Senior Theses 20152016
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Fundamental Groups of Simplicial Complexes
(2016)We define two different simplicial complexes, the common divisor simplicial complex and the prime divisor simplicial complex, from a set of integers, and explore their similarities. We will show that if one is connected, ... 
War
(2016)The card game War is known for taking a long time to play. There are many different variations of the game of which could possibly make the game shorter. Using a program which we wrote in Java, we calculated the length of ... 
Generalization of Riemann's Rearrangement Theorem
(2016)In this paper, we will examine Riemann's rearrangement theorem for sequences of real numbers. Continuing on, we will briefly discuss previous generalizations of the theorem to the n dimensional case. Because of the difficulty ... 
The Mathematical Modeling of Forest Fires
(2016)With worsening severity of forest fires in America, it has become a necessity to understand the behavior of these phenomena. Not only will this understanding assist land managers with preventing the start and spread of ... 
Mathematical Models of Conventional Warfare
(2016)Modern conventional warfare consists of multiple forms of battle that can be mathematically modeled using differential equations. One such basic and widely analyzed system of differential equations is the Lanchester ... 
The Mathematics of Power Outages
(2016)The power grid in the United States suffers from unpredictable blackouts that affect millions of individuals, but what results in a total blackout rather than a simple power outage is not yet known. Through a Mathematica ... 
Classification of Sets that Force a Group
(2016)In standard group theory, a group is formed from a set and a binary operation, then properties of the group that results are studied. However, there are some underlying structures in the sets that form groups. By considering ... 
The Effects of School Year Length on Fourth Grade Standardized Test Scores in YearRound Schools and Traditional Schools
(2015)This research study was designed to determine if there are academic benefits in attending a school with a yearround calendar compared to a traditional school calendar. This research analysis compared the standardized ... 
Euler’s Smallest Squares
(2016)Leonhard Euler approached a problem involving x, y, and z for which x^2+y^2+z^2 and x^2 y^2+y^2 y^2+x^2 z^2 are perfect squares. Euler believed that he had found the absolute smallest solution to this problem. However, ... 
An Analysis of the Game Tenzi
(2016)In the game Tenzi, a player has ten sixsided dice and repeatedly rolls any subsets of the dice in order to have all ten show the same number with as few rolls as possible. A simple strategy is to choose a number at the ...