What’s ν?News from the Department of Mathematics and Computer Science

Mount St. Mary’s UniversityEmmitsburg, MD 21727

Issue No. 11 June 2015

Contents

What I Do . . . . . . . . . . . . . . . . . 2Department Activities and Awards . . 3The 2015 COMAP Competition . . . . 6A History of Computer Science at

Mount Saint Mary’s, Part 2 . . . 6Reflections on REUs . . . . . . . . . . . 9MAA Student Chapter Report . . . . . 12ACM Student Chapter Report . . . . . 12

PME and UPE Induction . . . . . . . . 13CS in 5 . . . . . . . . . . . . . . . . . . . 15Mount Math Madness . . . . . . . . . . 16Smalltalk . . . . . . . . . . . . . . . . . 17Math in 5 . . . . . . . . . . . . . . . . . 18An Interview with Dr. Petrelli . . . . . 222015 Seniors . . . . . . . . . . . . . . . 24

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What I Do By Jennifer Moczulski, Class of 2005

It’s hard to believe in just a month I’ll be celebrating my 10 year reunion with the Mount. It wasMount Saint Mary’s College when I first attended, but that’s not the only thing that’s changedduring my time away. My husband Dave (class ’05) and I recently visited the Mount and wereexcited to see the enhancements made on campus since we last walked those paths, and alsodelighted to see some familiar scenes and faces. I, too, have accomplished much since graduatingin 2005, and the Mount guided me to the path I’m on today.

It started back in my sophomore year. Professor Weiss presented our Comp Sci class with ascholarship opportunity, which some students and I seized. I was working as a student super-visor at the Information Technology HelpDesk at the time, raising tuition and spending money,so receiving a scholarship would be a great benefit. The scholarship was awarded by the In-dependent College Fund of Maryland as part of the National Security Scholarship Program. Inaddition to the scholarship, the program afforded each recipient an internship with one of sev-eral Department of Defense contractors. I was one of just a few that year selected to receive thisaward, and I had the unique choice of picking the contractor with which to intern. I selected TheBoeing Company. During my internships and later as a full-time employee, I worked for Boeingunder their National Security Programs division. At the time, they were particularly interestedin graduates with technical backgrounds in math, computer science and information technologyto aid and protect our nation. I knew I would be doing something important and I knew myeducational background and experience would help me accomplish that.

Over ten years later I am still with Boeing, protecting our nation. As a systems engineer, with afocus on system design and integration, I am able to leverage both my programming knowledgeand my IT experience in this role. My team and I evaluate requirements from the customer andtranslate those requirements into a cost-effective, integrated solution. We stage systems in a lab,integrate those systems with other systems, test and evaluate, deploy the systems worldwide,train operators and system administrators on the system, and finally provide sustainment supportfor all fielded systems.

I work with a variety of equipment including Dell servers, NetApp and DataDomain storageappliances, and Cisco and Brocade network equipment. Our primary platform is Linux (bothRedHat and CentOS). Recently we’ve been developing virtual solutions utilizing VMware/v-Sphere to reduce power, space, and cooling requirements and minimize procurement costs. Myteam is also responsible for the development environment of application software we install onthese systems. We manage the build servers, GIT repositories, track bugs in JIRA, monitor RFCs(request for change), and take part in the weekly CCB (configuration control board) meetings.We then build and package the software into RPMs and customize bash scripts for easy systeminstallation and upgrades. Once the application is installed on our system, we integrate it withother custom-developed software as well as commercial software. We set up dataflow paths andcontinuously monitor that information is reaching its end target databases.

During my time at Boeing, I’ve been project lead on copious system deployments, which haveallowed me the fortunate opportunity to travel the world. In an industry where there is no publicreward or recognition, I find intrinsic value in being able to see the world at such a young point inmy life. More often than not, Dave joins me and we share in those travel experiences together.I’m also constantly learning and honing my skills. Each project and deployment brings newchallenges, keeping me interested and yearning to continue in this field. While I can’t alwaysshow family and friends what I’ve accomplished during my career, I do have the satisfaction inknowing what I do matters and I have a sense of pride in the work I perform.

Outside of work, I keep equally as busy. Not long after graduating, Dave and I bought a town-home in Maryland and married in ’06. We now live in a beautiful single family home with alarge yard for our two-year-old husky, Rory. I obtained my MBA from UMUC in 2010. I keep a

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Jen and Rory

very active lifestyle by participating in several rec sports leagues with my husband and friends,my favorites being football, softball, and volleyball. In the winter we are avid snowboardersand take a trip out West every spring when the powder is perfect. We both enjoy going for runsand hikes with Rory, and of course he vacations with us! Rory and I also compete nationally in asport called K9 Nose Work, from NACSW (National Association of Canine Scent Work). If you’veever seen a drug or bomb sniffing dog then you get the idea behind Nose Work, except the dogsare trained to sniff and alert on specific scents (birch, anise and clove). Teams compete in trialshosted around the country. Rory and I have titled at the NW1 level with first place in one of theelements. We’re anxiously waiting to compete in an NW2 trial in May.

In addition to being very active, we enjoy unwinding by playing music. I took percussion lessonsat the Mount and since continued to progress my skills on the set. I can also add guitar and bassto my repertoire. Dave also plays several instruments, so he and I set up an area in the housewhere we have friends over every few months to jam. Also in my spare time you can find meat an Orioles or Ravens game. We’re season ticket holders and never miss a home game. Ourfavorite sports fan memory was going to Superbowl XLVII in New Orleans.

That’s me a nutshell. If I were to sum up my experiences and offer a piece of advice, it wouldbe to make your own path in life. Let your experiences shape you but not define you. Mostimportantly, find joy and fun in everything you do.

