annual report 2016-2017 wooster math & computer science · pdf fileannual report 2016-2017...

ANNUAL REPORT 2016-2017

Wooster Math & Computer Science

Professor Byrnes talks to Math/CS major Nan Jiang about his project at the Senior I.S. Symposium.

Zach Phillips-Gary encouraged audience participation in virtual reality at his digital I.S. presentation.

Day!


An Exploration of the Surreal Number System Aaron Brown, Math Major -advised by Matt Moynihan

The surreal numbers are an enormous and extensive class of numbers. The surreals contain familiar numbers such as integers and real numbers, along with less familiar numbers such as ordinals and strictly surreal numbers. Importantly, all surreal numbers can be represented as a specific combinatorial game known as Hackenbush. In this paper, we will explore the relationship between Hackenbush and the surreal number system, which will be useful for constructing the surreal numbers. Additionally, we will explore algebraic properties of the surreal numbers (e.g. transitivity, reflexivity, etc.) and surreal operations such as addition and multiplication.

Math Rules Everything Around Me: An Examination of Fractals and their Real World Applications Dana Faust, Math Major -advised by Pam Pierce

A fractal is a mathematical pattern that has several distinct features. Firstly, it must exhibit self-similarity within itself. Secondly, it must have a unique, non-integer dimension. These features of fractals are discussed for both regular and irregular fractals. Three regular fractals are examined: the Cantor set, the Koch curve, and the Sierpinski Triangle. Irregular fractals are discussed in the context of practical applications in the fields of geology and art. Relevant proofs and

equations for understanding these concepts are also included in their corresponding discussions.

Senior Independent Study


Two-Sided Eulerian Numbers Haven Wagner, Math Major -advised by Matt Moynihan

The Eulerian numbers count the number of permutations in the symmetric groups with a certain number of descents. The generating function for the Eulerian numbers can be sorted into terms that correspond to equivalence classes partitioned by the particularly elegant “valley-hopping” proof. The two sided Eulerian numbers are an analog of the Eulerian numbers that also count the number number descents of each permutation’s inverse. Gessel’s conjecture sorts the generating function for the two-sided Eulerian numbers, and it has been proven using recurrence relations, but a proof that matches the valley-hopping proof in elegance is yet to be found.

Sacrifice bunting and attempting stolen bases are popular strategies in baseball. We set out to determine if using these strategies helps collegiate teams win games, and if so, in what situations they can be used to maximize probability of winning. We found that, in most cases, sacrifice bunts and stolen bases decrease win probability. However, especially in late innings and in some specific base/out situations, sacrifice bunts and stolen bases can be beneficial. In 2016 SEC play, using our optimal strategy as opposed to the current usage, win probability increased by 1.7%.

We took play-by-play data from 2016 SEC baseball games, compiling batting order, plate appearance results and future runs, to develop average expected runs tables along with probability of scoring tables for each base/out situation. In our initial data we had a glimpse into the optimal strategy, but the sample size was too small to be statistically significant. Our next step was to create a simulation in Python to model SEC games. We used the simulation to create win probability charts based on every inning, and we compared simulations using various bunting and stealing strategies to develop an optimal strategy.

Smallball: A Statistical Analysis of the 2016 SEC Baseball Season Jacob Kail, Math Major -advised by Drew Pasteur


The emphasis on human capital formation as a means to achieve increased productivity and economic growth

led many countries to develop immigration policies that favored skilled worker migration from less developed countries. In recent decades, the increased demand from developed countries for high-skilled labor caused a surge in the rate of high-skill emigration. The increased circulation of skilled migrants from less developed to developed countries brings about many complex implications for both sending and host countries. Drawing from brain drain literature that focuses on emigration prospects and human capital formation in sending countries, this paper develops a game theoretic model that looks at the strategic interaction between prospective emigrants and the home country. Congruent with literature, theoretical results show that better emigration prospects induce investment in education in native workers, which under certain circumstances can lead to human capital accumulation in the developing country.

Monotonic Untangling to Solve the Unknotting Problem Dana Foley, Math & CS Double Major

-advised by Matt Moynihan (Math) & Nathan Sommer (CS)

In mathematics, a knot is a single strand crossed over itself any number of times, and connected at the ends. The Reidemeister Moves have been proven to be the three core moves necessary to fully untangle a knot. We define a set of generalized moves based on the Reidemeister Moves which only reduce or maintain the complexity of a diagram. We provide a proof that these moves are sufficient for untangling all knots, including hard unknots. Additionally, we construct a computer program which reads the projection of a knot in its Extended Gauss Code notation and uses our moves to untangle it to the smallest number of crossings.

Skilled Emigration, Return, and Human Capital Formation: A Game Theoretic Approach Ruben Aguero Quinteros, Math & Economics Double Major

-advised by Jennifer Bowen (Math) & Amyaz Moledina (Economics)


We created a computer program that allowed users to play “No Thanks!”, a popular card game that is both simple to learn and capable of involving complex strategies. Within this computer program are computer players, or AI, that were coded from scratch to follow certain strategies. Within these hard coded AI parameter tuning was used to improve the AI’s execution of the given strategy. In addition to these hard coded AI, we created a self-learning AI. This AI started with no knowledge of the game or strategy and by repeatedly playing itself came to understand the game and potential strategies. This was done using neural networks of varying sizes, with a temporal difference algorithm used to train the weights within the neural network. While very large computation time was associated with neural networks capable of learning the game well enough for the self-learning AI to rival the best hard coded AI, the self-taught AI was able to learn enough to pose a challenge for human players of average skill. An introduction to game theory and reinforcement learning is also discussed in order to facilitate an understanding of the results.

Reinforcement Learning in Card Games: No Thanks! Robin Morillo, Math & Physics Double Major

-advised by Drew Pasteur

This project delves into the underlying mathematics and applicative computer science of error-correcting codes. A brief overview of error-correcting codes and how they work is proceeded by an extensive look at the Hamming code. Then the mathematics of finite fields and their intimate connection with error-correcting codes is developed and analyzed. Following this, the applicable side of error-correcting codes are inspected through extensible error-correcting code and noise software created for this project.

Clear Communication: Construction and Implementation of Error-Correcting Codes Alex Iudice, Math & CS Double Major

-advised by Jennifer Bowen (Math) & Denise Byrnes (CS)


We investigated the two vector mode solutions to the spherically symmetric wave equation for a step function refractive index profile. The investigation

began with a discussion on the classification and boundary conditions of partial differential equations. We proceeded with the derivation of the numerical finite difference method for different types of partial differential equations. In addition to this numerical technique, we presented the analytical separation of variables method for cartesian and spherical coordinates. We then analyzed our physical system, a glass microsphere surrounded by another medium, by dividing the spherically symmetric wave equation into an unperturbed Hamiltonian and a perturbative correction term. This separation allowed us to determine the two families of unperturbed solutions, the vector modes, analytically and to perform first order perturbation theory on the numerically computer wavenumbers. We studied the dependence of the waves’ energy and propagation properties on the quantum numbers, vector modes, and different surrounding media. We finished our study of our wave equation by assuming our unperturbed solutions factorable in their spin and orbital degrees of freedom. Applying perturbation theory, we determined the vector basis that diagonalized the perturbation Hamiltonian.

