Mathematics Department
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Mathematics Senior Theses 20122013
Selected Mathematics Senior Theses submitted for the 20122013 Academic Year 
Mathematics Senior Theses 20132014
Senior thesis papers submitted during the 201314 academic year. 
Mathematics Senior Theses 20142015
A collection of senior thesis papers 
Senior Theses 20152016
A collection of senior thesis papers from the Mathematics Department at Carthage College 
Senior Theses 20162017
A collection of senior thesis papers from the Mathematics Department at Carthage College 
Senior Theses 20172018
A collection of mathematics senior thesis from the class of 2018.
Recent Submissions

The Double Exposure SI Model: A Senior Thesis
(20170531)The SI model of disease spread is a fairly simple and wellknown way to study disease. In the model, each person is either susceptible or infected, and the infection spreads when a susceptible person interacts with an ... 
ZeroDivisor Graphs of Direct Product Rings
(20170531)This research investigates zerodivisor graphs of direct product rings. In zerodivisor graphs, if elements are connected with an edge, they will multiply to the additive identity element of direct product rings, (0,0). ... 
Mathematical Representation of the Chlorine DioxideIodineMalonic Acid Reaction
(20170531)Mathematics is frequently used in chemistry to solve several different types of problems including thermodynamics, stoichiometry, and analyzing experimental data. However, there are more interesting ways to link these two ... 
The Impact of Graph Density and Infection Probability on Disease Spread in Temporal Networks
(20170531)Epidemiological processes, such as the spread of a disease through a population, can be represented in a simple way by applying SI dynamics to temporal networks. The spreading behavior is observed by running simulations ... 
Determination of TwoDimensional Solutions to the NavierStokes Equations
(20170531)The NavierStokes Equations describe the motion of a viscous fluid. Although they have a wide range of practical uses, finding an analytical solution is nearly impossible, except for under certain simplifications. We ... 
Automorphism Groups of Cayley Graphs
(2017)In this paper, we develop ideas in algebraic graph theory to look at the Cayley graphs of groups, and the automorphism groups of graphs. A Cayley graph can be defined using a group and a set; for a given group, a ... 
Solving the Schrodinger Equation for Infinite Potential Wells
(2017)We solve the Schrodinger equation, after a brief introduction to quantum mechanics, for systems where we have zero potential energy within a given region, and infinite potential energy elsewhere. First, square wells ... 
An Analysis of Probability Through the Medium of Games
(2017)By looking at the board game RackO, it is apparent that chance plays a large part in possibly winning the game. The work of this thesis is to derive probabilities of winning according to the game rules quickly and easily, ... 
On The Nonkth Elements of a Group
(2017)In Abstract Algebra, raising an element to a certain power can provide insight on various properties of both the element itself and the group it is a part of. This thesis is interested in the number of elements of a ... 
Sums of Reciprocals of Fibonacci Numbers
(2017)Though there are many proofs, this paper gives direct proofs of wellknown formulas for sums of reciprocals of Fibonacci numbers. 
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 ...