Off on a Tangent
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
  February 24, 2010 Vol. 8, No. 9 
http://www.math.hope.edu/newsletter.html


Tomorrow's colloquium


Title:  A Workshop on Hyperbolic Polygons
Speaker:  Prof. Mike McDaniel and Jillian Russo (student), Aquinas College Mathematics Department
Time:  Thursday, February 25 at 4:00 p.m.
Place:  VWF 104

Abstract:  Following Emmendorfer, Precup and Warren's work on nested Euclidean polygons, we will examine the hyperbolic version.  Some compasses and straightedges will be supplied; so that participants may construct hyperbolic polygons.  Using the Poincare disk model, we will find properties of lengths, angles, sums of sides and areas of spirals.

Next week's colloquium

 
Title:  Modeling the evolution of insect development time in response to climate change
Speaker:  Prof. Brian Yurk, Hope College
Time:  Thursday, March 4 at 4:00 p.m.
Place:  VWF 104

Abstract:  Since developmental timing in insects is temperature-dependent, it is likely that climate change will result in dramatic changes in insect populations.  In these populations, there are strong selective pressures for maintaining appropriate developmental timing.  To survive to maturity, insects must avoid coincidence of sensitive life stages with extreme weather while maintaining overlap with resource availability.  The degree to which development is synchronized in a population can also have important fitness consequences, determining the probability of finding mates, the likelihood of avoiding predators, and the ability to overwhelm prey.  As climate changes, populations that are well-adapted to local climate conditions will be forced to migrate, evolve, or go extinct.


In this talk, I will present a mathematical model of the evolution of temperature-dependent development time in response to selection on emergence time and density in insect populations. Steady distributions for the model under stable temperatures are determined using asymptotic methods.  In numerical simulations, the existence of these distributions determines population dynamics under warming temperatures as well.  The model is applied to predict population dynamics and evolution of development time in mountain pine beetle (MPB) populations under warming temperatures.  Recent MPB range expansion and increased outbreak frequency have been linked to warming temperatures.  The MPB is an important insect from both an ecological and an economic perspective because its outbreaks often result in massive timber loss.



LMMC

The 34th Annual Lower Michigan Mathematics Competition will be held at Grand Valley State University this year on Saturday, April 10.  Students from colleges and universities in Michigan will gather there to challenge themselves on 10 interesting problems, working together in teams of up to three people. The competition runs in the morning and then lunch will be provided. Further information about this event and how to sign up will be in a future newsletter.  You can also find information about the contest here.

Hope has a history of strong showings at the LMMC, including several championships, and we'd like to regain the title this year and bring the Klein Bottle Trophy back to Hope!



Congratulations Dan!

Hope has a series of courses to help students get into the field of actuarial science.  Part of the process to become an actuary is to pass a series of certification exams.   Hope student Dan Waldo recently passed the Financial Mathematics Actuarial Exam.  Congratulations!

Actuaries use mathematical models to put a present dollar value on future risky events.  They work mostly in the insurance and pensions industries and have one of the highest job ratings.  For more information about Hope's program of study for pre-actuaries visit http://math.hope.edu/tintle/actuarial_program.html.



Real Math in the Fake News


Mathemagician Art Benjamin from Harvey Mudd College recently squared off with Stephen Colbert on The Colbert Report.  The interview included such items as liberal versus conservative numbers, how the number of mathematics courses taken is correlated (positively of course) with a person's lifetime income, and Benjamin's ability to square large numbers quickly in his head.  For a clip of Benjamin's interview click here.





GRE preparation help available tomorrow

The Hope Pew Society and the Office of Career Services are sponsoring an information session on the Graduate Record Examination.  Professor Mike Pikaart of the Department of Chemistry will discuss the mechanics of the GRE, what students might do to prepare for the exam, and answer questions.  The session is Thursday, February 25, 4:00-5:00 PM in 1019 Schaap Science Center.

A couple of other resources for GRE preparation at Hope are:
Math Club News


It's a slow time here at math club. We do have a meeting tomorrow, Thursday, February 25th at 7:00 in VZN 299.

