30th Annual MAA Florida Section Meeting

Program

Friday: 9:00 a.m. - 4:30 p.m.
Saturday: 8:00 a.m. - 10:00 a.m.
Registration Fee: Regular $7.00, Student $1.00

Saturday: 7:30 a.m.
Cost: $6.95

Saturday: 12:45 p.m.
Cost: $8.00

Friday: 10:00 a.m. - 5:30 p.m.
Saturday: 8:30 a.m. - 11:00 a.m.

Friday, 28 February 1997

Saturday, 1 March 1997

30th Annual MAA Florida Section Meeting - Abstracts

Friday, 28 February 1997

10:00am-12:00 noon (parallel sessions)

Room 244 Workshop on Using/Programming the TI-82/83 Graphing Calculator

MICHAEL J. KELLER (St. Johns River Community College). Write programs for formulas, create menus, copy and delete programs.


Room 122 Workshop on Environmental Mathematics

BEN FUSARO (Florida State University).

The goal of this minicourse is to acquaint teachers with a calculus-free method for modeling environmental problems. This approach, which requires nothing beyond Algebra II, admits significant modeling applications into general education courses. The material can also serve as a unit in a standard modeling course. The approach uses a five-step solution pattern that analyzes energy flows.


Room 118 Workshop on MATHCAD + 6.0

MARCELLE BESSMAN (Jacksonville University).

Participants will have hands-on experience using the computational and symbolic capabilities of Mathcad +6.0 within the context of using it as a teaching tool for algebra through calculus.


Room 239 SUS Chairs Meeting

WILLIAM CALDWELL (University of North Florida).

(1) Effect of common prerequisites and leveling. (2) Use of technology in the curriculum; Distance learning. (3) How mathematics "reform" is affecting us. (4) Teaching loads & class size; Staffing needs. (5) Encouraging good students to become majors. (6) Graduate program status. (7) Articulation with public schools and the community colleges. (8) Service courses. (9) Budgets, other concerns.


Room 116 Community College Forum and Department Chairs Meeting

12:20pm-1:00pm Regional Meeting Reports Room 122

1:15pm-1:30pm Welcome Session Room 122

DON HILL, MAA-FL President (Florida A & M University)

CHRISTOPHER HUNTER, Department of Mathematics Chairman (Florida State University)

1:30pm-2:30pm Plenary Address Room 122

Euler and His Calculus

V. FREDERICK RICKEY

Distinguished Teaching Professor (Bowling Green State University)

Leonard Euler (1707-1783) was the most prolific mathematician of all time. Besides his hundreds of research papers, he wrote seminal books that reworked the calculus into a form that we can recognize today. After sketching his life, we shall concentrate on the three works which he wrote on the calculus.

2:45pm-5:45pm (parallel sessions)

2:45pm-4:15pm Panel Discussions Room 122

2:45-4:15 Assessment and the Reformed Mathematics Curriculum.

MARCELLE BESSMAN (Jacksonville University).

The panelists are MARILYN REPSHER (Jacksonville University) and DAVID A. SMITH (Associate Professor, Mathematics, Duke University, Co-author of Project CALC and the text Calculus: Modeling and Applications published by Heath (now Houghton Mifflin)).


4:35-5:35 To Phase or Not to Phase? Not!

NAZANIN AZARNIA & ANN STEEN (Santa Fe Community College).

This presentation offers the audience a brief overview for successfully bringing about change at a large community college. Participants will work in teams on materials used in both the classroom and laboratory settings for precalculus and calculus. Participants are encouraged to bring their graphing calculators since many of the activities can be approached from different viewpoints: graphical, numerical, and symbolic. Samples of students' work will be shared and both faculty and student reactions to the changes will be discussed.

2:45-5:40 Special Session: History of Mathematics Room 110

2:45-3:15 Erdos and Joint Work in Mathematics

JEAN A. LARSON (University of Florida).

The Erdos homepage lists 472 names of people who have written papers with Paul Erdos. He was a consummate collaborator in mathematics, and role model for many of us. A few specific examples will be discussed including his joint work with Kac in probabilistic number theory, his joint work with Hajnal in set theory and some of my own joint work with Erdos in combinatorics.


