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The Mathematical Association of America

North Central Section

Spring 2004 Meeting

April 23-24, 2004

Winona State University, Winona, MN

Preliminary Program

Friday, April 23, 2004 

7:00-8:00  Registration, Stark Hall Hyphen

8:00          Welcome by Dr. Steven Richardson, Vice President for Academic Affairs, Stark Hall Auditorium

8:05-9:00  "The Square Root Two Step: A Half Step Back, a Full Step Forward"

                 Professor Tom Sibley, St. John's University (2003 NCS Distinguished Teaching Award winner)

Abstract:  For the function f(x) = sin(x) it is easy to find its “compositional square”  fοf:  f(f(x)) = sin(sin(x)).  The other direction is harder:  Is there a square root g so that g(g(x)) = sin(x)?  We’ll explore when such square roots exist and develop a “square root two step” to generate square roots that do exist.

9:00-?      Reception, Maxwell Leadership Center (2nd floor, Maxwell Hall)

Saturday, April 24, 2004

8:00-11:00     Registration, Stark Hall Hyphen


8:00-12:00     Book Sales, Stark Hall Lounge

Morning Session

9:00                Welcome by Dr. Nancy Jannik, Dean of the College of Science and Engineering, Stark Hall Auditorium

  Concurrent Session I, Stark Hall Auditorium

9:05  NASA Return-to-Flight Program and a Brand of Texas Trail Mix, Richard D. Jarvinen, Winona State University and NASA
9:30  Symmetry and Integration, Bill Schwalm, University of North Dakota
9:55  Abel’s Solution of the Tautochrone Problem, Michael Tangredi, College of St. Benedict
10:20  A Didactic Differential Equation, Ralph Carr, St. Cloud State University

Concurrent Session II, Stark Hall 106

9:05  Exploring Geometry, A Discovery-Based Approach to College Geometry, Mike Hvidsten, Gustavus Adolphus College
9:30  Finding Tangent Planes to Quadric Surfaces without Calculus, Danrun Huang, St. Cloud State University
9:55  Electric Circuits and Symmetry Reduction, Cody Nitschke, UND
10:20  Characterization of Models Which Are Not Uniquely Solvable and the Potential Effect on Numerical Approximations, Jeffrey R. Anderson, Winona State University

10:40-11:00  Break

 

11:00-12:00  "WeBWorK:  A Web-Based Homework System," Stark Hall Auditorium

                     Professor Mike Gage, University of Rochester

Abstract:  We will give an overview of WeBWorK, a freely available, open source system which allows students to do standard calculus homework problems over the web.  The instant feedback encourages students to keep at the homework until they get it right.  Individualized versions of the problems allow student to collaborate while still doing their own work.  The homework is automatically graded for the instructor’s convenience.

 

12:00-1:00  Lunch, Jack Kane Dining Center, Kryzsko Commons

Afternoon Session

1:00-1:30  Business Meeting, Stark Hall Auditorium

                 (including vote on proposed by-laws change)
                 

1:30-2:30  “Connections Between Mathematics and Biology," Professor Carl Cowen, Purdue University

Abstract: Dr. Rita Colwell, a research microbiologist and current Director of the National Science Foundation, regards the mathematical sciences as the backbone for US Scientific and Engineering research.  Many scholars see the next few decades as a time of intensive progress in the biological sciences.  Dr. Colwell sees mathematics as being an integral part of the progress in biology, not a traditional view, but a forward looking one.    

In this talk, Carl Cowen will outline some of the research areas in the emerging collaborations between mathematical and biological scientists.  In addition, Cowen, who began his study of the mathematics of neuroscience last year at the Mathematical Biosciences Institute at Ohio State University, and who is this year beginning research with Professor Christie Sahley in Purdue’s Biology Department, will illustrate the connection between mathematics and neuroscience with a discussion of the Pulfrich phenomenon, an experiment that helps illuminate how the brain processes visual images.  There are few mathematical or biological prerequisites for this discussion.

