Florida Section NewsletterThe Mathematical Association of AmericaFebruary 2001 Volume 22, Issue 2 |

## In conjunction with FTYCMA, the 34th Annual Meeting of the Florida Section of the Mathematical Association of America, March 2 and 3, 2001, Florida Gulf Coast University, Ft. Myers, Florida

## Friday, March 2

## 9:30 - 11:30

A workshop on using TI Calculators in the Mathematics Curriculum by Doug Child - Rollins College

A workshop on Successful Grant Writing by Bill Bauldry - Appalachian State University

## 1:00

Presidential Welcomes

## 1:15 - 2:15

Pleanary Address from Barry Cipra, Freelance Writer, Northfield, MN

## 2:30 - 3:00

Room 101 Adventures in Number Theory via Mathematical Data

Scott Hochwald - UNFAbstract: The harmonic series is usually thought of as a creature from Analysis. However, when we look at partial sums of the harmonic series, we enter a world full of number theoretic possibilities. I will present some partial sums and let you look for patterns. We will discuss the patterns.

Room 265 My Erdos Number is Sqrt [-1]

Li Zhou - Polk CCAbstract: Ill discuss some useful problem solving strategies, such as collecting data, using calculators and computers, working backwards, and so on. In particular, Ill illustrate these concepts using my solutions to Problem 667 (College Mathematics Journal, Jan. 2000), Problem 1597 (Mathematics Magazine, Apr 2000), and Problems 10771, 10798, and 10814 (American Mathematical Monthly, Dec. 1999, Apr. and Jun. 2000).

Room 269 The Game of Cubic is NP-complete

Erich Friedman - Stetson UniversityAbstract: Cubic is a puzzle/video game/applet that can be played on the web. There are variously colored blocks that the player can drag around. The blocks are affected by gravity. When two or more blocks of the same color meet, they all disappear. The goal is to make all the blocks disappear. I will show that the question of whether or not a given Cubic position can be solved is NP-complete. That is, Cubic is easy enough so that a solution can be checked in polynomial time, but hard enough so that any polynomial time algorithm to solve Cubic positions would also yield a polynomial time algorithm to solve other hard math problems.

Room 264 Liberal Arts Math: A Project-Based Approach

Ann Cascarelle, Ken Chapman, & Bill Rush - SPJCAbstract: The basis for our liberal arts math course embraces the exploration of mathematics through group and individual projects. The presentation will show how to access the labs over the Internet and will include hands-on experience with a project. Participants have permission to use the materials for educational purposes.

Room 244 An Introduction to Ordinary Differential Equation Models of HIV Infection of CD4+ T Cells

Sanjay Rai - Jacksonville UniversityAbstract: In recent years a significant amount of work has been done in modeling HIV dynamics in the bloodstream using Ordinary Differential Equations and Delay-Differential Equations. It is well known that HIVs main target is white blood cells (CD4+ T cells). This virus uses the CD4+ receptors and the enzyme reverse transcriptase in binding with the host CD4+ T cells. In this binding the viral RNA is converted into viral DNA and it is integrated with the DNA of the host cell. Once integrated with the host cells DNA the virus divides itself with the host cell. We will present some of the basic models by Perelson and Nelson describing this interaction. We also consider a Delay-Differential Equation model by Culshaw and Ruan describing these dynamics. Effects of existing drug therapy on these models will also be explained. Our study will include steady states, stability and numerical properties of solutions based on the clinical data of HIV patients.

Room 131 A Tree for a Brain Tumor

Taeil Yi - University of FloridaAbstract: An earlier joint paper, by Yi and several others, presented automated unique sphere packing plans for each brain tumor by using spheres of different sizes to fill the tumor image. A topological classification of all possible brain tumors is produced by assigning a unique tree to each such sphere packing plan. A new code is developed to classify all unlabeled trees.

## 3:15 - 3:45

Room 101 Spectral Geometry, the Polya Conjecture and Diffusions

Pat McDonald - New CollegeAbstract: This talk surveys recent work involving the relationship between exit time moments for Brownian motion from smoothly domains in an ambient Riemannian manifold and the spectral geometry of such domains. The focal point of the talk is a comparison theorem for integral norms of exit time moments, a special case of which is an analog of the Polya conjecture for the Dirchlet spectrum of domains in R^n. The talk is expository. In particular, no prior knowledge of spectral geometry or diffusions is assumed.

