Speakers: Here are some SPEAKER GUIDELINES for this conference.
Title | Speakers | Institution | Room/Time |
Large Primes | Patrick Kessel & Westley Haggard | Northern Kentucky University | G219/3:00 |
Parallel Computation of the Polar Decomposition | Johnnell Parrish | University of Maryland Eastern Shore | G222/3:00 |
Error Bounds Involving Almost-Binomial Approximations | Abu Jalal | Wabash College | G219/3:25 |
The Irrationality of Pi | Amar Parmarr | Manchester College | G222/3:25 |
Farmer Ted Goes 3D | Shawn Alsburgh | Taylor University | G219/4:00 |
Patterns of Powers | Kendell Dorsey | College of Maint Saint Joseph | G222/4:00 |
Chaotic Behavior over the Naturals | Steve Young | Rose-Hulman Institute of Technology | G219/4:25 |
Good Sampling Times for Sampled-Data Systems | Mustafa Bashir | University of Nebraska-Lincoln | G222/4:25 |
Title | Speakers | Institution | Room/Time |
Energizer Fractions; They Keep Going, and Going, and ... | Erin Bergman | Saint Norbert College | G219/10:10 |
Rookies in the Math Modeling Contest | Michael Ewing , Peter Nei & Tom Schneider | Rose-Hulman Institute of Technology | G222/10:10 |
Roots, Roots and More Roots | Michelle Budzban | Saint Norbert College | G219/10:35 |
NP Complete Radio Tower Placement | Dennis Lin | Rose-Hulman Institute of Technology | G222/10:35 |
Bordered Klein Surfaces with Maximal Automorphism Groups | Shaun McCance | Purdue University - Calumet | G219/11:10 |
G222/11:10 | |||
Cwatsets and Graph Isomorphisms | Nancy-Elizabeth Bush | Wheaton College | G219/11:35 |
G222/11:35 |
LARGE
PRIMES
by Patrick Kessel & Westley Haggard of Northern
Kentucky University (G219 / 3:00 pm)
Abstract:
Public-key cryptography relies heavily on prime numbers. Anyone who
knows the definition of a prime number can show that a number a
is prime by showing that no positive integer divides a besides 1
and a. But for a public-key cryptosystem to be secure, the
number a must be hundreds of digits long. One certainly cannot
show that a is prime by showing that no positive integer divides
it besides itself and 1. This would take too much time. So
how can one show that a number, which is hundred of digits long, is prime?
PARALLEL
COMPUTATION
OF THE POLAR
DECOMPOSITION
by Johnnell Parrish of University of Maryland Eastern
Shore (G222 / 3:00 pm)
Abstract:
A nonsingular complex matrix A as a polar decomposition such
that A=UH, where U is a unitary matrix and H is a
Hermitian positive definite matrix. In this discussion, parallel computation
of the polar decomposition using a method by Higham and Papadimitriou is
considered, and specific applications of the polar decomposition are identified.
Furthermore, the efficiency of computing the polar decomposition on a distributed
memory computer is shown, and the importance of utilizing the computer's
resources effectively is pinpointed.
ERROR
BOUNDS
INVOLVING
ALMOST-BINOMIAL
APPROXIMATIONSOF
PROBABILITIES
INVOLVING
SUMS
OF INDEPENDENT
HYPERGEOMETRIC
RANDOM
VARIABLES
by Abu Jalal of Wabash College (G219
/ 3:25 pm)
Abstract:
Problems involving sums of several independent hypergeometric random
variables generally involve complex calculations. Straightforward approximations
have been developed using the Poisson distribution, the binomial distribution,
and the almost-binomial distribution, a generalization of the binomial
distribution where n is allowed to take on noninteger values. In
this talk, we give error-bounds for the almost-binomial approximation and
compare these with error- bounds for the other approximation methods.
THE IRRATIONALITY
OF PI
by Amar Parmarr of Manchester College (G222
/ 3:25 pm)
Abstract:
Everyone knows that Pi is irrational and yet proving this can be somewhat
of a challenge. Mathematicians have spent centuries studying and estimating
Pi. I will explain Ivan Niven's half-page elementary proof that Pi is irrational.
I was interested in also obtaining elementary estimates for Pi. Using
geometric methods, I was able estimate Pi with a scientific calculator,
but this method had many limitations. I then was able to obtain a good
estimate of Pi using only techniques from Calculus. I hope that my
clumsy estimates give you an appreciation for estimates of Pi that are
accurate to 200 million decimal digits.
