newsletter-FA14 - Providence College

Issue : Fall 2014
STUDENT NEWSLETTER
Department of Mathematics & Computer Science, Providence College
What’s in this issue?
• p 1 - Greeting from the Chair
• p 2 - Announcements
• p 3 - Independent Study, MAT
Courses for Spring 2015 &
Department Colloquium
• p 4 - 5 - In the Beginning, There
was a Die… by Abigail Alegi
• p 6 - 7 - Meet a Professor:
Dr. Emmanouli Drymonis
interviewed by Tommy Upton
• p 8 - My Summer 2014 PURE
Math Experience, by Meghan
Malachi
• p 9 - Math Puzzles
!
Welcome to the Fall 2014
Mathematics & Computer
Science Department Newsletter.
This newsletter is put together
under the direction of faculty
members Su-Jeong Kang and
Cayla McBee.
The student
editors are Thomas Upton and
Lilienne Lawson.
This semester we welcome Dr.
Leila Setayeshgar as our newest
assistant professor of
mathematics. Leila has a Ph.D. in Applied Mathematics from Brown
University and will be teaching courses in probability and statistics.
We also welcome Dr. David Ferrone, adjunct assistant professor of
mathematics. David has a Ph.D. from the University of Connecticut
and will be teaching some of the “service” courses required by
business and science students.
Programs of Study:
Mathematics & Computer
Science
• Bachelor of Arts:
✴ Mathematics
✴ Mathematics/Secondary Ed.
• Bachelor of Science:
✴ Computer Science
• Minors:
✴ Mathematics
✴ Computer Science:
Business Programming
✴ Computer Science
I want to let mathematics and computer science students know that
we have re-purposed room 217 in Howley Hall. This room is now a
lounge for mathematics and computer science students and faculty.
So If you want a place in the department to sit and work or talk, you
are welcome to use Howley 217. A bulletin board in this room will
have information on graduate schools, undergraduate research
opportunities, and other information that might be of interest to
mathematics and computer science students.
Our department sponsors a colloquium series, a student seminar, a
T-shirt designing contest, the Putnam Exam and Problem of the
Week. For other department activities and information, check out
this newsletter!
Jeffrey Hoag, Chair, Mathematics & Computer Science Department
Department of Mathematics & Computer Science
Howley Hall 218,
Phone (401) 865 - 2334 ,
Fax (401) 865 - 1356
1
Issue : Fall 2014
Announcements
• The Putnam Competition is an annual mathematics competition for undergraduate students in the United
States and Canada. The exam has been offered annually since 1938 and is administered by the MAA. This
year’s exam will be held at Providence College on Saturday, December 6, 2014. For more information contact
Dr. Boos. (Howley Hall 202)
• The MAA Fall Section Meeting will be held at Southern Connecticut State University, New Haven, CT on
Friday, November 21st! If you are interested in either of the events below please contact Dr. Boos: (All travel
costs and meals are paid for!!)
✓
✓
Collegiate Mathematics Competition
Presentation in the Undergraduate Poster session
• The Mathematical Contest in Modeling (MCM) is a contest where teams of undergraduates use mathematical
modeling to solve real world problems. MCM and ICM, a part of MCM, will take place February 5 - 9, 2015. If
you are interested in these contests, contact Dr. Joseph Shomberg or Dr. Cayla McBee. For more information,
visit http://www.comap.com/undergraduate/contests/mcm
• An REU (Research Experience for Undergraduates) provides an opportunity to participate in mathematical
research at a school other than Providence College. Students participating in an REU work during the
summer with a group of other math-loving undergraduates from around the country while under the
guidance of a faculty member. In addition to days spent working on exciting research projects, most REUs
also provide social activities and entertainment during evenings and weekends. Housing and food are
provided, and on top of all this, you even get paid a stipend!
To see a list of REUs currently available go to: http://www.nsf.gov/crssprgm/reu/list_result.jsp?unitid=5044
or: http://www.ams.org/programs/students/undergrad/emp-reu
To read more about the different types of REUs go to:
http://www.maa.org/programs/students/undergraduate-research/research-experiences-for-undergraduates/
is-an-reu-for-you
If you are interested in applying to an REU, you can talk to your
advisor or contact Dr. Boos at [email protected].
• Designs for this year’s PC Math & Computer Science T-shirts have
been submitted. Look for an upcoming email to vote on a design and
order your T-shirt!
