Northeastern Section of the MAA (NES/MAA)
Fall 2003 MEETING
The schedule of student papers is below followed immediately by the abstracts for the student papers.
Student Papers: Schedule
|
Speaker and Title |
Time |
Room |
|
Brian D. Ginsberg, The Nearly Secret Theorem of E. Midy |
|
270 |
|
Elizabeth
Bellenot, Effects of Biological Invasions on Ecological Communities |
|
270 |
|
Jessica
S. Lee, |
|
270 |
|
Michael
J. Coleman, Modeling iBOT Belt Dynamics |
|
270 |
|
Seila Selimovic, |
|
270 |
|
|
|
|
|
Iuli
Pascu, A Graphical Interpretation for Complementary Sequences |
|
274 |
|
Karin
Steece, The Chinese Postman Problem |
|
274 |
|
XinXin
Du, |
|
274 |
|
Paula
F. Popescu, Games with Hats |
|
274 |
|
Kathleen Leahy, College of the Holy Cross Enigma |
|
274 |
|
|
||
|
Charlie
Rossetti and Matthew Angelucci, Dynamica |
|
278 |
|
Brandon Dwyer, |
|
278 |
|
Jenny Kirouac, Naming Really Large Numbers |
|
278 |
|
Kari
Lock, Making Best Approximates Appear Through Magical Intervals |
|
278 |
|
Neil
Hoffman, Double Bubbles in Other Universes |
|
278 |
|
Speaker and Title |
Time |
Room |
|
Kathleen
Smith, Vertex Total Magic Labelings |
|
392 |
|
Solving ‘Rubik’s Polyhedra’ Using Three-Cycles, |
|
392 |
|
Joelle
Arnold, The Assignment Problem and Optimizing Registration |
|
392 |
|
Janet
Tsai, You Can Make Anything with One Straight Cut |
|
392 |
|
Ben
Kraines and Siddartha Rao, Extreme Points and Lipschitz Conditions for Functions in a Certain Zygmund Class |
|
392 |
|
|
|
|
|
Matthew Stephen Palmacci, The Golden Ratio |
|
396 |
|
Alison Fish, The Golden Ratio and Three-Dimensional Geometry |
|
396 |
|
Kaitlyn
ONeil, Pretzel Knots and Colorability |
|
396 |
|
Kevin
Roberge, Algebraic Topology and Elementary Circuits |
|
396 |
|
Michael A. Burr, Simplicial Depth: An Improved Definition, Analysis, and Efficiency for the Finite Sample Case |
|
396 |
Student Papers: Abstracts
Matthew Angelucci,
Dynamica
In this talk we present Dynamica, a software package running under Mathematica that helps researchers gain insight into the behavior of dynamical systems. The various features of the software are demonstrated on a biological model of Lyme disease described by a difference equation.
Joelle
Arnold,
The Assignment Problem and Optimizing Registration
Consider the arranged marriages of a fixed and finite number of heterosexual couples. Suppose that each woman gets to make a list of her preferred husbands, but that the men have no say. We will discuss the conditions under which each woman can be paired with a suitable husband - this is Hall’s marriage problem. The Assignment Problem is any scenario in which a group of people or other entities are to be matched to another group of people or entities, and in which both groups have the same number of members. By either one group or both groups ranking preferences, an optimization can be found. We arrange the data in a matrix and by using the Hungarian Method, may make the best matches. This procedure is used to solve job training, hypothetical marriage and shipping route problems. We will investigate using these two methods to optimize the registration process here at Olin. In this manner, we should be able to maximize student satisfaction with spring schedules.
Elizabeth
Bellenot,
In an ecological community with n distinct species, what happens when an invader species is introduced? By studying food webs using matrix analysis and simple graph theory, we examine cases where we can predict which resident species will increase, decrease, or has no change in population. We also look at cases where the outcome is ambiguous.
Michael A. Burr,
Simplicial Depth: An Improved Definition, Analysis, and Efficiency for the Finite Sample Case
As proposed by Liu
(1990) the simplicial depth of a point with respect to a probability distribution
on
is the probability that
belongs to a random simplex in
.
The simplicial depth of
with respect to a data set
in
is the fraction of the closed simplices given
by
of the data points containing the point
.