FARMER
TED
GOES
3D
by Shawn Alsburgh of Taylor University (G219
/ 4:00 pm)
Abstract:
Let s(n) be the minimum surface area of a three dimensional
rectangular box with integer sides and a volume of n. Let F(n)
be
the ratio n/s(n). Let A be the set of all integers
n
such
that for all integer .
Because of the similarity with a property of cubes, we define the set of
almost-cubes to be the set A. We attempt to characterize almost-cubes.
We note the relationship between almost-cubes and their two-dimensional
counterpart almost-squares. Three different classes of almost-cubes
are described, including how to calculate which almost-cubes fall into
each class. This is a generalization of the work of Greg Martin,
who characterized almost-squares in a 1999 paper.
PATTERNS
OF POWERS
by Kendell L. Dorsey of College of Mount Saint Joesph(G222
/ 4:00 pm)
Abstract:
In examining the sequence
with a calculator, one can see that the greatest integer less than or equal
to each term is odd. In this talk we establish this result and consider
which pairs (a,b) have the same pattern, i.e. the greatest integer
less than or equal to
is odd for all n. We also contemplate other parity patterns for
the greatest integer of .
CHAOTIC
BEHAVIOR
OVER THE NATURALS
by Steve Young of Rose-Hulman Institute of Technology
(G219
/ 4:25 pm)
Abstract:
Typically when speaking of a chaotic data set, the set resides in the
Reals. This talk intends to show how a chaotic data set can be extended
so that is can be thought of as residing in the Natural numbers and how
a subset of the Naturals can be thought of as a chaotic data set by transforming
it into the Reals.
GOOD SAMPLING
TIMES
FOR SAMPLED-DATA
SYSTEMS
by Mustafa Bashir of University of Nebraska-Lincoln
(G222
/ 4:25 pm)
Abstract:
We consider a continuous-time system modeled by a differential equation
with a continuous-time control. We examine its stability in terms
of a continuous-time solution. We apply a sampled-data control and
compare the stability of the new solution with that of the continuous-time
solution. Our primary interest is in relating these solutions and
understanding how the sampled-data control works on the system. We
finally examine the stabilities of several sample systems and form a conjecture
about the stability of an infinite-dimensional system using its finite-dimensional
truncation.
Saturday Morning
Abstract:
This will be an introduction to continued fractions. We will
give a variety of examples and discuss some elementary properties.
ROOKIES
IN THE MATH MODELING
CONTEST
by Michael Ewing, Peter Nei, and Tom Schneider
of Rose-Hulman Institute of Tecnology (G222 / 10:35 am)
Abstract:
We will describe our experiences in our rookie season in the math modeling
contest. Describing what we would have liked to know before hand
and what we will would do differently if we could repeat our rookie season.
ROOTS,
ROOTS,
AND MORE
ROOTS
by Michelle Budzban of Saint Norbert College (G219
/ 10:35 am)
Abstract:
We will review the time-honored method of hand-calculating square roots,
investigate the thery behind this method, and extend the method to other
roots.
Abstract:
One of the problems in this year's Mathematical Contest in Modeling
involved assigning frequencies radio towers arranged in a hexagonal pattern.
The purpose was to minimize span of the frequency assigned while avoiding
interference between towers. We showed that the general problem where an
arbitrary number transmitters is placed on a hexagonal grid is NP-Complete.
People have been unsuccessfully trying to solve NP-Complete problem for
many years now. Also, modern encryption depend on the fact that such
problems are hard. Thus, we conclude that we are unlikely to find
an efficient solution to our problem.
BORDERED
KLEIN
SURFACES
WITH MAXIMAL
AUTOMORPHISM
GROUPS
by Shaun McCance of Purdue University Calumet
(G219 / 11:10 am)
Abstract:
In this talk, we consider tilings of the upper half plane by hyperbolic
polygons. We use these tilings to construct Klein surfaces with nontrivial
automorphism groups. It is known that if Y is a bordered Klein
surface of algebraic genus p the order of its automorphism group
must be less than or equal to 12(p --1). We conclude the talk
by examining Klein surfaces that possess this maximal number of automorphisms.
CWATSETS
AND GRAPH ISOMORPHISM
by Nancy-Elizabeth Bush of Wheaton College (G219
/ 11:35 am)
Abstract:
Cwatsets were first introduced at Rose-Hulman as a topic suitable for
undergraduate research, and applications have been found for them in statistics
and coding theory. Here we introduce another important application to the
field of graph theory: we show how the equivalence class of a graph can
be described using cwatsets. Studying invariance leads to a discovery of
which of these cwatsets are groups