What’s ν?
News from the Department of Mathematics and Computer Science
Mount St. Mary’s University
Emmitsburg, MD 21727
Issue No. 9
May 2013
Contents
What I Do . . . . . . . . . . . . .
Student Activities and Awards . .
Fred Portier Steps Down as Chair
Introducing Karon Shorb . . . . .
SPARC Honored Faculty Address .
The Shake It Alarm clock . . . . .
Michelle Rose’s REU . . . . . . . .
Early Developments in Mathematics and Computer Science . .
MAA Student Chapter Report . .
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4
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5
6
7
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Faculty/Student Puzzle Competition
PME and UPE Induction . . . . .
CS in 5 . . . . . . . . . . . . . . .
A few puzzles . . . . . . . . . . . .
Perfect Proofs . . . . . . . . . . . .
Mount Math Madness . . . . . . .
Smalltalk . . . . . . . . . . . . . .
Math in 5 . . . . . . . . . . . . . .
An Interview with Dr. Butler . . .
2013 Seniors . . . . . . . . . . . . .
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22
What’s ν? 2013
What I Do
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By Andrew Cuga, Class of 2006
After six years as a software developer for various Department
of Defense contractors around Washington DC, I took the
plunge into the private industry as lead engineer at HotelMe,
a web startup dedicated to verifying the legitimacy of hotel
reviews.
The transition was a big decision – cleared DoD software consulting is typified by 9-5 hours, competitive benefits, and great
job security. On the other hand, the startup life’s atmosphere
is much more casual, job performance matters way more, and
there’s the ability to publicly show people, “Hey, I built this.”
I’ve come to realize the greatest satisfaction for an engineer
is to build something people actually use and appreciate, and
that’s goal that makes the job worth it.
In-shop, our development team uses the Java flavor of Google
App Engine, where the non-relational database BigTable has
been a breeze. We communicate with external systems primarily over web services, preferably via JSON, and our site’s
front-end is done entirely in GWT.
It’s enticing to evaluate new technologies and be able to freely adopt them into production,
so enticing that my brother followed suit in abandoning DoD contracting and joined the
company this past year as another developer. Having coworkers whom one can also goad
into helping do yard work on the weekends has turned out to be a great benefit.
Greatest of all, however, was the (bad?) decision by fellow Mount grad Emmy Lu Jones
(C’09) to marry me just over eleven months ago. More recently, we bought a home together
in West Virginia and are still busy settling in. My next big task will be convincing her that
this house should count as her first anniversary gift.
Student Activities and Awards
By Brian Heinold
Another year has flown by. The fall semester started with our annual picnic. A little later in
the semester we had our annual faculty/student puzzle competition. See Professor Weiss’s
article about it in this newsletter. In October, Maria Marinelli and Amy Strosser gave a
presentation at the MAA EPADEL meeting at Millersville University. Their talk was on
the middle levels problem, a well-known open combinatorial problem for which they have
developed a promising new approach. They started working on the problem after solving
a special case on a Discrete Math assignment last spring. In November, Mike Mugno won
our department’s programming competition.
Dr. Portier’s theme for the fall computer science senior project class was app development.
From the class, Julian Ptak’s Latin prayers app was published on the Google Play store and
John Martin’s Latin flash card app was published on the iTunes store.
At the start of the spring semester we had five teams participate in the COMAP competition,
a school record. Here are the teams:
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1. Joseph Appleton, Joe Lesniewski, and Isaac Zappe
2. Luis Bautista, Jeff Mercedes, and Emily Rodriguez
3. Emily King, Michelle Rose, and Camille Sanchez
4. Tim Evans and Julian Ptak
5. Maria Marinelli, Carmen Morales, and Amy Strosser
The team of Maria, Carmen, and Amy earned an honorable mention designation.
On April 8th, Charles Wessell of Gettysburg College gave an ACM/MAA Lecture Series
talk entitled “Electoral College Math.”
Mike Mugno and John Martin presenting at SPARC
The SPARC Festival had strong participation from the department. The winning poster
from the School of Natural Science and Mathematics was Michelle Rose’s poster based
on the research from her REU. Michelle has an article about this later in this newsletter.
The winning lightning talk was Maria Marinelli’s “The Square Cycle Problem,” and the
honorable mention lightning talk was Mike Mugno and John Martin’s “iPhone and iPad
Apps.” The app they revealed at the talk is now available on the iTunes store. See their
article about it in this newsletter. Also at the festival, Tim Evans gave a poster, “There
and Back Again: A Vector’s Tale, ” on programming with vectors. Nick Warthen gave a
talk, “Gettin’ into the Groove,” about the programming language Groovy. Mike Mugno
gave a talk entitled “Outlining Images using A.I.,” and Julian Ptak gave a talk entitled “An
Introduction to Android Development.”
On April 7 we inducted six students into PME and five into UPE. See Dr. Petrelli’s article
about the induction. At the April 28th honors convocation, Emily Gordon won the department’s McCollough and McGraw prizes, John Martin won the Kevin J. Carty Memorial
Award for service to the Mount, and Taylor Frock won the Monsignor Tierney Memorial
Prize for the junior with the highest cumulative GPA.
Amy Strosser was accepted to three of the nine REUs she applied to and will be attending
one at RIT.
Outside of the department, sophomore math major Michelle Rose was a member of the
winning CSI challenge team and junior math major Liz Duhring was elected Lieutenant
Governor for the Maryland Student Legislature.
A few of our seniors will be going to graduate school next year. Emily Gordon will be
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attending Johns Hopkins part-time for a Masters in applied math, while working full-time.
Branden Ehrenreich has been accepted to a number of schools and plans to pursue a Masters
in computer security. Mo Moriarty has been accepted to the Mount’s MBA program.