We propose an alternative definition for simplicial depth which continues to
remain valid over a continuous probability field, but also fixes some of the
problems for the finite sample case, including those discussed by Zuo and
Serfling (2000). Additionally, we discuss the effect of the revised definition
on the efficiency of previously developed algorithms and prove tight bounds on
the value of the simplicial depth based on the half-space depth.
Michael
J. Coleman,
The iBOT, a revolutionary personal mobility device developed by DEKA Research and Development Corporation, contains several belts that transfer mechanical power through the system. The dynamic characteristics of the belts are obviously important to the operation of the iBOT. Our task is to create a mathematical model of some aspects of the belt dynamics. Partial and ordinary differential equations and Lagrangian dynamics are employed to understand the elements of this electro-mechanical system. Ultimately, finite difference numerical methods are applied to solve the rather complicated system of governing equations developed. The results from our mathematical model are compared with those from actual experiments.
XinXin
Du,
Monte
Carlo Simulations on One Electron Per Site, Two-Dimensional
Square Lattices
I
used
Brandon Dwyer,
A Student’s Look at the First Actuarial Exam
If a student is looking seriously into a career as an actuary, they should begin the exam process while still in college. The Course I exam contains problems relating to calculus and probability (both discrete and continuous). This presentation will look at how to prepare for the exam including strategies for studying. Two typical exam questions will also be presented.
Alison Fish,
Merrimack College
The Golden Ratio and Three-Dimensional Geometry
The
golden ratio, represented by (phi) is found in many areas of mathematics.
This talk will discuss the golden ratio and how it can be found in
three-dimensional geometric shapes such as polyhedra. Golden rectangles, which exhibit this ratio,
exist within the polyhedra. Also the coordinates of the vertices of the
polyhedra and the relationship of the edges include the golden ratio.
Brian
D. Ginsberg,
The Nearly Secret Theorem of E. Midy An Extension after 165 Years
This work extends
Midy’s theorem a curious, old number theory result about
parts of decimals of even period
to
a wider class of fractions whose period need not be even. Avenues for further
extension are also explored.
Neil
Hoffman,
The
recently proved Double Bubble Conjecture says that the familiar double soap
bubble is the least-area way to enclose and separate two regions of prescribed
volumes in .
We report on extensions to other three-dimensional universes.
Jenny Kirouac,
Westfield State College
You know thousand, and million, and billion, and trillion. Ten thousand, ten million, ten billion, and ten trillion, but do you recall the numbers that come after them all? Shouldn`t we have names for bigger and bigger numbers? And what exactly is a zillion? This talk will delve into a system of naming numbers that not only exceeds our traditional system, but also allows us to keep naming larger and larger numbers without limit. Of course, we will also mention some of the famous numbers and say how they can be alternatively named in this new system: large numbers like the perplexing Googolplex number, the merciful Mersenne primes, and the invigorating Vinogradov`s number. After experiencing this talk you will know lots of amazingly large numbers AND you will be able to name any number you come across.
Ben Kraines,
Extreme Points and Lipschitz Conditions for Functions in a Certain Zygmund Class
The
Tagakivan
der Waerden function is an important example of a continuous nowhere
differentiable
function. Although it is nowhere
differentiable, it is possible to define an analogue to the derivative via the
“dyadic difference quotient” sequence. This paper concerns functions whose
dyadic difference quotients have modulus one.
We use the dyadic difference quotient to investigate Lipschitz points
and extreme points for such functions in a way that parallels the use of the
derivative in studying extreme points and Lipschitz behavior in real variable
calculus.
Enigma
The Code that Changed History
In this talk we will give a brief history of the Enigma code used by the Germans in World War II. We will describe the machine used to encode and decode as well as some of the mathematics involved. We will also discuss the connection between the breaking of the Enigma code and the creation of the first digital computer.
Jessica
S. Lee,
As early as 300 B.C., were prime for all primes
. While this conjecture is false, many people
now have joined the search for primes of that form, now dubbed Mersenne Primes
after the Frenchman who studied them at great length. This talk briefly outlines the history of
these rare primes, the current on-going search for them, as well as providing
an introduction to some of the unsolved mysteries surrounding Mersennes.
Kari
Lock,
Let be a real, irrational number. Given a positive
integer q, an important question in diophantine approximation is: how do we
determine exactly when q is the denominator of a “best rational approximate” to
?
Using the theory of continued fractions and their convergents, I show that if
the continued fraction expansion of
has the form
,
then a positive integer q is a denominator of a best approximate to
if and only if the interval