
The Mathematical
Association of America
North Central Section
Spring 2002 Meeting
April 2627, 2002
St. Cloud State University, St. Cloud, MN 
Preliminary Program
7:00
 8:00 Miller Center (New Library):
Registration $8.00 for members; students free.
Miller
Center B17 and B18: MAA Book Sale
8:00 
9:00 Miller Center Auditorium: Invited Address: The Problem of the
Gambler’s Ruin
Ted Vessey,
St. Olaf College
ABSTRACT: An
intrepid gambler plays a simple game for a dollar. With probability
"p" he wins any trial and with probability "1p" he loses
the trial. He begins the game with an initial fortune F and plays repeatedly
until either he has won
his goal of G
dollars (he would then have F+G dollars) or until he has no money left. We will try to compute the probabilities of
these events given various values for "p", F, and G. The problem is
easy to understand and the interest is in the various ways to solve the
problem, including guessing, matrix manipulations, and summing series. As an
analyst, I will choose the series approach.
9:00  ?? Valhalla Room – Atwood
Center: Reception
8:00
 12:00 Miller Center: Registration
8:00  3:00 Miller Center B17 and B18: MAA Book Sale
9:00  9:10 Miller Center Auditorium: Welcome
St. Cloud State University
President, Roy Saigo
Miller Center Auditorium: Morning Session 1
9:15  9:35 Algebra,
Computer Algebra,and Mathematical Thinking
Paul
Zorn; St. Olaf College
ABSTRACT:
Mathematical symbolism generallyand symbolic algebra in particularis
among mathematics' most powerful intellectual and practical tools. Knowing
mathematics well enough to use it effectively requires a degree of comfort and
ease with basic symbolics. Helping students acquire symbolic fluency and
intuition has traditionally been an important, and sometimes daunting, goal of
mathematics education. Cheap, convenient, and widely available technologies can
now handle a good
share of the
standard symbolic operations of undergraduate mathematics. Does it follow that teaching these topics,
and even some of the techniques, is now a waste of time? The short answer is “no.” The key question is how to help students develop
“symbol sense” and, above all, a feeling for mathematical structure. An answer concerns choosing mathematical
content and pedagogical strategies wisely, in light of technology, to highlight
what matters most.
9:40  10:00 Art
Inspired by Mathematics in Minnesota
Lisl
Gaal; University of Minnesota, Minneapolis
ABSTRACT: In the
December 2000 issue of the MAA Focus Magazine there is an article on “Art
Inspired by Mathematics in New York” by Ivars Peterson. The only illustrations in this article are of
sculptured Moebius strips, although the show also included paintings. I shall show six simple examples of
illustrations from combinatorics (counting), geometry, group theory, probability
,and transfinite arithmetic.
10:05 – 10:25 Betting
on the Outcome of the NBA Final: Can One Make Money?
M.
B. Rao; North Dakota State University, Fargo
ABSTRACT: In this
talk, I will explain how to set up a system of linear equations for betting on
NBA teams in winning the final. The technique is applicable to betting in horse
racing and some casino games. The treatment is accessible to any one who has
some rudimentary knowledge of linear algebra.
10:30 – 10:50 Take
Putnam Problem B1, 2001 for Example
Loren
Larson: Northfield, MN
ABSTRACT: I'll
present a number of solutions, including a natural approach that several
students attempted, but none successfully. I'll conclude with some
related problems of a recreational nature. The point of the title is that
a good problem produces good mathematics.
Miller
Center B31: Morning Session 2
9:15
– 9:35 Gnomonic Pythagorean
Triples
Dale
Buske; St. Cloud State University
ABSTRACT: A gnomon is a connected figure G which when suitably
attached to figure F produces a third figure similar to F. A characterization of all Pythagorean triples having
Pythagorean triangles as their gnomons is given. From this
characterization it will follow that fundamental
Pythagorean triples do not have Pythagorean gnomons.