Dr. Portier with Emily Rodriguez and Jessica Gardner at the SPARC Festival
Fred Portier Steps Down as Chair
By Brian Heinold
After 15 years as department chair, Dr. Fred Portier is handing over the reins to Dr. Melanie
Butler. Why? Dr. Portier said it was time for a change for both him and the department.
He said it’s is good to have a new set of eyes to look at things.
When asked what he thought his major accomplishments were as chair, he said the establishment of the Computer Science major, bringing Pi Mu Epsilon and Upsilon Pi Epsilon
to campus, and hiring a bunch of talented young faculty.
With his newfound free time, Dr. Portier plans to reconnect with his research. He also
hopes to be part of the effort to improve undergraduate research in the department.
Also moving on is Dean David Bushman. Dean Bushman is now president of Bridgewater
College in Virginia.
Introducing Karon Shorb
Karon Shorb is the department’s new administrative assistant,
taking over for Barbara Levy who retired last year. Karon is
originally from Emmitsburg and now resides just over the border in Fairfield, PA. Before coming to the department, Karon
worked in numerous positions around the Mount including in
Admissions, Student Affairs, and Housekeeping. Before that,
Karon worked at a number of places, including Gettysburg
Hospital and Lincoln Intermediate. She worked at a sewing
factory for 13 and half years. She also worked for a dentist, a
lung doctor, a midwife, and an interpreter for the deaf.
By Brian Heinold
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Karon’s husband, Dave, has worked here at the Physical Plant for the last 29 years. They
have one daughter, Brandy. Karon enjoys flowers, gardening, reading, and making crafts.
When asked how she likes working in the department, Karon said that she loves it absolutely
and that everyone has been sweet, helpful, and kind. (I didn’t ask her to say that.)
SPARC Honored Faculty Address
By Brian Heinold
Our own Dr. Jonelle Hook gave the honored faculty address at this year’s SPARC Festival.
Her talk, entitled “Finding Patterns among the Stars: A Mathematical Search for Order,”
is about Ramsey theory, a branch of combinatorics with roots in the early part of the 20th
century.
Dr. Hook presenting at SPARC
Dr. Hook talked about some of the famous problems of Ramsey theory and told interesting
stories about the developers of the theory, including Ron Graham and Paul Erdős.
Dr. Hook gave the example of how many people need to be at a party in order for there to
be either three mutual friends or three mutual strangers. The answer is six. She described
how the problem is equivalent to coloring the edges of a complete graph red or blue such
that you can always find a complete subgraph of three vertices (a triangle) whose edges are
either all red or all blue.
She talked about how the problem can be generalized to finding groups of n mutual friends
or n mutual strangers. But these problems turn out to be really difficult. Even the n = 5
case has not been solved. Dr. Hook quoted Paul Erdős:
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Suppose aliens invade the earth and threaten to obliterate it in a year’s time
unless human beings can find the Ramsey number for red five and blue five.
We could marshal the world’s best minds and fastest computers, and within a
year we could probably calculate the value. If the aliens demanded the Ramsey
number for red six and blue six, however, we would have no choice but to launch
a preemptive attack.
Dr. Hook concluded her talk by discussing some of her own research in Ramsey theory,
focusing on critical graphs and star-critical Ramsey numbers. The idea is as follows: Given
two subgraphs G and H, how large of a complete graph do you need so that if you color
its edges red and blue, you can always find either a red G or a blue H? If it turns out the
answer is n vertices, then n − 1 would not be enough. This means that you could color the
edges of a complete graph on n − 1 vertices and avoid both a red G and blue H.
Such a coloring is referred to as a critical graph. Part of Dr. Hook’s research is classifying
critical graphs for various Ramsey numbers. On the other hand, suppose you start with a
complete graph on n − 1 vertices, add a vertex, and start adding edges from it to the others.
What is the minimum number of edges you need to add in order to find a red G or a blue
H? This is the star-critical Ramsey number which Dr. Hook has found for different classes
of graphs.
The volleyball game at the annual picnic
The Shake It Alarm clock
By John Martin & Mike Mugno
This past semester Michael Mugno and John Martin have been studying
the iPhone Operating System (iOS). Their areas of interest included geolocation, a gyroscope sensor, and an accelerometer sensor. By the end of the
semester, they used all three of these to build an iPhone app called Shake
It. Shake It is the first of its kind alarm clock app, with the key feature
of turning the alarm off by shaking the phone. The app was inspired by
their roommate, who always had a hard time waking up to his alarm clock
in the morning. The accelerometer and gyroscope sensors are used to detect the shaking
movement of the phone, carefully designed to wake the person up before the alarm stops
ringing. Geo-location is used to find the current location of the person and display the
weather based on where they were. The app intelligently determines the zip code, and it
changes the background hue based on the temperature and current conditions outside. For
example, if it is 90 degrees outside and humid the phone will turn the background a bright
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red.
Screenshots from the Shake It app
During the 2013 spring semester, the app was presented at the SPARC festival lighting talk
series. The following day the app was available for download on the iTunes App Store. So
far the app has been sold in several different countries and has a steadily increasing number
of daily downloads. When asked whether or not new features were in the works, Mugno and
Martin laughed and said, “we don’t talk about any unannounced features.” Look for Shake
It Alarm Clock in the iOS app store and give it a shot at waking you up in the morning.
Michelle Rose’s REU
By Michelle Rose
After my first semester at Mount St Mary’s, one of my math professors asked me if I would be
interested in applying for an REU (research experience for undergraduates). I was flattered
but had never heard of such a thing before. Since the particular REU he was talking about
was open to rising sophomores and juniors who didn’t have too much experience in math, I
figured that it was worth a try. Basically they wanted fresh minds and ideas, and I definitely
had no idea what 99% of the things we did were going into the REU.
