Mathematics
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Mathematics Department Documents [1]
This collection includes documents from the Kalamazoo College Department of Mathematics. 
Mathematics Senior Integrated Projects [274]
This collection includes Senior Integrated Projects (SIP's) completed in the Mathematics Department. 
Mathematics Syllabi [0]
This collection contains syllabi from the Mathematics Department.
Recent Submissions

Usage of Python in Differential Equations
(Kalamazoo College, 20230101)This paper is a chronological record of the transition from the usage of wxMaxima, a downloadable computer algebra system used in previous iterations of the course to assist students with the computation of differential ... 
Recognizing Simple Groups by Their Codegree Sets
(Kalamazoo College, 20230101)An arithmetic property of a group G is a property that can be expressed solely in terms of numbers. The restrictions that certain arithmetic properties place on the structure of a group is a wellstudied and fruitful area ... 
Mathematics Education Foundations : Developing Math Materials for Students and a System for PeerEducators
(Kalamazoo College, 20230118)Learning mathematics is hard, and learning college mathematics is made even harder by textbooks which are primarily used as vessels for homework exercises. These two facts motivated my Senior Integrated Project (SIP) or ... 
Exploring Algebraic Themes in Calculus
(Kalamazoo College, 20230101)This paper outlines two different approaches to studying the algebra underlying the ideas of differentiation and integration typically presented in analysis. In the first section we approach the notion of derivative by ... 
Algorithmic Methods for Computing Monomial Invariants of Abelian Groups
(Kalamazoo College, 20220601)Given some arbitrary polynomial ring, an invariant polynomial is a polynomial that is unchanged by the action of a group G. We investigate the ring of invariant polynomials under the action of some abelian groups with the ... 
Topic Modeling and its Applications
(Kalamazoo College, 20211101)The amount of data online is growing rapidly, and while most people think about numbers when they hear data, there is a huge amount of textual data available that can prove to be useful. Analytics involving numbers has ... 
The Data of Community Safety
(Kalamazoo College, 20220301)One way communities can keep each other safe is through being informed. This writ ten report explains the background, process, and purpose behind the interactive web page, Data of Community Safety, found at https://rut ... 
A National Assessment of Racial Disparities in Prehospital Pain Management by Paramedics
(Kalamazoo College, 20220301)The United States has a pervasive history of racism ingrained into the fabrics of many American institutions, including healthcare. The goal of this project is to utilize statistical methods to examine nationwide racial ... 
Building a Sales Calculator
(Kalamazoo College, 20211101)The goal of this paper is to provide insight on what a Sales calculator built for a company that sells Consumer Processed Goods Ads does and what it looks like. This paper contains figures and equations that show what it ... 
Roots and Derivatives in the Complex Plane
(Kalamazoo College, 20211101)In this paper, we explore the relationships between roots and derivatives in the complex plane. Unfortunately, there exists no onesizefits all solution like Rolle’s Theorem which describes the relationship between solutions ... 
Modeling Vibrating String Wave Forms
(Kalamazoo College, 20220301)This project is aimed to construct a simplified, but justifiable model, for vibrating strings so that we are able to explore questions related to musical instruments. We begin with solutions to the 1dimensional wave ... 
Logistic Regression Analysis: Predicting Match Outcomes In Professional Tennis
(Kalamazoo College, 20211101)In this SIP project, A logistic regression model is created in Rstudio to predict the outcomes of professional tennis matches solely based on one player's performance. Statistics were collected about every grand slam tennis ... 
The Promise and Peril of Database Technology in American Public Healthcare
(Kalamazoo College, 20211201)Preventative medicine is an integral part of quality healthcare, and one way it can be supported is through federal funding. AllCare Health, a local branch of Medicaid located in Southern Oregon, has integrated a new program ... 
Professor Effects on Student Trajectories : a Statistical Data Analysis in R
(Kalamazoo College, 20210401)Parameters quantifying the quality of instruction can be difficult to come across. One commonly used measure comes from course evaluations, which are largely subjective reviews that pertain to personality in conjunction ... 
Coxeter Groups and the Bruhat Order
(Kalamazoo College, 20210101)In an introductory course on abstract algebra, one will learn about algebraic structures that are seen in many areas of mathematics. In particular, the study of groups include finitely generated groups, the dihedral group, ... 
Experiential Senior Individualized Project as a Global Markets Summer Analyst at Nomura Securities International
(Kalamazoo College, 20201101)Throughout the summer, I was able to learn about Nomura itself, beginning from its vast client base to its large amounts of assets under management. I was able to learn about the main businesses within Nomura from Asset ... 
Coding Theory Analysis : an Algebraic Analysis on Linear Block Codes with Application
(Kalamazoo College, 20210201)This paper has discussed the linear block codes from an algebraic approach. Linear block codes are created to solve the noisy channel problem in communication, and they are characterized by their specific errorcorrecting ... 
Poisson and Gamma Models for Predicting Bundesliga Results
(Kalamazoo College, 20201101)Soccer is unpredictable. Picking the winner of a soccer league has many variables that affect the final standings, from the performance and health of the individual players, to the environment and timing of games, to the ... 
On Mutually Unbiased Bases and Hadamard Matrices : An exploration from quantum mechanics to number theory
(Kalamazoo College, 20210503)The goal of this paper will be to study the behavior of mutually unbiased bases in complex dimensions by looking at equivalent objects that preserve the mutually unbiasedness property. Of the many equivalent objects, this ... 
The Importance of Data Visualizations for the Identification and Reduction of Racial Disparities in Michigan Counties’ Infant Mortality Rates
(Kalamazoo College, 20201101)Infant mortality rate is a measurement of the number of infant deaths in a community, and it is an important rate to record as it is used to assess the health of a community. In the state of Michigan for the year 2018, the ...