Tim Burke, Cameron Dixon, Christian Winkle, Joe Appleton, and Isaac Zappe at the SPARC Festival

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Department Activities and Awards By Brian Heinold

Yet another school year has come and gone. Here’s a recap of this year’s activities. We startedthe year with our annual picnic in September. In early November, Alan Jamieson of St. Mary’sCollege of Maryland gave a talk entitled Dijkstra’s Elegant Note. Later in the month, Prof. Weiss,Dr. Heinold, and several CS students went to the CCSC Eastern Regional Conference at YorkCollege.

In January, Michelle Rose presented a talk entitled The Unit Bar Visibility Number of Graphs atthe Joint Math Meetings in San Antonio, based on her REU research. In February, we had fourteams compete in the COMAP competition. One of the teams was designated as a MeritoriousWinner and another was an Honorable Mention. See the article later in this newsletter for moreinformation. In April, Isaac Zappe won our annual programming competition. We also held ourannual PME/UPE induction in April. See the article on it later in this newsletter.

The department once again was well represented at the SPARC Festival. Michelle Rose presentedher honors project, Cheating at Cards: Using the Mathematics of Game Theory to Master the CardGame 31. Here’s a brief summary: In the game 31, players try to accumulate cards of the samesuit with hands of three cards. When a player thinks they have a good enough hand to beat atleast one other player, that player knocks. Everyone else gets one more turn, and then playerscompare hands. The player with lowest hand loses a quarter. Michelle used mathematics andcomputer simulations to help players decide on an optimal knocking strategy.

Derrick Kaas, Emily Gipe, Justin Miskiel, and Josh Testa at the SPARC Festival

Macon Calton, Jenna Glassman, Michelle Rose, and John Schultz presented their senior projectsat the festival. Macon’s project is an expense organizer for iOS that allows users to keep track oftheir receipts and expenses. Jenna’s project is a testing program for a certain type of psychologyexperiment. Michelle Rose’s project is an Android app that allows users to store info about themedications they own and get recommendations based on symptoms. John Schultz’s project isa program for Veritas advisors to help keep track of their advisees’ classes and needs.

Alex Wakuluk presented a poster, Comparing Sorting Algorithms. Christian Winkle, Isaac Zappe,and Joe Appleton delivered lightning talks. Christian’s talk was A Random Talk: EvaluatingTechniques to Generate Pseudorandom Numbers Using Math, Science, and a Little Creativity. Issac’swas Not So Random Number Generators: The Weakness of Linear Congruential Generators. Joe’stalk, Computer or Human? – Programming a Semi-Intelligent Chatbot, won the award for bestlightning talk from the School of Natural Science and Mathematics.

At Honors Convocation, Michelle Rose was awarded the McCullough Memorial Prize this year forexcellence in mathematics. Alex Van Neste received the McGraw Memorial Prize for maintaining

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Alex Wakuluk with his SPARC Festival poster

the highest average in mathematics. Freshman Molly Ousbourne shared the Monsignor Hugh J.Phillips Prize, given to the member of the freshman class who has attained the highest average.

On May 9, we graduated 9 students. See the article at the end of this newsletter for more onour graduates. Two of our graduates, Brenna Edmonds and Camille Sanchez will be attendinggraduate school next year. Brenna will be in the Mount’s MAT program. Camille will be pursuinga degree in education at Johns Hopkins University.

John Schultz presenting at the SPARC Festival

This year we offered Computer Security for the first time. There were 18 students in the class.We also graduated our first Cyber Security minors – Macon Carlton and Joe Lyons.

Joe Appleton is one of six Mount students to be studying at the University of Cambridge thissummer. He will be studying in the International Security and Intelligence program, led by theone-time head of the MI6.

Finally, On May 16, Dr. Butler gave birth to her fourth child, Eleanor “Ellie” Jane Butler. Elliewas 7lbs 4 oz. and 19 inches.

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The 2015 COMAP Competition By Brian Heinold

This year we had four teams compete in the COMAP math modeling competition. Problem Aasked students to assume that a cure for Ebola has been found. They had to build a model toget the medicine to where it is is needed in order to efficiently eradicate the disease. Problem Basked students to build a model for searching for planes that have gone down in the ocean. Allfour teams chose problem A.

Team 1 consisted of Emily Luetkemeyer, Matt Martin, and Jake Tate. Team 2 consisted of JoeAppleton, Carmen Morales, and Nick Navarro. Team 3 consisted of Rooshan Matih. Team 4consisted of Sasanthi Fernando, Kelly Weiss, and Katherine Wu. Team 4 was declared an Honor-able Mention, putting them into the top 40% of all teams on problem A. Team 2 was declared aMeritorious Winner. Of the 5000+ teams that attempted the problem, there were 10 Outstand-ing Winners, 12 Finalist Winners, and 641 Meritorious Winners. So this puts the team of Joe,Carmen, and Nick into a pretty exclusive group. I asked Joe for a few thoughts on the contest.Here’s what he had to say:

Meritorious COMAP team: Joe Appleton, Carmen Morales, Nick Navarro

“In this year’s COMAP competition the problems were extremely interesting. I likedhow both problems required participants to model real-world situations that we hadbeen seeing on the news for the past couple months. In the end, we chose to modelthe distribution of a hypothetical Ebola medicine because it seemed to be the moreinteresting of the two.

“Actually finding an approach to this problem was the most difficult aspect of thecompetition. As we decided how to build our model, we gained an incredibleamount of knowledge about the virus itself as well as epidemiology in general. WhenI came across the program we ended up using in our solution, I was floored. STEM(the Spatiotemporal Epidemiological Modeler) was a godsend to us. We used thisprogram to build our model and efficiently test every single variable that went intoour experiments.

“I did not expect us to get a Meritorious Winner designation, and when I heard thatwe did, I was absolutely ecstatic. I was hoping for an Honorable Mention at best,but I suppose the all-nighter I pulled from Sunday into Monday was actually worthit in the end. Nick, Carmen, and I now have a great idea of what it takes to placethis highly among the various teams. In order to do as well (if not better) in nextyear’s competition, we will have to redouble our efforts. I better start stocking upon coffee now.”