The REU that I applied for was at St Mary’s College of Maryland and was considered very
competitive due to limited space and a desirable stipend; I was very fortunate to be selected.
We worked 9-5, five days a week for six weeks, and there were also weekend trips like to the
zoo and the Baltimore Inner Harbor to see the math exhibit at the science center.
There were three topics to choose from: discrete optimization, graph theory, and imaging.
I chose graph theory, which I honestly knew nothing about. We read published papers for
background on the topics, talked about them together and helped each other figure out what
the authors were saying. The papers detailed algorithms that were both self stabilizing and
resulted in several different types of sets, but we focused on something called a dominating
set. My group created algorithms that would result in double dominating sets, Then we
proved that the algorithms would stabilize and that the stabilization would occur in a finite
amount of time.
Each week the three groups came together and presented the work that was accomplished,
which was good practice if the groups wanted to take these findings elsewhere. For instance,
my group presented our findings at a math conference at JMU, as well as the conference on
combinatorics and graph theory in Boca Raton, Florida. We are currently working finishing
up the paper we wrote on our research in hopes of getting published.
The REU was truly an amazing experience. I learned so much in those six weeks, both in
graph theory from my own research and in the other two topics from the presentations from
week to week. The REU at St Mary’s was funded by a grant from the NSF, and meals and
housing were provided. Besides that, I met a bunch of people from around America, from
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New York to Hawaii. I can’t wait until I get to see them again at future math conferences.
Students from this spring’s Math Seminar class. Front row (left to right): Rachel Baranoski, Taylor
Frock, Lindsay Ruhle, Keri Barnes, Lindsay Sneeringer, Emily Rodriguez. Back row: Maria Marinelli, Liz
Duhring, Mo Moriarty, Luis Bautista, Amy Strosser, Chris Coughlin, Rebecca Thiem
Early Developments in Mathematics and Computer Science
By Tom Ryan
I am very honored and pleased to use this mathematics newsletter to reflect on my rewarding career at Mount Saint Mary’s University. As you may know, I retired from my academic
position at the Mount two years ago (2011) after 47 years as a member of the faculty. The
last 29 years I taught in the Richard J. Bolte, Sr. School of Business. (The school was originally called the Department of Business, Accounting and Economics). During my tenure
in the business school, I primarily taught statistics in the MBA program and management
science in the undergraduate program. Prior to my work in The School of Business, I was a
professor of mathematics in the Department of Science and Mathematics for 18 years during
the 1960s and early 80s. My career at this great institution, which began in the fall of 1964,
was filled with interesting challenges, special relationships with students and colleagues, and
exhilarating learning experiences.
My early years as a member of the Science and Mathematics Department were especially
exciting and challenging. In the mid-1960s the mathematics curriculum needed to be restructured as a result of the powerful mathematical discoveries of the early part of the 20th
century and the looming electronic computer era. Professor Bill O’Toole became a department member in 1966, and we worked together to revise the mathematics curriculum with
new course requirements including courses in real analysis, abstract algebra and topology.
But the most substantive change came with our efforts to initiate computer courses into
the mathematics curriculum. In 1966 we collaborated with the mathematics faculty at St.
Joseph College (Sister John Francis and Don Shriner) to write a National Science Foundation
(NSF) proposal which resulted in an NSF grant to the colleges. The grant provided funds
to purchase some computer equipment and included additional financial support for initial
computer education. Each school purchased a Model 33 Teletypewriter which was then
connected to a remote computer (off-campus site). This setup then allowed our students
to share time with the off-campus computer site. But there was also a great need for
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fundamental computer education, especially for the mathematics faculty.
In the fall of 1967, students from both campuses, as well as the mathematics faculty, attended
class each Friday afternoon at the National Bureau of Standards (NBS) in Gaithersburg,
MD (now called NIST). Computer scientists from NBS provided our students and faculty
instruction in the fundamentals of computers and illustrated their contemporary applications. The second part of the course – with a BASIC programming component – continued
in the spring semester (1968) with class meetings held at one of the Emmitsburg campuses.
This was the first computer course given at the Mount.
Because of the limited computer resources, the two mathematics programs began to interchange students for the other computer offerings. This exchange of math students for
computer classes led to similar exchanges in elective math courses and subsequently spread
to other departments on the two campuses. The result of this initial cooperation generated
a very positive environment on the Mount campus.
As a by-product of the NSF grant, I was offered the opportunity to work in the summer
of 1968 at NBS. I was very fortunate to be assigned to the Technical Analysis Division
of NBS, a group of operations research analysts whose task was to solve technical problem in government using the contemporary methods of operations research (OR), including
computer programming, applied statistics, and optimization techniques. My work in that
summer of 1968 led to 10 consecutive summers (1968–1977) of employment at TAD, where
I learned much about the contemporary applicability of mathematics and computer science.
Those real-world problem-solving experiences became part of my teaching at the Mount for
30 years. By the mid-1970s there existed a couple of programming courses in computer
science; fundamentals of computer technology were introduced as an important component
of the required core mathematics course; and new mathematics courses such as mathematical modeling, probability, mathematical statistics, and numerical methods were added to
enrich the evolving curriculum. At the same time, many faculty envisioned the need for computer education to expand into other academic disciplines – a need for computer-assisted
instruction emerged.
