Abstracts of Student Talks

Speakers:  Here are some  SPEAKER GUIDELINES for this conference.

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Index

Abstracts

Abstract:   I present results on a study of an academic database used to predict the best prospective students based on data gathered preregistration.  Several mathematical programming methods for classification were used and I will introduce some of these.  Computational results will be given.

Abstract:  In this talk the numerical simulation of a generic two-stage chemical reaction to completion is presented: i.e., product A producing B and product  B producing C. This system is typical in chemical manufacturing processes. Each reaction component (A, B or C) has a price at which it is bought or sold. Thus, the goal is to maximize profit of the overall process. Using a single industrial process, we "fit" difference and differential equation models to the reaction data and determine reaction constants for each stage. With these constants, chemical reactions are numerically simulated for any choice of initial conditions for each component. This demonstrates the usefulness of simulation, as compared to full-scale experimentation, to optimize industrial processes.

Abstract:  Specialty Plastics & Packaging, Inc., located in Shelburn, IN, presented an engineering design project to the Mechanical Engineering department at Rose-Hulman concerning the manufacturing improvements of welding rod containers they produce.  As part of an Operations Research course, we developed a model that specified the amount of each product to be produced each month and which molds to use during each specified month.  Our discussion will focus on the problem and the model used, as well as directions for expanding this model to solve more difficult problems.

Abstract: Using Visual Basic and ActiveX, mathematical models can be created and rapidly deployed to the World Wide Web or compiled into stand alone applications with little programming experience. This session provides a brief overview of the technology and step-by-step instructions on how to go  from functions on a paper to a mathematical model on the Web.  Models of a basketball shot, a 2-body gravitational force, and predator-prey pursuit and escape strategy will be some of the examples used.

Abstract:  This research project was initiated by our school bookstore after recently increasing the amount of room available for customers to wait in line.  Before remodeling, the bookstore had problems with long lines as well as extreme congestion in the doorways and aisles during the "bookrush" period at the beginning of each semester.  Therefore, the purpose of our research was to use simulation and queuing theory to find a  new configuration of checkout lines that would ease congestion and minimize he time students spent in line.

Abstract:       The mind-boggling game of Lights Out can provide for many hours of frustration.  The objective is simple.  You are presented with a five by five grid of lights, some off, some on.  When you press a button, the four buttons that form a cross with the pressed button as the center change parity.   To win, get all the lights out.  To add to the headache, we have taken the challenge of solving this puzzle through the means of Linear Algebra.  By solving, we mean that given a board state, we can tell you exactly what buttons to press in order to turn all the lights out.  The solution requires only a basic understanding of Linear Algebra concepts. In addition, we will also engage in a discussion of the newest version of Lights Out, Lights Out 3D.

Abstract:  Many public facilities have capacity limits placed on the
lawful number of occupants.  How should such limits be determined? The
safety risks in an overcrowded area are explored, and computer
simulations are used as a basis on which general guidelines are
formulated.
 

Saturday Morning

Abstract: Many of the theorems that we use in modern geometry were discovered accidentally.  I will introduce another geometric theorem, that I found quite by accident, involving areas of triangles, generated by the squaring of the sides.  My fellow classmates and I found it to be quite interesting.  I will show proofs applicable to 10th grade students, and others applicable to 2nd or 3rd year math majors.

Abstract: Measure chains are special subsets of the real line.  The real line itself and all its discrete subsets are examples of measure chains, but many subsets containing combinations of continuous intervals and discrete points are also measure chains.  The calculus on measure chains is thus an extension of the differential and difference calculuses.  The axioms defining measure chains will be given, and basic concepts and theorems in the measure chain calculus will be presented.  Some results on stability (which culminate in Lasalle’s Invariance Principle) will be presented in both a differential calculus and a difference calculus
context; the hope is to extend these results to the measure chain calculus.

Abstract: Why does the familiar diatonic scale have such a wide appeal? Using the techniques of Brian J. McCartin, tonal music is explored by means of elementary geometrical reasoning. Musical ideas such as the circle of fifth, chords and transpositions are addressed.

Abstract: The problem of kaleidoscopically tiling a surface by triangles is equivalent to finding groups with certain properties.  In order to admit a tiling, a group must have a specific set of generators as well as an involutary automorphism, theta, that acts to reverse the orientation of the "tiles".  If a group has the appropriate generators but lacks a theta, then it represents a symmetry of a hyperbolic surface, but does not come from a tiling.  The purpose of this talk is to explore group theoretic and computational methods for determining the existence of theta and thus distinguish between symmetry and tiling groups on hyperbolic surfaces.

Abstract: Given a graph G, we find the associated Laplacian Matrix, L(G), by subtracting the adjacency matrix A(G) (Aij = 1 if there exists an edge connecting vertices i and j, and 0 otherwise) from a diagonal matrix D(G) whose entries equal the degrees of the vertices. We call the second smallest eigenvalue of L(G) the algebraic connectivity. For trees (connected graphs with no cycles), the algebraic connectivity is positive. The eigenvectors corresponding to the algebraic connectivity can be used in classifying trees as type 1 or type 2. We show that certain symmetric trees must be type 1.

Abstract: Various means of summing both finite, and infinite series will be covered.  In particular, these will include: power series, a derivation for the sum of the kth powers of the first n integers, as well as, an application of partial fractions to reduce infinite series to telescoping series.  Interesting properties of binomial  coefficients will also be presented.

Abstract:  What do subcommittee creation, emergency medical services and psychometric testing all have in common? These areas, like many others contain questions that are easily formulated as a set covering problem. The set covering problem is often stated as: Given a binary matrix A, find a binary vector X such that AX is vector with strictly positive entries. Much work has been done in finding minimal solutions to the set covering problem. This talk addresses the related question of finding multiple set covers with a minimal number of elements in common. Genetic algorithms are a technique, based on evolutionary biology, for finding approximate solutions to difficult optimization problems. This talks focuses on using a genetic algorithm to find maximally disjoint solutions to the set covering problem.

Abstract:  After a brief history of Blaise Pascal, some old properties and one newly-discovered one will be discussed.