Off on a Tangent
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
  April 4, 2011 Vol. 9, No. 13
http://www.math.hope.edu/newsletter.html


Next week's colloquium focuses on graph theory

Title: Convexity and Independence in Multipartite Tournaments
Speaker: Darren Parker, Grand Valley State University
Time:  Tuesday, April 12 at 4 p.m.
Place:  VWF 104

Abstract: In geometry, a convex set is any set of points such that, given any two points in the set, all points on the line segment between the two given points are also in the set.  This is a simple but powerful idea in geometry, but it turns out we can look at convexity in other contexts as well.  Since the definition of a convex set depends completely on points and line segments, we can generalize the concept of convexity by looking for structures that include things that act like points and things that act like lines.  Directed graphs are a perfect environment in which to work with convexity.  Here the "points" are the vertices, and the "lines" are directed paths.  In this talk, I will discuss some work my collaborators and I have done on convexity in multipartite tournaments.

The end is near!


For those of you waiting until the last minute to complete your colloquium credits, we are now fairly close to that last minute.  There are two problems of the fortnight left (including the one listed in this newsletter) and there are three remaining colloquia scheduled for the semester at the following days and times.
  • Tuesday April 12, 4PM—Darren Parker, Grand Valley State University
  • Tuesday, April 19, 11AM—Matt Boelkins, Grand Valley State University
  • Tuesday, April 26, 4PM—Melinda Koelling, Western Michigan University

 

Integration Confrontation


The Integration Confrontation will be Wednesday April 20th at 3 PM in VZN 297.  Teams of 1-3 students will compete solving challenging
integrals.  Fabulous prizes for the winners.  Please sign up by by 1:00 PM on Tuesday April 19th  on Professor Edwards' door.  You may
sign up as a team or we will place individuals on teams if they desire.  Participation in this event is worth one colloquium credit and the students should be in Calculus II or beyond.

Hope students score well in the Putnam exam

 
A big congratulations goes out to Nathan Graber, XiSen Hou, Joshua Kammeraad, and Bobby Nash on their outstanding performance in the 2010 William Lowell Putnam Mathematical Competition.  As a team, they finished 121st out of teams from 442 colleges and universies from the United States and Canada.

The Putnam exam is so challenging that this year's median score was two points out of a possible 120.  Individually, each of the four students scored between 10 and 20 points on the exam, all ranking within the top 1,670 out of the 4,296 individual participants from 546 institutions.

"Putnam is an extremely difficult and prestigious competition," said Dr. Aaron Cinzori, mathematics department chairperson.  "For our students to finish 121st among the best mathematical students in two countries, and to score 10 to 20 individually when the median was two, is a remarkable achievement and we're proud of their performance."

The annual William Lowell Putnam exam is a two-part, six-hour exam administered on the first Saturday in December, with the students who compete taking the exam on their own campuses.  The exam consists of 12 problems, each worth up to 10 points, that cut across many areas of mathematics and are designed to test originality as well as technical competence.  The competition began in 1938 and is administered by the Mathematical Association of America.

 

Math Online:  Mathematics in Movies

 
Oliver Knill of Harvard University has developed a website dedicated to Mathematics in the Movies.  The site features a collection of clips from more than 200 movies in which mathematics plays a part and each clip comes with an explanation of the mathematics found in the movie.  

Dr. Knill's mathematics in movies website can be found here.


Problem Solvers of the Fortnight

 
In our last our last PotF:  A certain dodecahedron has edges of length 10 cm.  If a fly lands on a vertex of this dodecahedron and then walks along only the edges, what is the greatest distance the fly could walk before coming to a vertex a second time and without retracing an edge?  Justify that your solution is optimal.
The following students gave correct solutions of 200 cm: AJ Wickham, Greg Hubers, Kendra Donze, Josh Kammeraad, Kent Kammermeier, Erica Budge, Eric Lunderberg, Josh Zoerhof, Andrew Mc Cubbin, Emily Krupczak, Craig Blume, David Jenkins, and Kyle McLellan.


Problem of the Fortnight


Allyson, Bethany and Corey have a window washing business and are regularly hired by a strip mall owner.  They have found that together they can finish the job in 6 hours less time than when Allyson works alone, 1 hour less than when Bethany works alone, and in ½ the time than when Corey works alone.  The next time they need to wash the windows, only Allyson and Bethany will be able to work.  How long will it take them?

Write a complete solution (not just the answer) on a dodecahedron and drop it off in the Official Problem of the Fortnight Slot outside VWF 212 by 3:00 pm on Wednesday, April 13.  As always, be sure to include your name, the name(s) of your professor(s), and your math class(es) -- e.g. Candice Waite , Dr. Harriet Knight, Math 112 -- on your solution. 




Signs you may or may not see in your travels. 

Off on a Tangent