In the spring of 1975 the MSM faculty, after viewing a very impressive demonstration of the
Plato System, approved the leasing of the system. The Plato (Programmed Logic for Automated Teaching Operations) System consisted of more than 10,000 hours in programmed
subjects (lessons) ranging from remedial mathematics to biological simulations. The system hardware resided at the University of Illinois, and the Mount contracted to rent two
Plato terminals connected to the mainframe at U of IL. The system was unique in that
it possessed many valuable programmed lessons together with incredible graphics display
capability. The programming language for the system was called Tutor, and several faculty
members used existing lessons available on the system or created valuable lessons for their
courses using Tutor. While the potential educational value of the System was acknowledged
and some success was achieved, there were concerns with the endeavor. The system was
expensive; there were just two terminals available for student use; the effort to create usable
lessons was exhausting; and the use of the system was dominated by students regularly
utilizing the system’s incredible games and gaming capability to play games and to interact
with other students around the country – a very early indication of what was to come in
the future with the Internet. After two years the Plato System was terminated in favor of
a microcomputer lab.
At the same time, the department approved funding to purchase the Altair 8800 microcomputer. It was the first commercially available computer, but it came as a kit. Professor
O’Toole, together with several students, spent many hours building the computer. The
system was initially built as a single-user system, and it supported Microsoft BASIC programming language. But the system did not have an operating system and “crashed” pretty
regularly. To “boot” the system one had to actually flip the switches (on/off) on the front
panel in the proper sequence. It often took patience to accomplish this fundamental task.
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Pretty primitive! The system was enriched with the development of software and was used
primarily by math majors.
By the late 1970s – with the demand for computer courses dramatically increasing – the
faculty voted to create a microcomputer lab which offered much greater access to computer
courses for our students. The lab was built on the first floor of the Coad Science building
and contained eight carrels each equipped with a TRS-80 microcomputer. Each computer
had 4k of memory, a tape cassette drive for storage, and came with BASIC installed. It was
a relief for students to now have such a sophisticated system (ha!). External floppy drives
and additional memory increased the machines’ capability and set the stage for greater
advances of computer science at the Mount.
The late 60s and the decade of the 70s were exhilarating times with many computer developments – Model 33 Teletypewriter, the Altair 8800, The Plato System, TRS-80 microcomputers, BASIC programming, and many new courses. Those special times provided
significant contributions to the future development of mathematics and computer science
on campus today.
Rachel Baranoski, Taylor Frock, and Keri Barnes
MAA Student Chapter Report
By Keri Barnes
This year the Mount St. Mary’s chapter of the Mathematical Association of America helped
to continue and sponsor many traditional club events. The club members, under the advisement of Dr. Jonelle Hook, met at least once every month to discuss and organize these
events. Two of our members, Amy Strosser and Maria Marinelli, went to a regional conference at the beginning of the fall semester to present a mathematical talk on some research
they had been doing. Also during the fall semester we had our annual Halloween candy
counting event where the whole campus was able to get involved and place their guess of
how many pieces of Halloween candy were in a jar.
Spring semester brought our Valentine’s Day candy counting event as well as our Pi Day
event, which was our biggest event this year. Five of our Mount staff volunteered to allow
students vote for them to get “pied” in the face. After a week of voting for a minimal
charge, the students on campus voted on the top three staff members they would like to
see get pied. Dr. John Schwenkler, Philosophy professor, Eddie Wright, Admissions leader,
and Margot Rhoades, Registrar, were the three candidates chosen to receive a pie in the
face on Pi Day this year. On 3/14 staff and students gathered in Patriot Hall to witness
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and participate in the pie throwing. The money raised from this event went to help fund
the activities put on by the MAA this year.
Scenes from the MAA’s Pi Day Event
We finished off the semester by helping sponsor the Mount’s annual SPARC Festival. Some
of the members donated their time to help work the SPARC Festival’s informational booth
in Patriot Hall throughout the event. We also were able to share what we have done
throughout the year at the SPARC Festival’s closing ceremony. Overall it was a year filled
with traditional events and we look forward to continuing these traditions in the years to
follow!
Faculty/Student Puzzle Competition
By Scott Weiss
In October of 2012, the department hosted its annual puzzle competition. Prof. Weiss and
Dr. Bob Keefer (from psychology) co-hosted the event. This year, challenges were taken
from the book Crowd-Pleasing Puzzles by Patrick Berry and Todd McClary (Puzzlewright
Press, 2012). Three student teams participated in the preliminary rounds, each pair doing
a different competition.
In one event, teams were given half of two famous pairs of the form blank and blank. Near
and Jack would lead to far and Jill. They then needed to figure out rhymes for those words
that led to another pair. So, in the example, the final answer would be bar and grill. Can
you figure out what pair you end up with if you start at touch and straight? (Answers to
all the puzzles in this article are upside down on the last page.)
In the game “Bits of Wit,” a set of words at the beginning or end of a well-known phrase
were replaced by their initials. For example, float like a butterfly slab should be float like a
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butterfly, sting like a bee. Can you reconstruct go out in a bog?
In “Figure Eight,” teams needed to come up with as many answers as possible to a trivia
question with eight correct answers. One question asked them to name the teams in the
four major sports leagues (MLB, NBA, NFL, NHL) whose nicknames contained one of the
colors red, white, and blue. Can you get all eight?
The winning student team of Maria Marinelli, Lindsay Ruhle, and Amy Strosser faced off
against the faculty team of Dr. Heinold, Hook, Petrelli, and Portier for bragging rights for
the rest of the year. The competition was based on analogies like in the SATs. The twist
was that a pair of words in each analogy was spoonerized; the initial letters of the words
were swapped. So given the analogy sled is to beep as chair is to what?, the correct answer
is sit. You should change sled and beep to bed and sleep. Here’s one for you to try: sappy
is to smile as had is to what?
The students played an amazing game and easily defeated the faculty team. Will the
students be able to retain their title in 2013? Visit us this fall and find out. We’d love to
have an alumni team participate!