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Dr. Portier, Prof. Weiss, Dr. Heinold, and Macon Carlton at graduation

A History of Computer Science at Mount Saint Mary’s, Part 2 ByBill O’Toole

At the conclusion of Part 1 of this history, published in 2005, I promised to add stories about im-portant people and developments over the 48-year span of computer science at the Mount. I willtreat the Plato IV system and a special friend of the institution and members of our department,Dr. John Vincent (J.V.) Atanasoff.

Sometime in the late 1970s, we had the opportunity to take advantage of a National ScienceFoundation (NSF) grant to install and administer two Plato IV terminals from Control DataCorporation. These terminals had square, high-resolution, monochrome, orange gas-displayscreens and were connected by a dedicated phone line to a CDC super-computer at the Universityof Illinois in Champagne-Urbana. We got a good deal financially because our connection piggy-backed on a similar line for a larger Plato IV installation at the University of Delaware. It helpsto be in the right place at the right time. The terminals ran an extensive array of programswith applications in biology, chemistry, economics, art, music, and many other fields, as wellas math and computer science. I recall one simulation in which the student selected a matingpair of houseflies and specified any of several characteristics for each fly. The system wouldthen generate as many offspring as one wished to see, complete with images, gender, and othercharacteristics. Powerful stuff! And it was fast. The terminals were installed in the computer labon the first floor of the Science Building. Word spread quickly and both terminals were occupiedmuch of the day and often into the night.

Local programs could be written in the Plato IV native language and saved to the system wherethey could be made available to users at other installations, which were located in multiplecountries around the globe. The terminals had speech and music capabilities; the screens weretouch-sensitive so one could just point to make a selection. The Plato series (I through V) werequite advanced for their time, and many of their features found their way into later computersystems.

A very special friend of Mount Saint Mary’s

In January 1974 I picked up a Sunday edition of The Washington Post. The Outlook sectioncontained a three-page (including the cover page) article about the “inventor” of the computer.

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I thought, “Wait a minute! Everybody always said that the electronic digital computer wasinvented by Drs. John Mauchly and J. Presper Eckert at the University of Pennsylvania in 1946.”But here was a fascinating story that discounted that earlier “knowledge.” I read the articleand checked out the several photographs in the section, including one of an electronic digitalcomputer at Iowa State College in 1942. The large photograph on the cover of the section wascaptioned, “Shown is Dr. John Vincent Atanasoff in his workshop at his home near Frederick,MD.”

Here is a brief summary of the story of J.V. Atanasoff. You may recognize the name as Bulgarian.In fact, J.V.’s grandfather was a Bulgarian patriot who died defending his country against theinvading Turks. A famous work of art shows this patriot on his horse being shot and killedwhile handing off his son, J.V.’s father, to rescuers. J.V.’s father and his family immigrated tothe United States. In 1903, J.V. was born in Hamilton, NY. The family moved to Florida whereJ.V. earned a BS in electrical engineering at the University of Florida. Other degrees were amaster’s in mathematics (Iowa State College, 1926) and a PhD in theoretical physics (Universityof Wisconsin, Madison, 1930). He then accepted a position teaching math and physics at IowaState College, now Iowa State University.

Because of the drudgery involved in solving large systems of differential equations, J.V. beganto think of ways the process might be automated. He started to design an electronic digitaldevice to automate this process. He tells the story of working in his lab one winter night andbeing frustrated about a particular problem he was having with his circuitry. Since the area wasin a “dry” county, he got in his car and drove over to Illinois, stopping at a bar and having afew drinks. He was inspired and drew a circuit diagram on a cocktail napkin. He was fondof saying that Mauchly and Eckert would have you believe that the computer was born in aPhiladelphia ice cream and soda shop, but it was really born in a bar! J.V. received a grant for$650 with which he enlisted the help of his graduate student, Clifford Berry. Together they builtthe Atanasoff-Berry Computer in the basement of the physics building beginning in 1937. Itbecame operational in May 1942 – the month I was born!

Fast forward to the newspaper article in 1974. It told about lawsuits among several giant com-puter companies that began back in the 1950s. Essentially, multiple manufacturers were refus-ing to pay licensing fees for certain patented devices and processes. The patents were owned bySperry Rand, successors to the Mauchly and Eckert Computer Company, builders of the ENIAC(Electronic Numeric Integrator and Automatic Calculator) at the University of Pennsylvania. J.V.testified at several court hearings over the years, describing how Mauchly was his house guestin Ames, Iowa multiple times in the 1930s and had full access to J.V.’s papers and work. InOctober 1973, Judge Earl Larson issued his ruling, saying in part, “Eckert and Mauchly did notthemselves first invent the automatic electronic digital computer, but instead derived that sub-ject matter from one Dr. John Vincent Atanasoff.” The ENIAC patents were invalidated. Thenews was buried at the time because of that little burglary at Watergate, which happened thesame day as the court ruling.

I dug out the phone directory and found J.V.’s listing. I introduced myself and asked him if hewould like to come to campus to speak to my computer science class about his pioneering work.He said he’d be delighted, that he was preparing to go on a multiple-nation speaking tour, andthat he could try out his speech in my class! We scheduled his appearance in the auditoriumof the science building one evening. It turned into a media event. There were people standingin the back and sitting in every available spot on the floor and steps. The local press was therewith photographers and reporters. I taped the talk, which went on for over 90 minutes. I hadbrought only a C-90 cassette, figuring that would be more than adequate. But after 100 minutesof talking, J.V. took questions for another 45 minutes! This was the beginning of a friendship thatlasted until he died. He began a special relationship with the Mount, making several appearancesover 18 years, including the celebration of his 85th birthday in 1988, covered on campus by theBulgarian press and television, and culminating in the Mount awarding him an honorary degreein 1992.