Blinded by the Light: An Investigation of the Wave Propagation of Vector Modes of Light in a Spherically Symmetric Refractive Index Profile Preston Pozderac, Math & Physics Double Major

-advised by Drew Pasteur (Math) & Cody Leary (Physics)

Auction with a buy price is the combination of auction and fixed price market, where buyers can either make a purchase immediately using the buy price previously set by the seller, or enter a bidder process in order to search for a better deal. eBay has adopted this idea and created their own version of auction with a buy price where the choices are only offered to the first customer. Bidders, when fully informed of how this system works, would behave so that they can maximize their expected payoffs. Hence, sellers, based on how rational customers act, would like to see how their revenue is generated under two types of auction available in eBay right now: thermal auction-style listing and the Buy It Now auction listing.

Bidder’s Behavior Model and Seller Revenue in eBay’s Buy it Now Option Gina Trang Lam, Math Major -advised by John Ramsay


The introduction of the internet, and thereby digital goods, has drastically changed consumer behavior in the music market. Behavior of particular note is the tendency of consumers to pay more than required for an album without any material motivation to do so, which we call the generous payment phenomenon. We observe that traditional neoclassical economic theory has difficulty predicting behavior such as this, therefore further models must be developed. We attempt to create a new model for consumer behavior specific to the digital music market using game theory. Specifically, the public goods game is used as a baseline and we apply a Theory of Reciprocity developed by Falk and Fischbacher.

Infant Mortaility Rates, IMR, describes the number of infant deaths per 1,000 live births

and is considered one of the most comprehensive ways to measure population health. This is due to IMR’s ability to respond to the quality and access to health care, as well as a number of different social, environmental and economic factors that do not directly deal with health. Despite recent improvements in the U.S.’s IMR, the U.S. ranks poorly in this measure compared to other developed nations. This unfavorably high IMR is primarily attributed to health disparities between subgroups that have continued or have become exaggerated through the years. Using U.S. county census data, the primary objective of this study is to identify different social, economic, and behavioral indicators that contribute to infant mortality rates. The second objective is to evaluate how these indicators vary across temporal boundaries and across subgroups using different mathematical and statical modeling methods.

A Mathematical Modeling Examination of the Changing Social, Economic and Environmental Indicators for Infant Mortality Across the United States Sophia Anderson, Math Major

-advised by Drew Pasteur

Consumer Decision in the Digital Audio Market Using Behavioral Game Theory Max Mindlin, Math Major -advised by Robert Kelvey


Regression analysis is seen as a tool to predict the future. However, many times regression models create misleading predictions or completely fail. There are other times when unexpected circumstances render all of the data gathered about a topic useless. Instead, regression analysis is a subject that deals with the exploration of information. It begins by gathering one’s already known information on a subject and then expanding by gathering and testing data. Regression involves a lot of statistics along with other math concepts such as calculus. Ultimately, regression analysis is about understanding the relations between variables and a never-ending question of the results. In this study, we go through what a general regression analysis is and how it is used. Then two types of regressions will be explained, linear regression first and then logistic regression, followed by a real life example.

Recession Analysis: Understanding Rather than Assuming Jonathan Ledesma Chavez, Math Major

-advised by Robert Kelvey

The Search for GTO: Determining Optimal Poker Strategy Using Linear Programming Stuart Young, Math Major -advised by Matt Moynihan

This project applies techniques from game theory and linear programming to find the optimal strategies of two variants of poker. A set of optimal poker strategies describe a Nash equilibrium, where no player can improve their outcome by changing their own strategy, given the strategies of their opponent(s). We first consider Kuhn Poker as a simple application of our methodology. We then turn our attention to 2-7 Draw Poker, a modern variant onto which little previous research is focused. However, the techniques that we use are incapable of solving large, full-scale variants of poker such as 2-7 Draw. Therefore, we utilize several abstractions techniques to render a computationally feasible LP that retains the underlying spirit of the game. We use the Gambit software package to build and solve LPs whose solutions are the optimal strategies for each game.


A Markov chain is a unique random variable because it is memoryless and the probability of moving to the next state in the process depends only on the current state of the process. The uniqueness of this random variable makes it applicable across a range of topics including two problems in particular. The focus of this thesis is how a specific type of Markov model called a Hidden Markov Model (HMM) emits observations that are used to predict the actual state of the model that is unknown. Finally, the paper discusses how a HMM is applied to the stock market in order to help an investor make a decision regarding a particular stock.

An Exploration of Hidden Markov Models with Applications to the Stock Market Tyson Vogel, Math Major -advised by John Ramsay

The Rubik’s cube is a puzzle formed from a 3 x 3 x 3 cube and 6 different colors. The way the cube operates and the puzzle that it creates can be explained using mathematics. To be able to talk about the mathematics behind the Rubik’s cube, we introduce some important concepts in Group Theory and then see how these concepts directly affect the workings of the cube. We discuss one solution, The Layer Method, and how the algorithm uses the ideas of Group Theory. We also discuss the concept of God’s Number and how a solution for the idea was found.

The Rubik’s Cube: A Look into Group Theory Tori McCoy, Math Major -advised by Jen Bowen

This project investigates the proofs that Kurt Gödel published in 1931 for his incompleteness theorems. We first lay out the basic knowledge necessary to understand the incompleteness theorems and the foundations of mathematics. With Nagel and Newman’s Gödel’s Proof as the main reference, we then examine the motivation behind proving these theorems and walk through the main ideas of Gödel’s original proofs. We conclude the project with the implications of the theorems and some thoughts regarding truth and provability in the context of mathematics.

Understanding Gödel’s Incompleteness Proofs Nanako Ito, Math Major -advised by Ondrej Zindulka


For the majority of votes that take place in Congress, over 90% of legislators’ votes can be explained by pure ideology. In years when no party has a significant majority, party unity becomes imperative in the scope of advancing

the party’s agenda. Various theories seek to explain congressional voting behavior as a catch-all approach, and often fail to further our understanding of the inconsistencies in voting behavior. Our lack of understanding of against party-line voting hinders our ability to explain and predict voting behavior. This project seeks to utilize various machine learning techniques to gain a better understanding of what causes against party-line voting in Congress.

Research in mathematics impacted the undergraduate mathematics curriculum between 1930 and 1950. Though the scholarship on

American higher educational history is vast, mathematics as a subject has largely been ignored by historians. Furthermore, those works that discuss changes in mathematics curricula do not engage research happening in high-level mathematics. A study of mathematics curricula reveals that higher educational institutions shifted their approach to undergraduate mathematics due to developments in research, major pedagogical movements, and external historical events. This I.S. draws on archives of course catalogues from two higher education institutions as well as articles written by mathematicians and mathematics educators in the early twentieth century. This project strives to bring studies of mathematical research closer to related studies in mathematics curriculum by considering the historical impact of such research on the undergraduate mathematics experience.

