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Mathematics & Computer Science

Greetings from the chair...Thanks for your interest in our department newsletter! This year the department welcomed some new folks on our staff and we have found ways to keep life exciting on the upper floors of Taylor Hall. Matthew Moynihan joined us after completing his Ph.D. at Brandeis in June of 2012. Matt loves the friendly atmosphere in the department and has already been active with the Putnam Exam and with SMAAC—the student math club on campus. Bob Wooster also joined us this year, after spending three years at West Point. Bob has enjoyed becoming active with our colloquium series and helping to organize three very successful teams of student participants in the COMAP Mathematical Modeling contest. Ronda Kirsch officially took over the directorship of the Math Center in the fall of 2012, and business has been booming ever since! In addition to running the Math Center, Ronda teaches three courses per

year and works with student tutors and graders. As we begin this upcoming year, we are pleased to welcome back Professor Simon Gray (Computer Science), who has been serving for three years in an administrative position with the Great Lakes Colleges Association.

The number of majors in the department has continued to grow, and we are excited about the enthusiasm and interest that we see in our students. With 24 senior majors in the department this year, we were well represented at the Senior I.S. Symposium in April. Commencement this year was particularly notable. Senior Sam Swartz received the prestigious Galpin Prize for all-

around distinction in his college career. Sam is heading to a private boarding school in Maryland (Saint Anne’s) where he will be kept quite busy teaching mathematics and coaching several student athletic teams. In addition to winning the Wilson Prize in Mathematics, senior David Freund was chosen as one of the two student speakers at this year’s commencement. Not only were we very proud to have a mathematics major up on the podium, but we also enjoyed hearing David speak about the highlights of his four years at Wooster. David will be continuing his studies in mathematics as he enters the Ph.D. Program at Dartmouth this fall.

We wish all of our seniors well as they leave Wooster and hope that all of our alums will continue to keep in touch with us. Please send your news and updates to our fearless leader, Jackie Middleton, at jmiddleton@wooster.edu.

The College of Wooster

Contents

Class of 2013 Senior Independent Study

Faculty & Staff

Speaker for the Class

Honors and Awards

Contests & Conferences

Colloquia

Applied Mathematics & Research Experience

Taylor Bowl

A Degree in Math/CS

Sam Swartz and Sarah Smith-Polderman celebrate at Wooster’s 2013 Commencement.

A Yearly Newsletter

Sorry, Andrew Blaikie, your I.S. is very well done, but you are not allowed to keep the giant Tootsie Roll from the Registrar’s Office.

Pamela PierceDepartment Chair

www.wooster.edu/academics/areas/mathematics www.wooster.edu/academics/areas/computer-science

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Senior Independent StudyJohn Angelo (Mayfield Heights OH)Mathematics majorPredictive Analytics on First Year Retention at The College of Wooster(advised by John Ramsay, Mathematics)

The mathematics behind two statistical methods used for prediction are developed: principal component analysis and naive Bayesian classifier. Principal component analysis uses variables from a data set to create a smaller number of new, uncorrelated variables. The naive Bayesian classifier method predicts which class each sample in a data set belongs to based on an independence assumption, conditional probabilities, and Bayes’ theorem. To illustrate each method we implement to predict first year retention for College of Wooster students The data from College of Wooster students is used to show how the methods are implemented and how results from each method are analyzed.

Theresa Albon (Columbus OH)Mathematics and Physics double majorThe Entanglement and Relaxation of Liquid Crystal Shaped Granular Media(advised by Drew Pasteur, Mathematics and Shila Garg, Physics)

The intention of this research was to analyze properties of microscopic liquid crystal molecules. Since working with microscopic molecules can be difficult a macroscopic model was made out of wires shaped like H, U, V, and rod shaped liquid crystal molecules. An experiment was done to analyze the collapse or relaxation of entangled wires of various shapes under sinusoidal relaxation accelerations. A MATLAB program was made to find the centroid and total pixel area of the entangled pile in every other frame of the video during the collapse. The centroid data was fitted with double exponential fits, which yielded two characteristic times for the collapse process. From this analysis, we concluded that the V and rod shaped wires behaved similarly, they did not display entanglement and would easily collapse. The U-shaped wires displayed the greatest amount of entanglement and would remain entangled together the longest out of all of the wires analyzed. A computer simulation was written to recreate the experiment. Only rods were analyzed and they varied in number: 50, 100, and 200. In addition to analyzing the relaxation height, the decrease in height due to entanglement from when the rods were first placed in an enclosure and accelerated, was analyzed. Only the data runs with 100 rods displayed any decrease in height, due to their alignment within the enclosure. The decrease in height during the relaxations also were fitted with a double exponential fit. The V and rod wire shapes were easily untangled during the relaxation portion of the experimental research, this suggested that V and rod shaped liquid crystals have a low elastic energy. The rod wires would align parallel to one another in the experiment and computer simulation and form a layer of rods, this suggests that the rod shaped liquid crystal molecules have the greatest orientational and positional order. The ability to relax when the wires were free of their enclosure and subjected to an acceleration compares with a liquid crystal’s molecular viscosity. Since the U-shaped wires displayed the greatest entanglement, this research suggests that they have the highest viscosity, while the rod shaped liquid crystal molecules would have the lowest viscosity.

Anna Easterday (Tiffin OH)Mathematics majorOnly for Honest Men: A Survey of Voting Theory(advised by Jim Hartman, Mathematics)

This thesis surveys voting theory. The history of the development of the topic is discussed. A range of voting systems is described and examined, from the everyday to the fantastic. The fundamentals for analyzing voting rules are put forth and implemented.

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Senior Independent Study Class of 2013

Philip Wales (Great Falls VA)Mathematics and Physics double major

ξ.(advised by Drew Pasteur, Mathematics and John Lindner, Physics)

The ξ. (pronounced “spring dot”) body problem is a unique, two dimensional, three body problem where three point masses are gravitationally attracted to each other. The uniqueness of the system is a linear elastic force between two of the point masses as though they were connected by an ideal spring. The two masses connected by the spring are denoted as the “ξ” subsystem, with the third free mass denoted as the “.”. The equations of motion for the system were derived in multiple cartesian and polar form using both Newtonian analysis and the Euler-Lagrange equations. Code in C++ was developed to numerically solve the equations using primarily the classical Runge-Kutta method. The code was used to create a program that would perform parameter space sweeps which was used to confirm analytic solutions for certain circular orbits derived for the system. Such circular orbits where when the spring was not stretched and the masses were either formed a line or an equilateral triangle. The ξ subsystem alone proved to be complicated. The true rest length of the system as well as circular orbits for the system were derived. A general solution for the ξ subsystem could not be obtained but the system was greatly reduced to a dimensionless form and independent time.