3:25-3:55 Cantor and the Origins of Transfinite Numbers

CHARLES LINDSEY (University of South Florida at Fort Myers/Florida Gulf Coast University).

In this talk we will trace the origins of Georg Cantor's theory of transfinite numbers. Beginning with his early work on convergence of trigonometric series, we follow Cantor's study of exceptional sets (where a trigonometric series fails to converge) to his early notions of point sets and derived sets of real numbers. The set P' of limit points of a set P was called the first derived set of P; we may similarly define P'' = (P')', and so on. Cantor first defined these sets in trying to extend results on uniqueness of trigonometric series to functions with infinitely many discontinuities. We will show how these constructions, and Cantor's early work with them, formed the basis of his theory of transfinite numbers and led to his proof of the nondenumerability of the reals.


4:05-4:35 Integer Right Angles in the Premodern Chinese Tradition

PAUL YIU (Florida Atlantic University).

The final chapter of Jiuzhang Suanshu (Nine Chapters of the Mathematical Art) is the origin of a long tradition of the study of right triangles in pre-modern China (up to the end of the 19th century). In this talk, we shall examine (1) a few examples from Jiuzhang Suanshu to see how the ancient Chinese construct right triangles with rational sides, (2) an example in the late nineteenth century of solution of certain quadratic indeterminate equations using the traditional Chinese method.


4:40-5:10 Fermat's Motivation

FRED ZERLA (University of South Florida).

Fermat's interest in how numbers work together began at an early age. The influence of Claude Bachet de Meziriac's Latin translation of Diophantus of Alexandria's "Arithmetica", published in 1621 when Fermat was 20 years old, is well known. Less well understood is the relationship Fermat had with the followers of Francois Viete in Bordeaux. Fermat's reluctance to publish his methods and his search for ingenious solutions probably springs from his participation in the "challenge problem" tradition made famous in the cubic controversy of the preceding century and in the plight of his contemporary, Giles Personne de Roberval. Some ideas about how Fermat answered these challenge problems are suggested.


5:15-5:40 Bernoulli Numbers and Fermat's Last Theorem

SCOTT HOCHWALD (University of North Florida).

Bernoulli numbers appear in many different areas of mathematics. Their first appearance will be described. Some of Euler's uses of them and some of their properties will be examined. Their connection to Fermat's Last Theorem will be explored. Finally, some unsolved problems involving Bernoulli numbers will be posed.

2:45pm-5:45pm Pedagogy Room 116

2:45-3:15 Teaching Mathematics with a Graphing Calculator

LINDA SMITH (Tallahassee Community College).

Using examples from trig and calculus the presenter will share some "teaching scenarios" in which the graphing calculator can be used in a lecture/discussion setting to anticipate and motivate new concepts rather than demonstrate "what we've already learned". Concepts will include horizontal translations of periodic functions, the Mean Value Theorem, trig identities and the Chain Rule.


3:25-3:55 Math History Timeline

LEE ARMSTRONG (University of Central Florida).

A description and presentation of a Math History Timeline project being developed in our Math History course MHF 4404. The project uses HyperStudio multimedia software. The project is intended for middle school students. Classes in Central Florida will be able to contribute pages to the Timeline. The Timeline will be placed on the Internet.


4:05-4:35 Projects for Teachers and Students: Report on an NSF Program

LEONARD LIPKIN (University of North Florida).

This is a report of mathematical activities for in-service and pre-service teachers that were undertaken in an NSF-supported program Technology, Discovery, and Communication in High School Mathematics. The purposes were to (1) see how parts of mathematics are used in science and in other parts of mathematics (e.g., logarithms and exponentials to study the length of a year on planets; cubic polynomials to study floating balls), (2) integrate science and mathematics (e.g., floating balls, reflection of light and conics), (3) use technology appropriately (handling data, describing long-term behavior of functions), (4) introduce the use of writing as a means of student learning, and (5) have students get involved in mathematics through the discovery method.


5:05-5:20 Student Projects in a Liberal Arts Math Course

KEVIN CHARLWOOD (Saint Leo College).