A Machine Learning Approach to Understanding Against Party-line Voting in Congress John O’Neill, CS & Political Science Double Major

-advised by Sofia Visa (CS) and Bas van Doorn (Political Science)

Calculating the Course: The Impact of Mathematical Research on the Undergraduate Mathematics Curriculum, 1930-1950 Marjorie Zeager, Math & History Double Major

-advised by Pam Pierce (Math) and Christina Welsch (History)


This thesis uses the HTC Vive in Unity to compare two different types of object interaction systems in order to determine the effectiveness of physics based interaction systems in a virtual environment. There is no standardized method for defining successful object interaction techniques in VR. There are numerous interaction techniques in VR that fall short of simulating realistic object interaction. This project explores a physics base interaction system and examines how effective it is by comparing it to a non-physics based system. A model house with various intractable objects is created to compare the two interaction systems. The first system, the naive interaction system, parents an object to the controller model, allowing the user to pick up and throw things in a very simple fashion. This system is compared to a physics based Newtonian system that takes into account mass and velocity during object interactions. The Newtonian system promotes a much deeper sense of immersion for a user due to how accurately the system simulates real life physical interactions. It is clear that creating a high level of mental and physical presence is crucial for a VR experience. Object interaction systems are an integral component of a VR experience that directly contribute to the realism and levels of virtual presence that a user achieves with a virtual environment. The results conclude that physics based interaction systems provide levels of realism and immersion that the naive systems cannot achieve. The results are beneficial because they demonstrate the positive impact that physics based interactions systems have on a VR experience and the need for improved systems in the future of VR development.

Grasping the Void: Immersion Tactics Using Gesture Controlled Physics Interaction Systems in Virtual Reality Avery Rapson, CS Major -advised by Denise Byrnes


Are Virtual Things Real? An Investigation into the Nature of Virtual Reality Zach Phillips-Gary, CS & Philosophy Double Major

-advised by Denise Byrnes (CS) and Elizabeth Schiltz (Philosophy)

Situated within the context of interdisciplinary research, this thesis leverages concepts from the fields of metaphysics, experimental psychology, game design and human-computer interactions to answer the question “are virtual things real?” First we attempt to develop an ontological account of virtual entities, using as a starting point the framework proposed by philosopher David J. Chalmers in his 2016 talk, The Virtual and the Real. We then expand on Chalmers’ account using concepts from Husserlian phenomenology in order to describe the first-person phenomenal experience of virtual reality. Next, we demonstrate that our modified version of Chalmers’ thesis is compatible with several major contemporary ontological accounts of the universe (materialism, idealism, and property-dualism). Using this framework, we present a series of “rules of thumb” for designing virtual reality environments with a realistic feel. Next we describe a series of empirical non-technical virtual environment design factors confer a phenomenal experience of realism upon the user. To conduct these experiments, we designed and implemented a series of virtual environments, along with an automated data collection system to measure in real time the qualitative variables analyzed in the study. Concurrently, we utilized phenomenological techniques to better understand whether these variables map on to the subjective experience of realism many participants experience inside immersive virtual worlds. We then describe the implementation of the software using the Unity3D game engine and the technical background of the HTC Vive virtual reality hardware employed in the experiments. Finally, we report the results of the empirical experiments and comment on the data collected. Although the quantitative analysis of the data from the automated data collection system failed to yield any statistically significant results due to issues with experimental design, the qualitative study seems to demonstrate an empirical grounding for our claim that virtual things are real in an ontological sense.


Jack In: An Exploration of Immersion in Virtual Environments Lewie Roberts, CS Major -advised by Denise Byrnes

The Black-Scholes Option Pricing Model and a Test for Efficiency in the Underlying Stock Market Sanjana Kumbhani, Math & Business Economics Double Major

-advised by John Ramsay (Math) and John Sell (Business Econ)

Within the last few years virtual reality has quickly become more popular and available to a larger number of consumers. As this technology grows in popularity, one of the features that will define its usefulness is its ability to convey immersion. This project examines what makes virtual environments feel immersive to users. Different styles of movement in virtual environments are examined. Sensory feedback is discussed in an investigation of how our senses convey presence. Environment design is also examined, with a focus on the spaces of two virtual environments, which are tested on users who provide feedback as to what did and did not feel immersive. By the end of this paper, the reader should have a better understanding of how virtual environments are created as well as what affects our feelings of immersion within them.

Options are tradable financial instruments that give holders the right, but not the obligation, to buy or sell the underlying asset at a specific price at or before a certain future date. The classic mathematical model used to price an option is the Black-Scholes option pricing model. If stock markets are considered efficient, then prices must reflect all available information. However, past research suggests there is a degree of inefficiency in the market. This study investigates the impact of information obtained from the Black-Scholes option pricing model on the efficiency of the underlying stock market. Specifically, the hypotheses is that the implied volatility measure of the underlying stock’s returns obtained from the Black-Scholes model is a returns measure; thus the former can be used to explain improved efficiency in the underlying stock market. Data for this study are collected from Yahoo Finance for a total of 100 firms. The results suggest that the model with the implied volatility measure is a better fit, and is more efficient in predicting the bid-ask spread of the underlying stock’s returns than the model with the historical standard deviation of returns measure. Thus, this study suggests that the Black-Scholes model can be used to add information that improves efficiency in the underlying stock market and further, the existence of an options market is, in general, beneficial for the quality of the underlying stock market.


Building a Course Recommender System for The College of Wooster Nan Jiang, CS & Math Double Major

-advised by Sofia Visa (CS) and Robert Kelvey (Math)

The goal of this project is to investigate the approaches for building recommender systems and to apply them to implement a course recommender system for The College of Wooster. There are three main objectives of this project. The first is to understand the mathematics and computer science aspects behind it. The mathematic concepts built into this project include probability, statistics and linear algebra. The final products consists of two components: a collection of Python scripts containing the implementation code of the course recommender system, and a simple user interface to analyze the pros and cons of different approaches by comparing their performance on the same training data sets which have information about students and courses at the College in the last seven years. The final goal is to apply the best model to build the course recommender system that can provide helpful and personalized course recommendations to students.

On Rationality and Morality: Three Kinds of Approaches Emily Howerton, Math & Philosophy Double Major

-advised by Pam Pierce (Math) and Evan Riley (Philosophy)

This thesis explores the relationship between rationality and morality. I ask questions about the prudential rewards of being moral, the evolutionary origins of our moral norms and implications for morality if we accept a more robust theory of rationality. To investigate one’s prudential reasons to be moral, I use game theory. Specifically focusing on the Prisoner’s Dilemma, I mathematically demonstrate its seemingly surprising conclusion. Philosophers like David Gauthier are troubled by the outcome of the Prisoner’s Dilemma and its potential implications for morality, so I examine his response. I also use game theory to think about the evolution of norms over time. Using the work of Christina Bicchieri, I question the assumptions on which traditional game theory is based and explore a new approach. Lastly, I deviate from the mathematical philosophy and explore the work of Donald Davidson. I give an account of what it means to be moral, if we accept his theory of rationality. Each author comes to the table asking different questions and making different assumptions. This variety is an asset. Rather than revealing some deep truth about the relationship between rationality and morality, I conclude with the importance of examining the relationship from all angles, through asking different questions and taking different approaches.


