| OFF ON A TANGENT |
A Fortnightly Electronic Newsletter from the Hope
College Department of Mathematics
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Student Research Celebration Held in DeVos Fieldhouse
"I saw it there…but I didn't know
why."
By JENNICA SKOUG | Staff
Writer
As I entered DeVos Fieldhouse, still polished
and shining since it's recent completion, I was struck by the audacious
banners of orange and blue, and by the bustling, noisy crowd
below. The tall-ceilinged arena was filled wall-to-wall not with
uniformed basketball players, but with a different face of Hope's
orange and blue -- the face usually kept in classrooms among hooded
sweatshirts and chalk-smudged professors, or in labs, amidst safely
glasses, computer programs and data sets, where the unknown tirelessly
refuses to reveal itself at anything more than a crawling pace to its
eager seekers.
The 5th Annual Undergraduate Research Celebration seemed
the perfect way to officially open and dedicate DeVos Fieldhouse, and
present to the public not just the sparkling new basketball court, but
the depth and breadth of creative and analytical knowledge that has
been breached by hundreds of Hope students (and professors) in recent
years. Over 175 student researchers were present at the event,
each endeavoring to summarize months or sometimes years of in-depth,
detailed learning into a two or three minute spiel that would satisfy
the inquiries of many passers-by. If you happened to attend the
student research math colloquium last semester, you may have recognized
the small but distinguished section of mathematics researchers, who,
along with several non-Hope students, spent the summer of 2005 puzzling
away in the halls of our beloved VanderPlex.
Daniela Banu worked with the enthusiastic and coffee-drinking Dr.
Pearson to find matrix representations for elements of metacyclic
groups (which, for Algebra novices like myself, boils down to taking a
more general, hard-to-work-with group of objects and turning them into
small, understandable matrices equip for linear algebra). While
Shova KC and Dr. Stephenson endeavored to find the expected area of
Randomly Generated Triangles within a regular n-gon (and while expecting
something random sounds contradictory, it really isn't). Kim
Harrison and David Visser worked with the late Dr. Janet Andersen
on a long-term collaborative project with the biology department,
developing a PDE Model for grass-munching Fall Army Worm.
There were, of course, other math majors present at the celebration,
demonstrating their intellectual prowess in other disciplines (which,
in spite of themselves, often include mathematics). For example,
it was hard to miss Kyle Williams' presentation on the optimal design
for wind turbine blades, or Megan Patnott's computer science "plug-in"
that adds additional colors as well as underlining and bolding features
to hard-to-decipher computer code -- both worthy endeavors!
All of the research presented could not possibly be described here (nor
could I have visited all the posters in 3 hours), but you can get a
Sparknotes-like summary if you happen to pick up a copy of the
celebration's abstract booklet -- which, by the way, was also designed
by a Hope student. Reading it, and imagining the possibilities
for future quests into this ocean of knowledge…well, you get the
feeling that despite any of it's faults or criticisms, Hope College is
really on to something here.
As I left the arena, one question lingered in my mind: why all of this
work? Why all of this nitty-gritty? Is it just to stand for
a moment amid intellectual chatter about Power Point posters, the
product of many dead-ends, traversed with endless cups of coffee?
Perhaps, in part. But as one student researcher told me, "I saw
it there…but I didn't know why." And the finding out of this
'why' is the heart of the matter.
A summer research opportunity
If you would like to be presenting an exciting poster at next year's
Research Celebration, then the mathematics department has a program for
you. This year's research program is being lead by professors
Mark Pearson, Airat Bekmetjev, Aaron Cinzori, and
Tim Pennings. They will be working with students this summer on
four
different projects. Although students apply from all over the
country for this program, Hope students are given special
consideration.
Participating REU students will receive a stipend of $2600 for the
eight week program. Free apartment-style housing will be provided.
Funds for travel as well as books and supplies are also available.
Visit http://www.math.hope.edu/reu.html
for more information about the program. Application deadline is
February 28.
In our last two newsletters, we highlighted Prof. Pearson's and Prof.
Cinzori's projects.
This time we will look at Prof. Bekmetjev's project on combinatoric
and probabilistic methods. His project
description is as follows.
