos Section we make two attempts to analyze the tables, the first by methods used by Vladimir Arnold as …

The Expected Total Curvature Of Random Polygons, Jason Cantarella, Alexander Y. Grosberg, Robert Kusner, Clayton Shonkwiler

Robert Kusner

We consider the expected value for the total curvature of a random closed polygon. Numerical experiments have suggested that as the number of edges becomes large, the difference between the expected total curvature of a random closed polygon and a random open polygon with the same number of turning angles approaches a positive constant. We show that this is true for a natural class of probability measures on polygons, and give a formula for the constant in terms of the moments of the edgelength distribution.

We then consider the symmetric measure on closed polygons of fixed total length constructed by …

The Effects Of The Use Of Technology In Mathematics Instruction On Student Achievement, Ron Y. Myers

FIU Electronic Theses and Dissertations

The purpose of this study was to examine the effects of the use of technology on students’ mathematics achievement, particularly the Florida Comprehensive Assessment Test (FCAT) mathematics results. Eleven schools within the Miami-Dade County Public School System participated in a pilot program on the use of Geometers Sketchpad (GSP). Three of these schools were randomly selected for this study. Each school sent a teacher to a summer in-service training program on how to use GSP to teach geometry. In each school, the GSP class and a traditional geometry class taught by the same teacher were the study participants. Students’ mathematics …