KAMATYC/KSMAA Joint Conference 2009
May 1 - 2, 2009
Pittsburg State University
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The Mathematics of Identification Numbers
Joseph Gallian, MAA National President, University of Minnesota-Duluth |
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Because of the existence of inexpensive, fast, and reliable technology,
consumer products are identified with bar codes and identification numbers
that have a built-in ``check'' to partially ensure that the numbers have
been correctly entered into a computer or have been correctly scanned by
an optical device. In this talk we examine some of the common bar coding
and check digits schemes that you encounter everyday. Among them are the
UPC bar code, the ZIP bar code, and the check methods used on credit
cards, airline tickets, money orders, travelers checks, personal checks,
pop cans, books and magazines.
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Using Mathematics to Create Symmetry Patterns Joseph Gallian, MAA National President, University of Minnesota-Duluth |
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We use video animations to illustrate how mathematics can be used to
create computer generated symmetry patterns. Polynomials,
exponential functions, logarithms and modular arithmetic are used to
transform basic images into symmetry patterns. These methods were
used to create the image for the 2003 Mathematics Awareness Month poster.
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| The National Alliance of Concurrent
Enrollment Partnerships: What Accreditation Means for Concurrent
Enrollment Bill Osborn, Johnson County Community College |
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| The National Alliance of Concurrent Enrollment Partnerships
created a national accreditation process for quality concurrent enrollment
partnerships at both two-year and four-year institutions based on standards
for curriculum, faculty, students, assessment and evaluation. In 2006
Johnson County Community College's College Now program received accredited
status. This session will describe NACEP and the methods used to study
our College Now students to help ensure accountability in the area of
concurrent enrollment. |
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| Topical Discussion: Dual Credit Moderator: Steven J. Wilson, Johnson County Community College |
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| Last year, attendees at the KAMATYC Great Bend conference expressed
the desire to see KAMATYC take a position on the topic of dual credit.
This discussion time is intended to help the organization determine the
issues that you want to see addressed in a position paper. |
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Is the Ratio of Development and Recapitulation Length to Exposition
Length in Mozart’s and Haydn’s work equal to the Golden Ratio?
Ananda Jayawardhana, Pittsburg State University | |
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Morse-Smale Diffeomorphisms as a Family of Hénon Maps Shawn Wiggins, graduate student, Wichita State University | |
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In this talk, I will use the work of Sandra Hayes and Christian Wolf to discuss a family of
Hénon maps which are Morse-Smale. As a result of computational experiments, I will present a
possible extension of the work of Hayes and Wolf. An overview of dynamical systems will be
included with this talk.
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Creation of an Interdisciplinary Degree
Bobby Winters, Pittsburg State University | |
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I will discuss the creation of an interdiciplinary degree in
math and business. I will discuss the process and the politics.
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Studying Ramsey Numbers with Coxeter Diagrams and Cayley Graphs
Jonathan Denning, undergraduate student, Tabor College | |
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We present our observations having studied
Ramsey numbers using Coxeter groups to model the mutual
relationships among a room full of people. Choosing edges of
order two and of infinite order to denote mutual friends or strangers,
we can describe the Ramsey number from a different approach.
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Objective Assessment
Timothy Warkentin, Cloud County Community College | |
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A simple (and free) software program to analyze how the objectives
of a particular course are being met will be demonstrated. This
software was developed by the presenter to meet the requirements
of course assessment mandated by the HLC.
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| Studio College Algebra Andrew G. Bennett, Kansas State University |
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| In collaboration with colleagues at the Center for
Quantitative Education, we have developed a new version of the College
Algebra course at Kansas State University. In the studio version, students
carry out computer activities, usually spreadsheet based, to explore
conceptual ideas and applications of algebra. The studio course includes one
lecture, one studio, and one recitation per week and is offered as an
alternative alongside the traditional College Algebra course. Both the
studio and traditional versions also use online homework for skills
development and written homework for word problems. The new version has
proved popular with students and has a higher success rate than the
traditional version. In the presentation we will discuss the new
version and give participants a chance to see how the computer studios work. |
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| Some Common Situations in Teaching and Learning
Mathematics Prem Bajaj, Associate Prof. Emeritus, Wichita State University |
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During my stay at Wichita State University, I noticed many students spending
a lot of time for a course, but not getting the results. We discuss
some of the common errors made by students. For example, students like to
have a "make-up" to have more time; but it does not work. We will discuss pros
and cons of a make-up. Make-up is a problem for the instructor also; a solution,
that worked for me, will be given. In teaching, most situations occur again and
again. We will give some examples where students can benefit and some ways that the
instructors can help.
