# Independent Study

## Senior Independent Study

To meet the graduation requirements of The College of Wooster, the major in mathematics requires a two-course Independent Study Project, which culminates in an Independent Study Thesis along with an oral presentation describing the Thesis. The additional college requirement of one course in Independent Study is satisfied by work in courses above 212 taken to fulfill the major.

Independent Study is of central importance in the mathematics major and in the entire academic experience of the student. The ability to engage in independent study is one of the primary goals of the major, and the successful completion of the I.S. Thesis represents the culmination of the student's academic program.

Guide to Independent Study in Mathematics (.pdf)

## 2017 Senior Independent Study Titles

- Sophia Anderson
*A Mathematical Modeling Examination of the Changing Social, Economic, and Environmental Indicators for Infant Mortality Across the United States* - Aaron Brown
*An Exploration of the Surreal Number System* - Matthew Buranosky
*A Stroll Through Cantor's Paradise: Appraising the Semantics of Transfinite Numbers*(Math and Philosophy) - Dana Faust
*Math Rules Everything Around Me: An Examination of Fractals and Their Real World Applications* - Zhao Gao
*On Degree Bound for Syzgies of Polynomial Invariants* - Dana Foley
*Monotonic Untangling to Solve the Unknotting Problem*(Math and Computer Science) - Emily Howerton
*On Rationality and Morality: Three Kinds of Approaches*(Math and Philosophy) - Alex Iudice
*Clear Communication: Construction and Implementation of Error-Correcting Codes*(Math and Computer Science) - Nanako Ito
*Understanding Gödel's Incompleteness Proofs* - Nan Jiang
*Building a Course Recommender System for The College of Wooster (Math and Computer Science)* - Jacob Kail
*Smallball: A Statistical Analysis of the 2016 SEC Baseball Season* - Sanjana Kumbhani
*The Black-Scholes Option Pricing Model and a Test for Efficiency in the Underlying Stock Market*(Math and Business Economics) - Gina Lam
*Bidder's Behavior Model and Seller Revenue in eBay's But it Now Option* - Jonathan Ledesma Chavez
*Recession Analysis: Understanding Rather than Assuming* - Tori McCoy
*The Rubik's Cube: A Look into Group Theory* - Max Mindlin
*Consumer Decision in the Digital Audio Market Using Behavioral Game Theory* - Conor Maley
*Evolving Monkeys into Sharks: An**Analysis of Daily Fantasy Football Drafting Strategies*(Math and Computer Science) - Robin Morillo
*Reinforcement Learning in Card Games: No Thanks!* - Preston Pozderac
*Blinded by the Light: An Investigation of the Wave Propagation of Vector Modes of Light in a Spherically Symmetric Refractive Index Profile*(Math and Physics) - Ruben Aguero Quinteros
*Skilled Emigration, Return, and Human Capital Formation: A Game Theoretic Approach*(Math and Economics) - Tyson Vogel
*An Exploration of Hidden Markov Models with Applications to the Stock Market* - Haven Wagner
*Two-sided Eulerian Numbers* - Stuart Young
*The Search for GTO: Determining Optimal Poker Strategy Using Linear Programming* - Marjorie Zeager
*C*(Math and History)*alculating the Course: The Impact of Mathematical Research on the Undergraduate Mathematics Curriculum, 1930-1950* - Yunjia Zeng
*Modeling Double Major Data and Predicting Organic Chemistry Grade at The College of Wooster*(Math and Computer Science)