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J.V. and Alice became good friends of Dick and Lee Borst before Dick retired from the Mount. Thesix of us often socialized together, and the Atanasoff family treated the four of us as if we weremembers of their family. We frequently joined them for family picnics and restaurant meals.More than once, the phone rang in the office that Dick and I shared on first-floor science, and itwas J.V. calling to ask if Dick or I could go to his house and fix his personal computer. Usuallywe both went. After one of these repair trips, Dick commented, “Now there’s an entry for one’srésumé: Performed computer repair for the inventor of the computer!”

While being interviewed by lawyers for Honeywell in the cluster of lawsuits, J.V. was asked howhe could remain quiet all that time about patents, licensing, the ENIAC, Mauchly and Eckert,and the computer industry in general. Didn’t he feel cheated? He said in reply that he had hada good life and was pleased with his work. He also said that he was well-off financially, evenwithout the fortune that patents on the ABC would have brought. (Officials at Iowa State weresupposed to file for patents for the ABC when J.V. went to Washington during World War II,but the folders got lost in the back of a filing cabinet.) He continued, saying that his associate,Clifford Berry, did not remain silent, protesting the theft of their ideas. Berry was found deadin a flop-house on Coney Island in 1963, with a plastic bag over his head. The coroner ruled ita suicide! J.V. hired a private investigator who reported that definitely foul play was involved.Since hundreds of millions of dollars were involved, this came as no surprise.

J.V.’s pioneering work on the ABC involved four important principles that affected all later com-puter designs: 1) The use of the binary (base 2) number system for internal logic and calcu-lations. (Mauchly and Eckert rejected this idea for ENIAC, using instead a two-tier bi-quinarysystem, with a two-way switch followed in a serial line with a five-position switch to generate10 digits, 0 through 9. That was definitely a dead end.) 2) The use of electronic switches (thenvacuum tubes, later transistors and integrated circuits) for flow control and logic. 3) Rotatingdrums, incorporating capacitor memory elements, which regenerated the contents each revolu-tion. The read and write heads for the drums were part of this memory jogging process. Thejogging capacitor memory elements on the rotating drums were binary and their principle is usedin all DRAM memory chips today. 4) The separation of computation and memory components. Acriticism of the ABC was that it was a special-purpose computer and not programmable, a weak-ness of several early pioneering machines. On the other hand, ENIAC was a general-purpose,programmable computer.

There are many other stories that I can relate about J.V. and his pioneering work, probablyenough to fill this newsletter completely for more than one issue. But J.V. is one of those very im-portant Mount “alums” (Doctorate honoris causa, 1992) who have greatly influenced our world.Who has had greater impact on the way we live than the inventor of the computer?

Bill O’TooleProfessor emeritus(MSM class of 1966, taught math and computer science at MSM from 1966 to 2007.)

Reflections on REUs By Michelle Rose, Camille Sanchez, and Alex Van Neste

This past summer we had three juniors participate in REUs. We asked them for brief reflectionson their experiences.

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UPE members (left to right): Dr. Portier, Joey Naylor, Macon Carlton, Dr. Heinold, Michelle Rose, Tony Weaver, Dr. McGovern,Isaac Zappe, Christina Weaver, Joe Lesniewski, Amanda Malmstrom, Alex Wakuluk, Christian Winkle, Prof. Weiss, Prof.O’Toole

Michelle Rose

This summer I spent 8 weeks at a Research Experience for Undergraduates at the RochesterInstitute of Technology. The program consisted of 10 undergrads from a variety of colleges.We were broken into 5 pairs and each pair worked with an advisor on a certain task. Some ofthe other groups looked into the effects of concussions on neurological connections, combiningexisting methods to more accurately model heartbeats, and predicting groups based on graphconnectivity. My partner Emily Gaub and I worked with Dr. Paul Wenger on a topic of graphtheory involving bar visibility graphs. This is where a graph is represented by horizontal bars on aplane, where the bars represent the vertices in the graph and a vertical line of sight between twobars corresponds to an edge between those two vertices in the graph. We researched previouswork on bar visibility graphs, bar visibility numbers (the number of bars needed for each vertexin order to represent all needed edges), and unit bar visibility graphs (where the bars must bethe same unit length). Using this information, we created the idea of unit bar visibility numbers.This is the number of unit bars that each vertex needs such that the unit bar representation ofthe graph includes all of the edges in the original graph. For instance, a complete graph on 3vertices can easily be represented by one unit bar per vertex so the unit bar number is 1. Acomplete graph on 4 vertices requires one of the vertices to be represented with a second unitbar, and therefore the unit bar number is 2. Through quite a bit a work and the developmentof an algorithm, we were able to find the equations for the unit bar number of several types ofgraphs, such as complete, planar, and using an algorithm we developed, trees. In January ofthis year, each of the groups from the REU presented our work at the Joint Math Meetings inSan Antonio, Texas.

Camille Sanchez

This past summer, I had the opportunity to participate in a research experience for undergradu-ates (REU) at North Carolina State University. The program, with projects focusing on Appliedand Industrial Mathematics, lasted for nine weeks. This was a rather large REU, with over 40students and 14 different research projects. My project group consisted of my mentor Dr. Haider,a graduate assistant and two other undergraduates.

The title of our project was “Computational Modeling for Optical Coherence Tomography Imag-ining of the Human Eye.” Optical coherence tomography (OCT) is a medical imaging techniquethat utilizes light waves to produce images of internal tissues in the eye. We used data from theseOCT images to compute curvature maps of the human cornea. We quickly realized that curva-ture computation is extremely sensitive to small errors in surface measurements; therefore, our

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Coleman Myron and Josh de Aragao at the Math Seminar poster session

overall goal of the summer was to develop theoretical cornea models to validate the curvaturemapping algorithms and analyze the propagation of certain types of errors. We sampled ourmodels on a hexapolar grid to simulate data from an OCT scanner. We were also introduced toZernike polynomials, used by ophthalmologists in their field of study. Errors in the surface rep-resentation and additional noise in the OCT image data were also considered. We used MATLABto produce curvature graphs as well as displacement error plots.

