Mathematics, Reading Literacy, Self-Efficacy And Problem Solving: An Analysis Of The 2003 Pisa Data
Linda M. Martin
Florida State College

The results of an analysis of the 2003 Program for International Student Assessment (PISA) data will be presented. Several factors identified in the literature as important for mathematical problem solving were investigated, including specific mathematical skills, reading literacy, and student self-efficacy. The findings suggest that more than practice and proficiency with routine exercises is required for problem solving success.

Modeling Within-Host Virus Dynamics: The standard model, applications, and extensions
Cameron Browne
Graduate Student, University of Florida

Mathematical modeling of viruses has been a popular and fruitful research area over the past couple decades, particularly in the case of HIV. I will describe the standard within-host virus model, along with some historical applications to HIV. I will then present two mathematical extensions of the model that I have been working on. Specifically, I add periodic combination drug therapy in the first model, and age structure in the second model.

Solitons and the KdV Equation
Tom Vogel
Stetson University

Solitons are mathematical solutions to certain types of nonlinear partial differential equations. The first (recorded) observation of a naturally occurring soliton was in 1834 by John Scott Russell. It wasn’t until 1895 that the mathematics of such solutions was understood. This talk will discuss solitons in both a historical and technical context. The first mathematical derivation of a soliton solution was in an equation governing waves on a shallow water surface. Today, this equation is known as the Kortweg-de Vries (KdV) equation. This talk will include a derivation of a 1-soliton solution of the KdV equation. Examples of physical systems which admit atmospheric, optical, and other physical solitons will also be discussed.

Swallowtails, Bumpy Oranges, and Monkey Saddles
Dan Dreibelbis
University of North Florida

In Calculus III, the Second Derivative Test classifies critical points as min, max, saddle, or the test fails. But what happens when the test fails? The field of singularity theory answers this question. We will explore some of the ideas behind this branch of mathematics, describe some of the applications, and look at some of the exotic curves and surfaces that show up when we break the Second Derivative Test.

Jensen’s Inequalities
Patrick Bibby
University of Miami

Many important properties of real numbers are expressed as inequalities. In 1906, the Swedish mathematician Johan Jensen (Yen?-sen) derived two generic inequalities that have a whole host of classical inequalities as special cases. One of Jensen’s inequalities can be applied to any function that is convex (concave upward) on an interval, and the other to any function that is concave (concave downward) on an interval.

Workshop: LaTeX
Nancy Johnson, C. Altay Özgener, Brad Trotter
State College of Florida

LaTeX is especially nice for typesetting mathematical work. It has beautiful mathematical fonts and extremely powerful tools for handling tables of contents/figures/etc, citations, bibliographies and indices. The interface is more like programming than the Word-like “WYSIWYG” approach, but the initial learning curve is not too steep and is worth the effort. We will discuss the basics of certain presentation packages such as Beamer, PS-Tricks, TiKZ.

Trends in Presentation in Calculus Textbooks (a Thesis study)
Nancy Eschen
Florida State College

During the 1980s, calculus instruction became the focus of a reform movement. Many mathematicians felt that some aspects of traditional calculus instruction did not provide students with a true understanding of calculus. This thesis study examined two widely used college calculus textbooks to determine how calculus instruction has changed or not changed from 1994 to 2006. The study showed a definite trend toward incorporating more reform elements (graphical, numerical, verbal, and technological) with traditional methods.

Commutative Clean Rings
Warren McGovern
Florida Atlantic University

Recall that a ring is (loosely) a set with two operations: + and *. The study of clean rings has been keeping mathematicians busy over the last few decades. It is interesting and fascinating subject. Let R be a commutative ring with 1 and x ∈ R. We say x is a unit if there is some y ∈ R such that xy=1. We call x an idempotent if x^2=x. An element that is the sum of a unit and an idempotent is called clean. In this talk I will motivate the study of clean ring through the use of examples: modular arithmetic, matrix rings, finite group rings.

How big is a zillion?
Richard Decker, Jim Rhodes
Polk State College

The goal of our talk is to instill an appreciation of the size of large numbers such as a million, billion, trillion, zillion, and googol. We relate these numbers to familiar examples from the real world to promote an understanding of their relative size. We have used the presentation in our math club and professional development sessions and it will be made available for all who attend.

Sustainability and Energy-based Economics
Ben Fusaro
Florida State College

Economists tend to underestimate the value of natural capital. This leads to an emphasis on fiscal policy and currency manipulation rather than environmental or resource limitations. A crucial role is played by the bio-physical counterpart of Return on Investment (ROI). Using little beyond arithmetic, it will be shown that an economics based on energy-based ROI and a systems approach will provide realistic expectations for the successful replacing of fossil fuels – particularly oil – by such presumably sustainable “green energy” sources as biofuels, fish farms, wind, tides or the Gulf Stream.