Room 265 An Overview of Fuzzy Logic

Margie Hale - Stetson UniversityAbstract: In the 1960s an engineer named Lotfi Zadeh introduced a new system of logic and mathematics, which he called Fuzzy. Except for a small number of enthusiastic theorists, few scientists paid attention. Twenty years later, several Japanese companies began to offer high-tech gizmos described as smart: smart toasters, smart cameras, even a smart rice cooker. Shortly thereafter, an entire subway system was designed to operate on the same smart technology, and the rest of the world took notice. The theory and programming behind a smart system is none other than fuzzy logic. Many of us always thought of mathematics as the science which deals with the black or white, the true or false, the precise. But math is no longer limited to describing precise characteristics. This talk will give a general introduction to the mathematics behind fuzzy logic.

Room 269 Mathematics and MERLOT

Jim Rutledge - SPJCAbstract: MERLOT (Multimedia Educational Resource for Learning and Online Teaching) is an independent non-profit organization dedicated to creating a central clearinghouse for college-level peer-reviewed online learning modules. The review rating process combined with an easy-to-use database structure will allow faculty to easily locate high-quality digital learning materials with evaluations and guidance for use.

Room 264 Mathematics for Under-prepared Undergraduates: A Useful and Practical Approach

Lionel Rosen - Lynn UniversityAbstract: Irrespective of undergraduate students majors or areas of interest, most private and public universities expect completion of two or more courses in mathematics for graduation. This paper will cover several options which fulfill these requirements, while simultaneously stimulating interest in a heretofore undesirable subject, producing surprisingly good and useful results.

Room 244 Effects of RT and Protease Inhibitors on a Differential Equation Model of HIV Infection

Brian Boucher - Jacksonville University

(student, 15 minute presentation)Abstract: In a recent paper (Math.Biosci, May 2000) Culshaw and Ruan analyzed a differential equation model for HIV dynamics in the bloodstream. The model uses a system of nonlinear ordinary differential equations to model the populations of healthy and actively infected CD4+ T cells as well as free virus particles. We analyze the effects of the three common treatments on the behavior of the model, both quantitative and qualitative. RT inhibitors like AZT and abacavir prohibit the infection of a T cell once the virus has inserted its RNA into the host cell. Protease inhibitors like Norvir and amprenavir prohibit the formation of viral proteins in infected cells, preventing the infection of other cells. In the cocktail treatment, these drugs and their actions are combined. We propose an adjusted model that includes the effects of these treatments. We analyze the qualitative properties of the system, such as its stability and any steady states it might have. Then, using actual clinical data on HIV patients, we plot numerical solutions to illustrate the qualitative properties.

Room 244 The Effect of RT Inhibitor on the Perelson, Kirschner, De Boer Model for HIV Infection

Nancy Eschen - Jacksonville University

(student, 15 minute presentation)Abstract: We examine an ODE model for the interaction of HIV with CD4+ T cells that considers the effect of an RT inhibitor on the development of the virus. This model has four compartments: healthy CD4+ T cells, latently infected CD4+ T cells, actively infected CD4+ T cells and the free virus particles. We attempt to describe the effects of RT inhibitors on this model. Our model is based on the model developed by Perelson, Kirschner, De Boer (1993). We found two steady states for our model: an uninfected steady state and an infected steady state. Five levels of RT inhibitors were studied: 0%, 25%, 50%, 75% and 100% effective. In addition we applied a step function to delay the introduction of the RT inhibitor. In all cases we found that RT inhibitor decreased the amount of infected cells and the virus. We also found that the increased level of RT inhibitor reduces the virus faster over time.

Room 131 Computer Demonstration of the Global Classroom

Marcelle Bessman - Jacksonville University

& Douglas Quinney - Keele UniversityAbstract: The Global Classroom, an NSF-funded project at Jacksonville University, is a seamless learning environment that provides live interaction and collaborative use of commonly used mathematical and other software across the Web. The presenters will discuss the project and demonstrate its latest implementation.

## 4:00 - 4:30

Room 101 What is a Triangle?

