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The Mathematical Association of America

North Central Section

Spring 2002 Meeting

April 26-27, 2002

St. Cloud State University, St. Cloud, MN

Preliminary Program

Friday, April 26, 2002

                7:00 - 8:00            Miller Center (New Library): Registration  $8.00 for members; students free.

                                                Miller Center B-17 and B-18:  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 "1-p" 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              

 

Saturday, April 7, 2001

                8:00 - 12:00          Miller Center:  Registration

                 

8:00 - 3:00            Miller Center B-17 and B-18: 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 generally-and symbolic algebra in particular-is 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 B-1, 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 B-31: 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 Differential-Difference Equation

                                                Namyong Lee; Minnesota State University, Mankato

                ABSTRACT:  In this paper, we study a certain partial differential-difference 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 non-majors 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 annuities-certain 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 non-majors and majors. 

 

BREAK

 

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.  E-mail 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 Web-Based 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 B-31 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.