Abstracts
Speakers: Subhash and Sikha Bagui, University of West Florida
Title: Some Aspects of Skew Normal Distributions
Abstract: In this presentation we discuss various properties of skew-normal distributions. We talk about estimation of parameters by the method of moments for three-parameter skew-normal distributions. An approximate test for the skew parameter is presented. Lastly we provide Monte Carlo methods for computing the percentiles for various values of the skew parameter.
Speaker: Mary Benson, Pensacola Junior College
Title: Red Ringed Bologna and Bundt Cake: Innovative Models in Calculus
Abstract: In the teaching of calculus, we are challenged with providing students a visual reference in three dimensions in order for them to comprehend the integration formula for volume of a solid of revolution. In this presentation, I will demonstrate the use of a red ringed bologna to model this formula.
In addition, a bundt cake will be used to model the reasoning behind the shell method of volume. These simple demonstrations have been used in my classroom for the past twenty (20) years to successfully provide the students a visual reference.
Speaker: Davorin Dujmovic, University of West Alabama
Title: Developing Student Interest with Interactive Team Quizzes
Abstract: We are discussing the concept of team quiz with interactive content as applied in precalculus and computer programming courses. We share some insights based on experience of using these quizzes in regular coursework as well as proposals for applying the same methods in calculus sequences and upper level data analysis courses.
Speaker: Joerg Feldvoss, University of South Alabama
Title: Approximations of Square Roots: From the Babylonians until Today
Abstract: In this talk we will discuss different methods to approximate square roots from ancient times until today – some of them well known and some maybe not so. Since not every student takes a course in Numerical Mathematics, these examples can be used in a calculus course to introduce the students to some basic numerical methods.
Speaker: Ajith Gunaratne, Florida Agricultural and Mechanical University
Title: A Quasi Newton Method for Constrained Molecular Dynamics Simulation
Abstract: MD simulation can be used to study various dynamic properties of proteins, but a long sequence of iterations has to be carried out even for small protein motions due to the small time step (10e-15sec) required. The bonding forces are among those causing fast protein vibrations that require small time steps to integrate, but they may be replaced by a set of bond length constraints, to increase the step size and hence the simulation speed.
Lagrange multiplier methods have been developed for constrained dynamics simulation. However, the multipliers have to be determined in every step to satisfy the constraints through the solution of a nonlinear system of equations. This process is computationally expensive since every time step Hessian matrix has to be calculated. Alternatively, The penalty function method is easy to implement and costs less than a Lagrange multiplier method, which requires the solution of a nonlinear system of equations in every time step.
Here we propose a Quasi-Newton method for constrained dynamics. The simulation with the Qusi-Newton Method can be done by using a conventional unconstrained solver such as Verlet, only with the penalty parameter increased in an appropriate manner as the simulation proceeds. More specifically, we scale the constraints with their force constants when forming the penalty terms. The resulting force function can then be viewed as a smooth continuation of the original force field as the penalty parameter increases.
The penalty function method is easy to implement and costs less than a Lagrange multiplier method, which requires the solution of a nonlinear system of equations in every time step. We implemented the penalty function method in CHARMM and applied it to protein Bovine Pancreatic Trypsin Inhibitor (BPTI). We compared the simulation results with Verlet and Shake, and found that the penalty function method had high correlations with Shake and outperformed Verlet. In particular, the RMSD fluctuations of backbone and non-backbone atoms and the velocity auto correlations of Ca atoms of the protein calculated by the penalty function method agreed well with those by Shake.
We describe the penalty function method and its implementation details, discuss our results and the issues to be resolved, show the advantages as well as the disadvantages of the method, and demonstrate the potential of using the method for general constrained molecular dynamics and energy minimization.
Speaker: Jaromy Kuhl, University of West Florida
Title:Avoiding Partial Latin Squares
Abstract: Let P be an nxn array of symbols. P is called avoidable if for every set of n symbols, there is an nxn Latin square L on these symbols so that corresponding cells in L and P differ. Due to recent work of Cavenagh and Ohman, we now know that all nxn partial Latin squares are avoidable for n>3. We give a short argument that includes all partial Latin squares of odd order at least 9. We then ask the following question: given an nxn partial Latin square P with some specified structure, is there an nxn Latin square L of the same structure for which L avoids P? We answer this question in the context of generalized sudoku squares.
Speaker: Rebekah Lane, Florida Agricultural and Mechanical University
Title: How Graphing Calculators and Visual Imagery Contribute to Students’ Understanding of Functions
Abstract: The purpose of this study was to answer the following research questions:
• What is the role of graphing calculators in understanding functions?
