November 14, 2000 Volume 29, No.10

St. Olaf Mathematics Department

Math  Mess

November 14, 2000 Volume 29, No.10

This Week’s Colloquium
This week the math department presents it’s annual “To Be or Not To Be” extravaganza.  To be or not to be a math major is the question. Members of the mathematics faculty will discuss the math major, statistics and computer science concentrations, careers, graduate schools, summer opportunities, study abroad programs, math education, and all sorts of math related issues.  First years and sophomores are especially invited to join us, wishy-washy juniors had better come, and seniors should know by now to come early for the food.  The festivities begin at 4:30pm in SC282.

WWW Treasure Hunt
The inside back cover of November’s Math Horizons features a “World Wide Web Treasure Hunt,” asking questions such as “What is the value of pi suggested by the Egyptian Rhind Papyrus?” and “What is lucky about the number 2187 and why does Martin Gardner care?” Curious? Find one of the remaining copies of Math Horizons and send in your discoveries by the printed deadline. Please cc: them to molnar@stolaf.edu. The most successful mathematical archaeologists from St. Olaf will enjoy the fruits of their labors in the form of a t-shirt or other valuable prizes.

Math Contest!
Students can still sign up for the annual Carlson Calculus Contest to be held on Nov. 14 and 15. Students work in teams of three for 90 minutes (not two days). Details can be found in last week’s Math Mess, or talk to Cliff Corzatt. First prize team members receive $35 each, 2nd prize $25 each and 3rd prize $15 each, with the winning team immortalized on a plaque in the SC.

Need some cash?
The Academic Support Center is looking for  individual math tutors to meet the current demand for help. Apply at the ASC.

Interim Courses
*Knot Theory (Math 248); Prof. Jill Dietz; Prereq: Math 220, Linear Algebra.
Knot Theory is exactly what it sounds like: the mathematical theory of knots.  Yes, it is a legitimate field of mathematics and is an increasingly important one due to its connections with biology (supercoiling of DNA), chemistry (chirality of molecules), and physics.  The course is a basic introduction to knots and knot invariants, culminating in applications to the sciences as well as to other fields of mathematics. Girl/boy scouting is not a prerequisite. Fun is guaranteed.

*Seminar(CS-378); Prof Brown; Prereqs: CS-272 and CS-274, or permission of instructor.
We will study the algorithms and data structures used to control processes, input/output, memory management and file systems in modern computer operating systems. We will cover topics such as interprocess communication, process scheduling, swapping and security. In addition, we will study examples from UNIX, Windows and the Mac operating systems as well as examining Linux in detail.

*Modern Geometries (Math 356); Prof. Wallace; Prereqs: Math 220 and either Math 244 or 252 (preferably both).
Math 356 is designed to expand your geometric intuition and expose you to the central role that geometry plays in mathematics and culture.  We will study topics such as axiom systems, non-Euclidean geometries, Euclidean transformations and fractal geometry. This course will give you practice and feedback on proof-writing and will include historical and cultural context, primarily through student presentations. Class members will work in groups of three on all homework and on one class presentation.

MAA Executive Committee
The executive committee for the MAA student chapter has been chosen. Leading the chapter this year are President Mike Eliason ’01, Vice President Laura Johnson ’01, Treasurer Eric Brown ’01, Assistant Treasurer Brett Werner ’03, Publicity Chair Annie Farrell ’01, Communications Director Ned McGuire ’01, and Program Chair Brooke Rittger ’02. These folks will be responsible for planning, advertising and leading the MAA events of this school year.

Last Week’s Solutions
Problem: Find the exact value of the power series (1/4) + (1/8) + (2/16) + (3/32) + (5/64)  + (8/128)…, where the nth term is the nth Fibonacci Number divided by 2(n+1) .

Solution: Two solutions this week.  First, from Michael Zahniser ’04: The nth Fibonnaci number can be represented as  (1/sqrt{5})((alpha_1)^n-(alpha_2)^n) where alpha_1 and alpha_2 represent the roots of x^2-x-1.  So the series can be written as the difference of two geometric series, and the sum of the sums is 1.  A different view from David Molnar: Flip a fair coin until tails shows up twice in a row. The probability that you stop after two flips is 1/4, which is the first term in our series. The probability that you stop after three flips is the second term, after four flips the third term, etc. Since you will eventually stop, and these events are disjoint and exhaustive, the series converges to one.

Problem of the Week
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.

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

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