This is a data driven independent study. Using the data provided by the registration office of The College of Wooster, we (1) analyze the data related to the double major students to make a double major network, and (2) predict the grade in the organic chemistry class using information about previous taken classes. By analyzing the double-major network using random walk and Markov chain methods, we observe that STEM majors are more connected than the rest of the majors. By using multi-linear regression and pattern recognition neural networks for predictive modes of the students’ grades in organic chemistry class, we figure that the prerequisite, the accumulated GPA and the highest math class that a student completed are predictive to their organic chemistry grades.

A Stroll Through Cantor’s Paradise: Appraising the Semantics of Transfinite Numbers Matt Buranosky, Math & Philosophy Double Major

-advised by Ondrej Zindulka (Math) & Ron Hustwit (Philosophy)

Modeling Double Major Data and Predicting Organic Chemistry Grade at The College of Wooster Yunjia Zeng, Math & CS Double Major

-advised by Drew Pasteur (Math) and Sofia Visa (CS )

In A Stroll Through Cantor’s Paradise: Appraising the Semantics of Transfinite Numbers, we confront the mysterious role of infinite (i.e., transfinite) numbers in mathematics. Our analysis of the subject is divided into three chapters. In the first chapter, “Building the Concepts of Set Theory”, we lay out the Zermelo-Fraenkel axioms and show how they allow for us to express the content of finite arithmetic in the language of set theory. These axioms are then augmented with several others to give foundation for the concept of ordinality, which is used to extend the linear number line into the transfinite realm. In chapter two, “Goodstein’s Theorem”, we define the Goodstein sequence and invoke transfinite ordinal numbers to prove that every Goodstein sequence eventually reaches zero. We then discuss The Kirby-Paris Theorem, which shows that a system of higher-order arithmetic is needed to prove Goodstein’s Theorem. In chapter three, “The Philosophy of Set Theory”, we consider the requisites for a formal theory to succeed in advancing our theoretical knowledge. We argue, a’ la Immanuel Kant, that only the mathematical concepts that can be presented in intuition could tell us anything about the natural world. This implies that it is not justifiable to grant semantics to infinite numbers. Defining transfinite ordinals in a system of higher-order arithmetic fundamentally requires a bridge principle from the concepts of higher-order logic. We find, however, that none of these principles are sufficient grounds on which to do so.


On Degree Bound for Syzygies of Polynomial Invariants Zhao Gao, Math Major -advised by Ondrej Zindulka (Math)

and Mátyás Domokos

Suppose G is a finite linearly reductive group. The degree bound for the syzygy ideal of the invariant ring is given by Harm Derksen in “Degree bounds for syzygies of invariants”, Advances in Mathematics 185(2): 207-214, 2004. We develop the theory of commutative algebra and give the proof that the ideal of relations of the minimal set of generators of invariant ring of a finite linearly reductive group G is generated in degree at most 2|G|.

Evolving Monkeys into Sharks: An Analysis of Daily Fantasy Football Drafting Strategies Conor Maley, Math & CS Double Major

-advised by Drew Pasteur (Math) & Sofia Visa (CS)

The Daily Fantasy Football Sports industry has recently skyrocketed. Led by powerhouses FanDuel and DraftKings, the industry is estimated to be worth over a billion dollars. The games themselves have been declared “skill games,” meaning there is an underlying strategy behind Daily Fantasy Sports. This anomaly can be seen simply by the fact that only a few top players typically win most of the cash prizes. In this project we provide a deep exploration into the data science that lies behind choosing a team in Daily Fantasy Football. With team salary restrictions, Daily Fantasy Sports present an interesting optimization problem: users must make difficult decisions on which players to play on a given week. We investigate these decisions using analytics and machine learning to both model and analyze past data. The main goals of the investigation are to gain a better understanding of what statistics best predict player performance and find how we can produce the team to give contestants the best chance to profit. Through the investigation, we present our findings on the impact of past player performance, salary cost, and past opponent performance on a player’s future performance. Finally, we develop models to choose teams based on these statistics and evaluate the models in a simulated Daily Fantasy Sports environment.


Zhao Gao ‘17 THE ELIZABETH SIDWELL WAGNER PRIZE IN MATHEMATICS AND COMPUTER SCIENCE

Presented to student who showed greatest aptitude during the junior year and seems most likely to succeed in mathematics or computer science.

Honors & Awards (to Math/CS majors)

Sophia Anderson ’17 and Sanjana Kumbhani ‘17 THE FOSTER PRIZE IN MATHEMATICS

Presented to senior math major who has demonstrated the most improvement in mathematics

Rose Taylor ‘19 THE LYMAN C. KNIGHT SR. PRIZE IN MATHEMATICS AND PHYSICAL EDUCATION

Awarded to a sophomore who has demonstrated outstanding promise in mathematics and superior physical skills

Khoa Nguyen ‘18 THERON & DOROTHY PETERSON AWARD FOR OUTSTANDING ACADEMIC ACHIEVEMENT

Awarded to student majoring in science and has earned recognition as an outstanding scholar

Emily Howerton ‘17 WILLIAM H. WILSON PRIZE IN MATHEMATICS

Awarded to senior who has shown the greatest proficiency in mathematics

SOPHIA, ZHAO, KHOA, STUART, AVI

Joseph MacInnes ‘19 and Haidar Esseili ‘19 THE DR. DONALD DEWALD PRIZE

Presented to sophomore student who has shown commitment to learning in a STEM related field


Avi Vajpeyi ‘18 THE EDWARD TAYLOR PRIZE

Awarded to student who has attained the highest academic standing their first and sophomore years

Honors & Awards (to Math/CS majors)

Emily Howerton ‘17 WILLIAM GALPIN AWARD FOR GENERAL EXCELLENCE IN COLLEGE WORK

2nd, Women

Emily Howerton, Robin Morillo, Preston Pozderac, Stuart Young ‘17s

PHI BETA KAPPA

Emily Howerton, Preston Pozderac, Stuart Young ‘17s SUMMA CUM LAUDE

Zhao Gao, Nan Jiang, Gina Trang Lam, Robin Morillo ‘17s MAGNA CUM LAUDE

Alex Iudice, Marjorie Zeager, Bo Zhang ‘17s CUM LAUDE

MATH MAJOR EMILY HOWERTON RECEIVES HER DIPLOMA FROM PRESIDENT BOLTON


New Members CLASS OF 2017Brianna Bauer Leandra Forte Robert Gates Emily Howerton Alexander Iudice Sanjana Kumbhani Trang Gina Lam Sarah McGrath Jake Polster Preston Pozderac Katie Stock Todd Ulmer Michael Wolff Stuart Young Marjorie Zeager Yunjia Zeng

