OFF ON A TANGENT
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
February 14, 2007
Vol. 5, No. 10
http://www.math.hope.edu/newsletter.html

    Happy Valentine's Day! 

Bowlizza this Saturday
 This Saturday the mathematics department will host its annual bowling and pizza (bowlizza) extravaganza.  We'll meet at Holland Bowling Center, located at the corner of 9th and Central, at 11:00 a.m. on Saturday, February 17.  The competition is sure to be fierce but friendly as students and professors vie for various prizes -- e.g. highest score, most strikes, largest standard deviation, to name just a few.  After a couple games of bowling we'll return to the math department for pizza. 

Sign up sheets will be passed around in your classes.  There will also be a sign up sheet on Professor Pearson's door (VWF 212) for you to sign up before noon on Friday, February 16.  Through the largess of the math department, the event is absolutely free to students.  We hope you'll be able to join us!

Thursday's Colloquium
When categorical data is collected, we typically assume that individuals are categorized correctly.  However, errors of classification can occur.  Classification errors can significantly bias estimates and increase type I and type II error rates when hypothesis testing.  For some automated classification mechanisms, we can model the way that classification errors occur.  I will present a general model for classification errors in SNP data, and demonstrate how duplicate genotyped (re-classified) data can be included in genetic tests of association (an asymptotic Χ2 test and a permutation test) to increase statistical power.  No knowledge of genetics will be pre-supposed.  This talk will make use of some concepts from introductory statistics (Χ2 test of association; independence; type I and type II errors).  I will also talk about summer research opportunities in this area and work that current Hope students are involved with.

  Join us for Tea Time 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 3:45 pm.  If tea isn't really your cup of tea, have no fear -- we'll provide some other beverages and snacks, too.  So please 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.

Statistics Showcase

On Friday, January 19, the Mathematics Department hosted the 5th annual Statistics Showcase.  Robyn Smith, Nik Burkhart and April Muske unveiled the marketing strategies of cereal companies, concluding that cereals with high sugar contents were consistently placed at the eye-level of children while cereals lower in sugar content were higher on the shelves at grocery stores.  Benjamin Bach and Kayleigh Tubbergen weighed in on the ongoing Mac vs. PC debate, surveying Hope students about performance reliability of their computers to conclude that Mac users enjoyed a higher satisfaction with their computers.  (When asked, Benjamin replied that he himself uses a PC.)  And Michelle Zeiter studied whether Hope students' use of silverware in the cafeterias was wasteful.  She concluded that students often took more silverware than they actually used, thereby wasting energy in washing the unused utensils, but that given the current configuration of the cafeteria in Phelps, it would not be practical to rearrange the dining hall so that the silverware was at the end of the food line where students could take exactly the utensils they needed.  The presenters did a wonderful job, enlightening and entertaining faculty and students from across campus.

Research Celebration

The sixth annual Celebration of Undergraduate Research and Creative Performance was held Monday, January 29, at the DeVos Fieldhouse.  Among the more than 160 projects involving around 275 Hope students and their faculty mentors were two projects from last summer's mathematics REU at Hope.  Megan Patnott, who worked with Ashley Olson from UC-San Diego under the direction of Dr. Airat Bekmetjev, presented work she and Ashley had done on graph pebbling.  Dan Lithio, who worked with Eric Webb from Carnegie-Mellon under the direction of Dr. Tim Pennings, presented work he and Eric had done on optimizing a volleyball serve, answering questions posed by volleyball head coach Becky Schmidt.  The math REU crew from this past summer is pictured at right.

Hope Students Accept the Challenge

On Saturday, October 28, 2006, eleven Hope Students participated in the Michigan Autumn Take Home (MATH) Challenge.  The students spent 3 hours working in teams of 2 or 3 on 10 challenging mathematics problems.  They then enjoyed lunch courtesy of the Math Department at 84 East.

The participants were Jackie Lewis, Samantha Dunmire, Brian McLellan, Mandy Ferguson, Jeffrey Meyers, Kimberly Klask, Dan Lithio, Martha Precup, Forrest Gordon, Josh Kinder, and Chris Hall.  Dan, Martha, and Forrest were Hope's top team, placing 8th.  Taylor University, Michigan Tech, and Kalamazoo College were in a three-way tie for first place.

Another team mathematics competition, the Lower Michigan Mathematics Competition, will take place in early April, when teams from schools in Lower Michigan will vie for the rights to the coveted Klein bottle trophy above (shown in the first floor VWF display case, where we hope it will reside next year!).

This Day in Mathematics History . . .

On February 14, 1877, Leopold Landau and Johanna Jacoby were given the Valentine's Day gift of a son, Edmund.  Young Edmund demonstrated a precocity that presaged his mathematics career: according to legend, his mother had once left an umbrella in a carriage, and it was quickly recovered when 3-year-old Edmund informed her that she had left it in carriage #354.  He would go on to become one of the leading number theorists of his day.

