Mathematics Commons^™

Hurdle Models And Age Effects In The Major League Baseball Draft, Justin Sims

Mathematics, Statistics, and Computer Science Honors Projects

Major League Baseball (MLB) franchises expend an abundance of resources on scouting in preparation for the June Amateur Draft. In addition to the classic "tools" assessed, another factor considered is age: younger players may get selected over older players of equal ability because of anticipated development, whereas college players may get selected over high school players due to a shortened latency before reaching the majors. Additionally, Little League rules in effect until 2006 operated on an August 1-July 31 year, meaning that, in their youth, players born on August 1 were the eldest relative to their cohort. We examine the …

Parallel Design Patterns And Program Performance, Yu Zhao

Mathematics, Statistics, and Computer Science Honors Projects

With the rapid advancement of parallel and distributed computing (PDC), three types of hardware and their corresponding software (hardware-software pairs) are becoming more and more popular: Distributed Memory Systems with the Message Passing Interface (MPI) library, Shared Memory Systems with the OpenMP library and Co-processor Systems with a general purpose parallel computing library. Alongside the development of both hardware and software aspects of PDC, the process of designing parallel programs has also improved significantly over the years. A consequence of this is that researchers have been able to describe many parallel design patterns, which are recurring solutions to well-known problems …

The Effects Of The Melting Arctic Ice Cap On Florida's Coast, Anthony Atkinson, Nicholas Joseph, Louw Scheepers

CLAS: Colby Liberal Arts Symposium

We've set out to determine the effect of arctic ice melt on the coastline of Florida, more specifically its major cities and tourist attractions. To do this, we created multiple mathematical models on different bases to ensure that our models are behaving in an appropriate manner. We constructed one statistical model based on past sea level rise data, and one theoretical model based on our interpretations of different components that add to the total sea level rise. Our data and analysis showed firm indications of extreme effects on the coastline of Florida and some of its major tourist attractions by …

Modeling The Optimization Of A Toll Booth Plaza, Liam Connell, Zachary Schutzman, Erin Hoover

CLAS: Colby Liberal Arts Symposium

When designing a toll plaza, many factors have to be considered, especially the number of toll booths to build. In this paper, we try to determine the optimal number of toll booths by creating a model for car movement at a toll plaza. We define optimal as the number of toll booths that minimizes the waiting time, particularly at a high congestion time (i.e. rush hour). To model the movement of cars through a toll booth plaza, we break the problem into two parts: time spent waiting in line and then time spent merging back into traffic. Because each of …

Mathematical Analysis Of A Nim-Like Matrix Game, Edward Chuang, Stephen Morse

CLAS: Colby Liberal Arts Symposium

This poster presentation covers our research on a mathematical game that is somewhat similar to the popular game Nim. In this game, Players play a variation of Nim where the number of piles must be a perfect square and where the piles are actually situated within a matrix. In addition, players are only allowed to subtract one from an entry on their turn, where as in Nim there are typically more options. The game is over either when a player does not have a move to make (because all entries have been reduced to zero) or the when the game …

The Highway Game: Optimizing The Number Of Tollbooths, Meaghan Lewia, Tara Chizinski, Megan Lasher

CLAS: Colby Liberal Arts Symposium

One of the biggest woes of highway drivers is the amount of tolls along the road that require each vehicle to not only slow down significantly, but also pay sometimes up to -8 to the State. This inconvenience is protested on various levels, but since its clear that the government must institute some type of toll system, we have decided to find a model that will at least optimize the time for each driver while still saving the State as much money as possible. Our report constructs a model of the ideal amount of tollbooths for any number of highway …

Oscillation Theorems For Fourth-Order Half-Linear Delay Dynamic Equations With Damping, Ravi P. Agarwal, Martin Bohner, Tongxing Li, Chenghui Zhang

Mathematics and Statistics Faculty Research & Creative Works

This article is concerned with oscillatory behavior of a class of fourth-order half-linear delay dynamic equations with damping on a time scale. Some new oscillation criteria are established. © 2013 Springer Basel.

