Off on a Tangent
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
   November 5, 2008 Vol. 7, No. 5  
http://www.math.hope.edu/newsletter.html


Student research will be the focus of tomorrow's colloquium


Title:
 Undergraduate Research Presentations, Part 1
Speaker:
 Brian McLellan, Eric Lunderberg, and Zachary Mitchell
Time:
 Thursday, November 6 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.

A Linear Trend Test for Including Duplicate Genotype Data in a Genetic Test for Association, Brian McLellan (research with Bryce Borchers, Marshall Brown, and Faculty Mentors Dr. Nathan Tintle and Dr. Airat Bekmetjev)  In genome wide association studies researchers often duplicate genotype between 2 and 10% of the sample as a quality control measure.  Typically, duplicate data is discarded before testing for association between genotype and phenotype.  However, we demonstrate that statistical power is increased by including duplicate genotype data in the test.  To include duplicate genotype data we propose a modified linear trend test (LTT) of association and demonstrate its asymptotic properties.  Further, we demonstrate that in many practical cases, the most cost effective use of resources would be to collect duplicate genotype data on the entire sample, instead of only a small fraction.  We present software that assists researchers in deciding if the collection of duplicate genotype data is cost-effective, as well as to compute the modified LTT.  Work supported by NIH R15-HG004543 and the Tanis Fund for statistics research at Hope College.

Cost-Effectiveness of a Three Classification Prevalence Testing Design, Eric Lunderberg (research with Ben DeWinkle and Faculty Mentor Dr. Nathan Tintle)  We examine the practicality and cost-effectiveness of collecting triplicate genotype data.   In particular, we show examples where three classifications provide benefits over two (or fewer) classifications.  Work supported by NIH R15-HG004543 and the REACH program at Hope College.

Turning Out the Lights, Zachary Mitchell (research with Victoria Elandt, Nicholas James, Katie Johnson, and Faculty Mentors Dr. Stephanie Edwards and Dr. Darin Stephenson)  Lights Out is a game played on a finite graph. The standard game starts with some vertices “on” and other vertices “off,” and pressing a vertex toggles the state of that vertex and all adjacent vertices. The goal of the game is to turn off all of the lights. We have studied a generalization of the game with any number of colors, and have determined which graphs in certain families (spider graphs, theta graphs, and trees) are winnable for every initial coloring.  Work supported by NSF-REU #0645887 and a Hope College Dean’s Research Award.
Next week's show when bad derivatives go good


Title:
 The Freshman Rule
Speaker:
 Prof. Aklilu Zeleke, MSU
Time:
 Thursday, November 13 at 4:00 p.m.
Place:
 VWF 104


Abstract: The erroneous way of calculating the derivative of a product by taking the product of the derivatives has been referred as the Freshman Rule. After briefly discussing the history of the Freshman Rule, we present different cases when the Freshman Rule gives correct result. Extensions to other operations will also be presented. This talk will be accessible to students with calculus background.


Meet Me in St. Louis, Louis

Hope students Josh Kinder, Mark Panaggio, Scott Hawken and Blair Williams traveled to Washington University in St. Louis last weekend to present their research at the Undergraduate Research Symposium of the Midstates Consortium for Math and Science.  Roughly 80 students from consortium schools gathered there to give talks and present posters about research they had conducted. 

Blair Williams gave a talk entitled "Modeling with Calculus: As Simple as Riding a Bike" that surveyed the research he had done with Dr. Pennings last summer on the mathematical modeling of riding a bike.  Josh Kinder, along with his research partner Sarah Cobb, presented their talk "Necklaces, Symmetry and Irreducible Representations of Wreath Products" about the algebra research they conducted with Dr. Pearson last summer; Josh and Sarah are pictured at left.  Scott Hawken presented a poster "Synthesis and Electrochemistry of Dinitronapthalimides" about the chemistry research he conducted with Dr. Gilmore last summer.  And Mark Panaggio presented a poster "Study of Pressure Waves from Close-in Blasts" detailing the results of the engineering research he did with Dr. Veldman.  Congratulations to Josh, Mark, Scott, and Blair for their research accomplishments and for their contributions to an excellent symposium!


A pie-cosahedron makes a great Thanksgiving dessert

Tired of the same old Thanksgiving pumpkin pie?  Need to get a little more mathematics in your desserts?  If so, we have a recipe for you and is large enough to feed your family as well as the families of many of your friends.  We found instructions for making a pie-cosahedron (or a pecan pie icosahedron) online.  The complete pie is composed of 20 triangular shaped pies and will easily feed over 100.  You might want to get started early on this because your first steps involve making the pie plates.  Complete instructions for creating this dessert are located at http://www.instructables.com/id/modular-pie-cosahedron/.




The Problem of the Fortnight

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

Write your solution (not just the answer!) on a not perfectly square piece of paper and drop it by Dr. Pearson's office (VWF 212) by noon on Friday, November 14.  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. Ima Rhombus, Prof. Ernest Try, Math 289).  Good luck, and have fun!




Problem Solvers of the Fortnight

Find an expression for the continued radical

C = √ ( m + √ (m + √ (m + ...)))

in terms of m that does not involve a continued radical and determine all positive integers m so that C is a positive integer. 

Notice that C = √ ( m + C), and so upon squaring both sides we get C2 = m + C, or equivalently, m = C2 - C = C(C-1), and so m must be a product of consecutive integers; that is, m = 2, 6, 12, 20, 30, 42, . . . .  Xisen Hou's solution is posted on the bulletin board.

Congratulations to the following problem solvers of the fortnight: Zach Mitchell, Luka Levata, Xisen Hou, Colin Rathburn, Kyle Gibson, Lydia Benish, Mark Panaggio, Andrea Eddy, Ashley Gruenberg, Jill Immink, Mark Gilmore, Kristian Cunningham, Dan Waldo, and Mitch Brown.

For too long we've been told about us and them.  Each and every election we see a new slate of arguments and ads telling us that they are the problem, not us.  But there can be no them in America. There's only us. 

Bill Clinton
Off on a Tangent