We shall discuss several short individual/group projects suitable for a "Math for Liberal Arts" course or a "Math for Elementary Teachers" course. The projects focus on arithmetic in bases other than ten, and go beyond standard fare in the typical texts for such courses. Specific projects to be discussed in detail include working with fractions and "decimals" in bases other than ten, along with how to convert irrational decimals to representatives in other bases. The scope of the projects will be outlined, along with desired outcomes in student comprehension.


5:25-5:40 Making College Algebra More Bearable

CATHLEEN M. ZUCCO (University of North Florida & Rutgers).

The author will discuss some of the pedagogical techniques that she used recently to increase the success rate in a college algebra course at the University of North Florida. The author will explain how she used cooperative groups and spiral review techniques in both her small and large lecture sections of college algebra. She will also make some suggestions for group discovery activities for this course.

2:45pm-5:40pm Contributed Papers: Mathematics and Pedagogy Room 117

2:45-3:15 Random Knotting

STU WHITTINGTON (University of Toronto).

When a simple closed curve is randomly embedded in a three dimensional space, how likely is it that the embedding will be knotted? This kind of question has been attracting attention for thirty years, and some answers have emerged recently. This talk will review some problems, methods and results in this area. The results have applications in polymer physics and in molecular biology.

3:25-4:25 Interdisciplinary College Algebra and Physical Science for Honors Students

MOANA KARSTETER & CAROL ZIMMERMAN (Tallahassee Community College).

Moana Karsteter, from Mathematics, and Carol Zimmerman, from Chemistry, at TCC teamed up to teach College Algebra and Physical Science during Fall 1996. In this talk, Moana and Carol will provide more details about their experience and describe and demonstrate some of the activities used in the courses.


4:35-4:50 Ross Perot's Influence on the Last Election

JAMES ISSOS (Florida A&M University).

A statistical analysis will be made of presidential election data to determine which major candidate Ross Perot's candidacy hurt the most.


4:55-5:10 Three Feedback Proofs of the Infinitude of Prime Numbers

SIDNEY KUNG (Jacksonville University).

By using the properties of Mersenne numbers and the repunits, and the solutions of a unit fraction equation, three new proofs of the infinitude of prime numbers have been generated. They are simple and easy to understand for students at the introductory level of number theory.


5:15-5:40 Columns of Pythagoras: A Problem Solving Tool

HERB WILLS (Florida State University).

This is a talk on applying the Columns of Pythagoras to several classical and difficult problems. Among the problems dispatched with ease are: (1) It is an easy task to find Pythagorean triples one of whose legs and hypotenuse are consecutive integers. However, finding Pythagorean triples having consecutive legs is a challenge. Find the first six of these with the least legs; (2) Find all triangular numbers that are perfect squares (or oblong numbers). (3) The ancient Pythagoreans dreaded the number 17 since it resides directly between a square and twice a square. Moreover, 16 and 18 are the ONLY integers each of which is both the area and perimeter of a rectangle. But are there integers other than 17 that are directly flanked by a square and twice a square? (4) The numbers 355 and 113 have a ratio closer to pi than any other pair of positive integers less than 1997. Which pair of integers, each less than 1997, have the closest ratio to the square root of 2. Interestingly, theorems 9 and 10 in Book 2 of Euclid's Elements each independently justifies the recursive construction of the Columns of Pythagoras. Moreover, neither is restricted to a difference of 1 for a square and twice some square. This fact may be used to advantage in solving the problem of finding all these integers that lie directly between a square and twice a square. That is 3 consecutive integers in which either extreme is a square while the other is twice a square.

2:45pm-5:40pm Student Conference Presentations Room 244

2:45-3:00 Perceived Gender Bias in Academic Employment.

ALISSA ANDREICHUK (Jacksonville University).

The purpose of this project is to examine analytically the pattern of hiring of Ph.D.'s in the various types of universities over the last eight years to determine if the formerly rampant gender bias against women in mathematics is significantly decreasing as the "critical mass" of women Ph.D.'s increases. Our data shows that the percentage of women hired does not appear to increase in relation to the percentage of available women Ph.D.'s. Therefore this belies the claim that the gender bias can be accounted for by the lack of a "critical mass." The number of women with Ph.D.'s hired in the academic field is still below that of men. Moreover, the women who are hired are also discriminated against in salary and tenure awards. On the average, women's salaries are much less than that of men. The ratio of tenured men to women in mathematics is also greater.