Kyla Davis (Struthers OH)Mathematics majorThe Torus and Graph Theory(advised by Matt Moynihan, Mathematics)

Often we find properties of planar graphs that can be generalized for other surfaces. This study explores and compares such properties of planar graphs with toroidal graphs, with notable topics such as the Euler characteristic and formula, Kuratowski’s Theorem and the Four Color Theorem.

Matt Schmitthenner (Delaware OH)Mathematics and Physics double majorA Theoretical and Experimental Pattern Analysis of Electrohydrodynamic Convectionin a Liquid Crystal System(advised by Drew Pasteur, Mathematics and Shila Garg, Physics)

Patterns formed by the electrohydrodynamic convection (EHC) of a liquid crystal system were analyzed experimentally and through a computational model. For the experimental liquid crystal system, a setup consisting of a circuit to sup- ply and measure voltage, a

microscope mounted with a camera, a temperature controlled heating stage and a computer to collect data was assembled. A simulation of the Generalized Swift-Hohenberg equation was created using a finite difference method to solve the partial derivatives. The liquid crystal experiment found the transition parameters between non EHC and EHC behavior for two novel shaped liquid crystal materials, RB1115 and RB1189, synthesized at Kent State University. The transition between dynamic scatter modes was also examined using discrete Fourier transforms. The Generalized Swift-Hohenberg equation was solved in two dimensions, and the resulting pattern was interpolated. These two different dynamical systems produced images with comparable patterns, validating the simulation to a degree.

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Senior Independent StudyAllie Webb (Columbus OH)Mathematics majorExtensions of the Farey Sequence and Ford Circles(advised by Jennifer Bowen, Mathematics)The Farey Sequence of order n is the sequence made up of all non-

negative irreducible proper fractions between 0 and 1, arranged in increasing order, with denominators not exceeding n. (Note that in this definition, order does not refer to the size of the sequence). The terms of the Farey Sequence have geometric applications that include the Farey Starburst and Ford Circles. In addition, the sequence can be found within a graphic representation of non-negative rational values called the Farey Tree, which is contained within the Stern-Brocot Tree.

David Freund (Kirtland OH)Mathematics majorThe Machete Number(advised by John Ramsay, Mathematics)Knot theory is a branch of topology that deals with the structure and properties of links. Employing a variety of tools, including surfaces, graph theory, and polynomials, we develop and explore classical link invariants. From this foundation, we define two novel link invariants, braid height and machete number, and investigate their properties and connection to classical invariants.

Erin Davison (Maitland FL)Mathematics major

Quaternions and Octonions(advised by Jennifer Bowen, Mathematics)The purpose of this paper is to investigate the algebraic systems the Quaternions and Octonions. It includes an introduction with the purpose of providing definitions from calculus, linear algebra, and abstract algebra. We discuss the algebraic structure and geometric applications of the quaternions, as well as give an example of a special case quaternion. We consider the extension of the quaternions, the octonions, and conclude with the construction of these algebras by the Cayley-Dickson process.

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Senior Independent StudyAndrew Blaikie (Allen Park MI)Mathematics and Physics double major/ /(advised by Drew Pasteur, Mathematics and John Lindner, Physics)The // body problem (slash-slash) is the study of the gravitational

interaction between 2 extended line masses. The topic of this thesis is the study of the planar // body problem, where the universe is restricted to a plane. The analysis is performed using completely classical methods. The potential and kinetic energies are derived in the center of mass frame using polar coordinates. The Euler-Lagrange equations are then used to write down the equations of motion. Geometric vectors are used to radically simplify the equations. The equations of motion are shown to reduce to the planar /. body

problem and the Newtonian 2 body problem in the appropriate limits. Three classes of periodic orbits are solved exactly and one class is believed to be stable. The Runge-Kutta-Fehlberg method is used to find numerical solutions for a given set of initial conditions using 64 digit precision. We describe a robust numerical mechanism to detect collisions before they occur. A GUI application automates the numerical processes. Retrograde spin was observed to stabilize orbits while prograde spin destabilized orbits. Escape not possible in the Newtonian 2 body problem was observed in the planar // body problem. Using parameter space plots we found that the gravity gradient orbit generates a valley of stability around its theoretical curve.

Ashley Stopka (Akron OH)Mathematics and Chinese Studies double majorA Study of Modern Geometries and Felix Klein’s Erlanger(advised by Jim Hartman, Mathematics and Rujie Wang, Chinese)The purpose of this paper is to research modern geometries and introduce Felix Klein’s Erlanger Programm. It gives an overview of the Erlanger Programm approach to studying geometry using Euclidean Geometry, then introduces some modern geometries. These geometries include: hyperbolic geometry, elliptic geometry and Mobius geometry.这个论文的目的是用研究现代几何还有介绍克莱因的埃尔朗根纲领丮这个论文包 括用这个埃尔朗根纲领学习欧式几何的一个概述丬还介绍一些现代几何丮这些几何是为

双曲几何丬椭圆几何和莫比乌斯几何.

Kendal Wong (Farmington Hills MI)Mathematics and Psychology double majorExercise Intention and Motivation: Intrapersonal Relationships, Feedback, and Personality(advised by Jim Hartman, Mathematics and Gary Gillund, Psychology)Exercise is a common component of weight maintenance and weight loss strategies. In order to examine variables that can create effective health behavior change, this study surveyed 244 undergraduate female students with an online survey. Participants were randomly assigned to one of six conditions based on source (parent, peer, romantic partner) and feedback (positive, negative) and completed an online survey to examine the influence of source, feedback, and personality (BIS/BAS) on exercise intention and exercise motivation (internal and external). To analyze the data, three 3-way ANOVAs were conducted. Results indicate a significant main effect of personality on intention and internal motivation, a significant two-way interaction between source and feedback on exercise intention, and a significant three-way interaction between source, feedback, and personality on exercise intention. No other results were significant. The findings suggest that source, feedback, and personality all influence one’s exercise intention and motivation; however, future research should closer examine these differences to find larger effects.

