Description: P:\MAA\meetings\2005springprogram_files\logo_ncs.jpg

The Mathematical Association of America

North Central Section

Fall 2005 Meeting

October 14-15, 2005

South Dakota State University

Brookings, SD

 

Preliminary Program

Friday, October 14, 2005 

7:00-8:00  Registration, Crothers Engineering Hall (NW entry)

                  $10; students, first time attendees, and speakers free; $5 for MAA-NCS section NExT members

7:00-8:00  Book Sales, Crothers 205

8:00-9:00  Evening Session    Professor Ken Yocum presiding,    Crothers 204

                  Welcome: Dr. Lewis Brown, Dean of the College of Engineering, SDSU

      Lecture:  Professor Daniel Schaal, South Dakota State University

                                “Should You Take the Bet?  A Problem from Marilyn Vos Savant”


Abstract:  Marilyn Vos Savant is famous for having the highest IQ ever recorded.  She writes the weekly column “Ask Marilyn” for Parade Magazine.  She is also famous for some very controversial answers to readers’ questions, especially questions involving mathematics and logic.  In this talk we will highlight a few of these controversial problems in mathematics.  We will also look in detail at a fascinating question involving logic and game theory that she answered.  This problem has not received the attention that some of her problems have, but it is equally complex.  It is also not clear whether Marilyn was right or wrong in her answer.

9:00-?       Reception, Tompkins Alumni Center

Saturday, October 15, 2005

8:15-11:00     Registration, Crothers Engineering Hall


8:15-11:00     Book Sales, Crothers 205

9:00               Morning Session    Professor Ross Abraham presiding,    Crothers 204

                      Welcome: Dr. Carol Peterson, Provost and Vice President for Academic Affairs, SDSU

9:05     A Generalized Ratio Test, Dr. Sayel Ali, Minnesota State University Moorhead
9:25     The Monster Hidden in Basic Algebra Textbooks, Dr. Louis Blair, South Dakota State University
9:40     The Use of Guided Notes in College-Level Mathematics Courses, Drs. E. Hill and K. Montis, Minnesota State University Moorhead

9:55     Reed-Solomon Codes:  An Application of Linear Algebra, Dr. Steve Leonhardi, Winona State University
10:15   Similarity Measures, Dr. Colleen Livingston, Bemidji State University

10:35-11:00  Break

11:00-12:00  "A Church-Related Story Involving Moses and a Big Helping of Curry with LambDescription: CoffeeRevisited"

                     Professor Stephen Walk, St. Cloud State University


Abstract:  The field of combinatory logic was developed in an attempt to clarify the foundations of mathematics, with an eye toward explaining paradoxes.  The pursuit has had unexpected benefits:  inspirations for fundamental results in computability theory, applications for computer science, and the discovery of some mind-blowing examples of objects that by all rights shouldn’t exist . . . but do.

 

Students are encouraged to attend this talk.  For that matter, so are others.  An open mind and an interest in paradoxes will be helpful.  Knowledge of functions, logic, and infinity will be helpful but not absolutely necessary and may be twisted somewhat by the time you leave.

 

P.S.  Sorry about the spill.

 

12:00-1:00  Lunch, 169 University Student Union

1:00-1:30    Business Meeting, President Dale Buske presiding,  Crothers 204
                 

1:30            Afternoon Session      Dale Buske presiding,    Crothers 204

1:30  Games Played in Tall Warehouses, Dr. David Wolfe, Gustavus Adolphus College
1:50  A Web Course for Geometry, Dr. Timothy Peil, Minnesota State University Moorhead

2:10  Regiomontanus:  Trigonometry Problems from the 1400’s, Dr. Walter Sizer, Minnesota State University Moorhead

 

Abstracts

 

Evening Session

Daniel Schaal, “Should you take a bet?  A Problem from Marilyn Vos Savant”

Marilyn Vos Savant is famous for having the highest IQ ever recorded.  She writes the weekly column “Ask Marilyn” for Parade Magazine.  She is also famous for some very controversial answers to readers’ questions, especially questions involving mathematics and logic.  In this talk we will highlight a few of these controversial problems in mathematics.  We will also look in detail at a fascinating question involving logic and game theory that she answered.  This problem has not received the attention that some of her problems have, but it is equally complex.  It is also not clear whether Marilyn was right or wrong in her answer.