By the end of the program my group concluded which Zernike polynomials most affected thecurvature mappings, as well what degrees of error were associated with particular coefficients.This REU introduced me to several different aspects of mathematics. It was nice to apply what Ihave learned in the classroom to real-world applications. Although the computer programmingaspect was a challenge, I learned so much in only nine weeks. On a biweekly basis we werealso given the opportunity to present what we have researched to the rest of the NC State REUgroups. This allowed us to hear about the other groups’ research projects, as well as practiceour presentation skills. It was a great experience that I would strongly recommend to otherundergraduates. I was able to advance my math skills as well as network with other professors,mentors and undergraduates.

Left: Issac Zappe at the Math Seminar poster session. Right: Alex Van Neste creating minimal surfaces with soap films afterDr. Hook’s smalltalk on that topic.

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Alex Van Neste

During the summer before my senior year I was selected as one of 13 undergraduates to partic-ipate in the Carnegie Mellon Summer Undergraduate Applied Mathematics Institute. This pro-gram lasted 8 weeks and consisted of conducting research while also attending class. I chose,from 4 other projects, to design a trinomial model that could be used in mathematical finance.This project coincided with the the courses very well since we took a Maple programming classand an introduction to mathematical finance.

I learned how to effectively program using Maple, which my partner and I then used for ourresearch. We wrote a program that would take in real-world stock data from Yahoo Finance andthen would utilize our trinomial model to compute prices for call options. The purpose of ourmodel was to be able to compare the computed values to real-world values in order to determineany possible mispriced options to be able to invest in.

Overall the program was incredible because I was surrounded by a group of students that werejust as passionate about mathematics. It also showed me how applicable math really is outside ofthe classroom. I would recommend an undergraduate research opportunity to any math major,especially to those unsure of what they want to do with their major after college, because of theexperience that it gives the students outside of the typical class settings.

Scenes from this spring’s Computer Security class

MAA Student Chapter Report By Michelle Rose

The Mount’s chapter of the Mathematical Association of America had a great year! We hadseveral meetings to discuss upcoming events throughout the year, and our members were presentat most of the school’s events such as the opening block party and the SPARC closing ceremony.As always, we had candy counting for Halloween and Valentine’s Day, where anyone could guesshow much candy was in the jar and the closest guess won that candy. Then on March 14th, theMAA members had a pi day party, complete with several types of pies and other snacks. Sincethis was a hit, we later held a movie night for the members with pizza and popcorn and wewatched a great math-themed movie, Moneyball. We closed off the year with t-shirts for ourmembers; this year we decided on the phrase “Fibonacci: it’s as easy as 1,1,2,3.”

ACM Student Chapter Report By Joe Appleton

The Mount ACM got off to a fairly slow start this year. Christian and I were completely new tothe club, so any activity we planned was a foray into new territory. We made a large computerout of cardboard for the Activity Fair at the beginning of the year and ended up generating ahealthy amount of interest.

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Left: Christian Winkle with the MAA and ACM poster from Accepted Students Day. Right: Pi Day deserts.

At our first meeting way back in September 2014, we went through a handful of interesting web-sites that computer science majors would find useful, as well as a bunch of interesting websitesin general. We had a much larger turnout than we were expecting and made sure everyone hada slice of pizza.

ACM members (left to right): Danielle Beauchamp, Emily Gipe, Tan Tran, Brianna Thezard, Ali Diaz, Andrew McDonald,Austin McGinty, Joe Appleton, Isaac Zappe, Christian Winkle, Connor Simoncelli, Alex Wakuluk, Austin Walters

As the year went on, we held more meetings and discussed some other interesting topics in therealm of computing technology. We also provided input for a going-away present for the Powells.

We’re very excited about next year’s activities now that we have a good idea about which direc-tion to take the club in. Before we adjourned for the summer, we distributed brand new MountACM t-shirts to all members who had ordered one. We also agreed upon a project for next year:a Wii-mote controlled robot butler. We’re still looking at acquiring all the necessary parts (suchas a Raspberry Pi, chassis, Wii-mote, etc.) but we will be hitting the ground running as soon aswe arrive back on campus in August.

PME and UPE Induction By Brian Heinold

On April 12, the department held its annual Pi Mu Epsilon (PME) and Upsilon Pi Epsilon (UPE)Honors Society inductions. The UPE ceremony was led by Prof. Weiss, Macon Carlton, and JoeyNaylor. They inducted current students Joe Lesniewski, Amanda Malmstrom, Jennifer Powell,

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PME members (left to right): Christina Weaver, Anna Hnizda, Michelle Rose, Coleman Myron, Isaac Zappe, Dr. Heinold, Dr.Portier, Alex Van Neste, Prof. O’Toole, Josh de Aragao, Dr. Petrelli, Dr. Hook, Dr. Butler, Prof. Weiss

Michelle Rose, Christian Winkle, and Isaac Zappe. Dr. Virginia McGovern of the Departmentof Sociology and Criminal Justice, who teaches Cyber Security, was also inducted. Alumni in-ductees this year were from the Class of 1998. They include Laura Hoy, Gregory Kirby, PaulaKoontz, William Nallo, Mark Shipley, and Anthony Weaver.

The PME ceremony was led by Anna Hnizda and Michelle Rose. Inducted were Josh de Aragao,Anna Hnizda, Coleman Myron, Alex Van Neste, Isaac Zappe, as well as Christina Weaver of theclass of 1998.