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Inverse Electromagnetic Scattering: Uniqueness of Obstacle Deepak Aralumallige Subbarayappa, graduate student, Wichita State University |
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In this presentation I will talk about scattering of time harmonic electromagnetic
plane waves by an obstacle with the most general impedance boundary condition
known as the Leontovich boundary condition. Here I will prove the uniqueness of
obstacles when the scattering data is available for a set of frequencies but only
for one incident direction. First I will prove existence and uniqueness of the
solution to the forward scattering problem. Using the fact that solution is
analytic with respect to frequency I will prove the uniqueness of obstacle by a
simple contradiction.
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Pricing Options Using the Binomial Model Dusty Peterson, graduate student, Pittsburg State University |
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In the presentation, an introduction of derivatives options specifically
calls, puts, collars, and straddles will be discussed. Included will be
examples of who would want to purchase options, how options help
investors leverage his or her position, and when future assumptions about the
market will lead investors to purchase specific options. The fundamental
assumption used in most stock price models is that stock prices follow a
lognormal distribution. We will discuss the lognormal distribution and effects
of such an assumption. Also, we will explore the binomial model which can be
thought of as a combination of a random walk and the binomial distribution.
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| Topical Discussion: Liberal Arts
and College Algebra Moderator: Brian Howe, Barton County Community College |
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| At the Core Competencies meeting in Wichita last fall,
several individuals commented on the lack of commonality among courses
designed for the liberal arts student at the college algebra level.
This discussion session is intended to explore what each of us is doing for
these students (whether it be a standard college algebra course, a modified
college algebra course, or an alternative course), and to discuss what
direction we should be going and, if necessary, how to get there. |
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The Amazing E-6B Flight Computer (no electricity needed)
Elwyn Davis, Pittsburg State University |
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The E-6B flight computer is an instrument used by all navigators and pilots
from before WWII until the advent of computers in airplanes. One side is a circular slide rule with
aviation aids. The other side helps in drawing wind diagrams for plotting
courses. Examples will be given and history will be discussed. |
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Efficient implementation of web-based (Maple TA) skill exams for
Precalculus, Calculus I and Calculus II in one computer lab
Estela A. Gastovo, Erika Ward, and Lynne Yengulalp, University of Kansas |
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We discuss a successful framework for administering web-based skill tests to
more than 2000 precalculus and calculus students at the University of Kansas.
We explain how student, instructor, technology and process factors all influenced
the design of the testing system and protocols. We conclude with some
remarks about the adaptability of our approach to other math contexts with
similar teaching and learning goals. |
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| Using a Sympodium 101 Rita Drybread, Neosho County Community College |
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| This presentation will cover
the ease of using a sympodium in the classroom, the unique features of the
sympodium, and the software that is available for use with the sympodium.
The sympodium can be used with Microsoft Office and the internet to make
classroom presentations. The presenter will also demonstrate how to make
movies with the sympodium that can be saved and e-mailed to students. |
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Exploring Paint By Numbers Puzzles Jennifer Wagner, Washburn University |
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A Paint By Numbers Puzzle (or nonogram) consists of a grid
of squares, some of which are to be filled in to make a picture. To
help the solver fill in the appropriate squares, each row and column
is labeled with the sizes of blocks of contiguous filled squares in
it.
How many labelings have unique solutions? I'll talk about some of the
issues that have arisen in exploring this question for small grids.
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| Making Green's Theorem Accessible Carl Anderson, Johnson County Community College (retired) |
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| Green's
Theorem has always been a difficult one for students and faculty. By
approaching it using partitions similar to the techniques used in
earlier integration problems, students are able to better understand
where the theorem comes from and hopefully gain some insight. |
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Counting Parenthesizings with Decimals Steven J. Wilson, Johnson County Community College/td> | |
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Counting the possible parenthesizings for a typical binary operation on
n factors is a standard classical problem, which we shall apply to
the 4 basic operations upon single digits. After looking at proofs of this
problem, we shall extend the enumeration to include those "operations" that
affect place value, specifically concatenation of digits, decimal points, and
repeating decimals. |
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Malaria Occurrences in Paraguay: Correlating Malaria and Normalized
Difference Vegetation Index Nicole Wayant, undergraduate student, Kansas State University | |
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Malaria is a disease that has several different species of mosquitoes
as its vector. The disease is most prevalent in tropical and sub-tropical
regions of the world. Although not immediately deadly, if left untreated,
malaria can cause complications leading to severe incapacitation or death. Because of the high disease prevalence in the tropics and subtropics, there is a general assumption that malaria is related to precipitation. Precipitation is also linked to phenological cycles in vegetation, implying that observation of greenness cycles in vegetation might provide surrogate information about precipitation. We therefore hypothesize that occurrence of malaria is linked to cycles of vegetation greenness. To test this hypothesis, NDVI and malaria occurrence data for two departments in Paraguay were correlated. However, before the correlation tests could be run, the data for both departments was transformed into moving windows and the NDVI data was de-noised using Fourier Transform. After the data had been prepped, the malaria rates were correlated on a pixel by pixel basis to NDVI data throughout time. The ultimate goal of this project is to discover a relationship between vegetation and malaria that can be used as a decision support tool to help determine the occurrence of malaria outbreaks. |
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Principal Components Analysis and Microarray Data Emily Walters, undergraduate student, Pittsburg State University | |
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Microarrays are a recently developed tool for analyzing the expression of many thousands
of genes in a single biological sample. Because of the large amount of data generated by
even small microarray studies, bioinformaticists often rely on mathematical methods to
"mine" this data for biologically meaningful results. Principal components analysis (PCA)
is primarily a method to reduce the number of factors under consideration in multivariate
analysis. Because one of the greatest problems in microarray analysis is the
dimensionality problem (probe sets containing >50,000 genes are not uncommon, creating a matrix
with an unmanageable dimensionality), dimension reduction methods must be used.