2:35-3:00  WeBWorK lab workshop, Stark Hall 206

                 Professor Mike Gage, University of Rochester

Concurrent Session III, Stark Hall Auditorium

2:35  Survey of Winona State Graduates with a Mathematics, Mathematics Education, or Statistics Major, Scott Przybelski, Winona State University
2:55  Teaching Problem-Solving in Finite Math and Operations Research Courses, Daniel Rand, Winona State University

3:15  Freshman Seminar, Kevin Dennis, Saint Mary’s University of Minnesota

Concurrent Session IV, Stark Hall 106

2:35  Change the Constitution?  Ya, You Betcha., Dale Buske, St, Cloud State University
2:55  Automorphisms of Semi-Direct Products, Jason Saccomano, St. Olaf College

 

Abstracts

Tom Sibley, “The Square Root Two Step:  A Half Step Back, a Full Step Forward” 

For the function f(x) = sin(x) it is easy to find its “compositional square”  fοf:  f(f(x)) = sin(sin(x)).  The other direction is harder:  Is there a square root g so that g(g(x)) = sin(x)?  We’ll explore when such square roots exist and develop a “square root two step” to generate square roots that do exist.

 

Concurrent Session I

 

Dick Jarvinen,  “NASA Return-to-Flight Program and a Brand of Texas Trail Mix”

Dr. Jarvinen has done special projects for the NASA Johnson Space Center, Houston, Texas, in each of the past ten years.  Now at NASA/JSC while on sabbatical leave from Winona State University, his continued work in reliability and risk assessment in support of the Space Shuttle focuses on trend analyses and their connection to the safe return to space flight.  He will talk about one of his most recent Return-to-Flight NASA projects, which includes both mathematical and statistical modeling.

Bill Schwalm, “Symmetry and Integration”

            I = ∫ ,

            I=        etc.

One can apply rotation, reflection, inversion.

Michael Tangredi, “Abel’s Solution of the Tautochrone Problem”

Is it possible to design a curve so that frictionless beads released simultaneously from different positions along the curve all reach the bottom at the same (“tauto”) time (chrone”)?  The answer, in the affirmative, was first demonstrated by Huygens.  But in the 19th century Abel solved a generalization of the problem, namely to design a curve for which the time of descent is a specified function of initial height.  My talk will present Abel’s solution, the crux of which involves finding the inverse of a particular integral operator.

Ralph Carr, “A Didactic Differential Equation”

Many students carry misconceptions about the logical meaning of mathematical theorems well into their college mathematics careers.  Among these is the notion that the conclusion of a theorem may fail to hold occasionally even when the hypotheses are satisfied.  A simple first order differential equation with initial values can be used in conjunction with a standard existence and uniqueness theorem to help students detect and correct their errors.

 

Concurrent session II

 

Michael Hvidsten, “Exploring Geometry, A Discovery-Based Approach to College Geometry”

This talk will present a curriculum development project designed with the goals of integrating discovery-learning and the use of technology into the typical college geometry course.  The talk will present several examples of this approach and will illustrate new text/software materials that utilize this pedagogical philosophy.

Danrun Huang, “Finding Tangent Planes to Quadric Surfaces without Calculus”

There are many nice discussions on finding the tangent line to a conic section without calculus.  In this talk, I will show how we can define and find a tangent plane to a general quadric surface, totally independent of calculus.  We also can classify tangent planes for quadric surfaces without calculus.  The classification would be difficult or impossible if one uses only calculus. So students who hate calculus could find an opportunity to exclaim:  “Down with Calculus!”

Cody Nitschke, “Electric circuits and symmetry Reduction”

When resistors are connected to form the edges of a Platonic solid, one can use rotation/reflection symmetries, and time reversal symmetry, to reduce electric circuit equations.  I review Ohm’s law and basic ideas of circuits.  This review assumes nothing and compares the flow of electricity to the flow of water in pipes.  Then I solve for resistance between pairs of corners of the cube using symmetry.  Similarly, I show corresponding calculations for an icosahedron.

