OFF ON A TANGENT
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
February 2, 2005 Vol. 3, No. 9


Tomorrow's colloquium will focus on using mathematics to predict animal behavior

In tomorrow's colloquium Professor Shandelle Henson of Andrews University will not show us how animals can be used to predict the weather, but will speak on the title "Can Mathematical Equations Predict Animal Behavior?" She will show that differential equations are being used to explain and predict the behavior of marine birds and mammals at Protection Island National Wildlife Refuge, Washington. Undergraduate students are involved in every aspect of the research, from data collection to the construction and analysis of mathematical models. This talk will be interdisciplinary and accessible. Although a knowledge of calculus and differential equations is necessary to understand some details, everyone will be able to appreciate the main points.  The colloquium takes place tomorrow at 4:00 in VWF 104.  Don't forget that tea time is scheduled from 3:30 to 4:00 in VWF 222.


Next week's colloquium should all add up

Next week's colloquium will feature Prof. Matt Boelkins, who is here on sabbatical this year from Grand Valley State University.  His title is titled "Is it totally irrational to ask what is?"  In calculus, we learn several ways to test whether or not an infinite series,converges. Via the integral test, given a real number p > 0, the p-seriesconverges if and only if p > 1. From this, we know that the series has a finite sum. So, what's the sum of the series? 

In this talk, he will consider this question for the above series, as well as for several other sums that are difficult to sum. Along the way, you'll meet some famous historical figures, encounter an unsolved problem or two, and see some of the unusual difficulties that arise when trying to add an infinite number of numbers. 

The details of this talk will be accessible to students who have completed calculus II. Other students of mathematics will be able to follow most of the big ideas in the talk.  The colloquium takes place next week Thursday at 4:00 in VWF 104.  Don't forget that tea time is scheduled from 3:30 to 4:00 in VWF 222.


Hope College Celebration of  Undergraduate Research and Creative Performance was held last Friday

Among the more than 100 projects of original work by Hope College students displayed last Friday at the Research Celebration, the following six projects were by mathematics students. 
  • Daniela Banu:  Analysis of the Conditioning Effect of Future Polynomial Regularization
  • Kyle Williams: Why are Learning Curves S-Shaped? A Probabilistic Model of Neural Connections
  • Ryan Weaver and Ryan TerLouw: Barging Ahead: Optimizing a Trip up the River
  • Tara Baase, Erica Pagorek, Megan Scholten: What is the Most Effective Way for Hope College’s Future Elementary Teachers to Learn the Mathematics They Will Need in the K-8 Classroom?
  • Andrew Wells:  The Group of Units of the Quaternoins Modulo n
  • Sam Lien and Brandon Alleman (Mathematical Biology): Building and Testing a Two-electrode Voltage Clamp System to Measure Transmembrane Currents in Xenopus Laevis Oocytes Injected with System xc
There were also a few math majors that presented posters in other disciplines.  A hearty congratulations to all of them on a job well done.
In the above image, Klye Williams is explaining his poster to a fellow student.  Below, Tara Baase and Megan Scholten stand in front of their poster.


Summer opportunities for research should be investigated soon

As evident from the research celebration last Friday, there are many students doing research at Hope during the summer.  The mathematics students are no exception to this.  Our department typically has around 10 students doing some form of research in mathematics during the summer.  This summer should be no exception.  The following are the research opportunities that currently exist.

Math students enjoy bowling and pizza event

Over 40 students and 6 professors came out to bowl and enjoy some pizza at the Math Department's Bowling and Pizza Spectacular on Saturday. Students from seven different math courses competed in four different team categories. David Visser had the highest score of any bowler with a 188 and was rewarded with a game of Set. He led his compatriots from Multivariable 1 to convincing victories in the class competitions for number of strikes by a class (32) and total score for a class (2349). The Calculus 2 students had the highest average score of any class with 122. The Bridge to Higher Mathematics group was the most diverse with a standard deviation of 43.2 for their scores. A final observation: there is a strong negative correlation (-0.70) between course number and course average bowling score.


The Third Annual Statistics showcase was held recently

Some of the outstanding projects from the Introductory Statistics courses (Math 210) were presented in our Third Annual Statistics Showcase on January 21.  Mark Dondero's paper looked at the proportion of males that eat at Gregordog and also compared the number of hot dogs ordered between males and females.  Katherine Stritzke investigated the walking speed of men versus women on Hope's campus.  Laurie Parker looked at stereotypes in various dorms at Hope.  Nate Golomb determined the fairness of quarters, nickels, and pennies when they were spun on a table.  Andrea Johnson and Heidi Simmons  investigated the differences in the age at which Hope students think is ideal to be married versus the ages their parents married.  Congratulations go out to all of these students for their hard work and outstanding results.


Harvard mathematician solves Venus flytrap mystery

A team of scientists led by a Harvard mathematician Lakshminarayanan Mahadevan announced last week that they had determined how the Venus flytrap snaps shut.  The carnivorous plant can close its leaves on an insect in a fraction of a second.  Dr. Mahadevan and others found that the flytrap slowly builds up elastic pressure in its leaves.  The leaf then snaps shut as the insect touches the hairy trigger inside.  Dr. Mahadevan and his colleagues have also been working on some other mysteries around us.  For example, they were able to determine how flys are able to stick to a wall and then quickly get unstuck again.  For more information about the Venus flytrap discovery visit http://www.news.harvard.edu/gazette/daily/2005/01/26-flytrap.html.  For more information about Dr. Mahadevan's other work visit http://www.news.harvard.edu/gazette/2004/07.22/19-maha.html.