We have ordered t-shirts, so keep your eyes peeled for more news about when and where to pick them up!






Problem Solvers of the Fortnight

In our last problem of the fortnight we found Delia, Tracy, and Bella going cross-country skiing with a school group.  They were carrying packs and each pack could weigh no more than 10 lbs.  The packs are weighed 2 at a time.  Delia and Tracy weigh their packs together and the total is 24 lbs.  When Delia and Bella weigh their packs, the total is 20 lbs.  Tracy’s and Bella’s packs together weigh 18 lbs.  Which skiers had packs that were too heavy, and by how much?

Solution:  D+T=24, D+B=20, T+B=18.  Subtracting the first two equations gives the new equation T-B=4.  Then solving the last equation and the new equation gives that T=11.  Further D=13 and B=7.  Therefore Tracy's pack is 1 pound too heavy and Delia's pack is 3 pounds too heavy.

Congratulations to the plethora of students that correctly solve this problem:  Andrew McCubbin, Tess Sammaro, Austin Cross, Matt Izenbaard, Courtney Killeen, Cara Cannan, Kendra Donze, Paige Douglas, Shayna Moon, Andrea Pickelman, Kyle Gibson, Dan Waldo, Carmen Hirsch, Robyn Dewey, Jessica Frey, Nolan Wiersma, Kim Slotman, Courtney Cook, Emily Barcely, Elliott Barney, Peter Doorn, Brian Ward, Christopher Calyore, Bethenie Gallagher, Nate Martin, Kate Hickox, Brian Kurzana, Eric Gobrogge, Elesha Wagenmaker, Danelle Koetje, Clare Hubbard, Nate Bowerman, Alex Kitzham, Sarah Prill, Xisen Hou, Phillip Hallam, Eric Halliquist, Daniel Simpson, Scott Brandonisio, Kristian Cunningham, Andrew Smith, Leah LaBarge, Russell Fyfe, Becky Chicklon, David Webster, Jaqueline Kirsch, Megan Ludwig, Kyle Sutton, Eric Lauzon, Sammie Pahls, Courtney Kimmell, Nathan Graber, James Nichols, Steven VanHoven, Josh Borycz, Amanda Blacke, Drew Gudeman, Scott DeClaire, Laura Hunnell, Lute Olson, Rob Peterson, Emily Scott, Allie Cerone, Morgan Bell, Caitlin Taylor, Kyle Alexander, Wesley Rieth, Leslie Stuipbergen, Ben Fineout, Erin Hildebrandt, Candace Goodson, Howie Dobbs, Matthew Rybar, Matt Eiles, Rachel Diephouse, Tim Cooke, Adam Maley, Tim Wahmhoff, John Zona, Matthew Koster, Kelly Shugart, Stephanie Brown, Angelica Willis, Danny Cole, Rebecca Danforte, Colin Zoellner, Marcus Bradstreet, Anna Filcik, Ryan Core, Danielle Fegan, Layne Fowler, BenThomas, Samantha Steffens, Ariel DuVal, Sarah Canche, Zach Mitchell, and Mark VanderStoep.

Problem of the Fortnight

Consider the following alphametic


PEOPLE
+ COUNT
------------
CENSUS

As we conduct the 2010 population census for the United States, we want to count as many of the population as possible.  So, find the maximum value of COUNT that satisfies the alphametic.  Note:  In an alphametic, each letter must be replaced by a different digit.  There are nine different letters that appear, so exactly nine of the ten digits 0 through 9 will be used in the solution.

Write your solution on an official census form and drop it off in the official Problem of the Fortnight slot outside Dr. Pearson's office (VWF 212) by 3:00 p.m. on Friday, March 5.  As always, be sure to include your name, the name(s) of your professor(s), and your math class(es) -- e.g. Eva Destruction, Professor Babe Ruthless, Math 153 -- on your solution. 

Citius, Altius, Fortius.  (Swifter, Higher, Stronger.)

The Olympic Motto
 
Off on a Tangent