Landau's career brought him into contact with some of the greatest mathematicians of his era.  His doctoral work was supervised by Frobenius, and when he was appointed to a professorate in Göttingen, he replaced Minkowski, and his colleagues there were Hilbert, Klein, Carathèodory, Hecke and Courant.  Somewhat persnickety and rather arrogant, Landau had a tendency to annoy colleagues and students alike.  In fact, Teichmüller, who would later become a famous mathematician in his own right, once organized a boycott of Landau's lectures!  As a result, Landau retired from the university and lectured in Europe before dying of a heart attack less than a year after the boycott.

To read more about Landau, please visit http://www-history.mcs.st-andrews.ac.uk/Biographies/Landau.html.


Problem of the Fortnight 

Since this is the Valentine's Day edition of Off on a Tangent, we thought we'd stick with the theme.  And nothing says Valentine's Day like a cardioid . . . at least to a mathematician!

Find the area of the region between the inner and outer loops of the cardioid r = 1 - 2 sin (θ).   The cardioid is shown at right.

Write your solution on the back of an old Valentine and drop it (along with a box of chocolates) in the Problem of the Fortnight slot outside Dr. Pearson's office (VWF 212) by 3:00 pm on February 23.  As always, please be sure to include your name, your math class(es) and the name(s) of your professor(s) -- e.g. Karl DeOid, Math 214, Professor Valerie N. Tyne -- on your solution.


Problem Solvers of the Fortnight 

Congratulations to Brian McClellan and Dan DeHaan for solving the problem of the fortnight of the last issue.  The problem is actually a very famous one, known as the Buffon Needle problem, but we supplied sufficient (and perhaps necessary) obfuscations.  If a 1 cm pencil lead is dropped randomly on a piece of ruled paper where the lines are 1 cm apart, the probability that the pencil lead will intersect a line is 2/π .  For a complete solution, please see http://mathworld.wolfram.com/BuffonsNeedleProblem.html.  The Buffon Needle problem offers a neat probabilistic method for determining the value of π experimentally.  Of course, there have been many ingenious variations on the theme of the Buffon Needle problem over the years.  Dan Lithio sent us one we enjoyed a great deal (please see http://www.wikihow.com/Calculate-Pi-by-Throwing-Frozen-Hot-Dogs for details); it involves throwing frozen hot dogs onto a lined plastic sheet!   

50-Cent Book Sale!

The 50-cent math book sale continues!
Stop by VWF 222 to look at the available books, and when you find one,
drop off $0.50 in the math department office.  What a deal!


Math Teaching Opportunity in Ecuador

Once again, this letter from one of our graduates:

Greetings,

My name is Kyle Williams and I graduated from Hope in May of 2006.  I am currently working as a math teacher in a private elementary school called Centro Educativo Amauta, located in the outskirts of Loja, Ecuador, a city of approximately 150,000 in the Andes mountains in the south of the country.   I am writing to ask for your assistance in finding someone to replace me here in the coming academic year.  I would eventually like to establish an exchange program between Hope and Amauta so that each year a recent graduate would come down here and teach and have the experience of living in a foreign country and perfecting their Spanish.   The school here and the whole country are truly wonderful and magical - it is definitely a worthwhile experience.

The school is unique in Loja (and one of only a few in all of Ecuador) for its use of a pedagogical philosophy based on the work of Piaget and the theory of constructivism (this is in spite of the rather conservative educational philosophy of the government here).   It is a very progressive and dynamic education and I have learned so much in my time here.  There are a total of 55 children in the school in 9 groups that cover a range from kindergarten to about 5th grade.   I only work with the older kids which ends up being about 35 students in 6 groups.  Thus, I am in direct contact with each and every student every day and am able to give lots of individual attention.

As for compensation, the school provides me with a place to live (a beautiful little house here in the mountains), two meals a day, and an additional $150 a month, which is more than enough to live and do a little traveling here. The school year here starts mid-September.   For more information about my experience, I have a website with all my journals and photos at http://www.bluedoorproject.com/kw.

We are looking for someone who has had experience with children and is willing to learn and work with a somewhat original educational system..   They should also have a decent amount of experience in Spanish as all teaching is in Spanish.  In addition, as the position is that of a math teacher, they should have at least enough math background to be comfortable teaching up to 6th grade level math – fractions, decimals, multiplication, division, etc.

I would be very grateful if you could share this email with your students and have any interested parties contact me at kyle.w.williams@gmail.com for more information about the position.   Thanks in advance for your collaboration in this little project of mine.

Sincerely,
Kyle Williams


 Imagination is more important than knowledge.
~ Albert Einstein