Mathematics Senior Individualized Projects
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This collection includes Senior Individualized Projects (SIP's) completed in the Mathematics Department. Abstracts are generally available to the public, but PDF files are available only to current Kalamazoo College students, faculty, and staff. If you are not a current K College student, faculty, or staff member, email us at dspace@kzoo.edu to request access to this material.
All materials in the Kalamazoo College Digital Archive are subject to Title 17 of the U.S. Code. All rights reserved. Unless otherwise stated, authors retain the copyright for all content posted to the Kalamazoo College Digital Archive.
Recent Submissions

Fast Fourier Transformation in Noise Reduction in Audio Recording
(Kalamazoo College, 2019)Ambient noise is always unwanted during the professional recording whether is speech or instrument. Signalprocessing by Fourier Transformation can play a vital role in greatly reducing the ambient noise in the recording ... 
A GroupTheoretical Approach to Voice Leading in Tonal Music
(Kalamazoo College, 2015)In this paper, we will attempt to explore the underlying mathematical structures in tonal music through grouptheoretical models. Drawing from existing neoRiemannian literature and its mathematical/musical structures, ... 
Tonnetz and Beyond : In Search of Functional Representations of Harmonic Structures through Algebra and Geometry
(Kalamazoo College, 2015)In this paper, we wish to explore underlying mathematical structures of tonal music with the use of group theoretic and geometric models. We will begin by examining trends in the current literature on the subject in attempts ... 
Exploring the Effects of Socioeconomic Status on Student Learning : A Series of FirstHand Experiences
(Kalamazoo College, 2014)The following essays are based on my firsthand experiences interactingas a teacher, mentor, tutor, and friend with children and young adults. Before I started writing these essays, I knew I wanted to write about my ... 
Senior Individual Project : Harmonic Analysis
(Kalamazoo College, 2018)The purpose of this research paper is to analyze the harmony in musical works and to find the harmonic similarity between each Bach’s Suites. Usually, harmonic analysis is done by hand, but in this research, we want to use ... 
Construction of Convex Ideal Polyhedra in Hyperbolic 3Space
(Kalamazoo College, 2019)The purpose of this project is to provide a method to construct a convex ideal polyhedron in hyperbolic 3space given a set of internal dihedral angles that belong to a unique convex ideal polyhedron up to isometry. Thorough ... 
Exploration of the Laplace Transform
(Kalamazoo College, 2019)The author designed a Physics lab using the Laplace Transformation to be used in Dr. Tom Askew’s Physics 370 class. The Laplace Transform gives us another option when it comes to solving differential equations. In short, ... 
Extensions of the Mean Value Theorem on the Real Line and the Complex Plane
(Kalamazoo College, 2018)The goal of this SIP is to first analyze just a few of the many extensions to the Mean Value Theorem that have been proven in recent decades. This analysis follows a common structure that starts with stating each theorem ... 
Developing Software for Audio to Music Score Conversion
(Kalamazoo College, 2018)The idea of converting audio to music score provides a fascinating perspective of perceiving the music. As the amateur or folk musicians, they may want a more productive music application that can help them create music ... 
Generalized Linear Mixed Models for Putting Performance on the PGA Tour
(Kalamazoo College, 2015)In golf, putting is considered to be the single most important aspect of the game. With approximately 40 percent of total strokes having been putts in 2013 on the PGA TOUR, it is obvious that putting performance is a ... 
The Relationship Between Diversity and Firm Performance : A Statistical Analysis
(Kalamazoo College, 2017)The American workforce is becoming more diverse than ever, with the expanding representation of minority groups, including women, people of color, millennials, etc. Not only are these groups entering the workforce at such ... 
Patterns and Statistics on Set Partitions and Restricted Growth Functions
(Kalamazoo College, 2015)We consider partitions π of the set [n] = {1; 2,….., n}and denote the set of these parti tions by _n. We use the notation _ = B1=B2/ : : : =Bk ` [n] to indicate that [n] = ωiBi and call the Bi blocks. If S _ [n] and _ ` ... 
Generalizations of Triangle Relations to Spherical and Hyperbolic Geometry
(Kalamazoo College, 2018)We generalize relations known in Euclidean geometry to spherical and hyperbolic geometry. First we prove a theorem which produces analogues for certain Euclidean inequalities involving a triangle's circumradius, inradius, ... 
Data Science : The Data Tidying Process with R
(Kalamazoo College, 2018)An enormous amount of data is generated every day. All of this data can be analyzed using concepts from data science. Data science is the science of extracting information from a data set to gain knowledge (Nongxa, 2017). ... 
On a Generalization of the BestvinaBrady Construction
(Kalamazoo College, 2017)This work builds on work in [1] and [2] to study the homotopy fibre of a map between polyhedral products. The construction itself generalizes the definition of BestvinaBrady group. Here we compute the cellular chain complex ... 
Symbolic Computation with Maxima
(Kalamazoo College, 2017)The author describes a project created in Maxima, successfully fixing the bug that first inspired this project. The result product residue m() also has some new features that enable it to handle much more complicated ... 
An Introduction to the Statistical Bootstrap : Examining Confidence Intervals Using Flight Delay Data
(Kalamazoo College, 2017)Bootstrapping is an important resampling method with the ability to provide statistical inference with fewer assumptions then most other statistical inference methods. Bootstrapping can be more accurate than classical ... 
Bases for Integer Generalized Splines on Graphs, an Investigation
(Kalamazoo College, 2017)Let R be a ring and G a graph whose edges are labeled by ideals of R. A vertex labeling of G by elements of the ring is called a generalized spline if for each edge, the difference of the labels of the two connected vertices ... 
A Summer of Quality Control at Bell's Brewery
(Kalamazoo College, 2017)The author spent the summer of 2016 as an intern at Bell's Brewery in Comstock. Michigan, working within their quality control lab as the statistical quality control intern. Working under quality lab lead Lauren Torres and ... 
Impact of Averaging Period on a MediumScale Wind Turbine Power Curve and Prediction of Annual Energy Production
(Kalamazoo College, 2016)A reliable method for the prediction of Annual Energy Production is necessary for the United States to achieve its goal of 20% wind energy by 2030. Along with the pressure to reduce error in energy yield prediction is the ...