Axioms Of Set Theory And Equivalents Of Axiom Of Choice, Farighon Abdul Rahim

Mathematics Undergraduate Theses

Sets are all around us. A bag of potato chips, for instance, is a set containing certain number of individual chip's that are its elements. University is another example of a set with students as its elements. By elements, we mean members. But sets should not be confused as to what they really are. A daughter of a blacksmith is an element of a set that contains her mother, father, and her siblings. Then this set is an element of a set that contains all the other families that live in the nearby town. So a set itself can be …

Kernel Based Quadrature On Spheres And Other Homogeneous Spaces, E. Fuselier, T. Hangelbroek, F. J. Narcowich, J. D. Ward, G. B. Wright

Mathematics Faculty Publications and Presentations

Quadrature formulas for spheres, the rotation group, and other compact, homogeneous manifolds are important in a number of applications and have been the subject of recent research. The main purpose of this paper is to study coordinate independent quadrature (or cubature) formulas associated with certain classes of positive definite and conditionally positive definite kernels that are invariant under the group action of the homogeneous manifold. In particular, we show that these formulas are accurate—optimally so in many cases—and stable under an increasing number of nodes and in the presence of noise, provided the set X of quadrature nodes is quasi-uniform. …

A Numerical Model For Nonadiabatic Transitions In Molecules, Devanshu Agrawal

Undergraduate Honors Theses

In molecules, electronic state transitions can occur via quantum coupling of the states. If the coupling is due to the kinetic energy of the molecular nuclei, then electronic transitions are best represented in the adiabatic frame. If the coupling is instead facilitated through the potential energy of the nuclei, then electronic transitions are better represented in the diabatic frame. In our study, we modeled these latter transitions, called ``nonadiabatic transitions.'' For one nuclear degree of freedom, we modeled the de-excitation of a diatomic molecule. For two nuclear degrees of freedom, we modeled the de-excitation of an ethane-like molecule undergoing cis-trans …

Stochastic Modeling Of Energy Commodity Spot Price Processes With Delay In Volatility, Olusegun Michael Otunuga, Gangaram S. Ladde

Mathematics Faculty Research

Employing basic economic principles, we systematically develop both deterministic and stochastic dynamic models for the log-spot price process of energy commodity. Furthermore, treating a diffusion coefficient parameter in the non-seasonal log-spot price dynamic system as a stochastic volatility functional of log-spot price, an interconnected system of stochastic model for log-spot price, expected log-spot price and hereditary volatility process is developed. By outlining the risk-neutral dynamics and pricing, sufficient conditions are given to guarantee that the risk-neutral dynamic model is equivalent to the developed model. Furthermore, it is shown that the expectation of the square of volatility under the risk-neutral measure …

Algebraic Properties Of Generalized Rijndael-Like Ciphers, L. Babinkostova, Kevin W. Bombardier, Matthew M. Cole, Thomas A. Morrell, Cory B. Scott

Mathematics Faculty Publications and Presentations

We provide conditions under which the set of Rijndael-like functions considered as permutations of the state space and based on operations of the finite field GF(p^k) (p ≥ 2) is not closed under functional composition. These conditions justify using a sequential multiple encryption to strengthen generalized Rijnadael like ciphers. In R. Sparr and R. Wernsdorf provided conditions under which the group generated by the Rijndael-like round functions based on operations of the finite field GF(2^k) is equal to the alternating group on the state space. In [39], this paper we provide conditions under which …

An Introductory Look At Deterministic Chaos, Kenneth Coiteux

Mathematics Undergraduate Theses

This is a brief introduction to deterministic chaos. We will be studying the logistic map and the 'double-humped' logistic map.

