Abstracts of Student Talks

Emaan Abdul-Majid, Northampton Community College

Title: Females, Mathematics and the Soceity

Abstract: Many stereotypes exist concerning women in mathematics. These stereotypes have existed for years, but their affect on women and their mathematical interests are very strong to this day. The stereotypes that exist have no scientific background. Despite this fact, the stereotypes are still believed by many women and men. Stereotypes have a major effect on women going into math and related fields. This is still seen today and causes many biases towards women who decide to pursue mathematics despite many widely held biases.

Andrew Abraham, Moravian College

Title: The Space Elevator "Tower to the Sky"

Abstract: Is it possible to construct a freestanding object that stretches from the Earth into space? Would such a structure be stable? How easily can the force of gravity be overcome? Examining the Space Elevator concept has proved to be a challenge to physicists, engineers, and mathematicians alike. This discussion will focus on some of the benefits and challenges of this interesting concept.

Paul Bernhardt, Messiah College

Title: Mathematical Modeling: Emergency Facilities Location

Abstract: This is a presentation of a solution to "The Emergency Facilities Location Problem" from the 1986 Mathematical Contest in Modeling. The problem deals with optimally locating emergency facilities in a town. The process of mathematical modeling will be discussed so as to give insight to the methods used to find the optimal solution and then to expand the problem further.

Crystal R. Bourne, Rutgers University-Camden

Title: Pell's equation

Abstract: In this talk we give proof to the solutions of the Pell's equation using continued fractions. Then some examples will be given.

Colin Conrad, Marywood University

Title: Smooth and Semismooth Integers and Their Roles in Factorization Algorithms

Abstract: Since the RSA public key encryption was invented in the 1970's, factorization techniques have earned more attention than ever. Our inability to efficiently factor large numbers is the basis for the security of the system. Smooth integers are essential to the factoring process, and their distribution and generalizations formed our modern algorithms. This presentation summarizes the theory and application of the factoring process, highlighting the importance of smooth and semismooth integers.

Matt Fearnley, Lock Haven University

Title: How about a Little "Basel" with Your Lunch?

Abstract: For centuries, mathematicians tried to find the exact value of the infinite sum 1+1/4+1/9+1/16+Ľ but were unsuccessful. In 1731, at the age of 24, celebrated mathematician Leonhard Euler found the sum. Euler offered, not just one, but two proofs of the famous summation, which became known as the Basel Problem. We will discuss a brief history of the problem, both of its proofs, and some open-ended questions.

Kerri L. Hansen, Holly Turnage, Rutgers University-Camden

Title: RSA Method Cryptology

Abstract: We are giving a presentation on the RSA Method of Cryptology. We are presenting a brief overview of the history of the RSA Method and an explanation of what it is and what it's used for. Then, we will present a problem and show how one would go about encrypting and then decrypting a message using the RSA Method.

Justin Hughes, Lycoming College

Title: Google's PageRank

Abstract: How do search engines work? Why is Google so good? This presentation will explain the initial version of the algorithm used by Google to sort search results. This algorithm is called PageRank, and it involves the mapping of hyperlinks to calculate the importance of a webpage by using matrices.

Jeremy D. Keffer, David J. Rieksts, Kutztown University

Title: How Many Ants are Enough?

Abstract: Ant colony optimization (ACO) is a relatively new metahueristic for solving combinatorial optimization problems that is based on the foraging behavior of biological ant colonies. Starting with the 1996 seminal paper by Dorigo, Maniezzo and Colorni, ACO techniques have been used to solve the traveling salesperson problem (TSP). A key ACO parameter is the size of the artificial ant colony. For the TSP, the seminal paper argued that the optimal number of artificial ants should be equal to the number of cities in the TSP. Typically, subsequent papers dealing with ACO and TSP have set the artificial ant colony size equal to the number of cities in the TSP. In this talk, we revisit the number of artificial ants to use in solving a TSP. We clearly demonstrate through empirical and statistical arguments that more ants are better.

Brian T. Kolarovic, Rutgers University-Camden

Title: On Binomial Coefficients

Abstract: In this talk we give proof of identities for binomial coefficients, including Fibonacci numbers.

Jamie Long, Moravian College

Title: The cx + d Conjecture - When 3x + 1 Just Isn't Hard Enough

Abstract: For over half a century, mathematicians from across the globe have struggled to find a solution to Lothar Collatz's infamous 3x + 1 conjecture, but there may come a time when it is finally solved. My talk describes an even more challenging generalization of the problem, and showcases some of the surprising similarities and differences between the two.

Susanna Molitoris, University Of Scranton

Title: Truels

Abstract: The talk will cover an introduction to multiple-person dueling scenarios with a focus on the truel, or three-person duel. Other topics to be covered include the prisoner's dilemma and its relation to this problem, as well as the logic behind stronger opponent strategy and its sometimes surprising results.

Timur Nezhmetdinov, Lehigh University

Title: Multidimensional Frobenius Problem

Abstract: The original Frobenius coin change problem is to find the greatest integer that cannot be represented as a linear combination of given positive integers over the nonnegative integers. The problem can be generalized to multiple dimensional spaces. Several results for the generalized problem will be presented.

Kyle Pena, Messiah College

Title: Checkerboard Paths: A Combinatorial Exercise

Abstract: We examine arrangements of "checkers" on a square lattice with the aim of counting monotone paths from one corner to another. We reduce the initial problem to a readily solvable special case, and then pose generalizations to the discussed method.

Daniel A. Pitonyak, Lebanon Valley College

Title: InQE: Quantum Computation, Quantum Information, and Irreducible n-Qubit Entanglement

Abstract: This talk will present the work I did as a research assistant in the summer of 2006 with the Mathematical Physics Group at Lebanon Valley College. The talk will introduce relevant background mathematics, explain the significance of irreducible n-qubit entanglement (InQE) to quantum computation and quantum information, and report on the Group's current direction of research.

Matt Powell, Lock Haven University

Title: Toward a Definition of the Discipline

Abstract: After some remarks concerning the undergraduate mathematics curriculum and its historical foundations, we examine the role of open questions in the expansion of the discipline.

Brian Story, La Salle

Title: A Historical Perspective on Collaboration in Mathematics

Abstract: Historical highlights of interactions between mathematicians. Including Newton & Leibniz, Fermat's little theorem, and Godel's incompleteness theorem. The focus will be on the role of publishing and collaboration with other mathematicians.

Meredith L. Williams, Cedar Crest College

Title: Women and Girls in Mathematics

Abstract: Despite amazing progress to equalize women representation in fields such as the biological sciences and humanities, women continue to be a minority in the mathematical sciences. This presentation discusses the possible reasons behind this continued under-representation including gender stereotyping, possible differences between the sexes and sociological influences.

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On 13 Feb 2007, 19:02.