CLASS OF 2018John Bacher Savannah Binion Emma Brinton Junyi Chen Paige McKean Jack Mershon Khoa Nguyen Matthew Pleshinger Kelly Steurer Maxwell Taylor Haven Wagner Ruifeng Xu

National Mathematics Honor Society OHIO PHI CHAPTERINSTALLATION AND INITIATION CEREMONY, APRIL 18, 2017

WELCOMING REMARKS BY:DR. ANGELA SPALSBURY, PRESIDENT, PMEYOUNGSTOWN STATE UNIVERSITY

Pi Mu Epsilon

CLASS OF 2019Bhargav Bhalodi Allison Clough Haidar Esseili Wan Hang Hui Mijiti Mierkamili Callie Ogland-Hand Kory Sansom Benjamin Verschell

CLASS OF 2020Margaret McGuire

FACULTYJennifer Bowen Robert Kelvey Matthew Moynihan (charter member)

CHARTER MEMBERSRobin Morillo Dylan Orris Shiwani Varal


Faculty & Staff

Jennifer Bowen, Associate Professor of Mathematics & Chairperson

PH.D. VIRGINIA 2005

COURSES TAUGHT: BASIC STATISTICS, TRANSITIONS TO ADVANCED MATHEMATICS, LINEAR ALGEBRA (2 SECTIONS), 3 INDEPENDENT STUDY ADVISEES

In addition to serving as chairperson for the Mathematics and Computer Science Department, Dr. Bowen served on the College’s STEM Advisory Board and as an ARCH advisor for the College’s First-Year orientation program. She was a participant in GLCA’s Academic Leadership Institute in Ann Arbor, and she also presented at AAC&U’s Transforming STEM Undergraduate Education conference, “The STEMZone: A Coordinated Effort to Foster Community and Improve Persistence in STEM Majors”.

Dr. Bowen is very excited to be selected as mentor to the Posse program’s students attending Wooster. Posse is one of the most comprehensive and renowned college access and youth leadership development programs in the United States. Founded in 1989, Posse identifies public high school students with extraordinary academic and leadership potential who may be overlooked by traditional college selection processes. Posse extends to these students the opportunity to pursue personal and academic excellence by placing them in supportive, multicultural teams—Posses—of 10 students.


ON SABBATICAL FALL 2016COURSES TAUGHT: CALCULUS WITH ALGEBRA B (2 SECTIONS), PROBABILITY AND STATISTICS IDr. Hartman spent his sabbatical leave in the fall of 2016 at the University of Regina in Saskatchewan, Canada. While there he studied the Weyr form of a matrix and learned about the connections between algebraic geometry and linear algebra. He served as a referee of an article for The College Mathematics Journal during this time and submitted solutions to three problems from Mathematical Association of America journals. Dr. Hartman continues being an AP Calculus consultant for the College Board and continues to be involved in the grading of the AP Calculus exams. He and Pam Pierce collaborated on an article, “To Each Their Own: Students Asking Questions Through Individualized Projects” (2017) appearing in PRIMUS, a highly-noted, peer-reviewed journal in mathematics.

Jim Hartman, Professor of Mathematics PH.D. MICHIGAN STATE 2005

John Ramsay, Professor of Mathematics & Associate Dean for Experiential Learning

PH.D. WISCONSIN 1987COURSES TAUGHT: OPERATIONS RESEARCHDr. Ramsay served another year as Associate Dean of Experiential Learning. One of the AMRE teams that he co-advised in summer 2016 gave a presentation of their work at the Annual AAC&U General Assessment Conference. Title of their talk was Integrating Theory into Practice: Developing an Assessment Framework for Experiential Learning. The team developed an assessment tool for APEX (Center for Advising, Planning, and Experiential Learning). APEX provides College of Wooster students with a variety of support services that aid in developing their own academic, personal and professional goals. In summer of 2017, Dr. Ramsay directed the AMRE program which completed 10 projects with 32 student team members, including four students from Ashesi University in Ghana as well as one faculty advisor from Ashesi.


Pamela Pierce, Professor of Mathematics PH.D. SYRACUSE 1994

COURSES TAUGHT: FIRST YEAR SEMINAR “TOUGH CHOICES”, REAL ANALYSIS I & II, 3 INDEPENDENT STUDY ADVISEES

For the second time, Wooster hosted the Summer Symposium in Real Analysis with 48 participants from across the globe coming to The College of Wooster. Having organized the 2010 real analysis conference here at Wooster, Dr. Pierce wrote a successful NSF proposal to fund the 2017 Summer Symposium in Real Analysis XLI: The Black Squirrel Symposium. She and conference co-organizer Ondrej Zindulka organized the conference which featured topics such as theory of real functions, geometric measure theory, descriptive set theory, Banach spaces, and dynamical systems. The invited speakers included Juan Bes (Bowling Green State University), Bruce Hanson (St. Olaf, Northfield), Mikhail Korobkov (Novosibirsk), Artur Nicolau (Barcelona), Anush Tserunyan (University of Illinois Urbana-Champaign).


COURSES TAUGHT: FIRST YEAR SEMINAR “COMPUTERS CHANGING OUR WORLD”, DATA STRUCTURES AND ALGORITHMS, PROBLEM SEMINAR, MACHINE INTELLIGENCE, SCIENTIFIC COMPUTING, BIOINFORMATICS, 6 SENIOR I.S. ADVISEESSofia Visa has been generous with her outreach, sharing workshops in computer programming for fifth- and sixth-grade girls with the local Expanding Your Horizons organization, students at the B-Wiser camp, and fourth-graders at Melrose Elementary. In Scientific Computing, Dr. Visa used two kinds of robots: the Ozobots and the Finch robots. Students worked in class with these robots and developed solutions that encouraged algorithmic thinking. She continued research in bioinformatics and her collaboration with University of Georgia, Boyce Thompson Institute, University of Valencia, University of Florida, and University of Massachusetts. With several Wooster students, she worked on identifying structural variants in tomato fruit genomes and on associating genes with tomato fruit traits.

COURSES TAUGHT: MATHEMATICAL MODELING, DIFFERENTIAL EQUATIONS, NUMERICAL ANALYSIS, 3 INDEPENDENT STUDY ADVISEESDrew Pasteur has recently taken on the role of co-director in the College’s summer Applied Methods & Research Experience (AMRE), in which teams of students work as mentored consultants for corporations and other clients. Last fall, he served as Local Arrangements Coordinator for Mathematical Association of America’s Ohio Section meeting at The College of Wooster. Together with former colleague John David, he authored a chapter on American football quarterback and kicker evaluation in the recently published, “Handbook of Statistical Methods for Design and Analysis in Sports.”