Math in Action Conference set for next month

As mentioned in the last newsletter, the Math in Action Conference is coming up this month.  This conference is intended for those interested in mathematics education at the K-12 level.  The conference is schedule from 8:40 a.m. to 3:00 p.m. on Thursday, February 24 at the downtown campus of Grand Valley State University in Grand Rapids.  This year's theme is "Assessment Through Algebra and Number: Utilizing Multiple Benchmarks." 

Prof. Mary DeYoung has conference brochures available outside her office (209 VWF).  They are also available online at http://www.gvsu.edu/math/MathInAction/.  The mathematics department will pay the registration fee for those attending and transportation will be available.  You simply need to fill out a registration form that is in the conference brochure and return it to Prof. DeYoung by February 7.


Problem Solvers of the Fortnight

Congratulations to Jeff Ambrose, Sommer Amundsen, James Daly, Erica Dickinson, Brett Jager, Beth Leahy, Megan Patnott, Jennica Skoug, and Benjamin Crumpler for finding the distance between two skew lines in three-dimensional space.  Most folks found a vector perpendicular to both lines and measured the distance by taking the component of a vector that joined the lines along the vector perpendicular to both.  Another elegant solution came by writing distance as a function of the parameters s and t and minimizing this function.  A third ingenious tack put the skew lines in parallel planes and found the distance between the planes.

Problem Solvers are invited to drop by Dr. Pearson's office (VWF 212) to claim their prizes.


Problem of the Fortnight

Punxsutawney Phil came out of his den today to determine whether winter would persist another six weeks.  As he was contemplating the skies, he noticed two goats, Harry and Billy, tethered in a pasture together and engaged in a spirited debate about their grazing areas.  "I wish I were tethered with a longer rope," complained Billy.  "You get to so much more to eat than I because you have a longer rope.  And that's especially important during these winter months, when the grass isn't growing very quickly, if at all." 


"No need to get gruff, Billy goat," countered Harry.  "It's true," Harry ruminated, "that my rope is 11 feet long, while yours is only 10.  Mine, however, is tied to a ring on the outside wall of this circular silo, and I can just reach the point on the wall diagonally opposite the ring, so I get no grass at all in that particular direction.  You, on the other hand, can graze over a complete circle, so it seems you are much better off than I.  So stop your bleating!" 

"Oh," sighed Billy, "I wish I had continued my studies of math.  Then I could prove to you that I'm right!"

"Well, I don't agree that math would prove you right," rejoined Harry.  "But I do agree that if we had taken calculus, we could probably settle this question for ourselves."  Because Punxsutawney Phil has finished calculus before going to meteorology school, he just chuckled to himself and slid back down into his den.

Settle the great goat debate once and for all by computing the area each goat has for grazing.

Tether your solution to a circular slice of goat cheese (wrapped in cellophane, of course) and drop it in the Problem of the Fortnight slot outside Dr. Pearson's den (VWF 212) by 3:00 on Friday, February 11.


Mathography: Bartel Leendert van der Waerden (1903 - 1996)

Our featured mathematician this fortnight hails from---you guessed it---the Netherlands.  As a child, he proved for himself the laws of trigonometry, and his fascination with geometry led him to the field of algebraic geometry, where he made his greatest mathematical impact.  His work in geometry uses the theory of ideals in polynomial rings developed by Emil Artin, David Hilbert and Emmy Noether.  (Hilbert and Noether have been the subjects of previous Mathographies.)  Perhaps best known for his 1930 text on algebra, van der Waerden was also keenly interested in the history of mathematics and authored several books on the subject (available in Van Wylen library).  Van der Waerden spent most of his early academic life in Germany, but because he refused to give up his Dutch citizenship during World War II, the Nazis made his life difficult and van der Waerden eventually landed a post at the University of Zurich, where he stayed for the rest of his life.  Born on February 2, 1903, B.L. van der Waerden passed away in Zurich on January 12, 1996.


Got a Math Question?

Ask Elvis ...

... email him at elvis@hope.edu

Dear Friends,

While we all know that dogs know calculus, some people also think that groundhogs know weather prognostication.  Well, you probably heard that Punxsutawney Phil saw his shadow this morning and that means that we will have six more weeks of winter.  I for one know that we will have at least six more weeks of winter and I don't need some rodent to tell me that.  A prediction of at least six more weeks of winter in Michigan on February 2 is like a prediction that your cat will take a nap today---it's going to happen. 

Speaking of winter---you know the registrar here at Hope calls this the spring semester.  I think that is kind of like calling a cat friendly.  We all know that it really is the winter semester (and that the day after winter break is really a Wednesday and not a Monday).

Enough about the weather.  As you can see by my picture, I have not needed to come out of my den and answer any of your questions for quite some time now because I haven't received any.  Don't be shy.  If you have a question about mathematics (or perhaps about the animal kingdom) just send me an email at elvis@hope.edu and I or one of my colleagues will try our doggonest best to answer it.

Take care,

  Elvis

 
This is one time where television really fails to capture the true excitement of a large squirrel predicting the weather.
Phil Connors in Groundhog Day