Mathematics
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Mathematics Department Documents [1]
This collection includes documents from the Kalamazoo College Department of Mathematics. 
Mathematics Senior Individualized Projects [242]
This collection includes Senior Individualized Projects (SIP's) completed in the Mathematics Department. 
Mathematics Syllabi [0]
This collection contains syllabi from the Mathematics Department.
Recent Submissions

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 ... 
A Quantitative Modeling of Rushing Ability in the NFL
(Kalamazoo College, 2016)In professional football, rushing has often been considered one of the most important aspects related to moving the ball on offense. In the past, the ability of rushing players has been measured strictly by the number of ... 
Fringe Pairs in Generalized MSTD Sets
(Kalamazoo College, 2016)A More Sums Than Differences (MSTD) set is a set A for which A+Aj > jA  A. Martin and O'Bryant proved that the proportion of MSTD sets in {0, 1,…, n} is bounded below by a positive number as n goes to infinity. We ... 
The Student Affairs Perspective : Looking at Underrepresented Students in STEM Through a Different Lens
(Kalamazoo College, 2016)The education gap in STEM is a growing national concern in the United States. With the growing emphasis on STEM skills in the workplace, it is more important than ever that we figure out how to support diverse students in ... 
A New Shape to the RUG : Further Exploration of the Region Unknotting Game
(Kalamazoo College, 2016)A region crossing change is an unknotting operation on a knot diagram. In the past, knot games have been used to demonstrate and discover properties of families of knots. We will find winning strategies of knot games to ... 
The Mapper Algorithm for the Qualitative Analysis of Drug Molecules
(Kalamazoo College, 2015)The world of computational drug design has seen tremendous progress in the last 40 years. Most of these methods rely on quantitative techniques through quantitative structure activity relationships. This approach works ... 
Creation and Evaluation of Probability Models for March Madness
(Kalamazoo College, 2016)For years, the NCAA Tournament has fascinated fans due to its unexpected outcomes. For this reason, an accurate prediction of the tournament bracket is considered to be a very respectable accomplishment. As a result, ... 
Geographic Variation in Healthcare Costs : A Statistical Analysis and Review
(Kalamazoo College, 2014)Geographic variation in the costs of healthcare exists at both the national and regional levels. Studies have shown that the differences in healthcare spending and costs across the United States do not result in better ...