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Senior Independent StudySpencer Hall (Mansfield OH)Computer Science and Mathematics double majorOptimizing Integer Arithmetic for Public Key Cryptography(advised by Drew Pasteur, Jim Hartman, Mathematics and Sofia Visa, Computer Science)Public key cryptography describes a family of systems that allow for secure communication between two parties in the presence of eavesdroppers. We

examine the history of cryptography and how the advent of public key cryptography irreversibly changed the science. The Diffie-Hellman key exchange protocol and the RSA cryptosystem and their applications are described in detail, as well as the mathematical theory behind them. The concept of radix representations and radix-sensitive arithmetic algorithms are explored. We create a simple arbitrary precision integer arithmetic system in Java and explore how arithmetic algorithm choices affect the performance of RSA implementations and RSA-related arithmetic functions.

Ruth Steinhour (Mason MI)Mathematics majorThe Truth About Lie Symmetries(advised by Jennifer Bowen and Robert Wooster, Mathematics)Differential equations are vitally important in numerous scientific fields. Oftentimes, they are quite challenging to solve. This Independent Study examines one method for solving differential equations. Norwegian mathematician Sophus Lie developed this method, which uses groups of symmetries, called Lie groups. These symmetries map one solution curve to another. They can be used to determine a canonical coordinate system for a given differential equation. Writing the differential equation in terms of a different coordinate system can make the equation simpler to solve. This I.S. explores techniques for finding a canonical coordinate system and using it to solve a given differential equation. Several examples are presented.

Samuel Swartz (Rocky River OH)Mathematics majorMy Ticket to Becoming an Athletic Director: An Analysis of the Graph Theory Behind Sports Scheduling

(advised by Pamela Pierce and Matt Moynihan, Mathematics)Through graph theory, sports scheduling can be achieved with more efficiency. The basic correlation between graph theory and a league of teams that uses a single round-robin tournament is the complete graph K2n where 2n represents the number of teams. Through factorization and oriented coloring, a scheduler can create a tournament where teams play each other once during a season and the Home-and-Away Pattern (HAP) displays this schedule through the profiles of every league member. Two rules presented by Swiss Mathematician Dominique de Werra guide the process of creating a canonical schedule. A canonical schedule will contain breaks and we look to minimize them while abiding by predetermined games in an HAP. Extended profiles and sequences provide us with the necessary information to achieve this goal. One can also create a schedule with 2n breaks or form a double round-robin tournament where all teams play each other twice.

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Senior Independent StudySarah Smith-Polderman (Cleveland Hts, OH)Mathematics majorLet’s Get in the Mood: An Exploration and Implementation of Data Mining Techniques to Predict Mood

Based on Musical Properties of Songs(advised by Jim Hartman, Mathematics)This thesis explores the possibility of predicting the mood a song will evoke in a person based on certain musical properties that the song exhibits. First, I introduce the topic of data mining and establish its significant relevance in this day and age. Next, I explore the several tasks that data mining can accomplish, and I identify classification and clustering as the two most relevant tasks for mood prediction based on musical properties of songs. Chapter 3 introduces in detail two specific classification techniques: Naive Bayes Classification and k-Nearest Neighbor Classification. Similarly, Chapter 4 introduces two specific clustering techniques: k-Means Clustering and k-Modes Clustering. Next, Chapter 5 implements these previously discussed classification and clustering techniques on a data set involving musical property combinations and mood, and makes conclusions about which musical property combinations will most likely evoke a happy, sad, calm, or agitated mood.

It can be concluded very generally that songs that are in major keys, have consonant harmonies, faster tempos, and firm rhythms will most likely evoke a happy mood in a person. Songs that are in minor keys, have slower tempos, and firm rhythms will probably evoke a sad mood in a person. Songs that are in major keys and have flowing rhythms tend to evoke a calm mood in a person. And last but not least, songs that are in minor keys, have dissonant harmonies, and firm rhythms will evoke an agitated mood in a person.

Matthew Lambert (Monroeville PA)Computer Science and Mathematics double majorAn Agent-based Model of Influenza Within a College Population(advised by Drew Pasteur, Mathematics and Sofia Visa, Computer Science)

Predicting the severity of a disease outbreak is an important task for health personnel and college administrators. Influenza is a disease that is commonly transmitted amongst college students. While traditional methods of mathematical prediction utilize systems of differential equations to predict results at the macro level that can be compared readily to historical disease data, agent-based models attempt to detail individual interactions on a daily basis. Agent-based models contain independent agents that follow a few given rules, so there is room for change and experimentation that would be difficult with the traditional mathematical models. Through these rules, one hopes to discover the underlying behavior of the system at hand. Specifically, how disease spreads throughout a population of these agents, given some number of initially infected agents. Once parameters are established so that normal runs produce results consistent with the mathematical models, the agent-based model can be modified, so different results can be seen from different behaviors. Here, we create an agent-based model of influenza with a population of roughly 2000 agents, and measure the effectiveness of two simple methods of lessening the severity of an outbreak.

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Senior Independent StudyBenn Snyder (West Salem OH)Computer Science majorComputer Vision: Object Recognition and Human-Computer Interaction(advised by Denise Byrnes, Computer Science)

This thesis focuses on computer vision and gesture-based human-computer interaction. In examining computer vision, the project covers existing computer vision systems, including OpenNI/NITE and libfreenect. It explores topics such as identifying humans and objects in scenes, recognizing gestures and context-specific movement, and more general scene analysis. The results of the computer vision work are applied to human-computer interaction. The project examines different types of user interfaces and the applicability of gesture-based interaction to those interfaces. One goal is a generic system for controlling user interfaces using a vision-based gesture system. The included software, consisting of three separate projects, covers both high-level HCI and low-level interaction with vision sensor device drivers. HighNI is a set of Java modules for OpenNI and NITE 1.5. It abstracts the existing Java classes to a higher level and provides some

skeleton examples for gesture callbacks. OpenNI2-FreenectDriver is a bridge driver that connects OpenNI2’s driver interface to libfreenect’s API. It allows OpenNI2 to use Kinect hardware on non-Windows platforms where Microsoft’s SDK is not available. FreeNUI is a new framework for natural user interaction, based around libfreenect and OpenCV. It is an experimental project that explores interface design and C++11 language features.

