30th Annual MAA Florida
Section MeetingThe 30th Annual Florida Section of MAA will be held on Friday and Saturday, February 28 and March 1, 1997 on the campus of Florida State University at the Turnbull Center/Center for Professional Development. The Turnbull Center is located on Pensacola Street one block west of the Tallahassee Civic Center between Railroad Avenue and Copeland Street (east/west) and Pensacola Street and St. Augustine Street (north/south).
Contents
MAA Student Conference
Check out "Things to do While in Tallahassee" (below).
Plenary Speakers:Don Albers, Director of Publications and Electronic Services for MAA (Mathematical Association of America), Problems: The Heart and Soul of Mathematics. 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.
V. Frederick Rickey, Distinguished Teaching Professor (Bowling Green State University) Euler and His Calculus. 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.
DeWitt Sumners (Florida State University) Knot Theory and DNA. 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.
go back to contents
Special Session: History of MathematicsPaul Ehrlich (University of Florida), Florida Deparments of Mathematics at the Turn of the Century. 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.
Robert Gilmer, Robert O. Lawton Distinguished Professor (Florida State University), Emmy Noether and Her Work in Commutative Ring Theory. 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. She proved that each ideal of a ring R satisfying a.c.c. is a finite intersection of primary ideals, and that a polynomial ring in finitely many indeterminates over R again satisfies a.c.c. Each of these results represented an extension to general commutative rings of results known in more concrete settings related to algebraic geometry or algebraic number theory. Another major contribution of Noether in the area was that of giving an axiomatic characterization of integral domains in which each nonzero ideal is uniquely expressible as a finite product of prime ideals; in the literature today, such domains are called Dedekind domains, while rings satisfying the ascending chain conditions for ideals are called Noetherian rings, in honor of Emmy Noether.
Scott Hochwald (University of North Florida), Bernoulli Numbers and Fermat's Last Theorem. Bernoulli Numbers appear in many different areas of mathematics. Their first appearance will be described. Some of Euler's uses of them will be discussed. 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.
Jean A. Larson (University of Florida), Erdos and Joint Work in Mathematics. The Erdos homepage lists 472 names of people who have written papers with Paul Erdos. He was a consumate 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.
Charles Lindsey (University of South Florida at Fort Myers/Florida Gulf Coast University), Cantor and the Origins of Transfinite Numbers.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.
Paul Yiu (Florida Atlantic University), Integer Right Angles in the Premodern Chinese Tradition. 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.
Fred Zerla (University of South Florida), Fermat's Motivation. Fermat's interest in how numbers work together began at an early age. The infulence 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.
go back to contents
Panel Discussions:Assessment and the Reformed Mathematics Curriculum. 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)). M. Bessman (Jacksonville University).
Reformed Courses: What Should We Leave in and What Should We Take Out? Chaired by, 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?
go back to contents
Workshops:MATHCAD + 6.0. Chaired by, 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.
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.
Contributed Papers in PedagogyLee Armstrong (University of Central Florida), Math History Timeline. 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 contibute pages to the Timeline. The Timeline will be placed on the Internet.).
Nazanin Azarnia & Ann Steen (Santa Fe Community College), To Phase or Not to Phase? Not!. 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.
Kevin Charlwood (Saint Leo College), Student Projects in a Liberal Arts Math Course. 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.
Byron Dyce & Bert Simmons (Santa Fe Community College), A Non-Traditional Approach to Teaching Introductory Statistics. 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 learing and 5) interactive learning.
Harley Flanders (Jacksonville University & University of North Florida), Some Applications of Taylor Series Solutions of ODE. 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 Method"s for solving non-linear equations.
James Issos (Florida A&M University), Ross Perot's Influence on the Last Election. A statistical analysis will be made of presidential election data to determine which major candidate Ross Perot's candidacy hurt the most.
Moana Karsteter & Carol Zimmerman (Tallahassee Community College), Interdisciplinary College Algebra and Physical Science for Honors Students. Moana Karsteter, from Mathematics, and Carol Zimmerman, from Chemistry, at TCC teamed up to teach College Algebra and Physical Science during Fall 1996. A section of college algebra and a section of physical science were offered back to back three days per week. Students were required to register for both sections and Carol and Moana were present for both. The courses were intended for non-science majors. The purpose of the courses was to help the students make the connection between mathematics and science. Using graphing calculators interfaced with "calculator based laboratory"(CBL) modules for data acquisition, the students got hands-on experiences in collecting and analyzing data. The students learned mathematical concepts in context with physical science problems. In this talk, Moana and Carol will provide more details about their experience and describe and demonstrate some of the the activities used in the courses.
