OFF ON A TANGENT
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
February 22, 2006 Vol. 4, No. 9
http://www.math.hope.edu/newsletter.html


Professor Bekmetjev will speak on pebbling
 In tomorrow's colloquium, Professor Airat Bekmetjev will give us an insight into one of his areas of research; graph pebbling.  Pebbling is a game that can be played on any connected graph.  Some number of pebbles are first placed on each vertex.  The player can move pebbles along the edges, but there is a toll for any move.  For every pebble moved across an edge the player loses one pebble. A configuration of pebbles is called solvable if the player is able to place a pebble on any vertex.  Two of the interesting questions that arise from this game are, "How many pebbles are enough to guarantee that any configuration is solvable?"  and "What are the optimal ways to move pebbles?"  In this colloquium Dr. Bekmetjev will answer these questions and discuss the existence of the threshold phenomenon in pebbling.


Professor Tanis will show how Maple can help you become an artist  If you thought the computer algebra system Maple could just help you solve a differential equation or evaluate an integral, you are wrong.  Professor Emeritus Elliot Tanis will show us, in next week's colloquium, that Maple can be used to make art.  On  Thursday, March 2, at 4:00 p.m. in VWF 104, Professor Tanis will present  "Using Maple to Construct Repeating Patterns and Several Tessellations Inspired by M.C. Escher."  Using Chinese Lattice Designs, M. C. Escher’s tessellations, and other sources, examples of the 17 plane symmetry groups will be shown.



  Tea at 3:30 in VWF 222 (Reading Room) on Thursdays before colloquia

As part of our colloquium series, the mathematics department will host a "tea time" in the Reading Room (VWF 222) at 3:30.  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. 


Math students enjoy bowling and pizza












Approximately 45 students and faculty came out to bowl and enjoy some pizza at the Math Department's Bowling and Pizza Spectacular a couple of weeks ago. Students from seven different math courses competed in four different team categories. Andrew Abela and Stephanie Poll received prizes for the highest and lowest score (we won't say which was which). 

Statistics were also kept for each class.  The Multivariable 2 class had the most strikes (50) and highest total score (2493). The Calculus 2 students had the highest average score of any class (121) as well as the largest standard deviation (29.7).  Statistics weren't kept on the amount of pizza that was consumed, but that is something to think about for next year.

A summer research opportunity

If you are interested in summer research in the mathematics department, the deadline is fast approaching.  This year's research program is being lead by professors Mark Pearson, Airat Bekmetjev, Aaron Cinzori, and Tim Pennings.  They will be working with students this summer on four different projects.  Although students apply from all over the country for this program, Hope students are given special consideration. 

Participating REU students will receive a stipend of $2600 for the eight week program. Free apartment-style housing will be provided. Funds for travel as well as books and supplies are also available.  Visit http://www.math.hope.edu/reu.html for more information about the program.  Application deadline is February 28.

In our last three newsletters, we highlighted the projects led by Professors Pearson, Cinzori, and Bekmetjev.  This time we will look at Prof. Penning's project on mathematical modeling.  His project description is as follows.

Mathematical modeling is the process of describing a simplified physical situation via mathematical formulas and then using the formulas to predict or otherwise gain information about the physical situation. Dynamical systems is the study of the qualitative behavior of differential equations (and their discrete counterparts: difference equations) in which the independent variable is time. That is, dynamical systems are systems that change with time.

This summer we will be spending several weeks studying dynamical systems (using "Nonlinear Dynamics and Chaos" by Steven Strogatz). Then students will have an opportunity to choose their own physical situation to model (either their own (approved) idea, or from a list of possibilities that I have collected).

Recent models have included a neural model that explains why learning curves are often s-shaped, optimizing a trip upriver against a variable current, modeling Frisbee flight, the spread of forest fires, timber wolf populations in Yellowstone National Park, and finding the optimal time to leave a ball game. (This was published in The Rose Hulman Undergraduate Mathematics Journal.(See http://www.rose-hulman.edu/mathjournal/archives/2003/vol4-n2/paper3/v4n2-3pd.pdf)

Students should have a background in multivariable calculus, differential equations and linear algebra. A background in physics and familiarity with computer algebra systems (such as MAPLE) is also beneficial.


From the Margins of My Textbook
A Math Major’s Musings 

By JENNICA SKOUG | Columnist
There is a certain face that every math major knows.  It arises, quite innocently, from the classic college icebreaker: “So, what’s your major?”  However, when the answer is math, it is not surprising that the question-asker, unless he or she is also a math major, will in fact enter a state of temporary shock, only recovering a few seconds later with a half-awed, half-scared look that means precisely “Are you crazy??”  Not knowing exactly how to express this profound feeling, many of these face-wearers put on a one of several visages, all of which are somewhat hard to describe.  Perhaps it is a look of wonder and trepidation, or one of great confusion combined with the I’m-glad-I’m-not-you eye roll.  

However, if you are or ever were a math major, I am sure you know what I am talking about.  This is the face that almost invariably precedes the statement “Oh, you must be so smart.  I could never do math – always hated it.  Too boring and complicated for me.”  Other majors – except, perhaps, for Physics – rarely get this reaction.  How often does Biology come face-to-face with the Nose Wrinkle, or English meet the Raised Eyebrow, both of which Mathematics knows so well?  Are Mathematics and its patrons condemned to this awed-yet-icy reaction?  And should it cause offense, or be read as flattery? 

Whatever your response to this social peculiarity experienced by math majors of every age and genre, the fact remains that math is usually categorized as a discipline to be revered, feared, and often resented.  Math, think some, is a field of study only available to its Chosen Few, leaving everyone else bruised and bleeding from the wounds it has inflicted on their academic persona, on their more artistic or more practical intellect. 