Emily Williams (Ann Arbor MI)Mathematics majorThe Golden Ratio(advised by Pamela Pierce, Mathematics)The golden ratio, or phi ( φ = 1.6180339887...), is a ratio that has

interested mathematicians as well as artists, philosophers, and many others for over 2,000 years. For some this interest stemmed from its vast mathematical properties, while others were more interested in its supposed aesthetic appeal. This Independent Study explores the

properties and appearances of the golden ratio throughout mathematics, the arts, and nature. It examines topics in mathematics including connections to the Fibonacci sequence, continued fractions, fractals, geometry, and Penrose tiling. In addition, it discusses other subjects in which the golden ratio is present including its history throughout art, architecture, and writing as well as looking at the more scientific appearances in quasicrystals and phyllotaxis.

Digital I.S.Competition

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Senior Independent StudyRutendo Ruzvidzo (Harare Zimbabwe)Mathematics and Economics double majorThe Gift that Keeps on Taking: Modelling the Impact of a Natural Resource Shock on an Economy(advised by John Ramsay, Mathematics and James Warner, Economics))Natural resource abundance can have a negative impact on the growth of an economy. An increase in natural resources leads to a movement of labor from the other sectors of the economy to the natural resource sector. However, once the increase

subsides, the labor cannot easily move from the resource sector. The cost of training and time make the movement back to the other sectors harder for the workers in the resource sector. This paper contributes to the literature by developing an economic model that explores the effects of an increase in the natural resource sector output on the overall economy. Labor is divided into skilled and unskilled labor. The model predicts that overall output suffers from a positive shock in the resource sector. Empirical analysis is performed using time series and Vector Autoregression models and data from Nigeria. Time series results reveal that natural resource abundance has had a negative impact on the growth of Nigeria. Results of the Vector Autoregression model show that a shock in the natural resource sector causes a decline in the real GDP in the first few time periods following the shock.

Joe Wilch (Albion MI)Mathematics and Geology double majorInsights into the tectonic evolution of the northern Snake Range metamorphic core complex from 40AR/39Ar thermochronologic results, northern Snake Range, Nevada(advised by Robert Wooster, Mathematics and Shelley Judge, Geology)Located in eastern Nevada, the Snake Range represents a classic example of a Cordilleran metamorphic core complex, where large-scale crustal extension has formed a detachment fault that separates highly strained and metamorphosed rocks in the footwall and normally faulted sedimentary rocks in the hanging wall. There is still considerable debate about the formation of metamorphic complexes. This study presents multiple diffusion domain modeling of K-feldspar 40Ar/39Ar thermochronologic results in order to better assess the tectonic evolution of the northern Snake Range. The thermal histories show a phase of rapid cooling occurring at 20 Ma near the center of the range and 16 Ma near the eastern flank. This paper also gives background on the mathematics of diffusion, discussing

Fourier series and the heat equation; the backbone to 40Ar/39Ar thermochronologic analyses. Previous thermochronologic studies in the area have incorporated irregular muscovite age spectra in their interpretations. Compositional data as well as analyses of step heating data of muscovite separates show that original muscovite samples may be a combination of at least two separate muscovites, each representing different tectonic stages. Therefore, drawing conclusions from these muscovite data should be approached with caution. 

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Faculty and StaffFrom left: Matt Moynihan, John Ramsay, Mary Jo Kreuzman, Jennifer Bowen, Ronda Kirsch, Drew Pasteur , Pam Pierce, Jim Hartman, Robert Wooster

New Math Faculty

Matthew MoynihanVisiting Assistant Professor of MathematicsBA St. Olaf 2007PhD Brandeis 2012

Robert WoosterAssistant Professor of MathematicsBS, MS, PhD Connecticut 1999, 2004, 2009

Professors Wooster and Moynihan were the first faculty members to ever participate in the “Humans vs Zombies” moderated tag game held on campus last spring.

Professor Wooster attended the MAA Ohio Sectional Meeting at Baldwin Wallace University as well as the MAA/AMA Joint Math Meeting in San Diego. At the Joint Meeting, he participated in a minicourse called “Teaching differential equations with modeling”. Dr. Wooster has a publication entitled “The Touchy-Feely Integral: Using Manipulatives to Teach the Basic Properties of Integration” to appear in the journal PRIMUS.

In 2012, Professor Moynihan completed his Ph.D. thesis in the area of combinatorics: “The Flag Descent Algebra and the Colored Eulerian Descent Algebra” and received his degree from Brandeis University. He gave a talk at Oberlin College entitled “Permutation Statistics and Algebras”. He also presented “The Colored Eulerian Descent Algebra” at the Joint MAA/AMS meeting in San Diego.

TeachingMath in Contemporary SocietyCalculus & Analytic Geometry I (2 sections)Problem Seminar (fall and spring semesters)Calculus with Algebra B (2 sections)Senior Independent Study (2 students)

TeachingCalculus & Analytic Geometry II (2 sections)Differential EquationsCalculus for Social SciencesProbability and Statistics ISenior Independent Study (2 students)

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Faculty and StaffOld Math/CS Faculty

John RamsayProfessor of MathematicsAssociate Dean of Experiential Learningat Wooster since 1987BA Berea 1980MS, PhD Wisconsin 1984, 1985

Pamela Pierce, ChairpersonProfessor of Mathematics

at Wooster since 1994BA Amherst 1985

MEd Massachusetts 1986MS, MPhil, PhD Syracuse 1988, 1992, 1994

Jim HartmanProfessor of Mathematics

at Wooster since 1981BA, Manchester 1975

MS, PhD Michigan State 1977, 1981

Dr. Hartman continues his heavy involvement in the Advanced Placement Program in calculus by presenting in numerous one day workshops, teaching AP Summer Institutes, and writing AP Calculus problems. He also helped develop a programmed one day workshop for calculus entitled A Day with an AP Reader. He was invited to attend and present at a two-day workshop in Las Vegas to pilot test this workshop. He then worked to revise the workshop based upon the pilot test and presented it at the AP National Conference.