3:05-3:20 Fractal Music.

RACHEL AUERBACH (Lake Highland Preparatory School).

Fractals are graphical representations of an iterated complex function on a complex plane. The purpose of this project was to see if the graphical points of fractals, when translated into musical notation, would make aesthetically pleasing music. This result would indicate that mathematics and music are deeply similar, maybe even the same at their root with only the expressions being different. By coding a program that gave the number of iterations of the coordinate points generated from a Julia set equation, then translating them into musical notes (using A=1, B=2 etc.), writing the notes in musical notation and playing them on the piano, music was created. The fractal music created was both aesthetically pleasing and musical in it's nature, and exhibited many traits of classical music including clearly audible patterns and tempos. The applications of this project may be a simple as creating a new form of popular entertainment, or as far-reaching as helping us to understand the basis of aesthetics and perhaps the nature of the human mind and its interpretation of the natural world.


3:25-3:40 Mixing Machines.

HAN DUONG & ED GRECO (Jacksonville University).

This is a solution to the 1997 Mathematical Contest in Modeling discrete problem. The problem asks for an assignment of 29 board members to various discussion groups, given constraints intended to assure mixing.


3:45-4:00 Predicting the Dow Jones.

MATTHEW GALATI (Stetson).

To be a step ahead of the market is every investor's dream. I will present a simple probabilistic model that can be used to predict the Dow Jones Industrial Average on a short-term basis. The model relies on a trend analysis of the last seventy-five years of data. Through compiling a database of trends in the past, I produced a model to predict the daily close of the Dow. In my presentation, I will explain the primary elements of the probabilistic model, including the major parts of the algorithm, and how the model works. I will present some of my recent predictions, and discuss any deviations from the actual close.


4:05-4:20 Determination of Optimum Time for Selling a Farm Animal.

LAURA GUNN & VALERIE HORSLEY (Jacksonville University).

The objective of this paper is to determine the optimum time for selling a farm animal. Solutions are obtained by solving a system of first order differential equations model.


4:25-4:40 A Two-Parameter Family of Curves.

MARK F. LEGEAR (St. John's River Community College).

The two-parameter family of curves satisfying the nth order ODE satisfied by the equations of harmonic motion is derived and given in five alternate forms depending upon certain constants in the equation. Next, some explicit solutions of the IVP involving the aforementioned ODE are given. During this development, such theorems as the product rule for the nth order differentiation and the reduction of order formula for the nth order homogeneous differential equations are proven and used.


4:45-5:00 Dinomatics.

MATT LITTLE & JIM LYNCH (Jacksonville University).

This is a solution to the 1997 Mathematical Contest in Modeling continuous problem. The problem asks for the strategy a velociraptor would use in pursuing a thescelosaurus.


5:05-5:20 Self-Complementary Degree Sequences.

JENNIFER PELKA (Lake Highland Preparatory School, Orlando).

Let n be the number of vertices in a graph. Only graphs for which n0(mod 4) or n1(mod 4) can have self-complementary degree sequences.


5:25-5:40 Hunting Strategies: A Mathematical Model.

SHAUN SMITH (Jacksonville University).

This is a solution to the 1997 Mathematical Contest in Modeling continuous problem. The problem asks for the strategy a velociraptor would use in pursuing a thescelosaurus.

4:45pm-5:40pm Contributed Student Papers Room 107

4:45-5:00 The Velociraptor Problem

PHIL WEINBERG (Jacksonville University).

This is a solution to the 1997 Mathematical Contest in Modeling continuous problem. The problem asks for the strategy a velociraptor would use in pursuing a thescelosaurus.

5:05-5:20 Resolvents of M-Accretive Operators in Banach Spaces

ERIC LEHR (Eckerd College).

In a real Banach space X, an accretive operator T is "m-accretive" if R(T+1)=X for all positive . Moreover, the resolvents for an m-accretive operator T are denoted by J and defined by the relationship J:XD(T) with J=(I+T)^-1 for all positive . In this talk, we develop a number of theorems concerning these resolvents and their associated Yoside approximants.