• Game Night: Come to Board Game Night, Thursday, October 23
starting at 7pm in Howley 217! Snacks and drinks will be provided. Bring your own game or play one of ours. Everyone is welcome! • Get Ready for Spring 2015! Registration starts at 7:30 am ✓
Class of 2015 & 2015 Dec. graduates - Nov. 14
✓
Class of 2016 & 2016 Dec. graduates - Nov. 17
✓
Class of 2017 & 2017 Dec. graduates - Nov. 19
✓
Class of 2018 - Nov. 21
Math/CS Department
Help Sessions !
Mathematics
Mon 5 - 7 pm at Howley 321
Tue
6 - 8 pm at Howley 321
Wed 4 - 9 pm at Howley 321
Thurs 4 - 9 pm at Howley 217
!
Computer Science
Mon 7 - 10 pm at Howley 321
Tue
7 - 10 pm at Howley 321
Wed 7 - 10 pm at Howley 321
Thurs 7 - 10 pm at Koffler 118
2
Issue : Fall 2014
Independent Study for Spring 2015
Master of Arts in Teaching
Mathematics (MAT) courses for
Spring 2015
!
Students interested in taking an independent study
course should speak with their advisor and the
professor offering the course.
Stochastic Processes, Dr. Setayeshgar
In probability theory, a stochastic (or random)
process is the probabilistic counterpart to a
deterministic process. Unlike a deterministic process
which can evolve in one way, in a stochastic process
there are several (often infinitely many) directions that
the process may evolve. Some familiar examples are
stock market, and medical data such as a patient's
EKG. In this course we will learn about some of the
most important stochastic processes, including
markov chains, martingales, and the famous
Brownian motion. Prerequisites: MTH 325
!
Differential Geometry, Dr. Kang
Differential Geometry is an area
solving problems in geometry
techniques of differential & integral
as linear algebra and multilinear
include arc lengths, curvatures
surfaces, geodesics, vector fields,
forms. Prerequisite: MTH 215, 223
in Mathematics
by using the
calculus, as well
algebra. Topics
of curves and
and differential
MTH 500 Foundations of Mathematics, Dr. Ishizuka Online - A course in the foundations of mathematics
designed to help prepare students for the study of
graduate-level mathematics. Topics in set theory,
class theory, the philosophy of mathematics, and
formal systems will be discussed. Emphasis will be
placed on the rigorous deductive process
characteristic of the study of mathematics.
!
MTH 502 Algebraic Structures II, Dr. Kang - Thursday
4:00 - 6:30 pm - This course is a continuation of Math
501. Topics include vector spaces and linear
transformations including the eigenvalue problem
and canonical forms.
!
MTH 512 Mathematical Analysis II, Dr. Ishizuka Tuesday 4:00 - 6:30 pm - This course is a
continuation of Math 511. Topics in sequences of
functions, Riemann Integration and measure theory
will be discussed.
!
MTH 523 Probability and Statistics, Dr. A. Shomberg
- Thursday
4:00 - 6:30 pm - Classical versus
subjective probability, probability models, limit
theorems, statistical inference and data analysis,
categorical data analysis and regression, correlation
and prediction will be discussed.
Department Colloquium (Fall 2014)
Organizers: Dr. Joanna Su & Dr. James Tattersall
✓
Sept. 17 - Meghan Malachi & Tucker Kibbee (Providence College)
✓
Sept. 24 - Kai Bartlette & Ben Wright (Providence College)
✓
Oct. 8 - Dr. Catherine Roberts (College of the Holy Cross)
✓
Oct. 22 - Dr. Lynette Boos (Providence College)
✓
Nov. 19 - Dr. Fred Rickey (United States Military Academy)
!
For additional information regarding talks and abstracts, visit
http://www.providence.edu/MCS/Pages/Colluquium.aspx
3
Issue : Fall 2014
In the Beginning There was a Die…
by Abigail Alegi (Mathematics ’14)
Mathematicians often find it difficult to pinpoint
exactly when the study of probability began.
Originating as an empirical study, it later became a
mathematical study believed to have originated
when Blaise Pascal and Pierre Fermat began
corresponding about the game of chance. However,
some argue its origin may have been developed by
Gerolamo Cardano and Galileo-Galilee.
The game of chance is crucial in the development of
probability study and theory. Historically, it has been
around for thousands of years and began with the
use of animal bones as game pieces. The bones,
specifically the astragulus and quoit bones from
animals, metals and stone were made to have
different, distinct sides. These game pieces were the
very primitive predecessor of what would become
the present day die. Images in Ancient Egyptian
tombs show the early use of these game pieces. The
pieces were used for gambling and games of
chance. The earliest known die date back to the third
millennium and were found in two separate areas,
Northern Iraq and Mohenjo-Daro, or Ancient India.
Both of which were made out of pottery.
