Browsing Mathematics Department by Title
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An Analysis of High Deductible and Low Deductible Insurance Plans
(20140918)In this study, we analyze two health insurance plans, a high deductible and low deductible plan. We determine which plan is more cost effective for both an individual and a fourperson family. This study considers various ... 
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, ... 
An Analysis of the Effects of Age on Professional Golfers
(20130913)We examine statistics from professional golf, and find which statistics influence scoring average and success on tour. We develop an efficient practice routine that tailors to the age and the most important components of ... 
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 ... 
Analyzing Soccer Strategies Using Network Theory
(2015)Soccer has never been a game of statistics. A team’s style of play has always been reserved for analysts and commentators to explain to the masses. In my research, network analysis and invariant calculation is used to ... 
An Application of Differential Equations to Political Partisanship
(20140918)The current political climate suggests an overarching decrease in political partisanship in the United States. In order to test this theory, we will consider a differential equations model suited for twogroup competition ... 
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 ... 
Battle of the Sexes: Is Professional Golf Two Separate Games?
(2015)The popularity of the Ladies Professional Golf Association (LPGA) has exploded, but the quality of golf played has not. Despite easier course setups, LPGA players fail to match the scores recorded by members of Professional ... 
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 ... 
Closed Form Solution for a Specific Case on the Friendship Paradox
(2015)It is a common feeling among people that their friends are more popular than they are. With social networking sites like Facebook, many people find validation that, indeed, many of their friends have more "friends" ... 
Decay Rates of Native and Invasive Tree Species Leaves in Aquatic and Terrestrial Sites
(20140918)In this study, we look at the decay rates of native and invasive tree species leaves in aquatic and terrestrial environments. We also determine if invasive tree species leaves influence the decay rates of native tree species ... 
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 ... 
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 ... 
Dynamical Systems and Circle Maps
(20140918)Dynamics is a branch of mathematics that studies how systems change with time, and this can be done using function iteration or di erential equations. Our focus is on the dynamics of the circle map function, fn(x) = nx ... 
The Effectiveness of Blended Learning
(20140918)District of Columbia Public Schools, a school district aiming to improve proficiency rates by 2017, is experimenting with a new teaching technique called blended learning. Proficiency rates from 20082012 of 3rd and ... 
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, ... 
Factoring 2x2 Matrices with Determinant of ±1
(20130906)We examine properties of multiplying and factoring 2×2 matrices to prove that there exist two generators to which all other 2×2 matrices factor. We prove that all matrices fitting out specifications must have a dominant ... 
Factoring 2x2 Matrices with Determinant of ±1 and Integer Elements
(20140918)We prove that all 2x2 matrices, as long as they meet our specifications, have a dominant column in absolute value and can be factored to a product involving three specific matrices. 
The Fibonacci Sequence Through a Different Lens
(2015)While Fibonacci numbers have been the subject of numerous works over hundreds of years, the sequence presents still more opportunities for discovery. This paper introduces a new way of perceiving this well established ...