Dr. Ramsay began his term as the Dean of Experiential Learning and claims he “wore a path” between Taylor Hall and Gault Library, where APEX (Advising, Planning, Experiential Learning) is located. His role as Dean is a natural extension of his many years of experience as Director of the AMRE program (Applied Mathematics and Research Experience). As a result, the 2013 AMRE program expanded to employ 34 students working on 12 different projects.

Denise ByrnesAssociate Professor of Computer Scienceat Wooster since 1991BS, MS, PhD Ohio State 1985, 1987, 1992

TeachingFirst Year Seminar “To Infinity and Beyond”Functions of a Complex VariableTutorial for Probability and Stats ICalculus and Analytic Geometry II (2 sections)Advanced Linear AlgebraSenior Independent Study (5 students)

TeachingMultivariate CalculusOperations ResearchSenior Independent Study (3 students)

TeachingLinear Algebra (2 sections)Real AnalysisSenior Independent Study (2 students)

TeachingComputer Programming II (Fall & Spring)Computer Programming II LabTutorialAlgorithmsSenior Independent Study (2 students)

TeachingTransition to Advanced MathematicsMultivariate Calculus (2 sections)

Mary Jo KreuzmanVisiting Assistant Professor of Mathematics

at Wooster since 1990BS Xavier 1980

MS, PhD Notre Dame 1982, 1985As the PI on an NSF grant, Professor Pierce has served as the coordinator of the S-STEM Scholars Program during its first year. Twelve students from the Departments of Mathematics, Computer Science, Physics and Chemistry were designated as S-STEM Scholars during 2012-2013, and Dr. Pierce has coordinated programming and mentoring with this group of outstanding students. She is hoping to expand the program over the next year.

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Faculty and StaffMath/CS Faculty, cont’d

The Knot Theory research students of Dr. Bowen and Dr. Ramsay had several publication submissions, one of which has been published and two more are under review. The published paper, “Klein Links and Braids” by David Freund ’13 and Sarah Smith-Polderman ’13, appeared in the Rose-Hulman Undergraduate Mathematics Journal.

Drew PasteurAssistant Professor of MathematicsAssistant Director of AMREat Wooster since 2008BS, MEd Florida 1996, 1997MS, PhD North Carolina 2004, 2008

TeachingCalculus with Algebra AFirst Year Seminar “A Town, a Team, and a Dream: High School Athletics and Small Town America”Math in Contemporary SocietyNumerical AnalysisResearch TutorialSenior Independent Study (6 students)

Jennifer BowenAssociate Professor of Mathematicsat Wooster since 2007BA Boston College 1998MS, PhD Virginia 2001, 2005

TeachingAbstract AlgebraCalculus & Analytic Geometry INumber TheorySenior Independent Study (3 students)

Sofia VisaAssistant Professor of Computer Scienceat Wooster since 2008BS Sibiu (Romania) 1998MS, PhD Cincinnati 2002, 2007

TeachingComputer Programming I (Fall & Spring)Computer Programming I Lab (Fall & Spring)Problem SeminarMachine IntelligenceSenior Independent Study (2 students)

Dr. Visa gave an Invited Plenary Talk on Bioinformatics at the 25th Midwest Artificial Intelligence and Cognitive Science Conference (MAICS) “Linking genes to tomato fruit morphology”, at Indiana University Southeast. She attended together with two undergraduate women students (Michelle Blackwood, Vanessa Logan) the Ohio Celebration of Women in Computing in Perrysville OH. The students presented posters of their research. She also attended and presented at the ISCS Imagination, Creativity, Design, Development Conference in Romania.

Samer KhasawnehVisiting Assistant Professor of Computer Scienceat Wooster 2012-2013BS Al-Yarmouk University (Jordan) 2007MS University of Akron 2007PhD Kent State 2012

TeachingPrinciples of Computer OrganizationFile and Database SystemsAnimation, Gaming & 3-D Virtual WorldsTheory of Computation tutorialComputer Programming I LabSoftware Engineering

Ronda KirschInstructor of Mathematics and Coordinator of The Math Centerat Wooster since 2011BS, MA Kent State 2008, 2010

TeachingCaclulus with Algebra A (2 sections)Basic Statistics

Ms. Kirsch attended the annual meeting of the National Council of Teachers of Mathematics in Denver. She also taught the mathematics portion of the Wooster Youngstown Early Intervention Program held at the College this past summer.

At the 2013 Joint Mathematics Meetings in San Diego, Drew Pasteur served as organizer of two sessions on sports-related research in the mathematical sciences. He also presented the results of a project that developed new metrics for assessing the skill of NFL field goal kickers, based on collaboration with Kyle Cunningham-Rhoads ’12.

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Honors and Awards given to Math/CS Majors

Latin HonorsSumma cum laude• Andrew Douglas Blaikie• David Richard Freund• Sarah Anne Smith-Polderman

Magna cum laude• Alice Catherine Webb• Kendal MacKenzie Wong

Cum laude• Rutendo Ruzvidzo• Ruth Anna Steinhour• Samuel Howard Swartz• Joseph Thomson Wilch

Andrew Blaikie ’13Joseph Smith ’15Amanda Steinhebel ’15Pam PierceSarah Smith-Polderman ’13Allie Webb ’13

The Wm. A. Galpin Award for General Excellence in College Work•Samuel SwartzThe David Leach Memorial Prize in Psychology•Kendal WongThe William H. Wilson Prize in Mathematics•David FreundThe Proctor and Gamble Economics Prize•Rutendo RuzvidzoThe Vivien Chan Prize in Interdisciplinary Sciences•Andrew Blaikie (also awarded the Compton Prize in Physics)The Foster Prize in Mathematics•Alice WebbThe Barbara Ward McGraw Memorial Prize•Sarah Smith-Polderman•Alice WebbThe Elizabeth Sidwell Wagner Prize in Mathematics & Computer Science•Sarah Smith-PoldermanThe Elias Compton Freshman Prize•Amanda Steinhebel ’15•Erin Andrews-Sharer ’15The Joseph Albertus Culler Prize in Physics•Joseph Smith ’15The Lyman C. Knight Prize in Mathematics and Physical Education•Erin Andrews-Sharer ’15

Phi Beta Kappa• Andrew Douglas Blaikie•David Richard Freund•Sarah Anne Smith-Polderman

Dr. Pierce poses proudly with some of our math majors at the spring recognition banquet.