Euclidean Geometry is Officially Dead But It Shouldn’t Be
Scott Hochwald
University of North Florida

This talk will present fascinating results from Euclidean Geometry that do not appear in Euclid’s book. The intriguing results will often be complemented by unexpected proofs.

Workshop: Poker and Popcorn: the Mathematics of Eating
Timothy W. Jones
Edison State College/Collier

Like to lose weight, learn a language, understand your mind as a biological computer, help bring the world into sustainability, and, in general, be all you can be? In this workshop we will engage in various activities that highlight the biological problem of acquiring nutrients from environments. For us humans our chief biological strategy is to use language. We explore how a subset of natural language, the natural numbers, allows an optimal solution to this most pressing problem.

Teaching Calculus in the 21^st Century
Stephen Rowe
Wilkes Honors College, FAU

The technological resources for teaching are advancing rapidly Our current economy demands we look at ways to promote cost-effective, quality instruction in Calculus. We consider here the MAA e-book publication: Calculus, Modeling and Applications by David A Smith and Lawrence C. Moore. The CD containing this book, which includes two semesters of Calculus, can be purchased by students directly from the MAA for $25. I will discuss the book’s use, resources, current status and activities.

Incredible Irrational Numbers
Richard Tamburro
Daytona State College

Irrational numbers are examined from the perspective of an irrational number-line including density and the modular patterns between successive irrational numbers. Geometric and non-geometric expressions of irrational numbers are explored with the Cantor-Dedekind hypothesis and irrational Pythagorean triangles. In addition, the two types of irrational numbers and a simple proof that repeating decimals are not irrational provide creative classroom discussions.

Investigating Sport Trends
Carrie E. A. Grant, Julie A. Jurgens
Flagler College

In this session, discover how Drs. Grant and Jurgens linked an elementary statistics with a business computer course to engage students through active and collaborative learning. Students in these courses used spreadsheets to organize, present, and statistically analyze real data. The sport-themed projects covered graphical displays of data, descriptive statistics, regression analysis, confidence intervals, and hypothesis tests. Data was collected from professional and college sports websites, as well as, from student participation in Wii Sports.

Workshop: Writing Mathematics Well
Ivars Peterson
Director of Publications and Communications at the MAA

The importance of communicating mathematics clearly and effectively is evident in the many ways in which mathematicians must write, whether to produce technical reports, expository articles, book reviews, essays, referee's reports, grant proposals, research papers, evaluations, or slides for oral presentations. With a focus on exposition, this workshop offers tips for improving writing skills, from grammar and usage to organization and manuscript or slide preparation. It also suggests how participants can contribute to the public understanding of mathematics.

Cubic Spline with QR decomposition
Su Hua
Graduate Student, University of West Florida

To construct the cubic spline in an interval [a,b], a linear system is set up and there are two more variables than the number of equation. To make a square system, two arbitrary equations are inserted in all textbook, such as f''(a)=f''(b)=0 for the so called “cubic splines.” This is unnecessary. There is another way to do it: Just accept the linear system as “under-determined” and apply the QR decomposition and solve the under-determined system for minimum norm solution.

Bent out of Shape: Taking a look at Perturbed Eigenvalues
Rachel Levanger
Undergraduate Student, University of North Florida

In linear algebra we learn about finding the eigenvalues of a square matrix. What happens if the entries of this matrix change over time? How does this affect the eigenvalues? In this presentation, we will parameterize a matrix by a real variable and then see what can be said about the eigenvalues as the parameter changes, or as the matrix is perturbed. Will the eigenvalues exhibit a continuous or a smooth behavior? Let’s find out!

Spatial dispersion of interstellar civilizations: a site percolation model in three dimensions
Andrew D Hedman, Undergraduate Student, Thomas W Hair
Florida Gulf Coast University

A site percolation model is presented that simulates the dispersion of an emergent civilization into a uniform distribution of stellar systems. This process is modeled as a three-dimensional network of vertices within which an algorithm is run defining both the number of daughter colonies the original seed vertex and all subsequent connected vertices may have and the probability of a connection between any two vertices. This algorithm is then run over a wide set of these parameters and for iterations that represent up to 250 million years within the model's assumptions.

Optimizing Hamiltonian Paths in Jacksonville
Katie Bakewell
Undergraduate Student, University of North Florida

A real-life problem concerning visiting the bridges crossing the St. Johns River in Jacksonville is modeled by a graph and optimal Hamiltonian paths are sought. This presentation discusses the advantages of a two step Hamiltonian Path Problem (HPP) and optimization approach to traditional Travelling Salesman Problem algorithms. Ore’s theorem, HPP algorithms, and contextual applications are considered.