16th Century — Gerolamo Cardano and GalileoGalilei made early publications on gambling and the
game of chance, specifically the probability of the
outcome of tossing a die. Cardano was a physician,
philosopher, mathematician,
astrologer and gambler. He
published Liber de Ludo Aleae,
which translates to A Book on
Games of Chance. His writings
were not discovered until after his
death; he concludes that a fair or
honest die can be given equal
weight to all sides and therefore
the probability of rolling a
particular side can be determined.
He expanded further to determine the probability of
tossing two and three dice as well. Cardano’s
calculations regarding tossing honest die were correct
but his predictions beyond that were not. Although not
all his writings were determined to be accurate, he is
credited as the first person to put any type of
probability theory down on paper.
Galileo-Galilei was an astronomer & mathematician.
His writing, like Cardano’s, focused on the probability
of tossing three dice. He noted that certain sums
resulting from rolling three dice are more likely than
others. For example, 3 and 18 are only possible one
way. He shows that the more combinations there are of
getting a certain number for the total sum, the higher
probability of rolling that sum.
17th Century — Blaise Pascal and Pierre de Fermat are
believed by most to be the originators of probability
theory. Although the works of Cardano and Galilei
deserve recognition, Pascal and Fermat had the most
success in their early probability
theories. Pascal began his
studies when presented with a
question from Chevalier de
Mere, a noblemen of the time
and an avid gambler. This began
their correspondence and thus
the beginning of their study of
probability theory.
The probability method
developed by Pascal and Fermat
is known as the Classical
Approach today. In their method,
4
Issue : Fall 2014
they determine that a dice game of chance has a
total number of equally likely outcomes, and a certain
number of outcomes that provide a winning roll. They
determined that the chances of winning are: the
number of rolls that result in a winning roll/total
number of equally likely outcomes. The other
method, the frequency method, was used by Pascal
and Fermat to test their method. This method is
simply testing the situation multiple times. Their
theory is correct but it is based solely on situations
with equally likely outcomes, which in probability
theory as it is known today is not always true.
Building off of the developments of Fermat and
Pascal, Christian Huygens continued developing
probability further when he published De Ratiociniis
in Ludo Aleae. His writings focused on the
applications of calculus in probability.
18th Century — Following Huygens, Jacob Bernoulli
and Abraham de Moivre become essential
contributors to probability theory. Bernoulli, a Swiss
mathematician born to a family of Swiss scientists,
published Ars Conjectandi. In his work, he
established that both methods up to that point in
history, the classical and frequency method, were
consistent.
De Moivre was a French mathematician that made
significant contributions to the modern approach of
probability which can be found in The Doctrine of
Chance: A method of calculating the probabilities of
events in play. In this work he develops his idea of
statistical independence: the outcome of one event
does not make the outcome of another event any
more likely or less likely to happen. He also
established the “The Central Limit Theorem” as we
know it today, the idea of standard deviation and the
normal integral, all important aspects of probability
as it is known today. It was during this century that
probability began to move away from testing games
of chance to testing the chances of scientific
outcomes such as the probability of the sex of a child.
19th & 20th Centuries — Pierre-Simon marquis de
Laplace was considered by many to be one of the
greatest scientists of all time. He published Théorie
Analytique des Probabilités which is considered to be
the first fundamental probability book. This book
studies generating
functions, Laplace’s
d e fi n i t i o n
of
probability, Bayes
rules, mathematical
expectation, and
p r o b a b i l i t y
approximations. All
very well-known and
commonly used
probability concepts
today.
Pierre-Simon marquis de
Andrey Kolmogorov developed the second
fundamental book of probability Grundbegriffe der
Wahrscheinlichkeitsrechnun in 1933. In this work he
defines conditional expectation. This definition was
crucial for defining Brownian motion, stochastic
integration and Mathematics of Finance. Kolmogorov
later published Analytical Methods in Probability
Theory which establishes the basis for Markov
processes.
Today, probability theory has many branches,
mathematical statistics being one of its most
important. Research continues to take place today
and the ideas of probability are further being
developed. We use probability today, whether we
want to or not, to calculate the outcomes of many
different scenarios. From calculating the chances of
developing a rare, genetically transmitted disease to
calculating the chances of filling out a perfect March
Madness bracket the uses are endless.
Citations
Brief History of Probability. (n.d.). Retrieved May 6,
2014, from http://www.teacherlink.org/content/math/
interactive/probability/history/
Probability. A very (brief) history. Florescu, I. (n.d.).
Retrieved May 6, 2014, from http://jpkc.fudan.edu.cn
/picture/article/
A Short History of Probability. Polansky, A. (n.d.).