• How does visual imagery contribute to visual and non-visual College Algebra students’ understanding of functions?
Interviews and document reviews were the data sets used in this study. The data were analyzed by using two theoretical frameworks: O’Callaghan’s (1998) translating component for understanding functions and Ruthven’s (1990) role of graphing calculator approaches. The investigation utilized the qualitative case study method.
The two participants in this study were presented with mathematical tasks to complete over the course of a semester. Each task was given to the students individually. In order to thoroughly understand the students’ responses, task-based interviews were conducted and videotaped. In addition, each participant was interviewed based on his or her response to the mathematical tasks. The tasks captured different types of mathematical functions. These included linear, quadratic, cubic, absolute value, and exponential functions. Furthermore, prior to receiving the tasks, the students’ preference for processing mathematical information visually or non-visually were determined using Presmeg’s (1985) Mathematical Processing Instrument and Questionnaire. These tools were chosen because they measured how a student preferred to process mathematical information, i.e., visually or non-visually.
In this investigation, O’Callaghan’s (1998) translating component was present during the completion of linear, quadratic, cubic, absolute value, and exponential functions. One of the participants used the graphing calculator during the completion of all of the mathematical tasks and exhibited Ruthven’s (1990) approaches. The other participant used the graphing calculator during the completion of five of the tasks and exhibited Ruthven’s (1990) approaches. In addition, one participant relied on visual imagery during the completion of five of the mathematical tasks. The second participant relied on visual imagery during the completion of three of the tasks.
Speaker: Cynthia McGinnis, Northwest Florida State College
Title: Prepositional Logic, A Visual Approach
Abstract: This is a presentation on teaching logic through the use of “logic gates”.
Speakers: Rika Paul and Rohini Mankee, Florida Agricultural and Mechanical University
Title: Calculating the Void Fraction of Carbon Foam using a Tetrahedron Model
Abstract: Carbon foam has become increasingly important due to its low density; high porosity or void fraction (75 - 90%) and high specific thermal conductivity. This study develops a model for the creation of air bubbles in the carbon-foaming process. Currently, reliable and robust models are not readily available through of-the-shelf Computer Aided Design (CAD) software. Our model provides a low cost method that may be useful for testing thermal properties of graphite foam. This model is based on a tetrahedron which has spheres centered at each of its vertices. These spheres represent the bubbles that are produced during a carbon-foaming process. Void fraction calculations are done before and after sphere intersections. For a fixed distance between bubbles (a), sphere radii (R) are allowed to increase. Void fractions are then calculated for three cases: (1) before the spheres intersect, (2) at the point the spheres begin to intersect and (3) after intersection. This calculation is done analytically until R/a = 0.5. For R/a = 0.5, void fractions are calculated using the Monte Carlo Method. The graphical relationship developed here provides a model that can be used to predict the void fraction of the graphite foam for a given ratio R/a.
Speaker: John Perry, University of Southern Mississippi
Title: Determinants in Wonderland
Abstract: The Rev. Charles Lutwidge Dodgson, better known as Lewis Carroll, author of "Alice in Wonderland", was also a mathematician. He developed an easy, elegant method to compute determinants of matrices, re-described last year in a paper of the College Math Journal. Unfortunately, it sometimes fails! We describe a modified Dodgson's Method that allows it to work for many more matrices--but still not all.
Speaker: Vicki Schell, Pensacola Junior College
Title: Thinking about Statistics as an informed citizen
Abstract: This presentation looks at activities for Elementary Statistics students involving analyzing statistical reports. Samples of student work will be shared.
Speaker: Haiyan Tian, University of Southern Mississippi
Title: A meshless method with regularization for elliptic inverse problems
Abstract: A meshless method is developed for inverse elliptic boundary value problems. The chosen basis function results in an easy derivation of a particular solution. The method of fundamental solutions coupled with Tikhonov regularization is used for solving the corresponding ill-posed homogeneous Cauchy problem. Numerical results show that this method is accurate and stable against perturbed data.
Speaker: James Weaver, University of West Florida
Title: What do Perron, Frobenius, Kendall-Wei, and Google have in common?
Abstract: In this presentation we will explore results of Perron (1907), Frobenius (1912), Kendall (1955)-Wei (1952) and how they relate to the present day page rankings found by search engines. This exploration will involve matrices (rectangular arrays of numbers) which have strictly positive and nonnegative entries. These matrices will be used to make comparisons between multiple objects, a pair at a time. Using the results developed by the above named authors, we hope to show the connection between the ideas discovered in the early nineteen hundreds with the comparison techniques used by present day search engines which have been developed by companies such as Google. Round robin tournaments will be used as examples.
