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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.