## 2016 Senior Independent Study Titles

- Thomas Ames
*Logicism and the Continuum Hypothesis*(Math and Philosophy) - Michael Bush
*A Comparative Analysis of Photon and Electron Wave Functions in Spherically Symmetric Potentials*(Math and Physics) - Adam Coppock
*Applying Modern Portfolio Theory to Optimal Portfolio Construction* - Kiera Dobbs
*Optimal Placement of Family Planning Centers* - Jeffrey Giegold
*Shooters vs. Goalies: Analyzing Shootouts in the NHL with Game Theory* - Melissa Griffith
*The Ineffability of "Nothing"*(Math and Philosophy) - Katelynn French
*Bees in the Trap: A Mathematical Approach to Modeling the Mutualism Between Flowering Plants and Honey Bees* - Rob Handloser
*Hall of Fame Classification Using Logistic Regression Analysis* - Lucas Hunt
*The Extra Point Rule Change and Its Effects on Decision Making in the NFL* - Sayantan Mitra
*Holding Hands Against the Unknown: Using Markov Chains to Model Informal Insurance Arrangements in Developing Societies*(Math and Economics) - Nakesha Newsome
*Dirichlet Tesselations* - Varunavi Newar
*Legalization of Prostitution and Its Impact on the Market for Human Trafficking*(Math and Business Economics) - Paroma Palchoudhuri
*An Experimental and Mathematical Study of Avalanche Behavior*(Math and Physics) - Michael Sokolich
*An Investigation of the Burning Numbers of Graphs and Trees*(Math and Computer Science) - Jacob Solomon
*To Blend or Not to Blend: Understanding the Impact of Technology in Mathematics Education*

## 2015 Senior Independent Study Titles

- Gregory Yerkes
*Vector Space Modeling: An Intuitive Apprach to Information Retrieval* - Philip Sizek
*Set Theory Building: Numbers from Nothing* - Marjorie Etheridge
*An Examination of the Golden Ratio in Nature and Music* - Stephen Skoch
*I Don't Play Chess: A Study of Chess Piece Generating Polynomial* - Sebastian Weber
*The Scope of Fractals: Geometry, Iteration, and Application* - Christine Hagan
*The Cost of a Child: A Bayesian Model of FertilityDecisions of Women in Academic* - Joshua Foerst
*Why Apply: Building a Predictive Model to Quantify the Factors that Lead a Domestic Student to Apply to The College of Wooster* - Joseph Smith
*Topological Defects in Nematic Liquid Crystals and the Behavior Induced by Adding Polystyrene Microspheres to 5CB*(Math and Physics) - Ian Vernier
*The Mental Game: An Analysis of Game Theory and Baseball* - Anqi Huang
*Matrix-Analytic Methods in Queueing Theory* - Colin Woodward
*The Use of Data and Statistical Analysis to Predict an Outcome* - Elliot Wainwright
*Avalanches on a Critical Conical Bead Pile: Exploration of Tuning Parameter Space and Mathematical Foundations*(Math and Physics) - Brian Maddock
*Modifying the Virasoro-Shapiro Amplitude to Correspond to the Glueball Trajectory*(Math and Physics) - Eli Barr
*Read at Your Own Risk: An Analysis of Risk the Board Game Using Graph Theory* - Meredith Schervish
*XH-π bonding in systems of indole and benzene using IBBCEAS and a bioinformatics analysis of protein secondary structure using graph theory*(Math and Chemistry) - Priyanka Datta
*Glory, Glory Fan United! A Study of the Relationship Between Fan Loyalty and Team Performance in English Premier League Football*(Math and Economics) - Daniel Miller
*Modeling Crime Using Social Interaction*(Math and Economics) - Lindy Howard
*To Flip or not to Flip? A Study of the Effectiveness of the Flipped Classroom Model for Teaching Mathematics* - Andrew Hoover
*Conquering Carcassonne*(Math and Computer Science) - Paula Trautvetter
*Stopping Segregation: Using a Mathematical Model to RaciallyBalance Schools in the 1970s* - Jai Kedia
*Beyond β: An Analysis of Alternative Risk Measures*(Math and Business Economics)