After dinner, Christina Weaver, new PME inductee and professor at Franklin and Marshall, gavean interesting and inspiring talk on her research in mathematical biology, covering both mathe-matics and computer science as well as her journey to this point.

PME inductees: Isaac Zappe, Coleman Myron, Christina Weaver, Alex Van Neste, Josh de Aragao

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CS in 5 By Brian Heinold

CS in 5 is a short note on computer science that you can read in about 5 minutes.

A trie is a useful data structure that you may not have heard of. Trie is pronounced like “tree”or like “try,” depending on whom you ask. In Algorithms this past fall, just for kicks we wouldsometimes pronounce it in the continental style, like "tree-ay.” The name comes from the middleletters of “retrieval.”

Tries are a type of tree usually used to store text, like lists of words, for easy retrieval. Supposewe want to store the list of words ad, an, any, cab, can in a trie. It would look something likethis:

A C

D N

Y

A

B N

Each edge of the trie represents a letter. Nodes represent the concatenation of all the lettersleading from the root to the node. Leaf nodes and sometimes nodes in the middle of the triestore complete words. We use filled-in circles above to represent these nodes.

It’s relatively quick to code up a trie class in Python. Here’s one:

class Trie:def __init__(self, is_word=False, links=None):

self.is_word = is_wordself.links = {} if links is None else links

def add(self, word):n = selffor c in word:

if c not in n.links:n.links[c] = Trie()

n = n.links[c]n.is_word = True

It’s a recursive class since each node in the trie is a trie itself. The class has a boolean variableto keep track of whether a node represents a complete word or not. To tell which nodes areadjacent to which, we use a dictionary whose keys are letters. In the trie shown earlier, theroot node would have is_word set to false, and its links dictionary would have entries for aand c, each of those pointing to another node. The add method starts at the top of the trie andworks its way down, following the individual letters in the word and moving down the trie byfollowing the links dictionary.

The most common operation on a trie would be to find all the words starting with a given prefix.Here is code we can add to our class that would do that:

def starting_with(self, prefix):n = selffor c in prefix:

if c not in n.links:return []

n = n.links[c]

What’s ν? 2015 16

return self.all_below(n, prefix)

def all_below(self, n, s):M = [s] if n.is_word else []if n.links == {}:

return Mfor c in n.links:

M.extend(self.all_below(n.links[c], s+c))return M

The starting_with method walks down the trie following the characters in the prefix. It thencalls the recursive all_below method that finds all complete words located at or below a givennode.

Once the trie is created, lookups depend only on the size of the word, not on the size of thedictionary. This is very fast, but there is a cost for this speed, and that comes in the amount ofmemory required for the trie. However, there are various things that can be done to make triesmore space efficient.

Tries have a variety of uses. One use is for implementing an autocomplete feature. With that,you type in a few letters (a prefix), and you want all the words that start with those letters,which is exactly what the starting_with method returns. Another use is in IP routing, wherethe next hop a packet should take is based on the first so many bits (a prefix) of its destinationIP address.

Brenna Edmonds and Alex Van Neste at the Math Seminar poster session

Mount Math Madness By Jonelle Hook

The fifth annual Mount Math Madness bracket challenge was held in the spring semester span-ning eight weeks of competition. The number of students who participated in the contest thisyear was by far the highest since the inaugural year of 2011. Over the course of the first fiveweeks, three problems were released on Monday afternoons. Each problem was worth a speci-fied number of points – 100, 200, or 300 points. Students accumulated points and earned entriesinto weekly drawings for a $20 Amazon gift card. The weekly winners were Rachel Meyerhofer,Dylan Soller, Katherine Wu, Aidan McCormick, and Jiahao Lian.

After a tight race, the top eight students were placed into a bracket for three rounds of head-to-head competition. For each round of the bracket challenge, a single problem was released onSunday afternoon. The first of each pair to submit a correct solution advanced in the bracket.There was one upset in each round of the bracket challenge with the number 3 seed, Joe Apple-ton, taking the title of Mount Math Madness Champion for the second year in a row. The runner

What’s ν? 2015 17

Left: The bracket from this semester’s Mount Math Madness contest. Right: Mount Math Madness runner-up Jiahao Lianand winner Joe Appleton.

up was Jiahao Lian, the number 1 seed. Joe and Jiahao both received Amazon gift cards in theamounts of $75 and $40, respectively. In addition, both were awarded Einstein bobble headsand certificates of merit.

Find our “Mount Math Madness Problem of the Week” page on Facebook and “Like” it to see thecomplete list of problems from this year and to follow the contest next year. Here is a samplingof this year’s problems.

1. Green Chocolate Company encourages their customers to recycle by offering one chocolatebar in exchange for returning three wrappers. If you have $15 and each chocolate bar costsone dollar, then what is the largest number of chocolate bars you could possibly get?

2. How many three-digit numbers are made up of three different digits where one digit isthe average of the other two digits?

3. This year was the Pi Day of the century and so below is a circular number puzzle. Eachnumber in the problem will be described using its location as a digit of pi. A “11th digit”pointed star made out of circular spots is held together by wire. There are “4th and 5thdigits” circular spots. Place the numbers “38th digit” through “4th and 5th digits” in thecircular spots where each number is used “2nd digit” time and each of the “5th digit” largercircles have “11th digit” circular spots that sum to “71st and 72nd digits.” The “5th digit”ends of the star also sum to “71st and 72nd digits.”

Answers can be found upside-down on the last page.

What’s ν? 2015 18

Left: Professor Weiss after his smalltalk. Right: Macon Carlton and John Schultz.

Smalltalk By Brian Heinold

This was our seventh year of Smalltalk. We moved again this year to now having most of ourtalks in Room 314. It’s a bit less impersonal than the auditorium.