5:25-5:40 Newtonian Athletics: The Physics Behind Baseball's "Sweet Spot"

PATRICIA ALEXANDER (Eckerd College).

There are two principle theories as to why the "sweet spot" of a baseball bat is the optimum place to strike the ball. One theory proposes that the sweet spot is the center of percussion, the other theory postulates that the sweet spot is located at the node of secondary vibration of the bat's natural vibrational frequency. Both theories will be explored in this talk.

2:45pm-5:40pm Special Meetings Room 239

2:45-3:45 FAME Meeting. ELIZABETH JAKUBOWSKI (Florida State University) presides.

Florida Association of Mathematics Educators (FAME). Open meeting for all interested in mathematics education at all levels in Florida. During this meeting of FAME we will discuss the Sunshine State Standards focusing on several issues. These will include the role of higher education in the interpretation and implementation of the standards; student assessment with respect to the benchmarks; and the preparation of preK-12 teachers to maximize the learning opportunities for all students.


3:50-4:50 Student Chapter Advisors Meeting. V.S. RAMAMURTHI (University of North Florida) presides.


4:45-5:45 FTYCMA Business Meeting. GUESNA DOHRMAN (Tallahassee Community College) presides.

5:45pm-6:45pm Evening Social Fireside Lounge

Hors d'oeuvres compliments of Wes Burnham (Kendall/Hunt Publishing Company), Kimberly Dawson (Houghton-Mifflin Company), Pamela McCaleb (Internat'l Thomson Publishers), Ruth Ann Sweeney (Harcourt Brace College Publishers). Thank you.

5:45pm-6:45pm Student Hospitality Center Room 107

Enjoy snacks and conversation.

6:30pm Student Conference Banquet Room 123A

Magnetic Fields: Technological Impact

JACK CROW, Speaker

Saturday, 1 March 1997

7:30-8:30 Governor's Breakfast Dining Room

FRED HOFFMAN, MAA-FL Section Governor (Florida Atlantic University)

9:00-10:00 Plenary Address Room 102

Problems: The Heart and Soul of Mathematics

DON ALBERS

Director of Publications & Electronic Services (Mathematical Association of America)

One of the joy's of serving as MAA's Director of Publications is seeing beautiful problems crossing my desk before they reach a broader population. Big problems, little problems, surprising problems, not-so-hard problems, and problems with problems which provide continuing pleasure and inspiration for all of us. In this talk, the speaker surveys some of his favorite problems encountered during his five years in the Washington office.

10:10-11:20 (parallel sessions)

10:10-11:20 Panel Discussion Room 122

Reformed Courses: What Should We Leave in and What Should We Take Out?

LEN LIPKIN (University of North Florida)

Has technology made some material obsolete? What skills should students know? If new topics come in, what should go out? Panelists are DEBBIE GARRISON (VCC-East), FRED HOFFMAN (Florida Atlantic University), SUSAN WALLIS, (TERRY PARKER HS, Jacksonville)

10:10-11:20 Special Session: History of Mathematics Room 244

10:10-10:40 Emmy Noether and Her Work in Commutative Ring Theory

ROBERT GILMER, Robert O. Lawton Distinguished Professor (Florida State University).

Emmy Noether's mathematical career spanned 27 years, 1908-1935, and consisted of three fairly distinct stages. She initially worked in invariant theory, the area of her thesis advisor Paul Gordan. Inspired primarily by work of Richard Dedekind, her work then moved into what, at the time, was called the general theory of ideals, a part of commutative ring theory today. The third stage of her career was devoted to noncommutative algebra. This talk will focus on Noether's work in the general theory of ideals during the second stage (1920-26) of her career. In general she advocated the axiomatic approach in algebra, and she gained a following because she ably demonstrated its power. In particular, she was the first to recognize and establish the preeminent role of the ascending chain condition (a.c.c.) for ideals in a commutative ring. Such rings are called Noetherian rings, in her honor.


10:45-11:15 Florida Deparments of Mathematics at the Turn of the Century

PAUL EHRLICH (University of Florida).