Drew Pasteur, Associate Professor of Mathematics PH.D. NORTH CAROLINA STATE 2008

Sofia Visa, Associate Professor of Computer Science PH.D. UNIVERSITY OF CINCINNATI, 2007

Nathan Sommer, Assistant Professor of Computer ScienceCOURSES TAUGHT: IMPERATIVE PROBLEM SOLVING, OPERATING SYSTEMS, DATA STRUCTURES LABS, SOFTWARE ENGINEERING – MOBILE COMPUTIING, 2 SENIOR I.S. ADVISEESProfessor Sommer joined the department last fall after a two-year visiting position at Moravian College. His research interests lie in machine learning, computer music, and computer science pedagogical tools. This past summer, he has been working to complete his dissertation from the University of Cincinnati on the topic: A Machine Learning Approach to Controlling Musical Synthesizer Parameters in RealTime Live Performance.


Denise Byrnes, Associate Professor of Computer Science PH.D. OHIO STATE UNIVERSITY, 1992

COURSES TAUGHT: DATA STRUCTURES AND ALGORITHMS + LAB, THEORY OF COMPUTATION, COMPUTER GRAPHICS, 4 INDEPENDENT STUDY ADVISEES

Dr. Byrnes’ Senior I.S. students obtained Copeland Funding to purchase a Chronos High Performance PC and HTC VIVE Virtual Reality System in order to set up a virtual reality lab for Independent Study projects.

Ondrej Zindulka, Pocock Distinguished Visiting Professor of Mathematics

PH.D. CHARLES UNIVERSITY, PRAGUE, 1993

COURSES TAUGHT: CALCULUS AND ANALYTIC GEOMETRY I (2 SECTIONS) FUNCTION OF COMPLEX VARIABLE, MULTIVARIATE CALCULUS (2 SECTIONS), 3 INDEPENDENT STUDY ADVISEESDr. Zindulka, an Associate Professor of Mathematics at Czech Technical University in Prague, spent the academic year 2016-2017 as the Pocock Distinguished Visiting Professor of Mathematics at The College of Wooster. With Dr. Pierce, he co-organized the 2017 Summer Symposium in Real Analysis held at Wooster.


COURSES TAUGHT: CALCULUS AND ANALYTIC GEOMETRY I AND II (2 SECTIONS), ABSTRACT ALGEBRA, TRANSITION TO ADVANCED MATHEMATICS, PROBLEM SEMINAR, 4 SENIOR I.S. ADVISEESDr. Kelvey came to Wooster after obtaining his Ph.D. at Bowling Green. His research interests are combinatorial and geometric group theory. Dr. Kelvey advised one ACM/ICM math modeling team which earned a Meritorious Winner designation, and he was advisor for the Math Club.

COURSES TAUGHT: CALCULUS AND ANALYTIC GEOMETRY I AND II (2 SECTIONS), MATH IN CONTEMPORARY SOCIETY, PROBLEM SEMINAR, TRANSITION TO ADVANCED MATHEMATICS, 4 INDEPENDENT STUDY ADVISEES Dr. Moynihan advised two of the MCM/ICM math modeling teams which earned Honorable Mention and Meritorious Winner honors. Along with Dr. Rob Kelvey, he obtained a charter for a Wooster chapter of Pi Mu Epsilon, the National Mathematics Honor Society, and organized an induction ceremony of members in April. Dr. Moynihan has relocated to the Boston area where he has obtained a tenure track position at Framingham State University. We are sorry to see him leave, but we wish him the very best in this new endeavor!

Matthew Moynihan, Visiting Assistant Professor of Mathematics

PH.D. BRANDEIS UNIVERSITY, 2012

Robert Kelvey, Visiting Assistant Professor of Mathematics

PH.D. BOWLING GREEN STATE UNIVERSITY, 2016

COURSES TAUGHT: MATH IN CONTEMPORARY SOCIETY, MULTIVARIATE CALCULUS, CALCULUS FOR SOCIAL SCIENCE

Mary Jo Kreuzman, Visiting Assistant Professor of Mathematics

PH.D. NOTRE DAME, 1985

Ronda Kirsch, Instructor of Mathematics and Math Center Coordinator

M.A. KENT STATE UNIVERSITY, 2010

COURSES TAUGHT: CALCULUS WITH ALGEBRA A (3 SECTIONS)Ronda is active in the ARCH orientation program and the Youngstown Early Intervention Program at Wooster. She was recently honored at the College’s annual staff recognition luncheon for five years of service.


September 8: Summer Research Experiences Part I, S-STEM Scholars

LEANDRA FORTE (CHEMISTRY ’17), EMILY HOWERTON (MATH ’17) AND PRESTON POZDERAC (MATH & PHYSICS ’17)

Math/CS Colloquium Series

September 15: Summer Research Experiences - Part II

THAO NGYEN (MATH & BUSINESS ECON ’18), MAX TAYLOR (MATH & COMPUTER SCIENCE ’18) AND JACOB DENBEAUX (MATH ’19)

October 6: Immersion in Mathematics via Digital Art

JUDY HOLDENER, PROFESSOR OF MATHEMATICS, KENYON COLLEGE

February 23: Cubing the Pyramid, or, Why We Need Calculus (and Measure Theory!)

KEVIN WOODS, ASSOCIATE PROFESSOR OF MATHEMATICS, OBERLIN COLLEGE

April 24: Innovation for a Connected World BEN NUSSBAUM, CTO & SENIOR SOFTWARE ARCHITECT, ATOM RAIN


Shiwani Varal and Shuwen Pang MERITORIOUS WINNER, ICM PROBLEM D

ADVISED BY MATTHEW MOYNIHAN“Measuring the Evolution and Influence in Society’s Information Networks” - Top 20%

CoMap MCM/ICM Math Modeling Contest

Aditya Zanwar, Rahul Roy, Mijiti Mierkamili MERITORIOUS WINNER, ICM PROBLEM D

ADVISED BY ROBERT KELVEY“Measuring the Evolution and Influence in Society’s Information Networks” - Top 20%

Hieu Tran, Thuy Dinh, Manh Tri Dao HONORABLE MENTION, MCM PROBLEM A

ADVISED BY MATTHEW MOYNIHAN“Modeling a Hot Bath”

HIEU, THUY, MANH TRI, SHUWEN, SHIWANI, RAHUL, ADITYA, MIERKAMIL


ACM/ICPC Programming Contest EAST CENTRAL NORTH AMERICAN REGIONAL PROGRAMMING CONTEST

YOUNGSTOWN STATE UNIVERSITYOCTOBER 2016

Khoa Nguyen, Nan Jiang, Avi Vajpeyi THE WOOSTER TEAM SOLVED TWO PROBLEMS:

THE KEY TO CRYPTOGRAPHY AND FOOSBALL DYNASTY(ADVISED BY SOFIA VISA)

HackOH5

Team “WooHoo”


Conor Maley ’17 (Math & Computer Science) “Monkeys into Hawks: Analyzing Optimal Drafting Techniques Used for Daily Fantasy Football using Mathematical Modeling and Machine Learning”, presented at the National Joint Meeting of the MAA/AMS, Atlanta GA, January 2017.