Principal components analysis applies a linear transformation to the matrix, reducing
it to a manageable dimension. This matrix of gene expression data can then be analyzed
in terms of those variables responsible for the greatest amount of variance; the
assumption is that these "principal components" will be biologically relevant. This paper will
attempt to explain the mathematical foundation upon which PCA is based. All examples
and equations, unless otherwise noted, are taken from Applied Multivariate Statistical
Analysis, 2nd Edition, by Richard A. Johnson and Dean W. Wichern, 1998, pp 340-366. |
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Astrophysics and Undergraduate Mathematics Craig Masters, Kansas Wesleyan University | |
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Astrophysics is an area of study which has gained a degree of cachet in the popular
media. As such, it has given me a way to stimulate student interest in some of my mathematics
courses. In this talk, I will present some simpler examples from my dissertation,
and other astrophysics-related topics, with which I have had success in engaging
students in the undergraduate mathematics courses I teach. |
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Development of a Course on Discrete Wavelets and Applications Qiang Shi, Emporia State University | |
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I will introduce my experience on developing a new wavelet course in Fall 2008.
The strategies, benefits and challenges of designing and offering such a course will
be discussed. A few Maple projects on image processing using wavelets will also
be shared.
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| Winplot's 3D Graphing Features Uwe Conrad, Cowley College |
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| This workshop will provide detailed instructions on the use
of many of Winplot’s 3D graphing capabilities. Participants will learn how
to generate Surface Plots, Normal Vectors, Tangent Planes, and Tangent
Lines. Winplot differs greatly from the capabilities of graphing calculators
since it allows the user to plot multiple surfaces on the same 3D coordinate
system. The program is self-contained and can be installed on a portable
drive (memory stick) or even a floppy disk (1.44 Meg). Participants are
encouraged to bring a memory stick in order to save their work. Winplot is
not a Mathematics Program like Maple or Mathematica – it therefore forces
the user (Teacher and Student alike) to think about the task at hand.
Winplot is a Free Program provided by Rick Parris and available for download
on the “Peanut Software Homepage” http://math.exeter.edu/rparris/. |
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| The Obstacle Problem William Carlson, undergraduate student, Kansas State University |
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| I will give a brief introduction to free boundary
problems arising in partial differential equations. For an example I will
focus on a description of the obstacle problem, using a 1-dimensional example
for visualization. I will also state without proof several modern results about
the regularity of solutions to the obstacle problem, for example the
Caffarelli alternative, which states that the modulus of continuity of the
solution (and that of its derivative) is related to the modulus of continuity of
the obstacle. My talk will be accessible to a general audience. |
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| Single-Site Parameters from Bulk Absorption Spectra:
Fitting Procedure and Error Analysis
Michael Reppert, undergraduate student, Kansas State University |
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| An important challenge in many spectroscopic applications is to
obtain detailed information on a "single-site" spectral profile, i.e. the absorption
spectrum of an individual molecule. In typically measured "bulk" spectra
(which correspond to measurements made on thousands of individual molecules), the
single-site spectrum is obscured by convolution with a distribution function
(typically assumed to be Gaussian) which results from slight differences in the micro-environments
of individual molecules in a sample. Although given an experimentally measured
distribution function and bulk spectrum, it is in principle possible to use
numerical Fourier Transform methods to obtain the single-site profile, experimental
uncertainties generally make the direct numerical computation unreliable in practice. We present a simple
fitting procedure which can be used to extract approximate values for a number
of basic single-site parameters from (noisy) experimentally measured bulk spectra
together with an analysis of the error involved in the approximation as a
function of several experimental variables. |
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