9:40 – 10:00 A Partial DifferentialDifference
Equation
Namyong
Lee; Minnesota State University, Mankato
ABSTRACT: In this
paper, we study a certain partial differentialdifference equation that arose
from a mathematical modeling project. We
show the idea of how to construct the solution and its asymptotic behavior.
10:05
– 10:25 Bijections Needed: Some Open Problems in Partition Theory
Tina
Garrett; Carleton College
ABSTRACT: We will
review the basic definitions in partition theory. We then describe several of the traditional
notations that are commonly used in bijective proofs of partition theorems,
including the Ferres diagram and Frobenius
notation. Several known theorems and conjectures are
stated for which bijective proofs may be expected but do not exist.
10:30
– 10:50 New Ways of Teaching
Mathematics of Interest and Life Contingencies
Ken
Kaminsky; Augsburg College
ABSTRACT: As part of our quantitative literacy program at Augsburg College,
I teach a course on the mathematics of interest. The course is a popular
one for nonmajors as the topic of money is fascinating to students but the
traditional actuarial notation used by existing texts often obscures the key
results. For example, although simple annuitiescertain differ from one another
only by a factor related to the valuation date, actuaries have given a distinct
notation for virtually every particular case. Recently, I decided to buck
this trend and unify the study of annuities using a comprehensive
formula. In this talk I will present new approaches to teaching using
this result. I will also discuss extensions to varying annuities and
insurances and I will discuss the implications for teaching both nonmajors and
majors.
11:00 –
11:55 Miller Center Auditorium: Invited Address: Fallacies in
Elementary Statistics
Ann Watkins,
President of the MAA; California State University, Northridge
ABSTRACT: We will
have some fun demolishing several enticing examples that commonly are used in
elementary statistics textbooks to illustrate the mean, median, and mode. Some
mathematics backed up by a little data show that these concepts are not as
intuitive as they appear. This talk is
actually more sophisticated than it sounds and includes some nice applications
to calculus.
12:00 –
1:00 Voyageurs Room – Atwood
Center: Lunch: $8.25.
Email reservations to Dan Scully, scully@stcloudstate.edu
1:05 –
1:35 Miller Center Auditorium: Business Meeting
Miller
Center Auditorium: Afternoon Session 1
1:40 – 2:00 Distinguishing
Gamblers from Investors at the Blackjack Table
David
Wolfe; Gustavus Adolphus College
ABSTRACT: A
skillful blackjack player, one who counts cards, maintains some information
about the distribution of cards remaining in the deck at all times. The player adjusts both betting style and
play based on this "count" information. Depending on the rules used by a particular
casino, the skillful player may have a slight edge over the casino. Without knowing exactly what the player is
counting, we would like to write a program which is able to assess the player's
playing skill
2:05 – 2:25 WeBWork – A WebBased Homework
System
Charles
Pastor; Gustavus Adolphus College
ABSTRACT: WeBWorK
is an online system for creating and grading homework problems. Problems can be individualized and students
receive immediate feedback. In this
presentation I will introduce WeBWorK, demonstrate how our
Department is
using this program and discuss student responses. WeBWorK is distributed for
free by the University of Rochester.
Miller Center B31 Afternoon Session 2
1:40
– 2:00 End Base Discriminatin
Now!
Tom
Sibley; St. John’s University
ABSTRACT: Do
you find it unfair that relatively awkward fractions like 17/32 can have finite
decimal representations, whereas seemingly simpler fractions like 1/7 confront
us with infinitely repeating decimals?
Would you like familiar numbers such as e and pi to have easily recalled
decimal representations? We will explore
alternative bases to achieve nice representations and encounter some pretty
mathematics and open conjectures along the way.
2:05
– 2:25 Disjunctive Rado
Numbers
Dan
Schaal (presenting) and Brenda Johnson (student); South Dakota State University
ABSTRACT: Rado
numbers are an area of discrete mathematics with applications in computer
science. In this talk we will present a
new variation of the classical Rado numbers.
Brenda Johnson is an undergraduate student at SDSU. This talk is based on joint research
conducted by the authors as part of Johnson's Honors Program.