Top: PME inductees Michelle Rose, Emily Rodriguez, Maria Marinelli, Nicole Vanagas, Josh Weaver,
Anna Hnizda
Bottom: UPE inductees Macon Carlton, Tim Evans, Amy Strosser, Chantel Lipkins, Evan Oliver
PME and UPE Induction
By Luca Petrelli
The Pi Mu Epsilon (PME) and Upsilon Pi Epsilon (UPE) induction ceremony was held on
April 7, 2013. It was the third time the Math and the Computer Science and Information
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Systems honor societies held their ceremony together.
PME inducted six new members: sophomores Anna Hnizda, Michelle Rose and Joshua
Weaver, and juniors Maria Marinelli, Emily Rodriguez, and Nicole Vanagas. UPE inducted
sophomore Macon Carlton, juniors Tim Evans and Amy Strosser, and seniors Chantel Lipkins and Evan Oliver.
The ceremonies were held in the Horning Hospitality room. Helping with the PME ceremony
were Taylor Frock and Rachel Baranoski, the officers of our Maryland Eta chapter, while
Zack Eick, president of the UPE chapter helped with its ceremony.
As usual following dinner the highlight of the evening was our guest speaker talk. This
year Dr. Marie desJardin of University of Maryland Baltimore County delivered a talk on
diversity (or better the lack of) in Computer Science. Dr. desJardin has done extensive
work in artificial intelligence, especially in the area of machine learning, multi-agent systems,
information management, and decision theory. Her talk was very informative and well
appreciated by the many students, parents, and faculty in attendance.
To join us next year simply contact me at [email protected] or Scott Weiss at
[email protected].
Drs. Portier, Petrelli, Hook, and Heinold at the picnic
CS in 5
By Fred Portier
CS in 5 is a short note on computer science that you can read in about 5 minutes.
Back in the day . . . I can remember a time when a computer was something you could
actually touch. You could physically pick it up and move it. You could turn it on and off
and when you opened your Word document you knew it was actually stored on that box
computer thingy.
OK, maybe that is still today but things are changing. It all started a few years ago
with virtualization. In virtualization you take a powerful computer and you place on it a
hypervisor. This is software that allows you to install multiple virtual computers on the same
physical device. At the Mount we have this set up on a pair of computers named Hal and
Deep Thought. On these we have installed Linux servers and Windows 2008 servers. The
hypervisor allows these virtual computers to run without stepping on each other’s binary
toes.
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Virtualization allows you to save a computer in the same way you save a file (a very large file).
This means you can also copy and duplicate computers without setting up any additional
hardware. The ability to quickly create exact copies of virtual computers is key in what we
have come to know as the cloud.
In cloud computing your data is stored somewhere and you don’t know exactly where. You
run applications that are found on a server (somewhere) and again, you don’t know where.
The basic premise is that it is out there in the cloud. In reality, your data is stored on a server
and probably duplicated over several servers. In many cases your data is in a distributed
database. Your application is running on one of many multiple copies of a virtual server.
A good example is Google Docs where you can run online versions of word processors and
spreadsheets among other applications. You can create, edit, and share documents using
software and data located somewhere in the cloud.
These cloud applications can be run on tablets and even cell phones. In the near future, cloud
computing will make it possible to perform most functions without a traditional computer.
There will still be a large number of computers but they will be located in large server
farms, out of sight for most users. In fact, some people are predicting the PC will soon be
replaced by mobile devices and the cloud. Major computer manufacturers are beginning to
experience a decline in sales. After all, why purchase an expensive computer when a tablet
provides everything you need?
Are we in the beginnings of a significant paradigm shift in computing? There are still a
host of technical and legal issues that need resolution. These include privacy and ownership
of online media. What will the world look like in a post-PC era and what impact will this
have on computer science in general and computer science education in particular?
Students and faculty at the PME/UPE induction. Front Row: Dr. Portier, Dr. Petrelli, Amy Strosser,
Keri Barnes, Rachel Baranoski, Taylor Frock. Back Row: Zach Eick, Prof. O’Toole, Rebecca Thiem, Prof.
Weiss, Michelle Rose, Emily Rodriguez, Maria Marinelli, Nicole Vanagas, Josh Weaver, Anna Hnizda, Dr.
Hook
A few puzzles
By Brian Heinold
People always talk about how math and music are closely related. Here are a few Jeopardy!
style before-and-after puzzles combining math and music. Answers are upside down on the
last page.
1. Beatles album released in 1970 that is also an expression used to tell if a quadratic
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has real roots
2. Detroit rapper who is the result of multiplying an m × k matrix by a k × n matrix
3. Reminiscent Bob Seager song about a guarantee that f 0 (c) = 0
4. Billy Joel song about a musician who is also a locally-Euclidean topological space
5. 1967 Otis Redding hit about prior probabilities
Perfect Proofs
By Melanie Butler
Paul Erdős, a Hungarian mathematician who lived in the 1900s, once joked about “The
Book,” which he said was God’s collection of perfect proofs of all mathematics theorems.
In fact, in 1985, Erdős said, “You don’t have to believe in God, but you should believe in
The Book.”
In the late 1990s, mathematicians Martin Aigner and Gunter Ziegler published Proofs from
THE BOOK in Erdős’ memory. Some of the proofs included in this collection are Euclid’s
proof that there are infinitely many primes and a proof of the Fundamental Theorem of
Algebra. This book is currently in its fourth edition, with each successive edition offering
updates in new areas of mathematics.
Inspired by THE BOOK, I asked some students to name their favorite mathematician and
favorite theorem. One student mentioned Pope Sylvester II, who lived around 1000 AD,
as a favorite mathematician. Pope Sylvester II is credited with popularizing Hindu-Arabic
numerals and the abacus.
Another student said that Newton was her favorite because he “gave us the laws of physics
that apply in everyday life.” A second student selected Newton for similar reasons. A
third student selected Newton calling him “the smartest man that has ever lived.” Cantor
was also selected as a favorite mathematician because “he proved that there are an infinite
number of infinities.”
