Math 
Mess
Math
Mess
December 12, 2000 Volume 29, No.13
Happy Holidays
Relax, Take It Easy...
Studying for finals got ya down? Are you tired of banging your head
against the wall trying to understand all those problems from Vessey's
M262? Or do you just need a break from that humdrum existence of studying?
Why not take one, and join us for a little cheer and relaxation that befits
the season, final exam season that is? Beginning this Thursday, and continuing
through next Wednesday, the Math Department will sponsor its biannual Relaxation
Station. Nestled in the beautiful not-so-rolling hallway that connects
OMH with the SC180 Strip, the Relaxation Station offers students and faculty
a wide variety of treats, including fresh popcorn, cookies, chips, soda
(pop for you real Minnesotans), and maybe a little fruit (we're trying
to cut down on the healthy offerings this year). Take a few minutes over
the next few days and join us! And of course, good luck on those final
exams!
Congrats to the Competitors!
The results from this year's NCS/MAA Team Competition are in! Held
Saturday, November 11, this year's event featured tremendous competition
from 56 teams of students from schools across the upper Midwest. Participants
from St. Olaf College included Jen Beilfuss, Julie Beilfuss, Eric Brown,
Andie Bykerk, Jason Grimm, Erik Johnson, Liv Anda Knatterud, Ned McGuire,
Eric Weinhandl, and Brett Werner. All of the St. Olaf teams performed admirably.
The team of Eric Brown, Ned McGuire, and Eric Weinhandl finished in 9th
place. Congratulations to all of you!
An Opportunity for Modeling, in Mathematics
That's right, modeling in mathematics. However, there's no need to
begin practicing your walk down the runway for this. The 2001 Mathematical
Contest in Modeling is scheduled for February 9-12. The registration deadline
is December 29, so if you are interested in participating, or just want
more information about the event, please contact Phil Gloor (gloor@stolaf.edu)
soon, or visit the MCM webpage at www.comap.com/ undergraduate/ contests/mcm/index.html.
Check it Out!
Congratulations to Nitish Dass '01, Jon McGrath '01,
and Erin Urbanski '00 on the publication of their paper "The determinant
of a (m,n) pretzel" in the Fall 2000 issue of the Pi Mu Epsilon Journal
(Vol 11, No 3). You can find the journal and their paper in the science
library.
Santa Fun Facts
Last Two Solutions
Problem: What is the largest positive integer n, such that (n-1)/n
can be written as a sum of fractions in the form 1/k where k is less than
100?
Solution: Nobody solved last week's problem correctly but here's
something to look at:
1/2+1/3+1/7+1/43 = 1805/1806
We want all the denominators on the left to be distinct. Can you do
better?
Problem from two weeks ago: Let f(x)= x_n + a_{n-1}x_{n-1} + ...+ a_1x + a_0 be any monic polynomial of degree n. What is the limit as x goes to infinity of [(nth root of f(x))-x]?
Solution: Bob Hanson, in the Chemistry Department solved the problem from two weeks ago. The answer is a_{n-1}/n. The justification is too ugly to print!
Problem of the Week
"The Game of X, Y, and Z" (as created by David Molnar): Two players
take turns placing stones on a Go board (a 19x19 grid). The object is to
make a set of 5 stones of your color, not (as in Go-Moku) in a straight
line, but in the shape of an X, a Y, or a Z. Describe a winning strategy
for the first player, or prove that the second player can always force
a draw.
**Please submit all solutions to Cliff Corzatt (corzatt@stolaf.edu) by the end of finals.
To subscribe to the Math Mess, please contact Donna Brakke at brakke@stolaf.edu.
Chief Elf:
Jill Dietz
Santa:
Jennifer Beilfuss
Problem Elf: Cliff
Corzatt
Elf Czar:
Donna Brakke
mathmess@stolaf.edu