Boris Shekhtman - University of South FloridaAbstract: In this talk, I plan to discuss several definitions of a triangle and, more generally, simplices in finite and infinite dimensional spaces. The equivalence of some of these definitions was established by Choquet, Kendall, Rothenthal and others, but one term remained an open problem for years. In this talk, I will indicate the solution of this problem, which is due to G.Goerz and myself.

Room 265 Convergence of Series: Beyond the Ratio and Root Tests

Lubomir Markov - Barry UniversityAbstract: This talk will examine the fine details of the theory of numerical series. Several interesting tests for convergence will be discussed.

Room 269 Teaching and Assessing Intermediate Algebra Students Online using WebCT

Alicia Giovinazzo - Nova Southeastern UniversityAbstract: This presentation illustrates some of the technologies available for the delivery of mathematics courses online. These illustrations focus on the use of a WebCT platform in the teaching and assessing of college students in an Intermediate Algebra online course.

Room 264 Equational Logic and Abstract Algebra

Taje Ramsamujh - Florida International UniversityAbstract: Equational Logic is used to study the set of equations that are derivable from a given set of equations and so is naturally associated with Abstract Algebra. The syntax and semantics lead to an easy completeness theorem but the decision problem for the logically valid sentences is undecidable.

Room 244 An Improved Perelson Model with Population Constraints

Thomas Bushaw - Jacksonville University

(student, 15 minute presentation)Abstract: This is a modified version of the Perelson model. The goal of this model is to more accurately reflect the infection rate of healthy CD4+ cells by HIV. Perelsons model is first simplified from a system of four equations to a system of three equations by combining active and latent infected CD4+ cells into one CD4+ population. Then, recognizing that infection rate should be a function of HIV population, we add kV/(alpha+V) a saturation term into the infection rate term. The steady states and characteristic equation resulting from our new terms is then analyzed. Numerical data and graphs are presented to illustrate the changes.

Room 244 A Differential Equation Model of HIV Dynamics via CD4+ T Cells

Josh Kilborn - Jacksonville University

(student, 15 minute presentation)Abstract: Perelson and Nelson (SIAM Review March 1999) introduced a differential equation model for HIV dynamics in the bloodstream. This model has three compartments consisting of lymphocytes CD4+ T cells, infected T cells T* and the virus v, a nonlinear system of differential equations. In the last decade a significant amount of work has been done in modeling HIV growth in the bloodstream via differential equations. Most of the models in the present literature are direct descendants of Perelsons and Nelsons model. In their model the differential equation governing the growth of the virus v has a linear virus removal rate. In our work, in this paper, we propose a differential equation model incorporating a nonlinear virus removal rate. We do a qualitative analysis of the solutions of this improved system of differential equations. Our results include steady states, stability and numerical properties of the solutions. We compare our results with the existing clinical data of HIV patients.

Room 131 Computer Demonstration of the Global Classroom

Marcelle Bessman - Jacksonville University

& Douglas Quinney - Keele UniversityAbstract: The Global Classroom, an NSF-funded project at Jacksonville University, is a seamless learning environment that provides live interaction and collaborative use of commonly used mathematical and other software across the Web. The presenters will discuss the project and demonstrate its latest implementation.

## Saturday, March 3

## 9:00 - 9:30

Room 101 Bezouts Theorem: A Taste of Algebraic Geometry

Stephanie Fitchett - Honors College, Florida Atlantic UniversityAbstract: Algebraic geometry is the study of zero sets of polynomials, and can be seen as a merging of ideas from high school algebra and geometry. One of the Great Theorems in algebraic geometry is Bezouts Theorem, which explains the intersections of polynomial curves in the (projective) plane. Bezouts Theorem will be illustrated through several examples, followed by a discussion of how the tools of modern algebra can be used to make intuitive geometric ideas precise.

Room 265 Rectangular Parallelopipeds with Integer Edges whose Volume is a Multiple of the Surface Area

John Goehl - Barry UniversityAbstract: This talk will give a complete solution when the volume is equal to the surface area and will look at the more general case.

Room 269 Technology and Concepts in Calculus

Marilyn Repsher - Jacksonville UniversityAbstract: This paper is a preliminary report on a project for the Carnegie Scholars program. We examine whether the availability of technology helps or hinders the development of understanding for three major concepts in elementary differential calculus: fitting a curve to data, rates of change, and optimization.