## 2014 Senior Independent Study Titles

- Zachary Sessa
*The Soviet War in Afghanistan and the Application of U.S. Special Forces: A Combat Analysis*(Math and Russian Studies) - Rebecca Wardop
*A Bayesian Model of Fertility Decisions in Relationship to Female Labor Force Participation* - Josephine Rey
*Analysis of Factors that Influence the Probability of a Goal in the >National Hockey League* - Xiameng Ye
*Evolving Lambda-Calculus Functions Using Genetic Programming*(Math and Computer Science) - Danielle Shepherd
*Go With the Flow: Developing Computational Fluid Dynamics Simulations According to the Navier-Stokes Equations*(Math and Physics) - Steve Hagen
*The Black-Scholes Options Pricing Model and its Implications on the Underlying Security Market*(Math and Business Economics) - Jarrod Mancine
*Applying Markov Chains to Baseball* - Julia Land
*Mistletoe Marketing: An Analysis of How Christmas Stimuli Affect Consumer Behavior* - Mary Sefcik
*Clarifying Chaos: A Look into Chaotic Dynamical Systems* - Prakrit Shrestha
*Universe from Scratch: Exploring Quantum Gravity in 2+1 Dimensions Using the Causal Dynamical Triangulation Method*(Math and Physics) - Cal Thomay
*Markov Chain Theory with Applications to Baseball* - Giang Nguyen
*The Analytic Hierarchy Process: A Mathematical Model for Decision Making Problems* - Kazuki Kyotani
*Twitter Can Predict Stocks*(Math and Computer Science) - Kelly Simmons
*Problem-based Learning in Early Childhood Education* - Sheharyar Khushnood
*Airline Fleet Assignments* - Mike Ries
*Ranking Systems and Their Applications to Sports* - Jacob Malone
*Modeling for our Lives: A Theoretical Study of HIV/AIDS Epidemiology Through Mathematical Modeling* - Trevor Pozderac
*Don't Get Boxed In: Connecting the Dots of Game Theory Through Computer Simulations*(Math and Computer Science) - Sarah Laper
*Creation of a Mathematical Model and Investigation of the Kinetics of the Reaction Between the Oxalic Acid Species and the Hydroxyl Radical*(Math and Chemistry) - Tyler Poppenwimer
*Generalist and Specialist Pollination Syndromes: A Theoretical Approach to Predict the Conditions Under Which a Generalist or Specialist Pollination Syndrome is Favoured*(Math and Biology) - Ryan Snyder
*Keeping Your Options Open: An Introduction to Pricing Options*

## 2013 Senior Independent Study Titles

- Theresa Albon

The Entanglement and Relaxation of Liquid Crystal Shaped Granula Media (Math and Physics) - John Angelo

Predictive Analytics on First Year Retentioin at The College of Wooster - Andrew Blaikie

// (Math and Physics) - Kyla Davis

The Torus and Graph Theory - Erin Davison

Quaternions and Octonians - Anna Easterday

Only for Honest Men: A Survey of Voting Theory - David Freund

The Machete Number - Spencer Hall

Optimizing Integer Arithmetic for Public Key Cryptography (Math and Computer Science) - Matt Lambert

An Agent-based Model of Influenza within a College Population (Math and Computer Science) - Rutendo Ruzvidzo

The Gift that Keeps on Taking: Modelling the Impact of a Natural Resource Shock on an Economy (Math and Economics) - Matt Schmitthenner

A Theoretical and Experimental Pattern Analysis of Electrohydrodynamics in a Liquid Crystal System (Math and Physics) - Sarah Smith-Polderman

Let's Get in the Mood: An exploration and Implementation of Data Mining Techniques to Predict Mood Based on Musical Properties of a Song - Ruth Steinhour

The Truth about Lie Symmetries - Ashley Stopka

A Study of Modern Geometries and Felix Klein's Erlanger Program (Math and Chinese) - Samuel Swartz

My Ticket to Becoming an Athletic Director: An Analysis of Graph Theory Behind Sports Scheduling - Philip Wales