S E Q U O I A C L U B

14 2012-2013

Speaker for the Class of 2013David Freund(Mathematics major)David will attend graduate school at Darthmouth.

David’s Commencement Address~Good morning everyone! As stated by Dumbledore, “I would like to say a few words And here they are: Nitwit! Blubber! Oddment! Tweak!” To the graduating seniors: don’t panic! This is our time to be recognized for the effort that we’ve put into our education over the past four years. We have friends and family who are here, or watching us via online streaming, simply to celebrate our academic accomplishments. This is supposed to be a happy occasion! We’re all aware of how much we’ve changed and grown since first arriving at the College of Wooster. So I would rather reflect on the freedom we’ve had during our time here.

Whatever the reason, we all ended up at Wooster. When I was first looking into colleges, I knew that I wanted a liberal arts education. To put it simply, I didn’t want to be forced down a specific academic path. However, other colleges have programs that enforce a strict liberal arts regiment, leaving little room for variation, and that’s not what I wanted either. At Wooster, the non-major course requirements account for only about a third of our classes (and that’s being generous). So it’s relatively easy to take on a second major or a double minor. While I did neither of these things, despite my attempts at a math/math double major, I’m appreciative of having had the option. And that’s what Wooster has truly been about for me – the freedom to build my education and college experience.

In a way, our education has been similar to making a sundae: we all have a similar foundation of course requirements or ice cream. And, naturally, the flavor of the ice cream depends on our major. From there, we can add toppings however we want – summer jobs, extracurricular activities, study abroad, sleep, or one of a thousand other toppings. Most importantly, no one sundae is essentially better than another: we have personal preferences and it doesn’t matter whether it’s a vanilla sundae with a drizzle of caramel or a complicated blend of flavors. ( continued->)

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The sundae I've created over the past four years has a lot of redundant flavors: I was a part of a math research group for two years, I assisted with an international math conference, I flew to another country to learn math, and I participated in math competitions. In case it wasn't clear, I love adding math on top of math.

Coming to Wooster, I knew that I wanted to major in math. When I was taking courses at Lakeland Community College, I had a wonderful professor, who is here supporting me today; who taught me calculus as well as even more advanced math. So I was prepared to jump right into the higher-level courses here. And I did: by the end of sophomore year, I had effectively decimated Wooster's supply of math classes. So a couple of faculty members wrote to the Budapest Semesters in Mathematics program on my behalf, stating “Please take him. We don't know what to do with him.” As a result, I found myself in Budapest, Hungary, and the math department had a year of peace.

My choice to study abroad was a combination of wanting to try something that terrified me conceptually, challenged me mathematically, and due to no small amount of prompting by my adviser. The me that arrived at the College four years ago would have laughed at the idea of studying abroad for an entire semester, let alone a year. But I couldn't pass up the opportunity to add extra ice cream to my sundae. What I learned while I was abroad is irreplaceable: how to accept being lost and confused and then making the best of it, how to wander through new cities and communicate without knowing the local language, and how to live independently.

However, studying abroad is only one option. As the graduating seniors are well aware, our time at Wooster has been about more than simply the courses we've taken. Instead, it's about the social experience of college – living in dorms or houses, either with roommates or independently; it's the new activities we've been engaged in, whether through a student-run organization or with a group of friends; and it's about our preparation for the rest of our lives – as scary as that may be – taking on internships, summer jobs, on-campus jobs, or simply discussing the future with our friends and professors. While it may be an obvious statement, we've all had a different experience at the College.

A lot of my favorite experiences have come from activities that I decided to try once and fell in love with, such as learning various forms of dance. Prior to freshman year, I had little-to-no dance experience. Now I feel comfortable with swing dance, Irish dance, and Highland dance.

For the past year, I've been one of the College's Highland dancers – performing with the Scot band and symphonic band. I wish I'd been a part of it sooner! Not only did it provide a healthy dose of exercise throughout the week, working my calves to the point that the legs of my pants didn't fit, but the Highland dancers created a wonderful community that I thoroughly enjoyed and I will sorely miss – they are one of the reasons this past year has been simply amazing.

In “Choices,” a song written by Mercedes Lackey, the opening verse goes “It's the choices that you make// and the ones that you don't// that define who you will be// what you are and what you see.” I feel that this aptly summarizes the Wooster experience – the College has provided opportunities and we chose what we wanted. As Gandalf said to Frodo, “All we have to decide is what to do with the time that is given us.” We've had four years here and we've made a lot of choices in that time and that has brought us here today.

Thank you for your attention.David Freund, Class of 2013

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Conference Presentationsby Math/CS Majors

The Classification of a Subset of Klein Links” (Danielle Shepherd ’14, Joseph Smith ’15, Sarah Smith-Polderman ’13, Jennifer Bowen, John Ramsay)

at Ohio Wesleyan University

Finding Regulatory Motifs in the Solanum Lycopersicum Genome, Michelle Blackwood ’14 and Sofia Visa

Purchaso Internship: Combining Web Development, Marketing and Social Media, Vanessa Logan ’14

Contests

Michele Blackwood ’14Professor VisaVanessa Logan ’14

MCM/ICM, an international contest in mathematical and scientific modelingAdvisor: Bob Wooster

Team 1: Amanda Steinhebel ’15, Joey Smith ’15 and Xiaomeng Ye ’15. This team tackled the problem of designing the Ultimate Brownie Pan. A team working on this problem had to develop a model that can be used to select the optimal shape of a brownie pan that maximizes(a) the number of pans that can fit in a rectangular oven,(b) an even distribution of heat, and

(c) a weighted combination of factors (a) and (b).In addition, they were to prepare a one to two page advertising sheet for the new Brownie Gourmet Magazine highlighting their design and results.Team 2: Hunter VanHorn ’14, Norman Chamusah ’14 and Tyler Poppenwimer ’14This team had to build a dynamic global network model of one aspect of Earth’s health. The model had to take into account how local factors affect global health. The team then had to identify factors that produce unhealthy global changes and make recommendations to prevent or limit these changes.

Both our teams earned Honorable Mention, which places them in the range of top 15% to top 46%. To put this in context, of the seven teams from Cornell, MIT, Harvard, and Princeton that attempted the brownie problem, Team 1 outperformed five of them!