Sidney Kung (Jacksonville University), Three Feedback Proofs of the Infinitude of Prime Numbers. By using the properties of Mersenne numbers and the repuints, and the solutions of a unit fraction equation, three new proofs of the infinitude of prime numbers have benn generated. They are simple and easy to understand for students at the intro-level of number theory.
Leonard Lipkin (University of North Florida), Projects for Teachers and Students: Report on an NSF Program. 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 lenth 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. The mathematics here is not new, but the activities take individual pieces and put them to use.
V.S. Ramamurthi (University of North Florida), Finding Inverses of Certain Tupes of Functions. 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.
I.A. Sakmar (University of South Florida), Atomic Transitions, Number Theory and Fermat's Infinite Descent. 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.
Linda Smith (Tallahassee Community College), Teaching Mathematics with a Graphing Calculator. Using examples from trig and calculus the presenter will share some "teaching scenarios" in which the G.C. 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.
Stu Whittington (University of Toronto), Random Knotting. 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 appplications in polymer physics and in molecular biology.
Herb Wills (Florida State University), Columns of Pythagoras: A Problem Solving Tool. Talk on applying the Columns of Pythagoras to several classical and dlfflcult problems. Among the problems dispatched with ease using the Columns of Pythagoras 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 ratia 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.
Cathleen M. Zucco (University of North Florida & Rutgers), Making College Algebra More Bearable. 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
go back to contents
Things to do While in TallahasseeFSU School of Theatre. Ticket Office (904) 644-6500, 11am-6pm Monday through Friday.
Studio Theatre Productions, The Boys Next Door by Tom Griffin, February 26-March 1 at 8:00pm.
Faculty Brass Quintet, February 28, 8:00 DRH
Visit your Florida Capitol, Mon-Fri 8am-5pm, Sat-Sun-Holidays 9am-3pm, State of Florida & US Government.
Tallahassee Museum of History and Natural Science, 9 - 5 Monday through Saturday; 12:30 - 5:00 Sunday. For more information on museum events and admission fees, call 575-1636.
Web Vista's Tallahassee Online
Save time & money!
Register now!To pre-register for the 1997 Annual Meeting, complete and return this form to Secretary Ernest Ross, 12229 69th Terrace N, Seminole, Florida 34642, along with a check made out to the Florida Section-MAA.
Pre-registration for everyone except students is $5.00, whereas registration at the meeting is $7.00. There will be no fee for students who pre-register.
You may also prepay for the Annual Luncheon ($8.00) and/or the Saturday morning Governor's Breakfast ($6.95).
go back to contents
Pre-Registration Form (print/copy, fill out & mail/email, this is not an on-lineform)
| first name: | last name: | title: |
| department: | institution: | city, state, zip: |
| email: | phone: | fax: |
| Pre-registration | $5.00 | $ |
| Luncheon | $8.00 | $ |
| Governor's Breakfast | $6.95 | $ |
| Total | $ |
For further information
or questions contact:Phil Novinger
Department of Mathematics
212 Love Building
Florida State University
email: novinger@math.fsu.edu
phone: 904.644.8711
fax: 904.644.4053
Motel/Hotel AccomodationsWhen making reservations, mention the MAA Florida Section meeting hosted by the Florida State University Mathematics Department. Rooms will be held at the indicated rates until February 1. Distances from motels/hotels to the Center for Professional Development are indicated in parentheses.
|
CAPITAL INN (1.2 miles) 1302 Apalachee Parkway (904) 877-3141 $38 + tax includes continental breakfast |
COLLEGIATE VILLAGE INN (2.5 miles) 2121 W. Tennesse St. (904) 576-6121 $40 + tax includes continental breakfast and evening cocktails. Free rides from airport. |
|
RAMADA LIMITED (1.5 miles) Corner Tennessee and Brevard (904) 224-7116 $45 + tax includes continental breakfast |
CABOT LODGE (4.0 miles) 2735 North Monroe (904) 386-8880 $57 + tax includes continental breakfast and two-hour evening cocktail reception |
|
RADISSON HOTEL (1.2 miles) 415 North Monroe (904) 224-6000 $82 + tax |
Last modified: 27 February 1997