Mathematics Senior Theses 20122013
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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 ... 
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. 
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 ... 
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. 
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 ... 
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, ... 
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.