The Behavior Of Midsets When Repeatedly Taking The Midset Of Two Lines In L1 Geometry, Joshua M. Fitzhugh, David L. Farnsworth

Articles

We study the outcome of taking midsets of two lines in ℓ1 geometry.We establish the algorithm for repeatedly finding these midsets and characterize the limiting midsets.We discuss the issue of angle measurement in Minkowski geometries, especially with respect to the limiting midsets.

Family-Wise Error Rate Control In Quantitative Trait Loci (Qtl) Mapping And Gene Ontology Graphs With Remarks On Family Selection, Garrett Saunders

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

One of the great aims of statistics, the science of collecting, analyzing, and interpreting data, is to protect against the probability of falsely rejecting an accepted claim, or hypothesis, given observed data stemming from some experiment. This is generally known as protecting against a Type I Error, or controlling the Type I Error rate. The extension of this protection against Type I Errors to the situation where thousands upon thousands of hypotheses are examined simultaneously is known as multiple hypothesis testing. This dissertation presents an improvement to an existing multiple hypothesis testing approach, the Focus Level method, specific to gene …

The Study Of Middle School Mathematics And Science Teachers' Practices, Perceptions, And Attitudes Related To Mathematics And Science Integration, Eliza Leszczynski

Theses, Dissertations and Culminating Projects

The purpose of this qualitative study was to investigate the nature of mathematics and science connections made by sixth and seventh grade mathematics and science teachers in their classrooms. This study also examined the extent to which these connections represented mathematics and science integration and described the teachers’ perceptions of and attitudes about mathematics and science integration. The primary data sources included classroom observations and teacher interviews.

Findings suggested that teacher practices in making mathematics and science connections in the classroom incorporated many of the characteristics of integrated instruction presented in the literature. Teacher attitudes toward integration were found to …

Tracking In Middle School Mathematics, Alexis Geisler

Mathematics Graduate Theses

This paper is a review of research pertaining to the issue of tracking in middle and high school mathematics. More focus is given to middle school because this is usually where tracking begins in mathematics. It supports research on the rationale behind detracking our schools and moving towards heterogeneous classrooms. Research behind the psychological effects of tracking is also provided, along with how tracking can segregate our school systems. There is a variety of research on the effect of tracking in mathematics. One of the most prevalent issues is how tracking is detrimental to the low tracked students. It not …

High Cognitive Test Item Development And Implementation, Ashley Salisbury

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

In secondary math classrooms there has been a movement toward discovery and problem solving based instruction. This type of instruction requires teachers to teach on what is often considered a higher level of cognition and allows students to discover more ideas and concepts on their own as opposed to traditional lecture style. Teachers with well thought-out examples, questions, and activities provide students with tools to solve problems on their own requiring students to make mathematical discoveries and connections. These skills not only benefit students in their math class but are analytical skills students can use throughout their lives.

With this …

A Three-Part Study In The Connections Between Music And Mathematics, Molly Elizabeth Anderson

Undergraduate Honors Thesis Collection

The idea for this thesis originated from my fascination with the studies of both music and mathematics throughout my entire life. As a triple major in Middle/Secondary Math Education, Mathematics, and Music, I have learned more than I thought possible of music and math. In proposing this thesis, I desired to use my knowledge of arithmetic and aesthetics to research how music and mathematics are intertwined. I am confident that the following three chapters have allowed me to develop as an academic in both music and mathematics. This thesis serves as a presentation of the connections of music and math …

Calculator Usage In Secondary Level Classrooms: The Ongoing Debate, Nicole Plummer

Honors College Theses

With technology becoming more prevalent every day, it is imperative that students gain enough experience with different technological tools in order to be successful in the “real-world”. This thesis will discuss the debate and overall support for an increased usage of calculators as tools in the secondary level classroom. When the idea of calculators in the classroom first came to life, many educators were very apprehensive and quite hesitant of this change. Unfortunately, more than 40 years later, there is still hesitation for their usage; and rightfully so. While there are plenty of advantages of calculator use in the classroom, …