But Math is innocent of such crimes!  In fact, this is not even a case of criminal offense, but rather, one of gross misunderstanding (and I’m not referring to that strange theorem in your calculus book).   For one, mathematicians, despite their particular quirks, are not the Chosen Few (although some might like to think they are), but rather have themselves chosen to pursue the scholastic ambition that most absorbs and enthralls them – just as someone might choose to study Writing because they lose themselves in turning words out on a page.  Furthermore, the notion that math has armed herself with symbols, theorems, and data tables for an unfair joust against the more “human” disciplines is, in fact, a beguiling fallacy.  We are quick to condemn what we have observed but do not fully understand.  Many people catch only a passing glimpse of mathematics, and, seeing only hard, impersonal facts, turn to something more tangible or subjective.  They would rather have Poetry than Proof.  But I contend that, metaphorically (and sometimes literally), Math is Poetry – and before you go around calling me an interdisciplinary nut case, grant me at least a fortnight of grace, and I will explain. 

to be continued


Problem Solvers of the Fortnight

Taking home the gold in the Off on a Tangent Problem of the Fortnight Olympics XXXII are: Jeff Ambrose, Trevor Bakker, Betsy Carlson, James Daly, Carleen Dykstra, Libby Hammon, Nicole Hartley, Clinton Jepkema, Alyssa Johnson, Josh Kortas, Jackie Lewis, Jacob Lyons, Brian McClellan, Heather McGovern, Jon Moerdyk, Keith Mulder, Karen Nordell, Matt Paarlberg, Allison Pautler, Chad Rector, Bill Rininger, Sam Rossman, Nathan Vance, Kevin Vanden Bosch and Ben Worrel.  Congratulations to all, and the judges have awarded 10 points extra credit to our first-time Problem Olympian Nate Vance!  All our gold medal winners correctly determined that the LEDs whose numbers are perfect squares will remain on after the 20,000th person has walked through the hallway.  These LEDs are toggled an odd number of times, and hence remain on, because the perfect squares have an odd number of factors.


Problem of the Fortnight

A 2x3x4 rectangular box is constructed from unit cubes, which divide each face of the box into a grid.  You have to travel from one corner of the box to the corner diagonally opposite along these grid lines, staying on the outer faces of the box.  (No fair going inside!  But it is fair to travel along the edges of the box.)

How many paths are there from one corner of the 2x3x4 box to the corner diagonally opposite such that the total distance traveled is 2 + 3 + 4 = 9, so that no back-tracking is allowed?

Write your solution on a piece of paper cut and folded into a 2x3x4 box, and drop it off at Dr. Pearson's office (VWF 212) by 3:00 p.m. on Friday, March 3.


Math Olympics

If the Problem of the Fortnight doesn't already occupy an unhealthy proportion of your "free" time, you might like to check out http://www.ewg.k12.ri.us/mathweb/winterolympicsmath.htm for some elementary and secondary Olympic math questions.  Math ed folks in particular might find some interesting ideas for future lesson plans.  Those of you whose free time follows a distribution skewed toward statistics might enjoy reading the commentary on figure skating scoring by Yale University Assistant Professor of Statistics Jay Emerson at http://www.stat.yale.edu/~jay/EC2006/.   



Got a Math Question?

Ask Elvis ...

... email him at elvis@hope.edu

Dear Friends,

It is nice to be an original. We all remember those who were first, like the first person on the moon (Neil Armstrong), the first American woman in space (Sally Ride), or the first living creature to orbit the earth (Laika whose picture is shown on the right).

You all know that I happen to understand and use some of the properties of calculus in my leisurely pursuits and was the first to demonstrate this.  There are, however, other dogs now coming forward to show their mathematical prowess. In particular, a Labrador named Salsa from France seems to be able to fetch a ball using similar concepts of calculus as those that I use. You can read more about her (but mostly about me) in an article that came out this past week at
http://www.sciencenews.org/articles/20060218/mathtrek.asp.

In the last newsletter I posed the question, "How much wood would a woodchuck chuck if a woodchuck could wood?"  I got four responses to that query.  Tim, Beth and Emily all gave similar responses.  They basically said, "It would chuck all the wood that a woodchuck could chuck, if a wood chuck could chuck wood."  I thought that was an interesting response.  Do you suppose if I asked this trio what 2 plus 3 was, that they would tell me it was the sum of 2 and 3?

In another response, David writes, "Though I'm not sure this would quite be considered an answer... with all this mention of woodchuck puzzles and tangents, the following occurred to me:  'How much sea could a secant see if a secant could can't see?'"  Well, using the above logic, I guess it could see as much sea as a secant could see if a secant could can't see.

Also in the last newsletter, I mentioned Austin, Minnesota was also known as Spamtown USA.  Well my relatives from Minnesota got pretty excited about this comment.  In fact, my sister Dee Dee writes me that Spam actually smells like canned dog food.  (That is a good thing from my point of view!)  She also wrote me the following.

The town of Austin, MN was officially nicknamed "Spam Town" in 1995.  I think the residents there were tired of being slandered for their association with SPAM so they decided to make the best of it and market themselves that way.  There is a SPAM Blvd, a SPAM museum (www.spam.com), a SPAM gift shop that sells SPAM cookbooks among other things, a SPAM mobile and a SPAM fan club.  At the museum you can learn all kinds of interesting statistics about SPAM.  Here are some of them:
As you can see, she gets pretty excited when the subject is canned meat.  That's all for this fortnight.  If you have a math question or one about canned meats, send me an email at elvis@hope.edu.





The struggle is what defines your success. If there is no struggle at all, the success doesn’t mean anything.
Bode Miller