ξ. (Math and Physics) - Allie Webb

Extensions of the Farey Sequence and Ford Circles - Joseph Wilch

Insights into the tectonic evolution of the northern Snake Range metamorphic core complex from 40 AR/39ar chronologic results, northern Snake Range, Nevada (Math and Geology) - Emily Williams

The Golden Ratio - Kendal Wong

Exercise Intention and Motivation: Intrapersonal Relationships, Feedback, and Personality (Math and Psychology)

## 2012 Senior Independent Study Titles

- Mohammad Saif Ahmad

Parity-based Measurement and Control of the Spatial Wave Function of Photons (Math and Physics) - Keisha Butler

The Prediction of Professional Basketball Games Using Artificial Neural Networks and Linear Models - Kyle Cunningham-Rhoads

Using mathematical models to evaluate NFL field goal kicking - Joshua Daily

Multivariate Statistics - Hannah Dauber

Wooster Problem: a staff scheduling problem with an application to student activities - Rachel Frank

An Exploration of Hyperbolic Geometry (Math and Studio Art) - Trisha Fultz

Exploring opinion dynamics from a computational science perspective (Math and Computer Science) - Yanlong Hu

Data mining and its applications (Math and Computer Science) - Norman Israel

Quantum Gravity: Exploring the Causal Dynamical Triangulation Approach (Math and Physics) - Meredith Kiefer

Modeling human papillomavirus with vaccination - Andrew Licking

Is Efficiency Optional? A study regarding the binomial options pricing model, transactions costs, and the implications of options on market efficiency - Daniel Pierce

Elements of understanding: mathematics, literature, and Nicolas Bourbaki (Math and French) - Evan Radkoff

Topical Web Crawlers (Math and Computer Science) - Kemal Ramic

Monte Carlo Simulations of the Clumpy Torus in Active Galactic Nucle (Math and Physics) - Kemar Reid

Entrapment and Determination of the Activity of Lipase Embedded in Swellable Organosilica: Modeling Particle Aggregation and Aging of Colloidal Sol-gels (Math and Biochemistry - Molecular Biology) - Hannah Roberts

Iteration Digraphs - Ian Sharp

Enigmatic magic: an analysis of the role of codes and ciphers within American intelligence (Math and History) - Joshua Stidham

Two-person Zero-sum Game Theory: Batter vs. Pitcher - Blake Sword

Model looking at the expected number of shots to hole out on a golf course - Nancy TInoza

Making Money, Making Sense: An analysis of the Modern Portfolio Theory and the Performance of alternative risk measures (Math and Economics) - Adam Trontz

Similarly Intriguing and Perspectively Odd: Fractal and Projective Geometry Explored in M.C. Escher's Art - Andrew Valerian

Traffic flow theory - Melissa Venecek

A Theoretical and Experimental Investigation of the Dimerization of Oxalic Acid, a Potential Reaction within Secondary Organic Aerosols (Math and Chemistry)

## 2011 Senior Independent Study Titles

- Kevin Nicholson

Bertolt Brecht and David Hilbert: A Connection through Formalism (Math and German) - Noah Hartley-Shepherd

Fish On: A Study of Nonlinear Elasticity and Tensors - Kaleb Reed

Going Inside the Rubik's Cube - Xiaoru Bao

The Derivation of the Black-Scholes Model and Its Application to Hedging - Anne Somers

Paradox - Pamela Wales

Exploring the Effects of Initial Conditions on the Kinetics of the Decomposition of Dichloroacetic Acid through a Hydrogen Peroxide and Ultraviolet Radiation Oxidation Process (Math and Chemistry) - Itai Njanji

Exploring the Branch-and-Cut Algorithm (Math and Computer Science) - Logan Garrity

Infinity (Math and English) - Sean Twining

Printed Circuit Board Layout Optimization - Wenyuan Wu

Bayesian Statistics: An Alternative Method to Insurance Pricing Practice (Math and Economics) - Jacob Haning