Retrieved May 6, 2014, from http://staff.ustc.edu.cn/
~zwp/teach/Prob-Stat/
Studies in the history of statistics and probability: a
series of papers, Pearson, E. S., & Kendall, M. G.
(1970).;. London: Griffin.
5
Issue : Fall 2014
Meet a Faculty Member
Dr. Emmanouil Drymonis
interviewed by Tommy Upton (Mathematics, ‘16)
Dr. Emmanouil Drymonis is an Adjunct Assistant
Professor of Mathematics here at Providence
College. Dr. Drymonis is originally from Greece,
where he grew up and his family still lives. He came
to the United States to pursue degrees in
Mathematics, and in December of 2012 he received
his Ph.D. in Mathematics from the University of
Rhode Island. He does research in difference
equations, and he is also interested in differential
equations and statistics.
Q: When did you decide you wanted to study
mathematics?
A: I realized that around 15 or 16 years old, because
the teachers that I had in school at that time in
Greece fascinated me. I am from Greece, as you
know. I had 4 teachers, one was in mathematics, one
in chemistry, another taught physics, and the last
taught writing. These teachers really got me excited
about the sciences in general, especially my
mathematics and physics teachers. They really
inspired me, and made me interested in discovering
truth and how things work in certain theorems. So I
decided to become a mathematician, even though it
was difficult for me to start thinking in a
mathematical way at the beginning.
Q: Was it your experience with these teachers that
ultimately made you want to teach?
Q: Tell me a little bit about your research?
A: I do research in difference equations, which is a
field of mathematics that began as a discrete analog
of differential equations; later on it evolved in its own
way and is interesting in its own right. The area that I
focus on is rational difference equations, which is an
area my advisor, Dr. Gerasimos Ladas, started almost
30 years ago. So it is a relatively new area, where we
try to develop new theorems: because there is little
known there. We are among the first ones to search
and develop this fertile and fascinating field of
mathematics, which is amazing. A professor at
Harvard also said recently that difference equations
can, at times, be better than differential equations for
modeling natural phenomena, so there is an
application to it as well. But mathematics is not only
applied mathematics it is pure mathematics. A
discovery that will move mathematics forward is an
important discovery, even if it does not have an
application right now.
Q: What was it like deciding to come to the USA from
Greece?
A: Many people ask me why I would leave such a
beautiful country like Greece. But I think that it has to
do with exploring, going to new places, and meeting
new people. Also, in my opinion, the US is the best
place to get a Ph.D.
Q: What are some of your interests outside of the
classroom?
A: Well on the school website I say that I like sports
and traveling, but I forgot to mention the arts. My
A: Yes. Besides getting me excited about teaching,
they also got me very excited in doing research in
mathematics. In my opinion they both go hand in
hand. A good researcher is a good teacher, and a
good teacher is a good researcher. Things balance
out between them.
Q: What is your favorite class to teach?
A: Next semester will be the first time I teach
differential equations here, and it is my favorite class
to teach so far. When I was a lecturer at URI, I really
enjoyed teaching it and by the way, I got my best
evaluations ever.
6
Issue : Fall 2014
mother and sister are artists. My mother is a painter
of byzantine iconography, and my sister is a painter
of modern art. They also do ceramic work, and my
sister graduated from the School of Fine Arts in
Athens. My whole family has a good background in
the arts. So I really enjoy going to exhibitions and
concerts.
Q: Do you have any advice for any current math
majors or anyone considering a degree in
mathematics?
A: Well, there are two main options. You can be a
math major and go into industry, or you can go into
academics and get a Ph.D. You can decide to get a
Ph.D. and work at a college and do research, you
will have a quality life where you are very happy and
do what you love to do. You also get the benefit of
free time. Or you can go into industry. You major in
mathematics and maybe you go and get a Masters
in economics and then you can work at a big
company, maybe on Wall Street, and make a lot of
money. Actually, if you have a degree in
mathematics, you can do many different things with
some further, specific training. So I would definitely
recommend a degree in mathematics because it
opens many doors.
Q: Is there anything you want to say about your time
here at Providence College?
A: I have really enjoyed the time I’ve spent here at
Providence College. It is a great community, and I
really like the students as well as my colleagues.
We are looking for student volunteers to
contribute articles and to help us put this
newsletter together. If you are interested in
getting involved, contact Dr. Kang or Dr. McBee
From
Mathematics &
CS Department
Happy
Halloween
Everybody!
The Actuarial Profession
A Most Satisfying Career Path
for Math and Finance Majors
!
When: October 15 at 6:00 p.m.
Where: Howley Hall 321
Alumni from the Mathematics/Computer Science
program will speak on the Actuarial profession and
how to prepare for this profession. They are eager
to help current student enter the field. The speakers
are: !
