December 5, 2000 Volume 29, No.12

St. Olaf Mathematics Department

Math  Mess

December 5, 2000 Volume 29, No.12

This Week’s Colloquium
Sadly, there is no mathematics colloquium this week.  Instead, you should all go out to the movies (after you’ve finished your math homework, of course).  The Grinch has been classic holiday fare since Vessey was a kid, but the movie version shows off the comic zaniness of Jim Carrey.  Charlie’s Angels was a television hit when the editor was kid, but the movie version shows off a bit more than Farrah ever did.  You can see Bruce Willis being tough and stoic in yet another movie, this time it’s Unbreakable.  For the afficionados of animated film there is 102 Dalmations — cute, cute.  Why anyone thinks Adam Sandler is funny is beyond the editor’s comprehension, but his latest movie for which he got paid about $20 million is Little Nicky.  Finally, the only movie the editor can truly recommend is You Can Count on Me.  A realistic portrayal of a sibling relationship with fantastic acting, writing and directing.

Gingerbread Houses
The MAA would like to invite all students to the annual Gingerbread House construction party on Thursday, Dec 7th. We will meet at 5pm in the math hallway of the SC where there will be supplies for creating your own gingerbread house out of edible goodies. Yummy!

Polyholiday Fun
In conjunction with the MAA’s Gingerbread House Making activity Thursday afternoon, David Molnar will hold a Polyhedreality Workshop. It’s a good way to discover what sorts of polyhedra exist by playing around with toys. Afterwards, ambitious types can cut some out and decorate them for Christmas ornaments. The materials will be in a classroom in the math hallway for people to play with while the gingerbread houses are being made. Around 6pm David will make a short presentation, followed by more hands-on model making.

Fellowship and Grant Info
The Graduate Research Program for Women (GRPW) is designed to increase female representation in science and engineering. GRPW provides financial support for outstanding women students who are pursuing full-time doctoral studies in many disciplines including Math, Computer Science, Operations Research, and Statistics. To obtain application forms for GRPW fellowships (annual stipend of $17,000) or grants ($2,000), visit http://www.bell-labs.com/fellowships/GRPW. The deadline for applications is January 8, 2001. Participants will be selected on the basis of scholastic attainment in their fields of specialization, and other evidence of their ability and potential as research scientists. Finalists will be invited to visit Bell Laboratories for personal interviews and to speak with members of the technical staff in their field of interest.

Why Math?
“In my experience, competency in mathematics – both in numerical manipulation and in understanding its conceptual foundations – enhances a person’s ability to handle the more ambiguous and qualitative relationships that dominate our day-to-day decision making. ”
— Alan Greenspan

Just For Fun….
Three statisticians went duck hunting. A duck was approaching and the first statistician shot and missed the duck by being a foot too high. The second statistician shot and was a foot too low. The third cried, “We hit it!”

Last Two Solutions
Last Week’s Problem: 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: Nobody correctly solved last week’s problem. For those of you who thought the limit was zero, consider letting the polynomial be (x+1)^n.

Problem from 2 weeks ago: Given that a,b are positive integers, show that if the arithmetic progression a, a+b, a+2b,… contains a perfect square, then it contains an infinite number of them.

Solution: (Submitted by Michael Zahniser.) If the whole number c^2 can be expressed as (a + bn) for whole numbers a, b, c, and n, then c^2 = a (mod b).  This means that (c + bx)^2 = c^2 + 2bxc + (b^2)(x^2) = c^2 (mod b), since any multiple of b, mod b, is equivalent to 0.  Thus, if c^2 is in the sequence of a + bn, so is (c + bx)^2, which means that the sequence will contain an infinite number of solutions.

Problem of the Week
Created by David Molnar’s Gateways Class: 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?

**Please submit all solutions to Cliff Corzatt (corzatt@stolaf.edu) by noon on Friday.

To subscribe to the Math Mess, please contact Donna Brakke at brakke@stolaf.edu.

Editor-in-Chief: Jill Dietz
Associate Editor: Jennifer Beilfuss
Problems Editor: Cliff Corzatt
MM Czar:   Donna Brakke
mathmess@stolaf.edu