Browsing Mathematics URC Student Scholarship by Issue Date
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Deletions and Collapsions with Partitioned Binary Matrices.
(20000101)It has been proven that, given any table of integers, one ? and only one ? of these statements is true: either some rows, excluding the first, can be deleted so that every column has an even sum, or some columns can be ... 
Simulating and Evolving Bipedal Locomotion.
(20000101)I endeavored to write a computer program in C++ which implements a 2D biped (stick figure) with legs and a torso, in which the biped learns to walk and achieve other human motions. The biped simulates human actions by ... 
Newton's Law of Cooling Heats Up.
(20010101)Newton's Law of Cooling (NLC) is a differential equation that attempts to predict the rate at which a body will cool when placed in an environment with an essentially constant ambient temperature. If the ambient temperature ... 
OnePalette n Color Maximizability.
(20010101)A graph is said to be OnePalette n Color Maximizable (OPNCM) if and only if, given a palette of n colors, the maximum probability of obtaining a coloring containing identicallycolored adjacent vertices occurs when ... 
An Artificial World and its Creatures.
(20010101)The project studies the evolution of some digital organisms in a simple world whose rules they learn by trial and genetic evolution. The creatures and the world are modeled to resemble a simple natural ecosystem. The world ... 
Bulgarian Choral Traditions:Music and Vocal Techniques Influenced byReligion, Education and the Singing Community
(20020101)As a living art form unique to every culture, choral music reflects strongly upon a country's history, culture, and people. It is an art form that is always evolving to depict changes within a culture. The sound of Bulgarian ... 
Bulgarian Choral Traditions:Music and Vocal Techniques Influenced byReligion, Education and the Singing Community Leanna Cooper and Akiko Minaga
(20020101)A tumultuous history is the cause of a rich cultural identity and unity that has enhanced music, particularly choral singing, in Bulgaria. Through religious, educational and communitybased institutions, choral music has ... 
Integer Partitions and their Applicationto Quantum Physics
(20020101)Combinatorial mathematics is not frequently associated with quantum physics. However, work in one discipline can motivate investigations in the other. A recent conjecture regarding allowed multiplets in the composite fermion ... 
Edge Coloring Graphs with Distance Restrictions
(20020101)Using probabilistic methods developed by Michael Molloy and Bruce Reed, we attempt to prove a conjecture that says the strong chromatic index for bipartite graphs is less than or equal to 5/4(D)^2$ where (D) is the maximum ... 
Nmaximizability of Thetaless Graphs
(20020101)A graph G is said to be nmaximizable if and only if we get the smallest number of proper colorings when using identical nlists for all vertices. First we prove that all cycles are nmaximizable for n>=3 (the n=2 case ... 
The Evolution of Altruism: Increasing the Amount of Realism in Evolutionary Simulations
(20030101)Our study is based on the research on altruism done by Robert Axelrod. With the use of mathematical game models, Axelrod created a computer model of altruism evolving from randomness. We have elaborated on his studies to ... 
Integer Partitions and their Applicationto Quantum Physics
(20030101)Combinatorial mathematics is not frequently associated with quantum physics. However, work in one discipline can motivate investigations in the other. A recent conjecture regarding allowed multiplets in the composite fermion ... 
Polygons with Rational Sides, Diagonals and Area: Constructions and Properties
(20030101)The majority of geometric constructions do not produce rational elements. This research was on so called rational polygons, which are polygons with rational sides, diagonals and area. We found a construction method with ... 
Variations on a Theme of Euclid
(20030101)Euclid is a simple game which can be played with paper and pencil, yet it is a wellspring of interesting ideas and surprises. This paper will explore the many variations of the game which are possible. Many of these ... 
New Nonstandard Finite Difference Methodsfor the Heat Equation
(20040101)Many physical phenomena around us can be described by mathematical models, which often take the form of a differential equation. Diffusion of heat through a homogenous bar or rod obeys a linear partial differential equations ... 
New Nonstandard Finite Difference Methodsfor the Heat Equation
(20040101)Many physical phenomena around us can be described by mathematical models, which often take the form of a differential equation. Diffusion of heat through a homogenous bar or rod obeys a linear partial differential equations ... 
Some Variations on the Tennis Ball Problem
(20040101)Our study looks at Catalan, Motzkin, and Schr?der numbers. Catalan numbers are very well known mathematically and extensive research has been done highlighting their interesting properties. In contrast, Motzkin and Schroder ... 
Modeling Airline Overbooking
(20040101)The airline industry uses mathematical models in order to increase its profits. Airlines face two major constraints: fixed capacity and the fact that seats on a certain flight represent perishableassets, as they are not ... 
The Mathematics of High Scores
(20040101)Many video games maintain a list of high scores. This paper investigates mathematical questions inspired by lists of high scores. First, we make the distinction between those high scores which were records when they were ... 
What a Tangled Web We Weave: Epidemiological Modeling and Graph Theory
(20050101)Network theory has recently received renewed focus for its applications in modeling the spread of diseases. Drawing upon a recent sociological study on the structure of adolescent sexual networks, as well as on previous ...