• Garret Hepburn (class of 2011)
✓
✓
!
Describe the program
(study time, rotations, 3-strikes, raises, etc)
Exams (Life vs. Cas, topics, etc)
• Mike Mazzona (class of 2010)
✓
✓
✓
✓
Day in the life of an actuary – outside of work
Sacrifices and Commitments
Life Balance
Studying/Groups
• Shannon Droge (class of 2013)
✓ How you can prepare now:
✓ What course do you take?
✓ Internships
✓ Online Research
✓ Day in the life – at work – Team
✓ What happens at work?
✓ Projects with example
• Steve Basson (class of 1979)
✓
✓
!
✓
How to Sell Yourself for THIS profession
What companies are looking for (and it is
more than exams)
How to interview
This presentation is sponsored by the Department
of Mathematics & Computer Science.
If you are interested in actuarial science, or financial
mathematics, please contact Dr. Asta Shomberg
7
Issue : Fall 2014
My Summer 2014 PURE Math Experience
by Meghan Malachi (Mathematics, ’16)
This past summer I spent five weeks as a Pacific
Undergraduate Research Experience (PURE) Math
intern at the University of Hawai’i at Hilo. I
remember when Doctor Brian Loft, the primary
coordinator of the PURE Math program, called me
only two weeks after applying to the program and
told me that I was invited to spend several weeks
doing research on the subject I love on the island of
Hilo. I remember feeling extremely embarrassed as
I cried over the phone in complete disbelief that I
was one of twelve students chosen out of more
than two hundred applicants to participate in this
highly competitive program. As soon as I learned
that my flights, boarding, and meals would be
covered by the program and that I would receive a
generous stipend at the conclusion of the
internship, I just knew that there was nothing
holding me back from going; I felt blessed that I
had received this once in a lifetime chance to delve
into true mathematical research and visit the
beautiful “Aloha state”. The next day I e-mailed
Doctor Loft an assured and confident acceptance of
his offer.
!
When I arrived at Hilo International Airport, Lisa
Waters, our PURE Math assistant coordinator,
greeted me with a heartwarming sense of
enthusiasm and welcomed me to the island with a
traditional Hawaiian lei. From that moment on, I
knew that while I had a lot of math to look forward
to, I would nonetheless have the opportunity to
truly experience the culture of the island as well.
Throughout the internship, we were taken to
various sites on the island. We hiked up to the
summit of Mauna Kea, a dormant volcano whose
apex lies nearly 9,000 feet above sea level. We
gazed at the beautiful colors of the active volcano
Mauna Loa. We hiked through Hawaii Volcanoes
National Park, where we gazed at the steam vents,
plant life, and the craters throughout the trail. We
swam with honu, massive Hawaiian sea turtles, at
black sand beaches, and we spent entirely too
much money on hair flowers, homemade jewelry,
and fresh coconut water at the Hilo Farmer’s
Market.
During the first three weeks of the internship I learned
about the wonders of numerical monoids and their
factorization theory as well as python-based
languages and computer programming; during the
last two weeks, however, I was able to partake in
hands-on research of such monoids and their
invariants. The PURE Math faculty divided the twelve
interns into three groups of four interns and assigned
each of us the duty of further researching one of the
invariants of numerical monoids that we had touched
upon during lecture. At the end of the research
portion of the program, each research group proudly
uncovered something about numerical monoids that
no one else knows about or no one else was able to
prove. Each group presented its findings at a
symposium at the University at the conclusion of the
program. We were all awarded certificates of
completion and personalized gifts at our farewell
banquet.
If I could do PURE Math all over again, I unhesitatingly
would. I left JFK International Airport with a somewhat
weak mathematical background and a non-existing
history of formal research; however, I returned five
weeks later with the ability to take a more logical
approach to solving problems, a sense of how to
perform research in an intuitive manner, and the
ability to confidently present mathematical research at
formal symposiums and conferences. I left Hilo.
If you are interested in REU program and would like
to get more information, please contact Dr. Boos
8
d
Issue : Fall 2014
MATH PUZZLES
In the illustration four flat cube-like shapes are shown. Their
patterns are drawn with bold black lines. Which of them can you
draw without taking your pencil off the paper or going along
the same line twice?PiWhich of them can't be drawn in this way?
9/12/14, 1
Author: Peter Grabarchuk
This Puzzle © 2008 Peter Grabarchuk. All Rights Reserved.
Pi
The Mathmatician
9/12/14, 11:09 AM
Test your knowledge about the most mystifying number known to humans--pi.
Crossword Puzzle
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