St. Olaf Mathematics Department
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
- To deliver his gifts in one night, Santa would have to make 822.6 visits per second, sleighing at 3,000 times the speed of sound.
- Pogonophobia is the fear of beards.
- There are currently 78 people named S. Claus living in the U.S. — and one Kriss Kringle.
- Average wage of a mall Santa: $11 an hour. With real beard: $20.
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 19×19 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