Room 264 From a Floppy Disk to a Pyramid

Carl Hensley - Indian River Community CollegeAbstract: This lecture/demonstration/audience participation offering will show how a paper circle can be transformed into various plane and 3-D geometric shapes. It helps introduce concepts, theorems, and definitions to students. This is aimed for teachers of students in grades 4-12, students in Liberal Arts Mathematics, or Elementary Education majors. Moreover, it is simply fun to fold paper.

Room 244 Applications of the New York Street Sweeper Problem to Software Testing

Daniel Nicholson & Mike Jones - Rollins College

(student co-presenters, 30 minute presentation)Abstract: A network of nodes and arcs, commonly called a digraph, can be used as a behavioral model for software, where nodes represent the states of a program and arcs between nodes represent transitional actions. One method of software testing involves using computers to test the actions a program can perform, where every sequence of actions begins and ends at the same reset state. When more than one computer is available, each computer may be used to test a different sequence. Since each such action sequence corresponds to a closed walk in the digraph model, by decomposing the arcs of the digraph into a collection of closed walks, we can assign these sequences to different machines, which can then be run concurrently. A natural objective is to try to minimize the run-time of those machines that execute the longest sequences. We present two algorithms that generate feasible solutions toward meeting this objective. The first assumes that an unlimited number of machines are available whereas the second assumes that the number of machines has been specified.

Room 131 An Algorithm for Finding Solutions of Phi(x) = k where Phi is the Euler Function and k is given.

James Rouzier & Andrew Royes - Barry University

(students, 30 minute presentation)Abstract: We develop an algorithm for finding solutions of the equation Phi(x) = k for a given integer k and will present the algorithm and its implementation on a computer.

Room 131 Algorithms for NP-hard Scheduling Problems

Joseph Corneli - New College

(student, 15 minute presentation)Abstract: We present a new development in the field of job-shop scheduling. Our result is a derandomized version of the best probabilistic approximation algorithm for the problem of finding minimal total weighted completion time for job scheduling in the online setting. Our algorithm can guarantee the 2*optimum bound on total weighted completion time for the scheduling problem.

## 9:45 - 10:15

Room 101 Galois Theory and Noethers Problem

Meredith Blue - Eckerd CollegeAbstract: Galois theory has been of interest to algebraists since the early 1800s. Noethers Problem arose during her approach to solving the Inverse Galois Problem. In this talk, I will review Galois extensions, define Noethers Problem and comment on its relation to the Inverse Galois Problem and to parametrization of Galois Extensions.

Room 265 Annual Business Meeting of FTYCMA and FTYCMA Forum

Mike Mears - Manatee Community CollegeRoom 269 The Global Classroom: Using the Web as a Live Active Learning Resource

Marcelle Bessman - Jacksonville University

& Douglas Quinney - Keele UniversityAbstract: The Global Classroom, an NSF-funded project at Jacksonville University, is a seamless learning environment that provides live interaction and collaborative use of commonly used mathematical and other software across the Web. The presenters will discuss the project and demonstrate its latest implementation.

Room 264 College Algebra Student Attitude Measurement: A Study of how using a Problem Solving Approach Impacts Beliefs

Michael Nancarrow - Jacksonville UniversityAbstract: By carefully measuring specific indicators, it may be possible to identify the impact non-traditional college algebra curriculums have on students attitudes and achievement. This presentation will briefly cover a specific example of instrument development, data collection, analysis, and interpretation in a college algebra setting where problem solving is the primary mode of learning.

Room 244 Balancing Survey Costs with Nonresponse Bias using Callbacks in Telephone Surveys

Jennifer Czuprynski - Stetson University

(student, 15 minute presentation)Abstract: In telephone surveys conducted by the Stetson Institute of Social Research, a phone number is called repeatedly (over several days) until contact is made. How many times should they call before they give up? Too many calls increases costs, and too few calls increases the bias of those surveyed. We look at several models, and attempt to calculate the optimal number of callbacks.

Room 244 Using the Fast Fourier Transform in the Analysis of Electron Diffraction Data

Hope Wymer - Stetson University

(student, 15 minute presentation)Abstract: There are various methods of obtaining information about the surface structure of a crystal. One new way involves sending an electron beam toward the crystal, measuring the scattering of the beam, and taking the Fast Fourier Transform of this data to get spacial information about the atoms on the surface of the crystal. We describe this process, why it works, and how accurate it is.

