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. 
Senior Theses 20182019
Senior Thesis papers submitted by student who graduated in the 20182019 academic year. 
Senior Theses 20192020
Senior Thesis papers submitted by student who graduated in the 20192020 academic year.
Recent Submissions

Infinite Snowman
(20190517)In this research paper we explore how to create an infinite snowman within an isosceles triangle to find the sum of its total area. Our main objective was to find the sum of the areas of the circles inscribed within the ... 
Minimizing Transpositions in Permutations with Indistinct Variables
(20190517)In any permutation within a symmetric group, the minimum number of transpositions required to return the permutation to the identity can be algorithmically determined. In fact, this algorithm determines this required number ... 
Mathematically Modeling the Josephson Junction
(20190517)Josephson junctions are widely used in applications where a very precise voltage source is required, one example being metrology, where they are used to help define the values of several fundamental constants of nature. ... 
ReactionDiffusion Equations and Biochemical Pattern Formation
(20190517)Many biochemical reactions can be modeled using reactiondiffusion equations, some of which form patterns. Reactiondiffusion equations are partial differential equations that describe how the concentrations of two species ... 
The Fair Mathematics of Fair Isle Knitting: A Study of Knitting Patterns
(20180517)Fair Isle knitting is a unique knitting style that follows a set of general rules. These rules include its use of only two colors within a knit row, its simple color changes, its repeats in pattern structure, and its ... 
Analysis and Manipulation of the Kruskal Card Trick
(20180517)In the Kruskal card trick, an audience member has a full suit of cards, ordered ace to King, and the magician has the rest of the deck. The audience member then picks out a card from the magician’s deck of his or her ... 
Has Polarization in the Senate Grown?
(20180517)There is reporting far and wide on all sides of the political spectrum that there is a rise in polarization in the nation and our politicians. The study by Andris et. al. proved this for the House of Representatives. ... 
The Optimal Path through the Crowd
(20180517)Have you ever arrived late at a concert and not been able to get a good view? Had the crowd already formed and there looked to be no good way to the front? Using collective motion models, we seek the optimal path to ... 
How Important is Putting the Ball in Play in Baseball?
(20180520)Baseball is a game in which the goal is to score more runs than your opponent. However, with the 2017 Major League Baseball season breaking home run and strikeout records, does putting the ball in play make a difference? ... 
Apportionment the 2016 Election
(20180517)The 2016 election between Hillary Clinton and Donald Trump was one of five cases where the winner of the popular vote was not the winner of the election. In this project, we examine the 2016 election to determine the ... 
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.