The Fundamental Theorem of Algebra and the Pythagorean Theorem were the two theorems
most cited as favorites. When talking about both theorems, students were excited about
the history and wide applicability of these theorems. The pumping lemma was also cited as
a favorite because it is “a simple problem that is hard to prove.”
When I asked the students to name their favorite mathematicians and favorite theorems,
they, of course, turned the question back to me. I didn’t have a good answer! My answers
change each semester, depending on the classes that I am teaching. Since I just finished
teaching Real Analysis this spring, I would probably select an analyst and a real analysis
theorem (Bolzano-Weierstrass maybe). By next spring, my answers will have changed.
However, I do have a favorite mathematics topic – one we often discuss in my house: the
fallacy of converse. I might tell my kids, “If you don’t eat your dinner, then you can’t have
dessert.” But, they are sometimes disappointed to learn, this doesn’t necessarily mean that
if you eat dinner, then you get dessert! They might be mad at me, but I’m just trying to
teach them logic! (I’m kidding – sort of.)
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Drs. Portier, Petrelli, Butler, and Hook hard at work
Mount Math Madness
By Jonelle Hook
The third Mount Math Madness competition commenced this past spring semester. Every
Monday, for five weeks, problems of various difficulties were posted and worth 100, 200, and
300 points. Students (and some faculty) participated and accumulated points in an effort to
make it into the elite eight. Also, each hundred points earned in a given week was equal to
an entry in a drawing. A weekly winner was randomly selected and awarded a $20 Amazon
gift card. Our weekly winners were Elizabeth Clark, Coleman Myron, Emily Wells, Alexa
Tuck, and Lydia Olsen.
The top eight students were placed into a bracket according to their rankings. For each of
the three bracket rounds, the students went head-to-head on a single problem and the first
person to submit a correct solution advanced in the bracket. This year we had six females
and two males make it into the bracket. The championship round ended up being between
the only two males, as freshman Coleman Myron, faced off against senior Michael Mugno.
Coleman was victorious and won the top prize of a $75 gift card to Amazon. As runner-up,
Michael won a $40 Amazon gift card. Both students were also awarded certificates of merit
and an Einstein bobblehead.
Below are some problems from this year’s contest. Find our “Mount Math Madness Problem
of the Week” page on Facebook and “Like” it to follow the contest next year.
1. The picture below shows the middle of a tic-tac-toe game. It is known that the game
ends with a win. Also, both players are equally skilled and do not miss any chances
to directly block a row from being formed. Can you tell which player will win? If so,
what are the moves?
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The final bracket
2. The event planner for the Superbowl decided to have all the players run down the fifty
yard prior to the start of the game. He ordered a decorative rope that was to be tied
from the goal post on one end of the football field to the goal post on the opposite
end of the field (the length of the field is 120 yards from post to post). When they
attached each end of the rope to the bottoms of the goal posts, they only had 4 inches
of slack in the rope. Are they going to be able to lift the rope at the 50-yard line so
that the players can run under it, or are the players going to have to jump over it?
3. Professors Keefer, Heinold, McGovern, and White play tennis in sets. Two of them
play a set and the winner stays on the court for the next set, with the loser replaced
by the player who was idle the longest. At the end of the day, Keefer played 61 sets,
Heinold played 22 sets, McGovern played 21 sets, and White played 20 sets. Who
played in the 33rd set?
4. Over spring break, I graded a lot of midterm exams. As I was grading, I came across
a student’s exam where a question was all smudged from the copier. There was no
possible way to read the question, but to my surprise the student answered correctly.
The answer choices were listed as follows.
A.
B.
C.
D.
E.
F.
All of the below.
None of the below.
All of the above.
Exactly one of the above.
None of the above.
None of the above.
How did the student get it right?
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5. Color the integers 1 through 13 using the colors red, blue, and yellow so that no color
group contains a solution to the equation a + b = c. (Note that a valid solution also
occurs when a = b.)
Mount Math Madness winners Coleman Myron and Mike Mugno
Smalltalk
By Brian Heinold
This was the fifth year of Smalltalk, our more or less weekly informal colloquium. It was our
largest year yet, in more than one way. We had more talks this year than in any previous
year, and we also had some trouble squeezing everyone into room 125. We seem to have
outgrown our room.
We also have a new record holder for most smalltalks by a student. Mike Mugno brought
his total up to nine smalltalks, breaking 2010 graduate Haley Blevins’s record of six. Here’s
a list of all of this year’s talks:
Fall:
A Magnetic Pendulum - Brian Heinold
Tux: The Penguin Revolution - Tim Evans
Graphs from Beyond the Grave - Michelle Rose
Graphing Prime Numbers - Mike Mugno
How to Make People Think You’re a Super Genius - Brian Heinold
Hypatia of Alexandria: An Egyptian Mathematician - Keri Barnes & Taylor Frock
Version Control Using Git - A Developer’s Best Friend - Dylan Bernard
The Middle Levels Problem - Maria Marinelli & Amy Strosser
Teaching a New Dog Old Tricks - Mike Mugno
Senior Project Demonstrations (Session 1) - Joey Gannon, Julian Ptak, Nick Warthen
Senior Project Demonstrations (Session 2) - Luis Beltran, Nathaniel Lewis, John Martin
Senior Project Demonstrations (Session 3) - Mike Mugno, Zach Eick, Branden Ehrenreich
Spring:
How Xerox Failed in the Computing Industry - Macon Carlton
There and Back Again: A Vector’s Tale - Tim Evans
Iterated Function Systems - Brian Heinold
iPhone Apps - John Martin & Mike Mugno
e - Brian Heinold
The Console - John Schultz
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Prof Weiss vs. Dr. Fill - Scott Weiss
Have You Tried Turning it Off and On Again? - Joe Garcia
Making Your LEGOS Move - Joey Naylor
Rstudio - Emily Gordon
A systematic method for calculating rook numbers - Michael Albright,
Brandi Jones, & Rachel Klado (from York College)
A look at general football probabilities using Markov Chains - Andrew Rhoads
I’m always looking for speakers, so if you would like to give a talk, just send me an email.