This summer we
plan to investigate graph pebbling problems. It is relatively new area
of combinatorics that studies a game on a connected graph. Suppose that
pebbles are configured on vertices of a connected graph G. A pebbling step consists of
removing two pebbles from a vertex v and placing one pebble on a neighbor
of v. A configuration is called r-solvable if it is possible to move
at least one pebble to vertex r by a sequence of pebbling steps. A
configuration is called solvable if it r-solvable for any vertex of G. We will look at open
problems in this area as well as algorithmic aspects of this problem.
We will also consider probabilistic models of pebbling t such that any configuration of t pebbles is solvable is called the pebbling number of G. For example, for a complete graph
on n vertices pebbling number is n.
Last summer, as a part of the research efforts, REU students developed
an applet to play pebbling game online. It is available at http://math.hope.edu/bekmetjev/pebbling/.
Students should have a
background in combinatorics and/or graph theory. A knowledge in
computer science, probability theory, familiarity with computer algebra
systems (such as MAPLE) is a plus.
The Fourth Annual Statistics showcase
was held recently
Some of
the outstanding projects from the Introductory Statistics courses (Math
210) were presented in our Fourth Annual Statistics Showcase on January
20. Katie Janczak's looked into how many
licks it takes to get to the center of a Tootsie Pop. (Now the
world does know, at least at the 95% confidence level.) Laura
Hauch and Ruth Arvalo investigated how Hope students' opinions about
Pres. Bush differ from those nationwide. Jennifer Rice examined
the difference between men and women and their ice cream flavor
preferences.
Laura Malpass explored the use of Facebook and other online web
postings by Hope students. Zachary Snyder and Mathhew McCabe
looked into gender differences when it comes to getting a speeding
ticket after being pulled over for speeding. (Ladies, you do seem to
have quite an advantage here!) Laura Nettleton
investigated gender differences and dessert choices in Phelp's
Cafeteria. Congratulations go out to all of these students for
their hard work and outstanding results.
Math in Action Conference set for
this month
The Math in Action Conference is intended for those
interested in mathematics education at the K-12 level. The
conference is scheduled from 8:40 a.m. to 3:00 p.m. on Thursday,
February 23 at the downtown campus of Grand Valley State University in
Grand Rapids. This year's theme is "Making Connections."
Conference brochures are available online at http://www.gvsu.edu/math/MathInAction/.
The mathematics department will pay the registration fee for those
attending. You simply need
to fill out a registration form that is part of the conference brochure
and
return it to Prof. DeYoung by this Friday, February 3.
Professor Stephenson will speak on polynomials
- Thursday, February 2 at 4:00 p.m.
- VWF 104
Tomorrow's
colloquium, presented by Prof. Stephenson, is titled "How Quickly do
Spaces of Polynomials Grow?" He will begin by considering the
growth of spaces of commutative polynomials. For polynomials in
one variable x, there is
exactly one monomial of degree n,
namely xn. For
polynomials in two variables, there are n+1 monomials of degree n, the monomials xj yn-j for j = 0, 1, …, n. Using some basic counting
techniques, this result can be extended to polynomials in any finite
number of variables.
Most of this talk will focus on extending such results to the case of
“noncommutative polynomials” in some number of variables. The
ordinary polynomials in two variables x
and y satisfy a “commutative
rule” for rewriting monomials, that is, yx = xy. By changing the rule
and/or adding additional rules, we can consider the growth of the
corresponding spaces of noncommutative polynomials.
This talk will detail recent work on this problem, much of it
undertaken with the help of undergraduate students. We will
arrive at a number of easily stated open research questions during the
course of the talk. The details of the talk will be best
understood by students who have taken linear algebra (Math 231), but
results and concepts will be stated intuitively, so that much of the
talk should be understandable to students at all levels.
Tea at 3:30 in VWF 222 (Reading Room) on Thursdays before colloquia
As part of our colloquium series, the mathematics department will host
a "tea time" in the Reading Room (VWF 222) at 3:30. If tea isn't
really your cup of tea, have no fear -- we'll provide some other
beverages and snacks, too. So please join us for a little food
and fellowship before you go to the colloquia. It'll be a great
time to chat with the speaker, your professors and other
students.