Zachary Phillips-Gary ’17 (Computer Science & Philosophy) “Virtual Reality Human Research Toolkit”, Poster presented at the ACM regional undergraduate research competition, CCSNE’17, April 2017, College of Saint Rose, Albany NY.

Avi Vajpeyi ’18 (Computer Science & Physics) “Chaotic Scattering of a Point Mass on a Complex Topography”, Poster presented at the ACM regional undergraduate research competition, CCSNE’17, April 2017, College of Saint Rose, Albany, NY.

Conference Presentations by Students

Numerically integrating

equations of motion

y

xx0 x1 x2 x3 xn–1 xn

Chaotic Scattering of a Point Mass on a Complex TopographyAVI VAJPEYI, DENISE BYRNES (ADVISOR), MATHEMATICS AND COMPUTER SCIENCE DEPARTMENT, THE COLLEGE OF WOOSTER, WOOSTER, OHIO, USA

Result: Chaotic vs.

Non-Chaotic Regions

Future Work

Result: Fractal Nature

Impact Parameter (b)-3.0

50º

0º

-50º

-2.0 -1.0 0.0 1.0 2.0 3.0

Scat

terin

g an

gle

(Θ)

Impact Parameter (b)-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0

50º

0º

-50ºScat

terin

g an

gle

(Θ)

VA L L E Y H I L L

b = 0.125

Θ = 82.1º

b = –2.26

Θ = –39.9º

b = 0.125

Θ = –21.4º

The parameters in the simulation are explained in Figure 3. On altering the impact parameter by small increments, we observe that the scattering angle varies:• Chaotic: scattering angle varies by large amounts,• Non-chaotic: scattering angle varies by small

amounts This can be understood by studying Figure 4. On this plot we have several paths with small differences in the impact parameter. The resulting paths are very different.

• Calculate the fractal dimensions to quantify and compare the fractal nature of the system with different initial velocities.

• Release a cloud of particles to study the interactions of multiple particles traversing a complex topography.

On focusing on chaotic regions (Figure 6), one observes similar patterns of repeating chaotic and non-chaotic regions in the data revealing inherent fractal properties in the system [3].

We use numerical integrators such as Runge Kutta 4 to calculate the position of the particle by using the equation relating the force experienced by the particle and its acceleration [2]. An example of how numerical integration works can be seen in Figure 2 where the midpoint technique is used to approximate the path of a particle (the curved line) given by a force equation.

Application: SimulatorThis application numerically integrates the differential equations of motion to simulate the movement of a point particle as it traverses through a region with four hills (blue contour plot) or valleys (yellow contour plot) as illustrated in Figure 1.

ACKNOWLEDGEMENTSThis project would not have been possible without the support and guidance of Dr. John Lindner, Physics Department, of the College of Wooster, Wooster, Ohio.

b = –2.26

Θ = –1.7º

ABSTRACT: Like classic scattering simulations [1], this program studies chaos in the scattering of a particle traversing a region with complex topographical obstructions. The obstructions cause the particle to deviate from its initial position. The relationship of deviation can be studied with the help of data taken from this application.

REFERENCES[1] Edward Ott and Tamás Tél. Chaotic scattering: An introduction. Chaos: An Interdisciplinary Journal of

Nonlinear Science, 3(4):417–426, 1993.[2] Konstantinos N Anagnostopoulos. Computational Physics, Vol I: A Practical Introduction to Computational

Physics and Scientific Computing, volume 1. Konstantinos Anagnostopoulos, 2014.[3] Harvey Gould and Jan Tobochnik. More on fractals and chaos: Multifractals. Computers in Physics,

4(2):202–207, 1990.

To study the chaotic nature of the system more quantitatively, we present graphs of the impact parameter and resulting scattering angle in Figure 5.

Particle

Four Hills

ScatteringAngle (Θ)

y

xImpact Parameter (b)

100º

50º

0º

-50º

-100º

Scat

terin

g an

gle

(Θ)

-0.765 -0.760 -0.755 -0.750

Impact Parameter (b)

100º

50º

0º

-50º

-100º

Scat

terin

g an

gle

(Θ)

-3 -2 -1 0 1 2 3

100º

50º

0º

-50º

-100º

Scat

terin

g an

gle

(Θ)

-1.0 -0.8 -0.6 -0.4 -0.2 0.0

100º

50º

0º

-50º

-100º

Scat

terin

g an

gle

(Θ)

-0.80 -0.75 -0.70 -0.65 -0.60 -0.55

Scat

terin

g an

gle

(Θ)

Scat

terin

g an

gle

(Θ)

Scat

terin

g an

gle

(Θ)

Scat

terin

g an

gle

(Θ)

100º

50º

0º

-50º

-100º

-1.0 -0.8 -0.6 -0.4 -0.2 0.0

100º

50º

0º

-50º

-100º

-3 -2 -1 0 1 2 3

Impact Parameter (b)

100º

50º

0º

-50º

-100º

-0.40 -0.35 -0.30 -0.25 -0.20 -0.15

100º

50º

0º

-50º

-100º

-0.286 -0.285 -0.284 -0.283 -0.282 -0.281 -0.280

VA L L E Y H I L L

FIGURE 2: A curved line being evaluated with a numerical integration technique. The rectangles are the approximated values.

FIGURE 4: Paths of the particle with slightly different initial b values. This demonstrates how small changes in b can result with very different final paths.

FIGURE 3: Schematic illustration of the scattering simulation with four potential hills in the particle’s path. The dashed line shows the trajectory of the particle.

FIGURE 6: Plots of the scattering angle versus the impact parameter, and successive expansions of a small region from the original plots shown top to bottom.

FIGURE 5: Graphs of the scattering angle plotted against the impact parameter. Each point on the graph represents one possible path.

FIGURE 1: Simulation interface with an animation of the particle traversing a region with four hills (yellow contour plot). The black dot is the particle and the green line is its path along the surface.


Math Club LEADERSHIP TEAMPresident: Shiwani Varal

Vice President: Manh Tri DaoTreasurer: Robin MorilloSecretary: Dylan Orris

Riddle of the Week: Hieu TranAdvisor: Rob Kelvey

Taylor Bowl XXVII Math/CS 113.6 Physics 100.1


Applied Methods & Research Experience

Goodyear Tire & Rubber Company

TIRE TREAD WEAR MODELINGAdvisors: Drew Pasteur (Mathematics) and Charlie Jackson (Engineering, Ashesi University) Team: Joe MacInnes ’19, Bhargav Bhalodi ’19, Kelly Steurer ’18, Maxwell Aladago (Ashesi ’18)

The main aim of this project was to identify and analyze the effects of some geolocational factors such as road roughness, road curvature, elevation change, weather, and traffic on tire tread wear. Goodyear provided us with data concerning the tire tread wear rates of different kinds of tires in several different zip codes. The majority of work done involved getting data for our factors, generating features from this data, and creating a model from these features. The main deliverable for the project was a model that explained the effect of the mentioned geolocational factors and enabled Goodyear to calculate a predicted tread wear rate for any region in the United States.

