OFF ON A TANGENT
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
September 8, 2004 Vol. 3, No. 1


Hope Students present at national conference: Mike Cortez wins award

Three Hope students -- Mike Cortez, Henry Gould and Andrew Wells -- presented papers at MathFest in Providence, Rhode Island this past August.

Andrew's talk was titled "Counting Symmetric Matrices of Rank one and two."  It was inspired by research he did in the summer of '03 under Darin Stephenson. He said, "Basically, we looked at how many matrices of specific ranks were contained in the span of a certain number of linearly independent n by n matrices."

"Mathematical Biology Curriculum Development" was the title of Henry's talk.  It involved research in which he participated during Summer 2003 with Janet Andersen.  Henry states, "I worked, along with a biology student, reading through biology research papers, revamping and creating new laboratory protocols, and things of that nature. All of this was done to improve the Mathematical Biology course offered each Spring."

Mike Cortez won an award for the best presentation on environmental issues at the Pi Mu Epsilon sessions of MathFest.  The award was sponsored by the Society for Industrial and Applied Mathematics (SIAM).  His talk, "A Mathematical Model of a Tri-Trophic Interactions," was based on research he did with Jennica Skoug and Mike Nelsen under the guidance of Prof. Janet Andersen and Prof. Thomas Bultman (Biology).  Their research used non-linear differential equations to model the interactions between a grass infected by a fungal endophyte, an herbivore (fall army worm), and a parasitoid (a wasp that ways eggs on the army worm and the offspring end up eating the army worm from the inside out).

From other research, it was known that the fungus was harmful to both the army worm and the wasp.  Mike stated, "In the end, we hoped to determine whether or not it was advantageous for the grass to have the fungus (the army worm is harmed more than the wasp, thus the army worm population is lower) or not (the wasp would be hurt more, therefore killing off the grass's control on the army worm)."  He also added, "This was different from previous research efforts since we were looking at the interactions of all three levels.  When looking at just two levels, the addition of the fungus is always better for the grass, but since the wasp is also harmed by the fungus, our model should be more accurate."

In addition to the student presentations at MathFest, Jennica Skoug, Brandon Alleman, Mike Cortez, and Mike Nelsen attended the Society of Mathematical Biology meeting at the University of Michigan in Ann Arbor.


Mike Cortez


New Faces: Matt Boelkins

Matt Boelkins is on sabbatical from Grand Valley State University this year and joins the math department as a visiting associate professor. At GVSU he has led several undergraduate research projects in the area of families of orthogonal polynomials.  His sabbatical is largely devoted to the development of further lines of inquiry for work with students. For fun he enjoys fishing, going to the beach, playing games, and all things sports-related, especially when done with his family. Matt received his B.S. from Geneva College, M.S. from Western Washington University, and Ph.D. from Syracuse University.


The first colloquium of the year is tomorrow

Professor Tom Jager from Calvin College will kick off the colloquium season this fall with a talk about the following intriguing question: If two positive integers are selected randomly and independently, what is the probability that they are relatively prime?  The answer is delightfully surprising!  His talk is titled "The Probability of Being Relatively Prime" and will be presented Thursday, September 9 from 3:30 - 4:30 p.m. in VWF 104.  Note the starting time is a half hour earlier than last year's colloquia.

  Bring a mug: Tea at 3:00 in VWF 222 (Reading Room) on Thursdays before colloquia

As part of our colloquium series this year, the mathematics department will host a "tea time" in the Reading Room (VWF 222) at 3:00.  If tea isn't really your cup of tea, have no fear -- we'll provide some other beverages and snacks, too.  So please bring a mug and 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.  (We'll provide some cups in case you don't bring one, but we'd like to encourage you to be eco-friendly and bring your own.)

             
Hope takes silver and bronze at the LMMC

Student teams from Hope College placed second and tied for third in the Lower Michigan Mathematics Competition held last April.  Albion College won the competition, and Calvin College was third along with Hope. The top five was rounded out by the University of Michigan at Flint.

The finishes continue a series of strong showings in the event for Hope. Teams from the college have won 10 times in the competition’s 28-year history, including in both 2002 and 2003.

Hope was represented by 16 students organized into six teams. The members of the college’s second-place team were Brandon Alleman, Henry Gould, Andrew Wells, while the students on the third-place team were Daniela Banu, Stefan Coltisor, and Heidi Libner.

The other participating Hope students were: Ben Bradley, Michael Cortez, Brandon Hazen, Natalie Hoogeveen, Brad Houzenga, Jennifer Kasten, Shova KC, Utsab Khadka, Luke Olinyk, and Jennica Skoug.



  Got a math question? 

  Ask Elvis . . .

     email him at elvis@hope.edu

Editor's note: Although it is unclear whether Elvis belongs to mathematics professor Tim Pennings or the other way round, they have collaborated on some calculus research, published articles on their findings, and can often be seen making their way across campus together.  If you haven't met Elvis yet, you should make a point of making the acquaintance of the world's foremost canine calculus expert.  He'll answer your questions even if he hasn't met you yet, so if you have a question you'd like to ask Elvis, please write it in an email to elvis@hope.edu with a subject heading of "Ask Elvis" to help him keep it separated from all his fan mail.  Because paws are an impediment to typing, Elvis can typically only answer one or two questions a week, but he appreciates receiving your questions even if he can't respond to them in his column.

Dear Elvis,
I'm interested in attending this week's colloquium, but I'm afraid I might be lost because I don't know what "relatively prime" means.  I know that the only divisors of a prime number are one and the number itself, but what does it mean for two numbers to be relatively prime?
                    -- Colloquially confused

Dear Colloquially Confused,
I'm an expert on calculus, but I don't know too much about numbers (although three different cats walk by my house everyday which I always thought was odd).  I asked around the department, though, and I think I have an answer for you: Two positive integers are relatively prime if their greatest common divisor is one.  For example, 2 and 3 are relatively prime, as are 3 and 4, but 2 and 4 are not relatively prime because the greatest common divisor of 2 and 4 is 2.

           Elvis
                   

Problem of the Fortnight

You have eight coins, all of which look, feel and smell identical.  One of them is counterfeit, and it is heavier than the other seven.  You also have a balance scale, on which you can put coins in the pans on each side and compare weights.  What is the minimum number of weighings you need to determine which coin is bogus, and how do you do it?

Tape your solution to a bogus Susan B. Anthony dollar and drop it in the Problem of the Fortnight slot outside Dr. Pearson's office (VWF 212) by 3 p.m. on Friday, September 17.  The Problem Solvers of the Fortnight and their just desserts (!) will be announced in the next issue. 


Say what!


Carl Friedrich Gauss, whom some consider the greatest mathematician ever to have lived, once said: "If others would but reflect on mathematical truths as deeply and continuously as I have, they would have made my discoveries."  Perhaps a good incentive to study hard for your math courses this year!  To read more about Gauss, please visit http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Gauss.html.
Carl F. Gauss



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