Here’s a list of the talks this fall:

Logic: Axioms, Logical Systems and Completeness – George HaglerBLAND: A More Interesting Method for Crystallographic Data Analysis – Joe LesniewskiQuestions of Prime Importance – Brian HeinoldUnit Bar Visibility Number of Graphs – Michelle RoseMaple’s Magic Money Tree – Alex Van NesteThe Imitation Game – Joseph Appleton & Christian WinkleThe Hardest Problem – Brian HeinoldThe RSA Algorithm: A Method of Public Key Cryptography – Sean StanleyIntroduction to Circuits – John Schultz

Joe Appleton and Christian Winkle giving a smalltalk

And the talks this spring:

Two Planar Curves: geometry and simulation – Fred PortierEx uno plures: Virtualization using VirtualBox – Joe LesniewskiWindows, Through Time: A look at the evolution of the Windows operating system from 1985 onward – Tim LyonsThe COMAP Math Modeling Competition – Joe Appleton, Carmen Morales, Rooshan MatihThe Mathematics of Bitcoin – Brian HeinoldMinimal Surfaces: An exploration with soap films – Jonelle HookA Series of Unfortunate Events: If the Trees Were Glass – Tim LyonsThe Perfect Poker Player – Scott Weiss

What’s ν? 2015 19

Dr. Heinold’s Smalltalk ducks

Math in 5 By Fred Portier

Math in 5 is a short note on mathematics that you can read in about 5 minutes.

The topic for the Spring 2015 Math Junior/Senior Seminar was a study of a broad collectionof curves that are all, in various ways, geometrically inspired. A circle is geometrically inspiredsince it can be defined geometrically. A circle is a collection of points, (x , y), of distance r froma point (a, b). The equation of the circle is then

(x − a)2 + (y − b)2 = r2

and is an immediate consequence of its definition. If you think of it, we now have two formula-tions: a geometric definition and a “cartesian” equation. Another representation is “parametric”by defining

x = a+ r cos t

andy = b+ r sin t

where the parameter t ranges 0 ≤ t ≤ 2π. A t moves from 0 to 2π we trace out the shapeof the circle. Finally, we can use a “polar coordinate system” to come up with yet anotherrepresentation but that is a bit beyond this scope of this article.

The ellipse, hyperbola, and parabola are all common examples of geometrically inspired curves inthat they can be obtained by forming various slices through a cone. As such, they are collectivelyreferred to as conic sections. Each has nice geometric properties which lead to relatively simplecartesian and parametric equations.

For example, a parabola is defined using a point, called the focus, and a line called the directrix.A parabola is then the set of all points where the distance to the focus is equal to distance to thedirectrix. The series of panes below shows the construction.

You start with the focus point, A, and the directrix line. Pick an arbitrary point P on the directrixand form the line segment PA. Let M be the midpoint of PA and form a perpendicular line throughM (the perpendicular bisector of PA). Now form a perpendicular to the directrix at P and let Fbe the point where these two lines intersect. It can be shown (think isosceles triangle) that thedistance from F to A is the same as the distance from F to P. This means that F is equally distantfrom the directrix and the focus making F a point on the parabola. Now imagine “sliding” Palong the directrix and “tracing” the path taken by F. The path formed is that of a parabola. The

What’s ν? 2015 20

last pane shows the entire parabola as the “locus” of points defined by F as P runs over all pointson the directrix.

More interesting curves can be formed that are “geometrically inspired”. Consider two circleswith one circle rolling along the outside of the first. In the figure below, the blue circle is rollingalong the edge of the yellow circle. We select a point on the blue circle and trace out the pathof that point. The resulting curve is called an epicycloid.

The relative sizes of the circles has a strong affect on the shape of the curve. Below are 4 curvesusing the same construction with different sized circles. Some of you may have played with atoy called Spirograph© that allows you to draw pictures using gears of various sizes. The shapes

What’s ν? 2015 21

produced by Spirograph© are epicycloids (like above) or hypocycloids (a circle rolling on theinside of another circle).

The parametric form of the epicycloid is

x = (R+ r) cos t − r cos�

R+ rr

t�

y = (R+ r) sin t − r sin�

R+ rr

t�

where R is the radius of the blue circle and r is the radius of the yellow circle and t is theparameter that ranges over all real numbers. In practice, the curve repeats itself allowing us tolimit t to some smaller interval .

These curves have been of interest to mathematicians for hundreds of years. In fact, many carrythe name of famous mathematicians. There is the Cissoid of Diocles, Fermat’s Spiral, and theFolium of Descartes. Many of the curves arose from engineering and physics especially in thecontext of constructing gears. A list of curves can be found at

http://www-history.mcs.st-and.ac.uk/Curves/Curves.html.

There are operations one can apply to derive one curve from obtain another. These includeinvolutes, inverses, pedals, envelopes, and caustics.

As a final example consider the red “infinity” shaped curve below. Technically, it is called alemniscate. Specifically, it is the Lemniscate of Bernoulli and satisfies the cartesian equation

(x2 + y2)2 = a2(x2 − y2)

where a is a constant.

We can construct the lemniscate as the pedal of the hyperbola (the blue curve in two pieces).We start with an arbitrary point (colored yellow) on the hyperbola and form a tangent line atthat point. Again at this point we form a normal line (a line perpendicular to the tangent line).We then construct a line through the origin, (0,0), parallel to the normal line. Next we identifythe point of intersection (colored green) of the tangent line and the line through the origin. We

What’s ν? 2015 22

then trace out the path of of this green point as the yellow point moves through all points onthe hyperbola. The path (or locus) of this point traces out a lemniscate.

The software I used to create the plots in this article is called GeoGebra (a cross between Ge-ometry and Algebra). It is free and can be found at https://www.geogebra.org/. There isa internet community building these constructions and sharing them with the public. You can“run” my construction of the Lemniscate of Bernoulli at

http://tube.geogebra.org/student/m1255537.

Just press the arrow in the lower left-hand corner to run the animation.