Woo330 Team consisting of Andrew Hoover ’14, Manish Aryal ’14 and Trevor Pozderac ’14 placed 60th out of 160 teams. For a better reference, considering schools of Wooster’s size only, they placed 10th.

Mission Chips Team of Spencer Hall ’13, Matt Lambert ’13 and Benn Snyder ’13 also participated in the contest.

Elastic constants and material properties of novel shaped liquid crystals, Matt Schmitthenner ’13, P.K. Challa, J.T. Gleeson, Shila GargEntanglement and Relaxation of Liquid Crystal Shaped Granular Media, Theresa Albon ’13, Wilder Iglesias, Antal Jakli, and Shila Garg

American Physical Society

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Math/CS Colloquium Series9/13/12 Off-campus Research ExperiencesRuth Steinhour ’13 George Washington University Summer Program in MathematicsDavid Freund ’13 Budapest Semesters in Mathematics

9/27/12 Approaches to Shape Modeling and Image SegmentationSofia Visa, Assistant Professor of Computer Science, CoW

10/11/12 Generating Functions and the Two Stamp ProblemKevin Woods, Associate Professor of Mathematics, Oberlin College

11/8/12 The Least-Squares Property of the Lanczos DerivativePaul Fishback, Professor of Mathematics, Grand Valley State University

11/15/12 An Overview of Functional EncryptionSusan Hohenberger, Associate Research Professor of Computer Science, Johns Hopkins University

2/21/13 The Fundamental Theorem of Calculus: History, Intuition, Pedagogy, and ProofV. Frederick Rickey, Professor Emeritus of Mathematics, West PointDistinguished Teaching Professor of Mathematics Emeritus, Bowling Green

4/4/13 How Many Skittles? Making Your Estimate CountBrian D. Jones, Associate Professor of Mathematics, Kenyon College

4/25/13 Research by Underclass Students in Math/CSJai Kedia ’15 and Sebastian Weber ’15 Competitive Balance and Season Length in Sports LeaguesRyan Snyder ’14 and Kevin Dinh ’14 Setting Strategy in College VolleyballMichael Bush ’16 and Joseph Smith ’15 Calculating Klein Link Crossing Numbers with Braids

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18 2012-2013

Goodyear Tire Sales ForecastingStudent Researchers: Jai Kedia, Giang Nguyen, Ryan Snyder

Faculty Advisors: Dr. Pasteur and Dr. Wooster

The purpose of this project was to predict future quarterly industry tire sales. More specifically, there are three tire markets within the overall tire industry: consumer replacement, commercial replacement, and commercial original equipment. The interesting aspect of our project was the fact that we did not use historical tire sales to aid in our predictions, but rather only used economic indicators, such as the stock market, unemployment, and business inventories. The main challenge of this project was determining which economic factors were the optimal predictors for each

market. We utilized regression techniques to choose the best indicators and artificial neural networks to make the predictions.

Applied Mathematics & Research Experience

Undergraduate Research in Knot TheoryStudent Researchers: Joseph Smith, Michael Bush, Katelyn French

Faculty Advisors: Dr. Ramsay and Dr. Bowen

Our research in knot theory was funded by HHMI Undergraduate Science Research Program and The College of Wooster’s Sophomore Research Program. Our team continued the College’s past research of Klein links. We focused on looking at the invariant of linking number for Klein links, as well as for torus links. With the use of braid words, we discovered equations that can calculate the

linking numbers of Klein and torus links. We have written a paper on this subject, which we hope to publish. We have begun researching the P-colorability of Klein links and have found very interesting results. We hope to better understand these results in the future. Lastly, we have

investigated the effect of Klein bottle hole placement on the created Klein links. We plan on finishing the write up of our conclusions and submitting them for publication.

Agbioscience Marketing Research and Methodology FormationStudent Researchers: John Lanz, David Brew, Jeff MayFaculty Advisors: Peter Abramo (Center for Entrepreneurship, APEX)

The purpose of the BioHio AMRE team was to conduct market research within the bioscience industries and to understand what industries could best be served at BioHio’s research park. The team created an entirely new research methodology that focused on Political, Economical, Social, Technological (PEST) trends. The findings will be used to help guide BioHio’s expansion and construction of the new research park.

S E Q U O I A C L U B

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Analysis of Sports Scheduling for the North Coast Athletic ConferenceStudent Researchers: Cal Thomay, Paula Trautvetter, Mike Ries

Faculty Advisors: Dr. Pasteur and Dr. Ramsay

The goal of the project was to analyze the current methods used by the North Coast Athletic Conference

in scheduling athletic contests in various sports. The primary objectives in scheduling are to minimize travel costs for NCAC member institutions and to minimize missed class times by student athletes. This optimization is subject to many sport-specific constraints. The team created a tool

that will enable the NCAC to schedule athletic contests

more efficiently as well as provide cost analysis of travel and missed class time to be used for comparison amongst different scheduling formats.

Applied Mathematics & Research Experience

Using Lasers to Cut Plastic FilmStudent Researchers: Deepika Sundarraman and Elliot Wainwright

Faculty Advisors: Dr. Pasteur and Dr. Lehman (Physics)

In this project students served as consultants for Kent Displays Incorporated in an attempt to help them better understand a CO2 laser cutting process of their polyethylene terephthalate (PET) film used to make Boogie Boards. Using Matlab, Excel, Mathematica, and other computational software, a model of the heat transfer process, including ablation of the material due to excessive energy from the laser, was written with the flexibility to change certain laser and material parameters and see the effect of the cutting. Welding strength of the heated material was also considered. The project involved knowledge of the physical and thermal processes, of numerical analysis, and the ability to quickly learn about a complicated process and computational techniques.

Competitive Intelligence: Analyzing Agency DataStudent Researchers: Daniel Miller, Xiangyu Li, Anqi Huang

Faculty Advisors: Dr. Pierce and Dr. Bowen

The purpose of this AMRE project was to analyze data collected from independent insurance agents to determine what characteristics or attributes determine whether a car insurance policy will be won or lost by Progressive Insurance. This analysis was done on comparisons between Progressive and six other insurance carriers.