We are always happy to have alumni back to give talks.
Mike Mugno’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.
This is an article about a recent breakthrough in the theory of prime numbers. First, a
quick refresher. A prime number is a positive integer greater than 1 that is divisible by
only 1 and itself. The first few prime numbers are
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101.
Thus, 19 is a prime because it has no divisors other than 1 and 19. The integer 20 is not
a prime since it has lots of divisors (2, 4, 5, 10) other than 1 and 20. Euclid (≈ 300 BC)
showed there were an infinite number of primes. In fact, we now know there are roughly
n
ln n
prime numbers that are less than are equal to n (Prime Number Theorem). This ratio,
n
ln n , grows very slowly meaning that, although there are an infinite number of primes,
they become less prevalent as you move further into the list of positive integers. In fact,
the expected distance between consecutive primes grows without bound as the primes get
larger.
Two primes are called twin primes if they differ by 2. You can see a number of twin primes
in the list above. We have 5 and 7, 41 and 43, 71 and 73. In fact, there seems to be no
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shortage of these twin primes. A quick google search found that the huge numbers below
are twin primes.
570918348 × 105120 ± 1
Most mathematicians believe there are an infinite number of twin primes. This conjecture,
the twin prime conjecture, was first posed by Euclid and has remained unproven. This
conjecture is a little surprising since the average gap between primes is growing and yet, it
appears, there are always primes that are really close to each other.
It then came as a shock in May when Dr. Yitang Zhang of the University of New Hampshire
made a significant contribution. Although he was not able to prove the conjecture, he did
show there were always pairs of primes that were somewhat close. The somewhat in this
case is 70 million. OK, I know that is a large number, but compared to infinity, this
number is tiny. No one else has been able to demonstrate anything like this. His paper
has been reviewed and will appear in Annals of Mathematics, where it will checked and
double-checked.
To be precise, Dr. Zhang was able to show that there are an infinite number of primes that
are no farther than 70 million apart. Reducing the 70 million to 2 would prove the twin
prime conjecture. We will probably begin to see papers where this 70 million is reduced to
smaller numbers. With luck, we will actually see the twin prime conjecture proven in our
lifetimes.
An Interview with Dr. Butler
By Brian Heinold
Where are you from?
I grew up in Eldersburg, MD.
What did you do when you were a kid?
I was a swimmer. I liked to play school. Those are
the big things. I played softball.
How did you get interested in math?
I always liked math. I liked everything. I don’t really know how it happened, but
it happened. I’m glad it happened. It’s hard to think back. I don’t remember
making a conscious decision.
Where did you go to school?
I went to St. Mary’s College of Maryland and graduate school at Temple.
What did you study at Temple?
I ended up studying abstract algebra and did my dissertation in ring theory.
After graduate school I know you were at West Virginia University. What did you do there?
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I was part of the Institute for Math Learning. We were working to improve
the classes at the calculus level and below. That’s when I got involved in doing
mathematics education research.
I probably started off doing a lot of research on technology in math ed because
at WVU, class sizes were 200 students per class and a lot of my research was
in using technology to improve classes. I’ve done some research on clickers and
interactive computer lab activities for math.
Recently I’ve gotten more interested in looking at service learning and how that
affects math students and their engagement.
Tell me about some of your research.
Some recent research showed that students who completed a math servicelearning project felt more strongly than other students that knowledge of math
is important for leading a successful life.
I’m going to a conference in May to work on my next big research project: in
the fall, I’m planning to study service learning to see if it has an impact on the
social and academic collaboration of students. I want to see if students that
complete a service learning project collaborate more and if collaborations are
longer lasting. I’m planning to use social network analysis, which is related to
both computer science and graph theory, in the research.
How do you feel about becoming department chair?
I like doing administrative work. That’s something I did to an extent at WVU.
At the Institute for Math Learning I was in charge of big course sections. I enjoy
doing stuff like that. I can’t really do a better job than Fred. I’m just trying to
live up to Fred.
What do you like about math?
I like that it’s creative. People don’t often experience the creative side of math
until later in their study of the subject. I think that is one of the things we are
trying to show students in MATH 111.
I enjoy looking at a problem and trying to find a way to tackle the problem
that’s not immediately obvious. I like thinking very logically.
Do you have any hobbies?
I like to read. I like to walk and run when I don’t hurt myself.
Tell me about your family.
My husband, Fred, teaches at York College. He teaches math also. We met in
high school. I’ve got three kids. My son Jack is seven, my daughter Josie is
three, and then my son Andy is seven months.
What is a typical day like for you?
21
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I’m still getting up one or two times a night. My day starts somewhere around
1 am, 3 am. I usually get up around six and deal with the kids for a while. I
might drop my son off at the bus stop at seven, come to school, teach, do some
stuff, plan classes. I might work on research a little bit. A large part of that
time ends up being email stuff. I come home fairly early and pick my son up at
the bus stop around 4:30. Then it’s dinner and the bedtime routine.
What are your plans for the future?
I’m excited about this conference in May. I’m a ”scholar” at the conference, so
I get a mentor to help develop a strong research project. I have a few family
vacations this summer with extended family.
We just moved into this house in December, so we will try to get the house fixed
up.
