|Off on a Tangent
|A Fortnightly Electronic
Newsletter from the Hope
College Department of Mathematics
research will be the focus of tomorrow's colloquium
|Undergraduate Research Presentations, Part
|Forrest Gordon, Dan Lithio, Blair
and Jill Immink
November 20 at
Abstract: Undergraduate mathematics research students
from Summer 2008 will give 15-minute presentations about their
work. We will also give details about summer research
opportunities in mathematics coming up in 2009.
Pseudo-Orbit Shadowing in Continuous
Decreasing Functions on the Unit Interval, Forrest Gordon
and Dan Lithio (research done with Alex Berrian (Tufts University) and Prof. Tim Pennings)
A discrete dynamical system is a
function in which the output from a point is repeatedly reinserted into
the function so as to form a sequence - which is called an orbit.
When a computer is used to generate these sequences, there is
inevitable round off error, so that what is in fact generated is called
a d - pseudo orbit, where d is the amount of possible error. If a
dynamical system has the property that there is an actual orbit close
to every d - pseudo orbit, then the system is said to have the
shadowing property. After giving explanation and examples of the above,
we provide conditions for a decreasing continuous function on the unit
interval to have the shadowing property. Work supported by
NSF-REU #0645887 and an HMMI grant.
a Bicycle Upright: A Mathematical Modeling Project, Blair
Williams (research done with Prof. Tim Pennings)
How does a bicycle rider keep from
falling? Anyone learning to ride a bicycle realizes that this is
not easy. One must continually steer so that the resulting centrifugal
force (inertia) counteracts the pull of gravity on a slightly tipped
bike and rider. But one must also steer so that the desired direction
of travel is achieved. In this project, students are led through the
process of forming a mathematical model of bicycle tipping, and then
they use the model to discover a way to keep a bicycle upright and
traveling on a straight path. Work supported by an HMMI
Development in the Sophomore Calculus Sequence, Jill Immink
(research done with Prof. Darin Stephenson)
The focus of my research project is
curriculum development for MATH 231 and 232 (sophomore-level math
courses) at Hope College. My responsibilities include writing exercises
for Darin Stephenson's MATH 231 and 232 textbook, creating labs and
projects to supplement traditional lectures, and developing assessments
to evaluate these labs and projects. One lab exercise that will be
discussed in detail involves a model of a population of bacteria, which
is altered each time a generation of genes replicates. Students use
their background of linear algebra and vector calculus to model the
behavior of this population with stochastic matrices. Furthermore, this
example of gene replication can also be utilized at the high school
level due to the relative simplicity of the model. Such an activity
would test the students' understanding of limits, probability, and
systems of equations.
Please join us for refreshments
outside VWF 104 at 3:45 p.m.
semester's last colloquium will take a look at Fermat's Last Theorem
|Andrew Wiles and others
December 2 at 6:30
Abstract: Fermat's Last
Theorem was first conjectured in 1637, but only
recently proved (in 1995) by Princeton mathematician Andrew Wiles.
spite of the simplicity of its statement, Fermat's Last Theorem puzzled
even the greatest mathematicians for over 350 years. During this
colloquium, we will watch a NOVA documentary that describes Wiles'
quest to prove Fermat's Last Theorem. The documentary provides
insights into not only the mathematics behind Fermat's Last Theorem,
but also some of the interesting individuals who contributed to the
Pizza will be served at around 6:15
pm, and a brief discussion will take
place immediately following the video. So that we can order the
amount of pizza, please put your name on the signup sheet on Prof.
Hodge's door (VWF 205) if you plan to attend.
(Note that the
time and day for this colloquium are different than usual.)
With the end of the semester right around
the corner, the ways to receive colloquium credit are also coming to an
end. The last problem of the fortnight appears below. There
will be two more colloquia, one tomorrow and one the week after
Thanksgiving. Details on each of these is given above.
If you have put off completing your colloquium credit, your
opportunities are quickly fading away. Like Greg Meyer shown to
the left, hopefully you will have a strong finish this semester.
Problem of the Fortnight
Problem of the Fortnight for this
A square is divided into three pieces of
equal area by two parallel cuts as shown. The distance between
the parallel lines is 6 inches. What is the area of the square in
Write your solution (not just the answer!)
on a sanitized square piece of paper and drop it by Dr.
Pearson's office (VWF 212) by noon
on Wednesday, November 26.
As always, be sure
to write your name, the name(s) of your
professor(s), and your math class(es) on your solution (e.g. Trap
E. Zoid, Prof. Hy Potenuse, Math 225).
Good luck, and have
Solvers of the Fortnight
of the positive factors of
36,000,000 are not perfect
There are 149 factors of 36,000,000 that are not perfect squares.
Adam Alexander's solution is posted on the bulletin board.
to the following problem solvers of the fortnight: Eric O'Brien, Shane
Kwapis, Ben Fineout, Adam Alexander, Forrest Gordon, Sean Eble, Dan
Lithio, Mark Panaggio, Jack Nummerdor, Laura Smallegan, Anna Brandes,
Lute Olson, Andrea Eddy, James Nichols, Ashley Gruenberg, Jose
Martinez, Ben Barkel, XiSen Hou, Beth Heisel, Kayla Lankheet, Joshua
Borycz, Dayna Waters, Lindsay Nieuwkoop, Lydia Benish, Jon Boldt, Zach
Mitchell, Heather Esfandiari, Andrew Quick, Chris Jordan, Heather
Borgeson, Laura Shears, Chris Hall, Joel Riegsecker, Dan Waldo,
Christian Calyore, Heather Thompson, Kristi Wu, Kaily Grumpper, Joy
Taylor, Kevin Browder, Luc Leavenworth, Terra Fox, Zach Petroelje,
Stephanie Pasek, Ben Bockstege.
it snows, you have two choices: shovel or make snow angels.