Fall Meeting October 26-27, 2001

University of North Dakota, Grand Forks, ND

Friday (evening), October 26, 2001

7:00 - 8:00 Gamble Hall Lobby: Registration $8.00 for members; students free.

8:00 – 9:00 Gamble Hall Room 1: INVITED ADDRESS

 Ethnomathematics and the Incas, Thomas E. Gilsdorf, University of North Dakota,

Abstract: In this talk we will explain some of the techniques involved in the study of ethnomathematics. The ideas involved will be illustrated by discussing the mathematics of the Incas.

9:00 - ? Alumni Center: Reception

Saturday, October 27, 2001

8:00 - 12:00 Gamble Hall Lobby: Registration

8:00 - 3:00 Gamble Hall Room 150: MAA Book Sale

Gamble Hall Room 1: Morning Session

8:50 - 9:00 Welcome from Dr. Martha A Potvin, Dean of Arts and Sciences.

9:05-9:20 Ron Rietz; Gustavus Adolophus College
Uncountable Subfields of the Reals

Abstract: A simple proof, using Zorn’s Lemma, that there exist (proper) uncountable subfields of the reals will be given. We will also point out a remarkable "interval-avoiding" property possessed by subsets of such fields.

9:25-9:40 G. Griffith; University of Saskatchewan
Solutions to a problem from the 2001 Invitational Challenge for Grade 11 students in Canada

Abstract: The Canadian Mathematics Competition, based in Waterloo, Ontario, offers annual "Invitational Challenges" to students in Grades 10 and 11. Some inspirational solutions appeared for one of the questions on the 2001 paper which may be of general interest.

9:45-10:05 Michael Tangredi; College of St. Benedict
Volterra’s Population Models

Abstract: This presentation will examine Volterra’s original approach to predator-prey problems. In particular, we first look at his well-known method of analyzing the solutions (which is quite different from the approach taken in modern textbooks.) Next we present Volterra’s refinement of this model, which was the origin of the mathematical discipline currently known as Volterra Integral Equations.

10:10-10:25 Daniel Hill (Undergraduate student) and Roxana Costinescu; University of Minnesota, Morris
Learning Sketchpad and Euclidean Geometry due to a Paper in Hyperbolic Geometry

Abstract: A senior seminar project about a different proof of the well-known theorem that gives the area of a triangle in hyperbolic geometry lead to interesting problems of a different nature. This presentation, designed primarily for undergraduate students exposed to geometry, will describe the challenges raised by using Sketchpad in illustrating proofs in the Poincarť half-plane model of hyperbolic geometry.

10:30-10:45 Michael Green; Metropolitan State University
Singularities of Hypersurfaces: The Milnor and LÍ Numbers

Abstract: Given an analytic function f of n-complex variables, the set of vectors at which {f=0} is called a hypersurface. A singularity is a point at which the hypersurface is not smooth. One way to study singularities is to define numbers that can be used to group singularieties into different "types." We describe two such numbers: The Milnor number and the LÍ numbers. Specific examples and computations will be given.

10:45-11:00 BREAK

11:00-12:00 Gamble Hall Room 1: INVITED ADDRESS

Touring a Torus, Joe Gallian, University of Minnesota, Duluth.

Abstract: This talk concerns the problem of traversing an m by n directed grid embedded on a torus so that each vertex is visited exactly once before returning to the starting position. We will also consider generalizations and variations on this theme. We conclude with an application to computer graphics.

12:00 – 1:00 Banquet Room Student Union: Lunch

Gamble Hall Room 1: Afternoon Session

1:05 – 1:35 Business Meeting – President Ralph Carr.

1:40-2:00 M. B. Rao; North Dakota State University
Number of Matchings in a Birthday Problem

Abstract: Not another birthday problem again! My service course classes in Statistics are big. I cannot resist throwing the birthday problem at the students and then set about checking whether or not at least two of them share a common birthday. I have noticed, on many occasions, several sets of students with each set sharing a common birthday. I will talk about this phenomenon of several mathcings.

2:05-2:20 Mizuho Schwalm (Graduate student); University of North Dakota
An Exercise in Computing Homology Groups

Abstract: Homology groups for chain spaces with real coefficients are computed as an exercise in linear algebra. The essential property of the boundary is that when boundary operations act successively, the result is zero. If we form chains with real coefficients, then the chain groups are vector spaces. Let the matrix representations of successive boundary operators be M and N so that MN = 0. The vector space representation of the homology group is then H = ker M – Im N. Since the matrices M÷ M and NN÷are Hermitian the problem is reduced essentially to an eigenvalue problem.

2:30-2:50 Dominic Naughton; St. Cloud State University
An Unexpected Encounter with some Famous Numbers

Abstract: The Bernoulli numbers arise when one computes the sums of powers of consecutive integers. . The first few 1, Description: P:\MAA\meetings\fall2001mtg\Image1.gif, and Description: P:\MAA\meetings\fall2001mtg\Image2.gif—are "hidden" in the coefficients of Description: P:\MAA\meetings\fall2001mtg\Image3.gif in the formulasDescription: P:\MAA\meetings\fall2001mtg\Image4.gif and Description: P:\MAA\meetings\fall2001mtg\Image5.gif. This talk will briefly describe their discovery and discoverer and mention some interesting places where they crop up.