Integrals From Room 27-132
Robert Shollar, Matthew Carr, Bradley Tratton, Thomas Haugh, Emre Özgener, Mike Mears, C. Altay Özgener
State College of Florida

Our calculus textbook "Larson et. al." contains a corner called "Putnam Exam Challenge." We investigated some of these problems during our regular "Room 132 Problem Sessions" on Fridays, and come up with some solutions. We will present these solutions.

Euler’s Identity, Leibniz Tables, and the Irrationality of Pi
Timothy W. Jones
Edison State College/Collier

There are several proofs of the irrationality of pi. We present a particularly simple one that uses Euler’s famous formula -- the one that combines all the great mathematical constants: pi, e, -1, and 0. We also introduce a way of computing all the derivatives of the product of two functions quickly using Pascal’s triangle: we show how to create a Leibniz tables. This table is the final step in the proof.

Words, DNA Codes, and Combinatorial Problems
Daniela Genova
University of North Florida

Mathematical limitations of classical computing have inspired many unconventional models of computation. In DNA computing, a problem is encoded on DNA strands, which then perform the computation according to Watson-Crick complementarity, and the result is decoded. This presentation will focus on some non-classical models of computation that were created to model molecular reactions more closely. These models are capable of defining the solutions to hard combinatorial problems and give rise to interesting mathematical questions.

Hands on Activities to help Students Understand Algebra Concepts
Debbie Garrison
Valencia College

Even college students can enjoy and benefit from hands-on learning. Come see what all the fun is about. I will share some classroom-tested activities that have helped my students better understand algebra concepts like slope, piece-wise functions and rate of change.

A Day Without Statistics Is Like a Day Without Sunshine
Penny Morris and Jim Rhodes
Polk State College

If there is significant personal meaning, the student will be engaged. In statistics, there is a wide range of possibilities for projects that can make a student feel invested to see it through. This presentation explores those possibilities and provides ideas to actively involve students in the learning process.

Workshop: Using GeoGebra to Analyze Pictures and Generate String Art
Steven L. Blumsack
Florida State University

Participants will use available GeoGebra sketches to determine whether pictures of familiar objects—both man-made and natural-- correspond closely to conic sections and identify key parameters of the conic section. In addition, participants will use other available sketches to generate several examples of string art. These ideas have significant potential in Honors Algebra 2, Analytic Geometry, and Mathematics Appreciation courses.

The Musicality of Continued Fractions
Nikki Holtzer
Undergraduate Student, Stetson University

It is commonly known that the customary twelve tone scale, used for music in modern Western culture, can be represented in terms of ratios. This is largely attributable to mathematics established by Pythagoras. Utilizing his original ratios to compute all frequencies of the chromatic scale, however, results in a contradiction. This discrepancy is commonly known as the Pythagorean Comma. This talk will focus on using continued fractions to create a mathematical model of the equal temperament, which cannot be achieved using Pythagorean ratios alone.

Support Vector Machines (SVM): It’s All About the Kernel
Anthony Ruble
Undergraduate Student, University of West Florida

In using Support Vector Machines (SVM) for classification, poor results may be caused by inappropriate use of kernels. Error rates are examined for different kernels in the use of SVM to classify Breast Cancer. The popular Wisconsin Breast Cancer data sets are used. We analyze techniques to find the best kernel values. We hope to show that by using some simple kernel selection methods better kernel values are obtained. These better values result in better classification results, improving the role Support Vector Machines having in classifying Breast Cancer.

A Study on the Fully Online Hybrid Program in Math at UWF
Kuiyuan Li, Raid Amin, Josaphat Uvah
University of West Florida

A fully online program in mathematical science using hybrid synchronous instruction developed by at UWF has been successfully implemented since 2008. Distance students are taught simultaneously with face-to-face students in the same classes. In spring 2011, an assessment on several courses was conducted. The assessment results showed that the developed model is flexible and cost efficient, and benefits both groups of students and the distance students do as well as the face-to-face students.

Fair Selection by Tossing a Coin
David A. Rose
Polk State College

A fair coin is tossed using geometric methods to randomly select one object of N. For N not a power of 2, two different methods, branching and modified imaginary complement, compete for best efficiency

Dynamic MAA-FL Program in 2013
Jacci White
Saint Leo University

This session is for you if you want to influence the MAA-FL program and conference for 2013. Come join us if you have ideas for keynote speakers, round table sessions, conference themes/strands, or other ideas or interests for the program. This is your section and your conference, have a voice and get involved.