CONSUMER SOFTWARE SALES PROFITABILITY RESEARCHAdvisors: Joe Histen (Business Economics) and Drew Pasteur (Mathematics) Team: Komal Mesvani ’18, Kory Sansom ’19, Jessica Verghese ’18

Saltillo Corporation is a local company that makes augmentative and alternative communication (AAC) devices for individuals with speech impairments. The objective of the project was to help Saltillo improve their marketing and pricing strategies to better cater to the demands of the education and consumer markets. Through extensive market research, the AMRE team recommended ways in which Saltillo could increase their social media and web presence, and adjust the price of their products using discounts or bundling strategies.

Saltillo Corporation



Western Reserve Group

AUTOMATED RATE IMPACT TOOLAdvisors: Jen Bowen (Mathematics) and Ronda Kirsch (Mathematics) Team: Constant Likudie (Ashesi ’18), Michelle Bae '19, Christian Betre ’19, Mary-Hannah Boyer ’18,

The goal of this AMRE project for Western Reserve Group is to automate the process of calculating the premium of auto insurance when underlying factors change. We were given excel spreadsheets with relevant calculation process and data. We rewrote this process in a program called R. Then we created an application using the algorithm. Now users can both graphically and numerically see the data of how much the premium has changed for how many people in a more efficient manner.

MARKET RESEARCHAdvisors: Brett Woodard (APEX) and Marina Rosales (APEX) Team: Charles Holt ’19, Kevin Gould ’18

This AMRE project focused on examining engagement factors for Outdoor Access, a two-sided marketplace that connects landowners and outdoor enthusiasts. Using regression analysis through STATA software, the team quantified the effect of listing characteristics on customer engagement, and surveyed Outdoor Access’ member base to better establish customer preferences. Ultimately the analysis and recommendations for the client served as methods to reduce marketing/acquisition costs and improve the long-run customer experience. The project concluded by presenting data analysis, survey findings and recommendations to Outdoor Access at their headquarters in Richmond, VA.

Outdoor Access



The College of Wooster/Calculus Labs

CURRICULAR RESOURCE STUDYAdvisors: Rob Kelvey (Mathematics) and Jen Bowen (Mathematics) Team: James Ma ’19, Julia Brooks ’19,Dylan Orris ’19

The goal of this project was to both find a lower cost alternative to the current textbook in use in Calculus courses at the College, as well as to revise, and for Calculus I and II, replace the aging Maple labs. The team researched textbooks and reached a consensus to recommend Openstax Calculus first and foremost, with secondary recommendations of three other books. After revising Maple labs for Linear Algebra and Calculus III, the team found an online course software, Ximera, and in addition to lab handouts, created online labs for Calculus I and II.

COMPETITOR PRICING INVESTIGATIONAdvisors: John Ramsay (Mathematics) and Rob Kelvey (Mathematics) Team: Cynthia Gouanfo (Ashesi ’18), Maggie Sestito ’19, Shuwen Pang ’18, David Wolshire ’18

A large insurance company was interested in determining what variables can predict or determine the sale of insurance policies. The College of Wooster AMRE Team was given three data sets to merge, clean, and analyze. In addition to those files, the team was provided with a glossary that listed all the variable’s descriptions.

Analysis Methods included: •Frequency Tables •Hypothesis Testing •Logistic Regressions •Binary Classification Trees •Clustering The team found a number of variables that influenced the sale of policies and provided the company with suggestions for further analysis.

Progressive Insurance



United Way

DATA CENTER FEASIBILITY STUDY AND POVERTY RESEARCH Advisors: Heather Fitz Gibbon (Sociology) and Anne Nurse (Sociology) Team: Celia Connolly ’17, Geoffrey Carney-Knisely ’18

This project focused on a feasibility study for the creation of a Data Center at The College of Wooster designed to serve United Way and the entire Wayne County community in assessing the collective impact of community investments, collaborations and partnerships on people's lives. The project team also researched and identified appropriate indicators to measure poverty locally, continuing the work of prior poverty research conducted with United Way and The College of Wooster.

Community Transportation

FEASIBILITY STUDYAdvisors: Vikki Briggs (APEX) and Nate Addington (APEX) Team:, Mary Cotter ’20, Shana Zelenka ’19, Pedro Oliboni ’20, Anna Addei (Ashesi ’17)

Traditionally, AMRE projects have been based in math and computer science; however the Community Transportation project was one of three projects completed in 2017 to be focused on social services. The Community Transportation team worked for seven clients with varying perspectives and goals for the project, including Wayne Economic Development Council, The Fund for Our Economic Future, and Job and Family Services, to generate interactive maps using ARCGis software, and to propose a spectrum of possible transportation systems for Wayne County. The Community Transportation team generated a final report and proposal which highlighted case studies of transportation systems across the United States, possible options for funding, stories of community members who struggle with transportation, and the Team’s proposed systems, among other topics. Additionally, a guide as to how to use mapping web applications created by the team was attached to the final report. The Community Transportation team presented on the following systems: four fixed routes generated by the team, a vanpool program, a paratransit system, and Liberty Mobility (an on-demand system managed by a private entity).


DATA MANAGEMENT TOOLAdvisors: Matt Moynihan and John Ramsay (Math) Team: Sarah Padrutt ’18, Scarlett Chen ’18, Sabrina Tobe ’18

APEX (Center for Advising, Planning, and Experiential Learning) provides College of Wooster students with a variety of support services that aid in developing their own academic, personal and professional goals. APEX would like to understand how each demographic of the student body engages with their services. The task given to the AMRE APEX Data Team was to perform an analysis of student engagement for the 2015-2016 academic year, and create an easy to use program that automates this analysis for subsequent years. In response, the team created a Microsoft Excel-based program named WISER (Wooster Interactive Student Engagement Report). This program will combine APEX student engagement data with College student demographic information to create a student engagement Excel database and a dashboard of interactive Excel Pivot Tables that will facilitate assessment of student engagement and APEX programming.


Social Services Coaches

FEASIBILITY STUDYAdvisors: Tom Tierney (Sociology) and Jim Foley (The Counseling Center of Wayne and Holmes Counties) Team: Randall Turner ’18, Emma Woods ’18, Oscar Bautista ’19

This AMRE project conducted a feasibility study to assess the possibility of developing a Social Service Coaches Program at The College of Wooster. The team organized a series of interviews with members of the community, faculty, and staff from the College, collected and analyzed alumni data, and created a literature review of academic sources to develop a model of best practices for the program. A comprehensive curriculum was developed to train students in the social work and mental health competencies they will need to conduct home visits and act as a mental health coach. Finally, partnerships with three mental health counseling centers willing to host College volunteers were established.

The College of Wooster/APEX Data

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