Jeffrey R. Anderson, “Characterization of Models Which Are Not Uniquely Solvable and the Potential Effect on Numerical Approximations”

We discuss the failure of Lipschitz continuity to be necessary for the unique solvability of various differential equations models.  Further, we examine the current state of work towards a characterization of uniqueness theories for reaction-diffusion models.  These models have application in a wide variety of physical situations, such as population movement, groundwater contaminant transport, and tumor-induced capillary growth. However, from a perspective of numerical analysis, concern for whether a model has unique solutions or not is often minimal.  Investigations on the wisdom of such an attitude have revealed an increase in the error of certain numerical approximations, potentially attributable to the lack of unique solvability of the model.

 

Mike Gage, “WeBWorK:  A Web-Based Homework System”

We will give an overview of WeBWorK, a freely available, open source system which allows students to do standard calculus homework problems over the web.  The instant feedback encourages students to keep at the homework until they get it right.  Individualized versions of the problems allow student to collaborate while still doing their own work.  The homework is automatically graded for the instructor’s convenience.

 

Carl Cowen, “Connections Between Mathematics and Biology”

Dr. Rita Colwell, a research microbiologist and current Director of the National Science Foundation, regards the mathematical sciences as the backbone for US Scientific and Engineering research.  Many scholars see the next few decades as a time of intensive progress in the biological sciences.  Dr. Colwell sees mathematics as being an integral part of the progress in biology, not a traditional view, but a forward looking one.

In this talk, Carl Cowen will outline some of the research areas in the emerging collaborations between mathematical and biological scientists.  In addition, Cowen, who began his study of the mathematics of neuroscience last year at the Mathematical Biosciences Institute at Ohio State University, and who is this year beginning research with Professor Christie Sahley in Purdue’s Biology Department, will illustrate the connection between mathematics and neuroscience with a discussion of the Pulfrich phenomenon, an experiment that helps illuminate how the brain processes visual images.  There are few mathematical or biological prerequisites for this discussion.

 

WeBWorK lab workshop

This will be a chance to use the WeBWorK homework system and to ask more detailed questions.

 

Concurrent Session III

 

Scott Przybelski, “Survey of Winona State Graduates with a Mathematics, Mathematics Education, or Statistics Major”

I did a survey of Winona State alumni with mathematics, mathematics education, or statistics degrees.  The survey was sent to those who graduated since 1980.  The survey assesses how well the WSU Mathematics and statistics Department prepared former students for the workplace or graduate school.  The results of this study will help to make improvements in WSU’s degree programs and to improve advising about potential careers for WSU mathematics, mathematics education, and statistics graduates.  I used a mail questionnaire and had a return rate of over 50%.  I will report on the survey and its results.

Daniel Rand, “Teaching Problem-Solving in Finite Math and Operations Research Courses”

In dealing with linear programming problems in both introductory courses and applied courses, the focus is on techniques of solution.  This is true even of operations research courses.  The question of formulating the problem is often overlooked.  In this paper I will show the means to emphasize problem-solving skills rather than the manipulation of the simplex method in introductory classes.  An operations research course outline that includes development of these problem-solving skills, the simplex method, and an overview of more powerful optimization algorithms will be summarized.

The tool featured in both courses is Solver, an add-in available in Microsoft’s Excel software.  Winona State University’s laptop program allows us to take advantage of widely available software to focus student efforts on problem-solving while de-emphasizing the operation of accepted algorithms.

Kevin Dennis, “Freshman Seminar”

The Saint Mary’s mathematics department offered a new course, Freshman Seminar, this year.  The purpose of this course is to introduce outstanding calculus students to different areas of advanced mathematics.  Details about the implementation of the course and reactions from students will be presented.

 

Concurrent Session IV

 

Dale Buske, “Change the Constitution?  Ya, You Betcha.”

With tenure comes the opportunity to discuss politics.  And this will be a political talk.  Along the way, I will present an efficient method of computing Banzhaf power indices in a weighted voting system such as the Electoral College.  Based on these calculations, I will propose ‘popular’ amendments to the U.S. Constitution.

Jason Saccomano, “Automorphisms of Semi-Direct Products”

Given any group G, an automorphism of G is an isomorphism of G onto itself.  In particular, this talk deals with automorphisms of groups that can be written as semi-direct products (a generalized direct product of groups).  We shall begin to uncover the structure of the automorphism group of such groups.