Off on a Tangent A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
 November 19, 2008 Vol. 7, No. 6 http://www.math.hope.edu/newsletter.html

 Student research will be the focus of tomorrow's colloquium

 Title: Undergraduate Research Presentations, Part 2 Speaker: Forrest Gordon, Dan Lithio, Blair Williams, and Jill Immink Time: Thursday, November 20 at 4:00 p.m. Place: VWF 104

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.

Keeping 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 grant.

Curriculum 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.

 The semester's last colloquium will take a look at Fermat's Last Theorem

 Title: The Proof Speaker: Andrew Wiles and others Time: Tuesday, December 2 at 6:30 p.m. Place: VWF 104

Abstract:  Fermat's Last Theorem was first conjectured in 1637, but only recently proved (in 1995) by Princeton mathematician Andrew Wiles.  In 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 proof.

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 right 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.)

 The end is near!

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.

 The Problem of the Fortnight

The last Problem of the Fortnight for this semester:

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 square inches?

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 fun!

 Problem Solvers of the Fortnight

How many of the positive factors of 36,000,000 are not perfect squares?

There are 149 factors of 36,000,000 that are not perfect squares.  Adam Alexander's solution is posted on the bulletin board.

Congratulations 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.

When it snows, you have two choices: shovel or make snow angels.

Unkown

 Off on a Tangent