Front row: Emily Gordon, Vicky Richards, Jessica Nase, Luis Beltran, Luis Bautista
Back row:Rebecca Thiem, Branden Ehrenreich, John Martin, Nathaniel Lewis, Julian Ptak, Mo Moriarty,
Mike Mugno
2013 Seniors
By Chris Jarvis
We are graduating 16 students this year.
In math, we have Luis Bautista, Chris Coughlin, Emily Gordon, Mo Moriarty, Vicky
Richards, and Rebecca Thiem. In Computer Science there are Luis Beltran, Branden Ehrenreich, Joseph Gannon, Nathaniel Lewis, John Martin, Michael Mugno, Jessica Nase, Julian
Ptak, and Nick Warthen. Zach Eick double-majored in math and CS.
We asked the graduates about their plans. Here’s what some of them told us:
Luis Bautista: After graduation I am taking the GRE in June to hopefully go to grad school
at The University of Maryland College Park campus to study mechanical engineering. Until
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then I am in the process of looking for an internship at Lockheed Martin, an engineering
firm, for the fall and hopefully help with grad school. If I am not able to find an internship
or job with them or somewhere else I will probably be working with my dad at his mechanic
shop in DC. (Hopefully I don’t have to, no AC!) I am also going to El Salvador over the
summer at some point with the family.
Luis Beltran: Upon graduation, I plan on working with Bechtel Corporation. I have been
working with them for almost three years, as their Computer Services Library Intern. I
started working with them as a summer intern my sophomore year, but things have gone
well and I have kept working with them during breaks and summers. However, I still plan
to keep searching for a job that is more suitable to my major, something more related to
software engineering, or programming.
I will probably be living in Frederick, as my wife and I are currently looking to rent in this
area, though this can change based on the jobs that she and I get.
I am planning on going back to graduate school in a year or so. I decided to take a year off
to take a break and to gain more experience in my field. At the moment I do not know what
to get my Master’s on; this is the reason why I want to gain more experience. Working will
hopefully give me a more precise idea of what I want to do with my life in terms of graduate
school.
Chris Coughlin: After graduation I am going to be working construction over the summer.
I am going to be living in Germantown and hopefully teaching in the fall. I am going to
Aruba in June. I am going to be starting graduate school in the winter of 2013.
Branden Ehrenreich: My plans after graduation are to attend graduate school. I plan to
get an M.S. in an information-security-related field.
The schools that I have been accepted to are:
DePaul University (M.S. Computer, Information, and Network Security)
Towson University (M.S. Computer Science with a concentration in Security)
Rochester Institute of Technology (M.S. Computer Security)
I am still waiting to hear back from:
George Washington University (M.S. Cybersecurity)
Johns Hopkins University (M.S. Security Informatics)
Zach Eick: I will be living in Baltimore after graduation and I plan to get a job in software
engineering. Once I have a job I will apply to grad schools.
Joey Gannon: I graduated in December and am employed at Raytheon as a software
engineer. I have been working there since January 21st.
Emily Gordon: After I graduate, I will be starting full-time as a mathematician at SAIC in
Columbia, MD. In the fall, I will be beginning my master’s program part-time at Johns Hopkins University. I will be receiving my masters in Applied and Computational Mathematics
with a specialty in Operations Research.
John Martin: As of now I am still searching for a job after graduation. I am talking to
several companies and want to make sure I find the right fit for me.
Mo Moriarty: After this year I have applied and been accepted to graduate school here at
the Mount. This summer I will be playing summer baseball in York while going to tryouts
to see if I can extend my baseball career beyond playing here at the Mount. If that does
not work out I will be here next year getting my MBA in business and will be a volunteer
assistant baseball coach at the same time. After completion of my MBA I hope to start
working towards my goal of getting into the FBI or some sort of government work along
those lines.
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Michael Mugno: After graduation, I will start a position with Booz Allen Hamilton, a
government contractor, as a Java developer. I will be working in Herndon, VA and living
with my parents until I save up for an apartment of my own.
Julian Ptak: I’m looking for a job either working with Android, Android app development
or web design. I’m looking to find my way into computer science through a programming
job.
Rebecca Thiem: After graduation I will be working for Optimus Technology, a company
I became associated with after the NSSP internship.
Nicholas Warthen: I have no plans other than trying to find a job which is still an on-going
process.
Luis Bautista
Luis Beltran
Chris Coughlin
Branden Ehrenreich
Zach Eick
Joey Gannon
Emily Gordon
Nathaniel Lewis
John Martin
Mo Moriarty
Mike Mugno
Jessica Nase
Julian Ptak
Vicky Richards
Rebecca Thiem
Nick Warthen
Answers to the faculty/student competition puzzles:
touch pairs with go, and straight pairs with narrow. go and narrow rhymes with bow and
arrow.
go out in a bog should be go out in a blaze of glory.
The teams are the Boston Red Sox, Chicago White Sox, Cincinnati Reds, Columbus Blue
Jackets, Detroit Red Wings, St. Louis Blues, Toronto Blue Jays, and the Washington
Redskins.
The corrected analogy is happy is to smile as sad is to what, making the answer frown.
Answers to before-and-after puzzles:
1.
2.
3.
4.
5.
Sittin’ on the Dock of the Bayes’ Theorem
Let it b2 − 4ac
Piano manifold
Old time Rock and Rolle’s Theorem
Eminem by n matrix
Answers to Mount Math Madness problems:
1. It can’t be X’s turn since O would have failed to block. So, O must block X’s winning
move by playing in the middle cell of the left column. Now, X plays in the upper right
corner leaving two winning moves (in gray) in which O can only block one on the next
turn and X wins.
2. The rope is lifted 93 inches or 7.75 feet and the players can surely run under it.
3. Keefer and White play in the 33rd set.
4. E.
5. Red (1, 4, 10, 13), Blue (5, 6, 7, 8, 9), Yellow (2, 3, 11, 12)
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