The Interpretation of Homology Groups - Prachi Saraogi

Impact of Financial Access on the Efficiency of a Portfolio: A Geometric Dissection of Portfolio Theory and Empirical Analysis of the Financial Diaries of Low-Income Households in South Africa (Math and Economics) - Hannah Kurtz

An Introduction to Game Theory and its Application to Biology - Jason Van Houten

An Evolutionary Study of Multimeric Phosphagen Kinases Using Ancestral Protein Reconstruction and the Prediction of Phosphagen Kinase Substrate Specificity Using Artificial Neural Networks (Math and Biochemistry/Molecular Biology) - Dustin Eisele

What Factors Affect Jurors' Decisions: A Mathematical Modeling Approach to a Common Psychological Question (Math and Psychology) - Joshua Thomas

Go with the Lava Flow (Math and Computer Science) - Bridget Kraynik

Boom! How the Human Population Explosion Affects Our Future - Louisa Catalano

Tighten Up: A Preliminary Study of Knots (Math and Physics) - Robert Taylor

Selection Pressure on a Selfish Herd: Evolution of Ecological Relationships in an Agent-based Model (Math and Computer Science) - Derek Wyman

The Impact of Calculators on Students' Test Scores

## 2010 Senior Independent Study Titles

- Elizabeth Ottie Agyeman

Let's See Who Takes Home the Cup this Year, 2010: Mathematical Sports Ranking - Marc Christian

Differential Gene Expression of H. Bacteriophora TTO1 in Response to Heat Stress (Math and BMB) - Eric Enoch

Analysis of Automotive Valve Train Springs - Jeff Lyman

NO MORE RED LIGHTS! A Cellular Automaton Solution for City Traffic - Kristine Mann

A Case Study Investigating Practices in Middle School Mathematics - John Mullett

Analyzing Insurgency Situations with an Emphasis on the Effect of Intelligence: An Adaptation of the Lanchester Model - AungMaw MyoLwin

Economic Benefits of Foot-Voting: Game Theoretic Approach (Math and Economics) - Mary Rhollans

An Introduction to Disease Modeling, with a Focus on Malaria - Priscilla Staples

Optimal Batting Order for The College of Wooster Fighting Scots Softball Team for the 2008 Season - Jared Steed

Investigation of the Kinetics of Aqueous Dicarboxylic Acids Under Tropospheric Light Conditions and the Application of Systems of Ordinary Differential Equations to Model Chemical Kinetics (Math and Chemistry) - Yang Tian

The Impact of Tariffs on Foreign Direct Investment (Math and Economics)

## 2009 Senior Independent Study Titles

- Robert Ashmead

Topics in Multivariate Statistical Theory - Jessi Baughman

Hydrogen Bonding Complexes of Cytosine and Uracil: A Spectroscopic Investigation (Math and Chemistry) - Corbin Boisvert

Riemann Zeta Function - Allyson Buytendyk

Kinetic and Thermodynamic Analysis of Calcium Binding to Phospholipid Analogs (Math and Chemistry) - Gregory Garris

MILE 1: Exploring the Connection Between Learning Styles and Preference for Mathematical Representations - Evan Heidtmann

A Differential Equations Model of Insulin Spherulite Growth and a Surprising Connection to Algebraic Topology (Math and Physics) - Sam Hickey

An Investigation of Mathematical Models Used to Optimize Bus Timetables in Urban Transit Systems - Lorna Johnston

DNA Geometry and its Biological Significance (Math and BMB) - Frank King

/. (Math and Physics) - Rachel Lipner

Investigation of Dioxybenzone-Alcohol Complexes through Spectral Deconvolution and an Analysis of Symmetric Groups and Character Tables (Math and Chemistry) - Sheldon Masters

Waste Load Allocation for Regional Wastewater Treatment Planning in the Willamette River Using Linear Programming - Natalie Offen

Classification of Surfaces - Ellen Wagner

Secret, Secrets are so Fun, If They're not for Everyone! (Math and Computer Science) - Jeffrey Willert

A Study of the Calculus of Variations