Room 131 Optimizing Robotic Aquatic Locomotion

Wendy Saintval - Barry University

(student, 15 minute presentation)Abstract: This is part of the research that was done towards his MARC thesis and the research started with a summer program at Cal Tech. He will discuss his research related to the calculation of the thrust force following earlier work by Ahlborn in 1997.

Room 131 Reliability of Stochastic Simulations

Leisis Martino - Barry University

(student, 15 minute presentation)Abstract: This is part of the research that was done towards her MARC thesis. The research involved the study of population growth which was governed by both logistic laws as well as stochastic events. The work was partially done in a summer program in Cornell University.

## 10:30 - 11:00

Room 101 Teaching AI Epistemology to Humans

Mark Fishman - Eckerd CAbstract: Intelligence seems integrally to involve recursion in the form of self-monitoring, but intelligent beings in the form of undergraduates seem pretty well immune to apprehension of the concept -- not to mention most of the important mathematical concepts essential to the practice and philosophical appreciation of artificial intelligence. The presenter describes an approach to the teaching of predicate logic, Goedels Theorem, formal languages, automata and recursion theory to undergraduates with no significant mathematical background, in the context of a philosophical examination of the history of artificial intelligence.

Room 265 Approximating Eigenvalues of a Class of Tri-Diagonal Matrices with Applications in Time Series Analysis

Walter Walker - Eckerd CollegeAbstract: Various statistics known as least squares estimates have been proposed to estimate the parameter from observations x(1), x(2), ..., x(n) on a first order autoregressive process x(t) = x(t-1) + epsilon(t) where the epsilon (t)s are independent standard normal random variables. All these statistics are known to be biased. Upper and lower bounds for the bias can be obtained by deriving approximations for the eigenvalues of a class of tri-diagonal matrices. We show how to approximate the eigenvalues and get the bounds on the bias.

Room 269 Vietas Formula and what we can do with it

Mysore Jagadish - Barry UniversityAbstract: Vieta gave a simple formula for 2/Pi as an infinite product. This can be easily presented in a calculus class. However, just a little more work leads to the ideas of statistical independence. Although this is well known material, it seems to be not presented in classes. The object of the talk is to bring it back into use in the classroom.

Room 264 Airplanes, Hurricanes, and the Simplex Method in Finite Mathematics

Pam Crawford - Jacksonville UniversityAbstract: Aviation is one of JUs most popular majors. Hurricane Floyd, which closed the university for three days, provided a real-life example of the use of the simplex method by airlines. After being given airplane redistribution data, students were then asked for best guess as to the most cost-efficient method to get an airline back on schedule. As a project, students used the simplex method to find the actual least cost method.

Room 244 A Variant of Pascals Triangle

Dennis Van Hise - Stetson University

(student, 15 minute presentation)Abstract: We define a triangle of numbers where each entry is the sum of all the entries in the two diagonals above it. Thus, the triangle begins:

1 1 1 2 2 2 4 5 5 4 8 12 14 12 8 We examine and prove some properties of this triangle.

Room 244 Material Derivatives

Wess Gates - Embry-Riddle Aeronautical University

(student, 15 minute presentation)Abstract: A brief history of the Material Derivative and its applications in Fluid Mechanics and Aerodynamics are discussed. Its use in solving complex flow problems is explored.

Room 131 Numerical Analysis for Rocket Systems

Thomas Galluzzo - Embry-Riddle Aeronautical University

(student, 15 minute presentation)Abstract: Often real world rocket engineering problems are so complex that they are too difficult to solve analytically. Many of these involve difficult differential equations. Solving these problems by numerical methods is discussed.

Room 131 Mathematical Analysis of SMARTS

Edward Springer & Sarah Kazukeiwicz

Embry-Riddle Aeronautical University

(students, 15 minute presentation)Abstract: A Spacecraft Mechanical Automatic Redundancy Thruster System (SMARTS) and the effects of a varying gravity environment on a mass-spring system will be mathematically analyzed.

## 11:15 - 12:15

Plenary Address from Frank Morgan, Williams College

## 12:15 - 12:30

Presidential Farewell and Thanks

## 12:30 - 2:30

Conference Luncheon and Annual Business Meeting

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