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  • The Double Exposure SI Model: A Senior Thesis 

    Stapf, Kerry (2017-05-31)
    The SI model of disease spread is a fairly simple and well-known 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 ...
  • Zero-Divisor Graphs of Direct Product Rings 

    Salzman, Emily (2017-05-31)
    This research investigates zero-divisor graphs of direct product rings. In zero-divisor 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 Dioxide-Iodine-Malonic Acid Reaction 

    Rutter, Elisabeth (2017-05-31)
    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 

    Northrup, Catherine (2017-05-31)
    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 Two-Dimensional Solutions to the Navier-Stokes Equations 

    Merritt, Mike (2017-05-31)
    The Navier-Stokes 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 

    Lato, Sabrina (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 

    Janke, Stephen (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 

    Hostetler, Bradyn (2017)
    By looking at the board game Rack-O, 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 Non-kth Elements of a Group 

    Grimes, Brett (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 

    Dobrowolski, April (2017)
    Though there are many proofs, this paper gives direct proofs of well-known formulas for sums of reciprocals of Fibonacci numbers.
  • Fundamental Groups of Simplicial Complexes 

    Wheeler, Erlan III (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 

    Valentine, Elizabeth (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 

    Weber, Benjamin (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 

    Shaw, Clarice (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 

    Schulter, Tod (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 

    Post, Rachel (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 

    Moen, Michael (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 Year-Round Schools and Traditional Schools 

    Jordan, Anthony (2015)
    This research study was designed to determine if there are academic benefits in attending a school with a year-round calendar compared to a traditional school calendar. This research analysis compared the standardized ...
  • Euler’s Smallest Squares 

    Harder, Malorie (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 

    Barhite, Justin (2016)
    In the game Tenzi, a player has ten six-sided 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 ...

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