Considering the ancestor institutions of U.F. and F.S.U., we will indicate how our Florida educational institutions in the early 1900's reflected a national pattern of graduate study at Hopkins, study in Europe especially Germany, then study at Clark and Chicago (which has been recently explored at length in the book by K. Parshall and D. Rowe on the emergence of the American mathematical research community.) Especially we will focus on Professor Albert Murphree of F.S.U. and Professors Karl Schmidt and Herbert Keppel of U.F.

10:10-11:15 Contributed Papers: Mathematics and Pedagogy Room 117

10:10-10:25 Atomic Transitions, Number Theory and Fermat's Infinite Descent

I.A. SAKMAR (University of South Florida).

Quantum mechanical equations are Diophantine equations, since the integer quantum numbers force the physical quantities like the mass, the charge, Planck's constant, the light velocity, et cetera, to conspire to give integer number relations. One such equation is the spectroscopic relation connecting the emitted wave's wavelength to the quantum numbers of the initial and final energy quantum numbers. We solve the problem for a given wavelength, a problem encountered in a physics course. Also we study the inverse problem for uniqueness. In the process, Fermat's infinite descent is used more than once. The uniqueness problem is closely tied to another theorem of Fermat, namely that the primes of the form 4N+1 can be expressed in a unique way as the sum of two squares.


10:30-10:40 Finding Inverses of Certain Tupes of Functions

V.S. RAMAMURTHI (University of North Florida).

The talk will describe a non-computational, map-oriented procedure for teaching the calculation of inverses of functions at pre-calculus and college algebra levels.






10:45-11:15 Some Applications of Taylor Series Solutions of Ordinary Differential Equations

HARLEY FLANDERS (Jacksonville University & University of North Florida).

Most of the talk will be a computer graphics show of solutions of physical problems: double pendulum, three-bodies, and related items. Some of the theory behind the "automatic differentiation" generation of high order Taylor polynomial approximations to solutions of ODE will be discussed, and possibly some other applications included, such as integration and higher order "Newton Methods" for solving non-linear equations.

10:10-11:10 Panel Discussion Room 116

A Non-Traditional Approach to Teaching Introductory Statistics.

BYRON DYCE & BERT SIMMONS (Santa Fe Community College)

This session will address a non-traditional approach to teaching Introductory Statistics with emphasis on: 1) using technology, 2) exploratory data analysis, 3) projects, 4) cooperative learning and 5) interactive learning.

10:10am-11:10am Panel Discussion Room 110

Reinventing Distance Learning.

Chaired by JUDITH BOETTCHER (Florida State University)

Assisted by EILEEN ST. GEORGE (Florida State University)

Is distance learning only for the remote and the hard to reach student? Will it always be viewed as second class learning? Creating quality interactive distance learning may now be possible with the use of high speed interactive technologies. This session examines the teaching and learning foundations that can make distance learning all that we have wanted teaching and learning to be: active, interactive, accessible, collaborative, customized, and excellent. A demonstration of an interactive distance learning course will be included.

11:30am-12:30pm Plenary Address Room 122

Welcome by SANDY D'ALEMBERTE, President, Florida State University

Knot Theory and DNA

DE WITT SUMNERS (Florida State University)

Cellular DNA is a long, thread-like molecule with remarkably complex topology. Many important cellular processes (including segregation of daughter chromosomes, gene regulation, DNA repair, and generation of antibody diversity) are mediated by enzymes which manipulate the geometry and topology of cellular DNA. Some enzymes pass DNA through itself via enzyme-bridged transient breaks in the DNA; other enzymes break the DNA apart and reconnect it to different ends. In the topological approach to enzymology, circular DNA is incubated with an enzyme, producing an enzyme signature in the form of DNA knots and links. By observing the changes in DNA geometry (supercoiling) and topology (knotting and linking) due to enzyme action, the enzyme mechanism can often be characterized. This talk will discuss topological models for the structure of DNA and the active enzyme-DNA complex. This will be an expository talk with lots of pictures, suitable for anyone with an interest in mathematics and/or biology.

12:45pm-2:00pm Luncheon and Annual Business Meeting Kissimmee Dining Room