Mathematics Symposium: "Mathematics Awareness Month at UNO"
Janna Eckhardt,
Mathematics and Signal Transduction in a Biological Network
This presentation will cover some basic aspects of networks and in more detail a specific biological network. Some topics include scale-free networks, biological versus man-made networks and ordered versus chaotic networks.
Laura Badger and Dustin Waderich,
The Euclidean Parallel Postulate
We will discuss our research on the Euclidean parallel postulate and explore attempts to prove the postulate. The Euclidean parallel postulate brings about different types of geometries. The two discussed will be Euclidean and Hyperbolic geometry, which are very different from one another. Using Geometer's Sketchpad we will recreate models to show these geometries and talk about who is responsible for these findings.
Gary Beck,
Clinical Experience and Examination Performance: Is There A Correlation?
Historically, medical education has focused on the principle that
the more clinical exposure students have to patients the more they will learn. No empirical evidence has been studied to determine the validity of such beliefs. This statistical study analyzes three years of students' patient encounter logbook data and test performance to ascertain if there is any correlation.
Eric Manley,
The Lang-Trotter Conjecture: A Computational Perspective
The number of points on an elliptic curve modulo a prime p is p+1- a_p where a_p is between -2sqrt(p) and 2sqrt(p). Lang and Trotter conjectured that for all p less than x, the number of times that a_p = n should be approximately c*sqrt(x)/log(x) where c is a constant depending on n and the elliptic curve. Previous computational studies have cast doubt on Lang and Trotter's conjecture. This study pushed the computations much farther and has found evidence greatly in favor of Lang and Trotter's conjecture.
Angela Storm,
The Purpose of Permutation in the Data Encryption Standard Algorithm
The DES algorithm implements a known initial permutation and its inverse. These permutations are the first and final steps of encryption respectively. Generally speaking, the goal of permutations is to create confusion in a message. However, with known permutations as the first and final steps, the effectiveness is questionable. The permutations appear to serve some function that is not cryptographic.
Jin Hui,
A New Model of Nonlinear Multiregression by Projection Pursuit Based on Generalized Choquet Integrals
A new nonlinear multiregression model is presented based on the generalized Choquet integral with respect to a signed fuzzy measure. The interaction among the predictive attributes toward the objective attribute is depicted a signed fuzzy measure. A linear transformation with unknown coefficients is applied to each attribute. The coefficients and the values of the signed fuzzy measure are optimally determined as regression coefficients by running an adaptive genetic algorithm based on given data.
Erin Carmody,
Seeking Solutions to x^4 + p^2y^4=z^4. Looking in Quadratic Fields
It is known that there are no rational solutions to the Fermat equation x^4 + y^4 =1. This equation does have a unique solution in the quadratic field Q(sqrt(-7)). However, the presence of p^2 in the modified Fermat equation x^4+ p^2y^4 = 1 has no non-zero solutions in any quadratic field for p congruent to 5 mod 8. I will show how this prime parameter can make such a difference.
Ni Yang,
Math and the Power Ball
This talk is about the most popular game in the American lottery - the powerball. We will look at the history of the game, basic rules of the game, and explore some related probability aspects.