Browsing Mathematics Department by Issue Date
Now showing items 120 of 45

Rolling Cups and Geometry
(20130905)We analyze the circular trajectory of a cup placed on its side and rolled. Using measurable components of the cup such as the radii and height we find the equation of the circle traced by the cup. 
Probability Distributions of Swishes in the Game of Swish
(20130905)We examine the game of Swish, where we look at the probability of certain events occurring on the first deal of n cards. We are interested in two specific cases, namely a swishless case, where no two cards form a swish, ... 
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 ... 
Making Connections: Is There Always a Winner?
(20130911)We analyze the board game Connections™ and prove that there is always a winner. We examine the scenario in which every space on the board is covered and one specific player has not yet won. Through a series of logical ... 
Using Markov Chains to Analyze a Volleyball Rally
(20130911)We examine a volleyball rally between two volleyball teams. Using the archived statistics of Carthage matches, we calculate the transition probabilities of the match. Results indicate the validity of our model. 
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 ... 
A Typed Lambda Calculus for Input Sanitation
(20131024)Programmers often wish to validate or sanitize user input. One common approach to this problem is the use of regular expressions. Unvalidated or insufficiently sanitized user input can cause security problems. Therefore, ... 
Surviving the End of the World: A Mathematical Model of the Zombie Apocalypse
(20131024)We develop differential equations models for a zombie invasion based on a variety of assumptions about zombies and humans. 
Symbolic Dynamics over Free Groups
(20131024)Symbolic dynamics is used to model functions acting on complex topological spaces. This work explores the symbolic dynamics over a nonAbelian group, the free group on two generators. We begin by introducing the fundamentals ... 
The Ultimate Lineup
(20131024)We explore the optimization of a youth baseball teams batting order, considering each players individual statistics. Specifically, we wanted to see if an alternating batting order of walkers and hitters (e.g. Highest Walk ... 
Using Markov Chains to Analyze Volleyball Matches
(20140918)In this study we examine how to model a volleyball match with the use of Markov chains and a computer program. We then use this model to examine the importance of different aspects of the game. 
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 ... 
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 ... 
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 ... 
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 ... 
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. 
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 ... 
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 ... 
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 ... 
Finding Harmonic Nine Crossing Knots
(2015)A knot is an embedding of the unit circle into real threespace. Harmonic knots are de fined as trigonometric polynomial parameterizations ofthe unit circle. In this paper we construct harmonic nine crossing knots. To ...