Off on a Tangent
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A Fortnightly Electronic
Newsletter from the Hope
College Department of Mathematics
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Title:
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Death
and Dismemberment in a Petri Dish:
Modeling a Three-Level
Interaction Using Nonlinear Dynamics
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Speakers:
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Tim Boman,
Ryan Johnson, Bryan
McMahon, and John Molenhouse, Hope College students
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Time:
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Thursday,
October 4 at 4:00 p.m.
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Place:
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VZN
240
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Abstract: We
studied a three-level food chain (a tri-trophic interaction) between
Tall Fescue grass, Fall Armyworms, and parasitic wasps and how this
relationship changes when a fungal endophyte (a fungus that lives
inside the grass) is introduced. Tri-trophic interactions are not only
interesting because of their intriguing dynamics, but also because
there are few tri-trophic models that have been fully analyzed. Using
three nonlinear differential equations, one equation for each
population, we attempted to analyze this system and predict the
population patterns in environments with and without the fungal
endophyte. Our goal was to find the fixed points of these systems,
which are where the populations settle down into an unchanging
equilibrium. Some of these fixed points were easily analyzed, while
others required a novel approach. Aside from the mathematical analysis,
we also got our hands dirty working with the caterpillars and wasps
(the grass was pretty clean).
Title:
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Optimizing
a Volleyball Serve
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Speaker:
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Dan Lithio,
Hope College student
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Time:
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Tuesday, October 9
at 4:00
p.m.
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Place:
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VZN 240
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Abstract: An optimal volleyball serve is one
that gives
the receiving team minimal time to react. That is, it is one in
which the ball goes over the net and hits the floor in the shortest
amount of time. In this talk I'll develop a model for the flight
of a volleyball acted upon by gravity, air resistance and spin.
Coefficients of drag and spin were determined via crude but ingeniously
effective experiments, and the trajectories of theoretical models were
compared with actual trajectories of volleyballs shot from a
launcher. Finally, we use the model to find the optimal serves
while varying the height of the serve, the amount of spin, and the
total distance traveled.
As
part of our colloquium series, the mathematics department
will host a "tea" in the Reading Room (VWF 222) at 3:45 p.m. on
Thursdays before colloquia.
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. We encourage
you to be environmentally friendly by bringing a cup for beverages, but
we'll provide cups if you can't bring your own. Please join us
for tea on Thursdays before colloquia! It's a
great time to chat with the speaker, your professors and other
students!
Two
mathematics competitions that
take place each fall are the MATH
Challenge and the Putnam Exam. Students can compete in either of
these competitions without leaving Hope's campus. Information
about each of these follows.
The MATH Challenge
The 2007 Michigan Autumn Take
Home Challenge (or MATH Challenge) will take place on the morning of
Saturday, November 3 this year. Teams of two or three students
take a three-hour exam consisting of ten interesting problems dealing
with topics and concepts found in the undergraduate mathematics
curriculum. Each team takes the exam at their home campus under
the supervision of a faculty advisor.
The department pays the registration
fee for each team and will provide lunch to participants afterwards.
The sign-up deadline is Monday, October 22
at
4:00 p.m. Interested students can sign up by
sending Prof. Edwards an email at sedwards@hope.edu or by signing up on
the list on her door (VWF 218).
A group of students may sign up as a
team. Individual students are also encourage to sign up; they
will be assigned to a team on the day of the competition. For
more information, please talk with any member of the
Mathematics Department or visit http://www.mcs.alma.edu/mathchallenge/, where you can also view old copies of
the exam.
The Putnam Exam
The William Lowell Putnam
Mathematical Competition, administered by the Mathematical Association
of America, is the most prestigious mathematical competition for
undergraduates in the nation. If you are interested in taking the
68th Annual Wm. Lowell Putnam Exam, you must email Professor Stoughton
by 4:00 p.m.
on Tuesday, October 9. The date of the exam is Saturday,
December 1, 2007. There is both a morning and an afternoon session of
this exam; lunch will be provided by the mathematics department during
the break. For more information about the Putnam Exam visit http://math.scu.edu/putnam/. For questions and solutions from past
exams visit http://www.kalva.demon.co.uk/putnam.html.
The Department of Mathematics at Michigan State University will host
tenth annual Michigan Undergraduate
Mathematics Conference (MUMC) on Saturday, October 27, 2007. Hope
College will be taking a group of
students and faculty. They will
leave early in the day and return in the evening.
Undergraduate students will be giving
20-minute oral presentations on many areas of mathematics, statistics
or related disciplines. Such areas include undergraduate research
projects, interesting class projects, history of mathematics, or
expository talks on interesting mathematics. Students are also
encourage just to attend as there will be presentations on careers in
mathematics, information about mathematics graduate programs and REU
programs.
Students interested in
attending need to sign up with Prof. Darin Stephenson by Monday, October 8
(he has a sign-up sheet
outside his office door, VWF 219). Visit the MUMC web page at http://www.lymanbriggs.msu.edu/mumc2007 for more information about the conference.
The
Problem of the Fortnight
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The Problem of the
Fortnight has gone national! More precisely, the Problem of the
Fortnight will now be part of the national
Problem Solving Competition. The Hope College student who submits
the greatest number of solutions from now until the end of the year
will be eligible for a prize!
The problem for the upcoming
fortnight involves a regular tetrahedron, a solid whose four sides are
congruent equilateral triangles. The problem is:
A regular tetrahedron has edges 36
units in length. What is the
altitude of the tetrahedron? Give your answer in simplest radical
form (i.e. x √ y form) and make sure you justify your answer.
Write
your solution on a piece of paper, fold it into a tetrahedron and
drop it by Dr. Pearson's office (VWF 212) by noon
on Friday, October
12. As always, be sure
to write your name, the name(s) of your
professor(s), and your math class(es) -- e.g. Al T. Tude, Professors
Newton and Leibniz, Math 131 and 132 -- on your solution.
Problem
Solvers of the Fortnight
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A number of students brushed
off their trigonometry skills and were able to come up with a correct
solution to last week's problem of finding the length of L in terms of 
. There are a number of ways to write a correct
answer to this problem. One way is
.
Dear Elvis,
We heard you had your second surgery
and that it went well. We miss you coming by for your snacks here
in the office. Get well soon and come to see us!
Jil, Marlene and Cathy
Dear Jil, Marlene and Cathy,
Thanks for the get well
wishes. It is nice to be back in the office enjoying everyone's
company and the delicious snacks that are made available to me.
While I haven't been that active
lately, I have been keeping my big ears open (and my big mouth
shut). I have heard three rumors of some interesting mathematical
locations around campus.
- There is a "whispering bench" in front of Graves Hall.
Typically you hear of this type of phenomenon in terms of a whispering
gallery. Rooms such as these have ellipsoid shaped
ceilings. When one whispers at one focus, the sound is clearly
heard at the other. You and a friend might want to check out the
bench by Graves to see if it truly is a whispering bench.
- The floor in Room 207 in the Dow Center is in the shape of a
golden rectangle.
- The plaza in between the Science Center and VanZoeren is almost a
perfectly shaped ellipse.
Does anyone else know any
interesting mathematical things about the Hope College campus? If
so, let me know via email at elvis@hope.edu.
I would also love to hear from you if you have any mathematical
questions.
Your
pal,
It's supposed to be
hard. If it wasn't hard, everyone would do it. The hard... is what
makes it great!
~ A line from A
League of Their Own