An Interview with Dr. Petrelli By Brian Heinold

How did you get interested in math?

I’ve always been interested in math. It seemed justnatural that I would end up doing math, studyingmath.

Tell me about taking math in Italy.

I went to the scientific high school, scientific concen-tration, I guess, which meant I took a lot of math. Wecovered up to Calc 3. And university was vastly dif-ferent since if you’re a math major that’s all you take.So I took 120 credits of math, 10 computer science,20 physics, and that was it.

I took 15 courses. Every course grade was estab-lished only at the final, where you would take a written exam and an oral exam.

What’s ν? 2015 23

If you didn’t pass them you’d get another chance a month later and after third orfourth failed chance, you would have to retake course. You had about a year to passthem.

Which undergraduate classes did you like best?

I liked Advanced Calculus and Functional Analysis. I also liked Rational Mechanics.I liked that one mostly because of the professor. I didn’t like Abstract Algebra.

Which was the hardest?

In terms of the exam, Analysis 1. With the first exam they tried to weed people out.There was a very low pass rate in those exams. In terms of the course, FunctionalAnalysis.

What classes did you like in graduate school?

I liked Finite Element Methods since I didn’t know anything about it before, so itwas interesting. I liked Calculus of Variations. I liked its applied nature, but it wasstill within the functional analysis environment that I liked. The professor wouldgive us open questions. There wasn’t a solution; there was just a point where yousaid I think I’ve done enough. People were very upset about this since you neverknew if it was enough.

What are your favorite classes to teach?

Differential Equations, Operations Research, and Calculus 2.

What do you like about math?

I’m a very rational person, so I like the idea that something is correct and somethingis incorrect, something logically flows from something else, which is not always therein other subjects.

Any memories that stand out over your 11 years here?

When I brought the students to the CURM conference. After they did a year ofresearch they went to present their results at a conference. That was nice; we flewto Utah.

Any hobbies?

I like to do some gardening in the summer. I used to play soccer; now I just watch it.I like to travel. I’ve been in about 40 different countries. I’ve been all over Europeand Central and North America. This summer we’ll be going back to Russia andItaly.

Tell me about your family.

I’m married to Anna, a graphic designer, and we have two daughters Stella, 5, andMaya, 1. And we have a beagle named Lucky. We live in Frederick now.

What’s ν? 2015 24

Any future projects?

We just bought a house that needs a lot of work; that’s been our present and ourfuture project. In the immediate future I promised a camping trip to my daughter.

Any future projects at the Mount?

I would like to have a very applied course where all the students do is solve a real-life problem tied to some math, whether it is statistics or differential equations oroperations research. That would be the goal. I see it as an interdisciplinary class, notjust math students, but math, computer science, and science students would form agroup to solve such problems.

Andy Alfaro, Pat Mastrorill, Rob Jones, and Andrew McDonald at the SPARC Festival

2015 Seniors By Brian Heinold

We are graduating nine students this year.

Math seniors: Anna Hnizda, Michelle Rose, Josh de Aragao, Camille Sanchez, Alex Van Neste, Brenna Edmonds

In Mathematics we have Josh de Aragao, Brenna Edmonds, Anna Hnizda, Camille Sanchez,and Alex Van Neste. In Computer Science we have Macon Carlton, Jenna Glassman, and JohnSchultz. Michelle Rose double-majored in Math and CS.

What’s ν? 2015 25

CS seniors: Michelle Rose, Jenna Glassman, Macon Carlton, John Schultz

We asked the graduates about their plans. For what might be the first time ever, all of thegraduates replied!

Macon Carlton: “I will be working as a software engineer for Raytheon in the Dulles, VA locationstarting in August and plan in the near future to pursue a masters degree working part time.”

Josh de Aragao: “After graduation, I will be working for Atinum Energy Investments as a Reser-voir Analyst in Houston, Texas. In addition, I plan on getting my accreditation to be an actuary.”

Brenna Edmonds: “After graduation I will be continuing at the Mount to attain my Masters ofArt in Teaching (MAT). I plan on becoming a teacher but hope to do something prior dealingmore with mathematics.”

Jenna Glassman: “After graduation, I plan on getting a job related to Cyber Security in theBaltimore, MD and Washington D.C. area.”

Anna Hnizda: “I will be teaching mathematics within a secondary school in Carroll County. Ialso plan to pursue a master’s degree in mathematics or administration in the near future.”

Camille Sanchez: “After graduation I will begin my 2 year commitment with Teach for America.I will be teaching high school math classes in Prince George’s County. During these next 2 yearsI will also receive a Masters of Ed from Johns Hopkins University.”

John Schultz: “I will be working for Raytheon as a software engineer in Annapolis Junction,MD. I’ve discussed plans with my supervisor to pursue a Masters in Computer Science in a fewyears.”

Alex Van Neste “I am currently going through applicant processing in hopes to work for thegovernment. I don’t have any other definite plans currently.”

Michelle Rose “I am currently searching for a job – most likely with the government or a gov-ernment contractor – that will allow me to use both my math and computer science majors.”

What’s ν? 2015 26

Josh de Aragao Macon Carlton Brenna Edmonds

Jenna Glassman Anna Hnizda Michelle Rose

Camille Sanchez John Schultz Alex Van Neste

AnswerstotheMountMathMadnessquestionsonpage17:

1.Youcanget22candybars.First,youbuy15candybarsfor$15.Thenexchangethe15wrappersfor5morecandybars.Exchange3ofthe5wrappersforonecandybar.Thentheremainingwrappersforonelastcandybar.(15+5+1+1=22)

2.Thereare20differentincreasingarithmeticsequencesoflengththree:012,123,234,345,456,567,678,789,024,135,246,357,468,579,036,147,258,369,048,159.Thereare3!=6waystopermutethesequences.Thus,20·6=120minus8sequencethatbeginwithzerogiveus112three-digitnumbers.

3.