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Developing an Assessment Framework for APEXStudent Researchers: Adam Donnelly, Varun Bhandari, Sebastian Weber

Faculty Advisors: Dr. Byrnes and Dr. Johnson (Communication)

Our project was a continuation of the 2011 AMRE project: College of Wooster Assessment, and related to the 2012 AMRE project: Experiential Learning Assessment. We were tasked with developing a framework for the assessment of the newly established center for Advising, Planning, and Experiential Learning (APEX). Our AMRE project was to renovate current assessment strategies that exist in the centers within APEX, and create a plan to incorporate the whole of APEX. Our tasks consisted of: 1) researching assessments implemented in organizations similar to APEX; 2) developing an understanding of current assessment structures at the Registrar, Learning Center, Advising Center, Career Planning, Experiential

Learning, and Entrepreneurship; 3) working with an outside expert to prepare and implement an assessment workshop; 4) creating an APEX-wide mission, goal, and measures. This assessment plan will help APEX in increasing its effectiveness and assistance to students.

Applied Mathematics & Research Experience

OARDC Molecular and Cellular Imaging Center: Integrating R ModulesStudent Researchers: Doug Code, Liang Cheng, Dagmawi Zegeye

Faculty Advisors: Dr. Byrnes

R is a data analysis programming language widely used by statisticians. Integrating R modules directly into Galaxy (an application used by OARDC biologists) will simplify data analysis, making the process accessible to a larger audience.While R offers a broad range of functionality, the significant learning curve associated with R, particularly for individuals without programming backgrounds, can intimidate new users. The goal of this project is to build a graphical user interface that gives users with little to no R experience quick and easy access to the ggplot2 graphics package.

The application uses RStudio’s Shiny package, which allows for the rapid development of R web applications.Shiny drastically decreases the amount of code and time needed to implement new features and build interface elements, making our R application easily maintainable and extendable.

Finding transcription factor binding sites in the Solanum Lycopersicum genomeStudent Researchers: Michelle Blackwood, Hunter Van Horn

Faculty Advisors: Dr. Visa

We computationally identify potential transcription factor binding sites in Solanum Lycopersicum genome. For such an exhaustive search, an algorithm for Hadoop (a platform that supports distributed processing of large datasets across clusters of servers) is designed and implemented. Several potential motifs are identified in four different clusters of genes of interest. In addition, the Arabidopsis orthologs of the genes having these potential motifs are mapped into regulatory and co-expressed networks of genes.

S E Q U O I A C L U B

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Analysis of Recent Trends in Children Services CasesStudent Researchers: Annie Godonoga, Sheharyar Khushnood, Rebecca Wardrop, Andreja Siliunas

Faculty Advisors: Dr. Burnell (Economics)

The goal of this project was to identify some possible factors that led to the increase in the number of children in the custody of Wayne County Children Services. The AMRE team approached this project in two ways. The first was a comparison between Wayne County and the other 87 counties in Ohio in 2007 and 2011. The purpose of this approach was to determine whether Wayne County was behaving differently than the state in some way and to analyze possible factors that could affect custody numbers on a statewide level.

The second approach was an internal assessment of the classification of cases in Wayne County comparing 2008 and 2012. The team read over 200 individual cases and extracted variables of interest. Through this approach, the team was able to identify case characteristics that were more likely to lead to custody. The two years were then compared to determine any changes in the important characteristics. Together, these two approaches created a comprehensive picture of possible factors that led to the increase in custody numbers.

Applied Mathematics & Research Experience

Market Segmentation Analysis of MIS Business UnitStudent Researchers: Jola Pham, Thanh Dang, Julia Land

Faculty Advisors: Dr. Ramsay and Dr. Verdon (Economics)

The AMRE team performed an analysis of the manufacturing operations and product pricing data of Will-Burt’s MIS Business Unit. The project scope was to analyze data to determine “where Will-Burt loses money.” The team made recommendations to Will-Burt as to which items are least profitable and thus prime targets for focus and reassessment.

Performance Analysis of MPO and Related Optimization ToolsStudent Researchers: Andrew Mueller, Andrew Hoover, Torger Miller

Faculty Advisors: Dr. Visa and Dr. Wooster

The MPO Goodyear project entailed researching ways to speed up Goodyear’s Multi-Performance Optimization (MPO) software. The MPO tool allows its user to specify particular tire performance metrics and then an optimization is performed to produce an “optimal” tire. The team developed a multithreaded version of the

MPO which achieves an average of 35% speedup. In addition to the multithreaded MPO tool, the team also developed ideas for future improvements on the MPO tool.

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22 2012-2013

Math/CS wins again...The annual bowling contest between Math/CS and Physics is a long standing tradition. In fact, there was no room left on the giant slide rule trophy to post the results of Taylor Bowl XXIV. But fear not, we have devised an extension to the slide rule that will allow the Taylor Bowl tradition to continue for at least another decade! Congrats to Professor Moynihan who bowled the high score of 160. He’s a beast!

Taylor Bowl XXIV

What our grads do with a degree in Math or CS...Divya Thadani ’99(Math & International Relations)Divya is senior director of strategy and new business development at J.M. Huber Corporation, NYC.

Wenyuan Wu ’10(Math & Economics)Wen is an actuarial analyst for Liberty Mutual Insurance in Boston MA.

Steve Elmore ’07(Math)

Steve teaches math and coaches football at San Manuel HS in

Tucson AZ.

Bryan Prusha ’98(Computer Science & Physics)Bryan is an iOS software engineer for Apple Computer.

Itai Njanji ’11(Math & Computer Science)Itai has accepted a position in Redmond, WA at Microsoft’s Bing search engine unit.

Jeff Lyman ‘10(Math)

Jeff is a commercial loans banker at

Huntington National Bank in Columbus

OH.

Denise Koessler ’08(Math)Denise is a Ph.D. candidate in computer science at the University of Tennessee.

Mike Liberatore ’10(Computer Science)Mike is a program engineer for Turning Technologies in Youngstown OH.

Vikas Malhotra ’98(Math & Economics)Vikas is the Director of HR Metrics and Measurement for AIG in NYC.

Elizabeth Stroud ’08(Math)Elizabeth is a business analyst for FirstEnergy Corp. in Akron OH.

Adam Hanley ’06(Math)

Adam is an attorney at the law firm of

Frost Brown Todd in Columbus OH.