Characterization of the divergence of test functions
Xiaoming Wang
Florida State University

Utilizing integration by parts, we show that a scalar test function (smooth function with compact support) on a domain in Rn is the divergence of a vector valued test function if and only if its integral over the domain vanishes. Using this result, we are able to provide an elementary proof of the characterization of the gradient of a distribution, i.e., when a vectored valued distribution is conservative. Applications to mathematical analysis of fluid problems will be mentioned at the end.

Ten (or More) Ideas for Writing the Best Possible Final Exam
Dennis Runde
State College of Florida, Manatee-Sarasota

Many teachers find the task of writing a final exam a truly daunting task. This talk will focus on several ideas to make this task easier and on ideas that will produce a better instrument to measure students’ learning. Discussion will include writing a departmental common final exam as well as final exams given to individual classes. The talk will conclude with participants providing feedback on sample questions from a real final exam.

Modeling Linear Functions Using Temperature Conversion Scales
John T. Taylor
Florida State College
Sharon E. Sweet
Brevard Community College

The functional relationship between the Fahrenheit and Celsius scales are derived using the corresponding boiling and freezing points of water. Students then each create a unique scale using the student’s body weight and the student’s age as the boiling and freezing points of water respectively. This “student” scale is then compared to the Fahrenheit and Celsius scales. The resulting functions are graphed and compared. We will illustrate this on the webpage: http://www.lsua.info/mathworkshop1/frametemp2.html

Workshop: Clickable Calculus
Marcelle Bessman
Florida State College

Recent versions of the software Maple have reduced the need for programming skill by supplying menus from which you can pick mathematical symbols such as derivative, integral, radicals then use the Tab key to fill in the information you need. The learning curve to utilize Maple for visualization, computation and creating project reports has lost much, if not all, of its steepness. This presentation will focus on visualization and project reports mathematical “laboratory” reports.

Folding & Unfolding Convex Polyhedra
Joseph O'Rourke
Smith College

The surface of a convex polyhedron can be cut open and flattened to the plane as a simple polygon. In particular, the unfolding does not self-overlap. So the polygon may be cut out of paper and folded to the convex polyhedron. It is most natural to restrict the cuts to follow the edges of the polyhedron. It remains an open problem to settle whether or not every convex polyhedron can be cut open to a "net" along edges. Without the edge restriction, there are several methods known to cut open any convex polyhedron to a polygon. I'll describe two recently discovered methods, both based on an idea of Alexandrov from the 1940's. The reverse process is equally interesting: Given a planar polygon, can it be folded to a convex polyhedron? I will show that every convex polygon folds to an infinite variety of distinct convex polyhedra. Nonconvex polygons are less well understood. I will show that the standard "Latin-cross" unfolding of the cube refolds to precisely 23 different convex polyhedra.

Understanding Cortical Folding Patterns in Development, Aging and Disease
Monica K. Hurdal
Florida State University

There is controversy and debate regarding the mechanisms involved in cortical fold formation. Current cortical morphogenesis theories describe folding using tension-based or cellular-based arguments. Modeling and understanding cortical folding pattern formation is important for quantifying cortical development. Hypotheses concerning brain growth and development can lead to quantitative biomarkers of normal and abnormal brain growth. Cortical folding malformations have been related to a number of diseases, including autism and schizophrenia. In this seminar I will present a biomathematical model for cortical folding pattern formation in the brain. This model takes into account global cortex characteristics and can be used to model folds across species as well as specific diseases involving cortical pattern malformations that can occur in human brain folding patterns, such as polymicrogyria. We use a Turing reaction-diffusion system to model cortical folding. Turing systems have been used to study pattern formation in a variety of biological applications. They use an activator and inhibitor and under certain conditions a pattern forms. We use our model to study how global cortex characteristics, such as shape and size of the lateral ventricle, affect cortical pattern formation. Due to the complex shape and individual variability in folding patterns and the surface-based functional processing of the brain, “flat” maps of the brain can lead to improved analysis, visualization and comparison of anatomical and functional data from different subjects. It is impossible to flatten a surface with intrinsic curvature (such as the brain) without introducing linear and areal distortion but it is possible to preserve angular (conformal) information under flattening. I will also discuss a method called “circle packing” which I am using to generate quasi-conformal maps of the human brain. I will present examples of some of the brain maps I have created and discuss how 150-year-old and modern mathematics may be applied to enable neuroscientists to better understand the functioning of the human brain.

The Jungles of Randomness
Ivars Peterson
Director of Publications and Communications at the MAA

From slot machines and amusement park rides to dice games and shuffled cards, chance and chaos pervade everyday life. Sorting through the various meanings of randomness and distinguishing between what we can and cannot know with certainty proves to be no simple matter. Inside information on how slot machines work, the perils of believing random number generators, and the questionable fairness of dice, tossed coins, and shuffled cards illustrate how tricky randomness can be.