Problem Solvers of the Fortnight
We received a record-setting 68 submissions to the Problem of the
Fortnight in the last issue! Sudo-kudos -- which are kudos for
conquering the sudoku puzzle and not, by any means, pseudo-kudos! -- to
all who tried the puzzle. It wasn't easy, but a record number of
you found the solution. Making the Honor Roll this fortnight:
Amanda Allen, Jeff Ambrose, Sam Baker, Trevor Bakker, Betsy Carlson,
Jenni Compton, Benjamin Crumpler, James Daly, Laura DeHaan, Anders
deJong, Mary DeYoung, Derek Duncan, Carleen Dykstra, Meg
Estochen, Jay Gibbs, Lindsay Goodell, Libby Hammon, Kim Harrison, Tara
Henderson, Katie Heneveld, Beth Heisel, Katie Hinkle, Maya Holtrop,
Mark Humberstone, Brett Jager, Clint Jepkema, Mike Jipping, Alyssa
Johnson, Katie Johnson, Jessie Jones, Lisa Kallemeyn, Deanna Kenafet,
Lauren Kucera, Christina Larson, Emily Mannenbach, Brian McLellan, John
McNutt, Jon Moerdyk, Keith Mulder, Karen Nordell, Ben Onken, Lucas
Osterbur, Stephanie Pasek, Martha Precup, David Rawlinson, Karena
Schroeder, Laura Shears, Jennica Skoug, Laura Smallegan, Chip Spires,
Darin Stephenson, Todd Swanson, Dirk Van Bruggen, Kate Vance, and
Rachel Van Kempen.
The solution to the sudoku puzzle is:
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Congratulations to all, and a special thanks to those of you who
provided your solution on the back of Super Bowl tickets. If you
see us on TV Sunday when the camera pans the stands, please be sure to
let us know!
Problem of the Fortnight
A long hallway has 20,000 LED lights (let's be environmentally
friendly, as long as we've got so many lights and are making it
up!). Each is operated by a switch that turns the LED light
either on or off. As coincidence would have it, 20,000 people
form a line at one end of the hallway. Initially the lights are
all off. The first person walks through the hallway and turns
each light on. The second person walks through the hallway and
hits the switch on every second light, thereby turning all the
even-numbered LEDs off. The third person walks through the
hallway and hits the switch on every third LED, turning some on and
others off. The fourth person hits the switch on every fourth
LED, and so on.
Which LEDs are on after the 20,000th person has passed through the
hallway?
Write your solution on a camping LED headlamp with elastic headband,
and drop it in the Problem of the Fortnight slot outside Dr. Pearson's
office by 3:00 p.m. on Friday, February 10.
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Got a Math Question?
Ask Elvis ...
... email him at elvis@hope.edu
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Dear Friends,
Did you know that tomorrow is Groundhog Day? It is tradition that
if February 2 is sunny and a groundhog sees its shadow, then we can
expect six more weeks of winter. If it is cloudy, however, a
groundhog will not see its shadow and we can then assume that spring is
"right around the corner."
You may have heard of the famous
groundhog named Punxsutawney Phil out in Pennsylvania that is the focus
of the news media on his special day. Did you know, however, that
Sun Prairie, Wisconsin is called the Groundhog Capital of the
World? Their favorite groundhog these days is Jimmy IX. If
fact, this town is so into groundhogs that it once held a wedding for
two of these large rodents. If you want to find out more about
the Groundhog Capital of the World visit http://www.groundhogcentral.com/.
I didn't receive any questions this past fortnight, so I think I will
pose one for you. Since a woodchuck is the same thing as a
groundhog, this made me think of the question, "How much wood could a
woodchuck chuck if a woodchuck could chuck wood?" If you
have a nice answer to this, send it to me at elvis@hope.edu.
Also, send me an email with any questions you have as well!
P.S. I've run across some other interesting town nicknames besides the
Groundhog Capital of the World. For example, Austin, Minnesota is
also know as Spamtown, USA. I'll have to ask Prof. Pearson (our
resident Minnesotan) if that name is referring to canned meat or bad
email. Either way, it makes one wonder....
An Ugly Monster
A freak, a most unusual pike,
Was caught at Jackson's Point by
Mike.
This fish was ugly, huge and strong,
With head alone twelve inches long.
Its body equalled, so Mike said,
Just half its tail plus twice its
head:
A third the monster's total length
Was tail, grotesque, but built for
strength.
So now maybe you'd like to see
How long this curious fish would be.
from More Fun with Figures by J.A.H. Hunter