 

Morning Session

 

Sayel Ali, “A Generalized Ratio Test”

Let {a} be a positive sequence.  Let L=, L= , and let

L = max{L, L} and l = min{L, L}.

(i)                  If  L<, then  converges.

(ii)                If  l >, then  diverges.

This result can be used to test the convergence of some series that are not easy to test with the known convergence tests.

A proof of this result and examples of it will be given.

 

Dr. Louis Blair, “The Monster Hidden in Basic Algebra Texts”

Unexpected complications arise in the simplification of certain common basic algebra problems (for example, ) if negative numbers are allowed.  It this talk, a project suitable for undergraduates is proposed, and consideration is given to the limits of what can be realistically expected of basic algebra students.

 

E. Hill and K. Montis, “The Use of Guided Notes in College-Level Mathematics Courses”

A summary of the technique of using guided notes to increase student participation, interaction, understanding, and retention of material in a college-level mathematics course will be presented.  Included will be some practical experiences from a veteran of the use of guided notes and from a newcomer to the practice, as well as considerations that drove the decision to use guided notes.

 

Steve Leonhardi, “Reed-Solomon Codes:  An Application of Linear Algebra”

Coding theory is used to improve reliability of compact discs, DVDs, computer hard drives, cell phones, and satellite communications.  The goal of coding theory is to add redundancy to messages in a systematic manner that facilitates simultaneously the efficient transmission of information and the detection and/or correction of transmission errors.

Coding theory uses basic (mostly undergraduate level) linear algebra and abstract algebra—matrices, vector spaces, linear transformations, and finite fields.  As such, it is a nice application topic to introduce to undergraduates, using anywhere from one class period to an entire semester.  I will give special attention to the Reed-Solomon codes.  I will also put in a plug for a series of classroom modules being developed by participants in a DIMACS 2003 Reconnect Conference, along with other resources for teaching this topic.

 

Colleen Livingston, “Similarity Measures”

The Jaccard’s, Dice’s, Overlap, and Cosine coefficients each provide a way to measure set similarity.  In particular, the Jaccard’s coefficient is defined as the ratio of the intersection to the union of the two sets.  The focus of this talk will be on the applications of the Jaccard measure in a variety of disciplines.  These applications are relevant to any course that introduces the ideas of set union and intersection.

 


Stephen Walk, “A Church-Related Story Involving Moses and a Big Helping of Curry with LambDescription: CoffeeRevisited

The field of combinatory logic was developed in an attempt to clarify the foundations of mathematics, with an eye toward explaining paradoxes.  The pursuit has had unexpected benefits:  inspirations for fundamental results in computability theory, applications for computer science, and the discovery of some mind-blowing examples of objects that by all rights shouldn’t exist . . . but do.

Students are encouraged to attend this talk.  For that matter, so are others.  An open mind and an interest in paradoxes will be helpful.  Knowledge of functions, logic, and infinity will be helpful but not absolutely necessary and may be twisted somewhat by the time you leave.

P.S.  Sorry about the spill.

 

Afternoon Session

 

David Wolfe, “Games Played in Tall Warehouses”

Partizan End Nim is a variation of the classical game known as Nim.  Partizan End Nim is played by two players called Left and Right.  The game begins with stacks of boxes lined up in a row, each stack containing at least one box.  Players (with forklifts) take turns removing boxes from the stacks on their respective sides.  (Left removes from the leftmost stack, while Right removes from the rightmost stack).  The player removing the last box wins.  One added twist is that the piles can be of any ordinal height.

We give an efficient recursive method to compute the outcome of (and winning moves from) any position.

This research is joint work with two undergraduates, Adam Duffy and Garrett Kolpin, and extends the work of Michael Albert and Richard Nowakowski.

 

Timothy Peil, “A Web Course for Geometry”

I am developing a web course in geometry for pre-service teachers.  I will give illustrations of an online book I am developing for the course including video illustrations, interactive java diagrams, video lectures and self-assessment quizzes.  I will also look at strengths and weakness of the e-book format.

 

Walter Sizer, “Regiomontanus:  Trigonometry Problems from the 1400’s”

In his book De Triangulis Omnimodis  (On Triangles) the fifteenth century mathematician Regiomontanus presents theorems on plane and spherical trigonometry.  Many of these results correspond to problems we would find difficult.  A few will be presented, with solutions either by Regiomontanus or the presenter or to be supplied at their leisure by the audience.