I have just finished the book, "Fermat's Enigma," by Singh. A wonderfully written book, it reminded me of how exciting mathematics can be and of the challenge we face as conveyers of a difficult subject field. Singh does a wonderful job of setting an exciting moment in an historical context. He also does a wonderful job of remembering who his audience is.

I think that is our daily challenge. Our audience has expanded dramatically. What was once a class of science and engineer hopefuls has expanded to those who must be exposed to the mathematical models that know no discipline boundaries. These students have far different and differentiated backgrounds from those we taught in the past. They have different needs when it comes to mathematics. I am still of the opinion, as I wrote in my first article some two years ago, that we, as a professional

community, have not thought out what the content and approach we should be taking in our classrooms given this broader student body, the existence of graphic and symbolic manipulators and the needs of the varied disciplines that depend on quantitative models.

This office has been a source of much pleasure. A large part of that derives from the opportunity it has provided to better know some of my Kentucky colleagues. Of course, we all have that opportunity at our Annual Meeting in March. I encourage you to join us at the University of Louisville and to bring this opportunity to the attention of your colleagues and students who may not be as active in the Kentucky Section as you are.

John Oppelt

On Friday afternoon, from 4:00 to around 5:30, we will have a problem solving workshop. This will be an opportunity for students to get involved in working on some interesting mathematical problems and to get to know students from other schools! Afterwards, we will gather for pizza and then will go to the evening lecture and the "Aftermath" social hour.

Student talks will be given on Saturday morning. Please contact me via email (elderbrockl@nku.edu) if you plan to give a talk or have any questions.

Lisa Elderbrock

The Joint Math Meetings were held in San Antonio, Texas this year. Unfortunately, I had to leave all the ice and snow behind to attend the Board of Governors meeting on January 12. I even had to miss the first week of classes to attend the many useful sessions, but I was happy to serve as your representative. I did think of you often as I walked around town in shirtsleeves or watched the Weather Channel reports.

The Board did approve Mathfest 2000 to be held at UCLA on August 3 - 5. Mathfest 1999 will be held closer to home in Providence, Rhode Island July 31 - August 2 this summer. I hope many of you will be able to fit a trip East into your summer plans. The financial picture for the association has certainly improved. Both the Atlanta and Toronto Mathfests appear to have broken even. The Board did approve a 4% dues increase for 2000.

Plans for the International Mathematics Olympiad, to be hosted by the USA in 2001, are going well under the direction of Walter Mientka, who directed the American Math Competitions (AHSME and AJHSME, as well as the advanced AIME and USAMO) for over 22 years. The AHSME test is being expanded next year into a two-tiered exam. One test will be open only to grades 9 and 10, and the other for up to grade 12 students. I would encourage you to talk with area high school and junior high school teachers to get involved in these competitions.

Project NExT is still going strong. Nine NExT fellows presently teach in Kentucky. Visit their website at http://archives.math.utk.edu/projnext/. The new draft of the NCTM Standards document is now published and your input is requested. Visit NCTM.org for more info or talk to your mathematics education faculty.

The Board solicits your imput on a strategic plan for the Association for the next five years. If you have ideas about how the MAA can better serve you, or what the major goals or objectives of the organization should be, please send them to me or Marcia Sward. In one last bit of news, Marcia will leave her position as Executive Director at the end of 1999, after 10 years of service. A search is currently underway to find a replacement. The Board thanked Marcia for her many years of faithful service to our organization.

Ballots will be distributed shortly to elect my successor as Governor of the Kentucky Section. I hope you will all exercise your right to vote. I have enjoyed serving you for the past three years.

Peter Moore

The Holiday Inn Louisville-Downtown is located at 120 W. Broadway, just off of I-65. The hotel is holding a block of 80 rooms until March 12. Rooms in the Louisville area will be extremely scarce on March 26, due to the Midwest Trucking Association Meeting at the State Fairgrounds that weekend, so make your reservation today!

Coming from the south on I-65, take the Broadway exit. Turn left on Broadway, continue under the interstate, and turn left into the parking lot of the Holiday Inn.

Coming from the north on I-65, take the St. Catherine Street exit. Proceed to Second Street, turn right, and continue down to Broadway, where the Holiday Inn is located immediately on the right.

To go from the Holiday Inn to UL’s Belknap Campus, get on I-65 South from the ramp on First Street just off the parking lot of the Holiday Inn. Take the Eastern Parkway exit and proceed through one traffic light to Eastern Parkway. Turn right onto the Parkway, and then turn left at the first traffic light into the Speed Scientific School (SSS) parking lot. Please park only in the green and blue spaces in that lot. Alternatively, one can avoid the interstate and take Third Street south to Eastern Parkway, turn left there, and then turn right at the traffic light into the SSS parking lot.

Those proceeding directly to UL’s Belknap Campus on I-65 South should follow the directions in the paragraph above. Those approaching the campus on I-65 North should pass over Eastern Parkway and take the Eastern Parkway West exit. Turn right onto Warnock Avenue at the bottom of the ramp, bear right on Crittenden Drive, and turn right onto Eastern Parkway. Continue under I-65 to the first traffic light, which is the SSS parking lot, and turn left into that lot.

Registration and the bulk of the sessions of the meeting will take place in the Natural Science (NS) Building, which is located on Eastern Parkway, directly across from the SSS parking lot. Cross at the light and go directly through either front door of the NS Building. Signs will direct you to the registration area.

Recall that reservations for meals MUST BE MADE by Monday, March 22. If you miss the preregistration deadline, you must make meal reservations via Dick Davitt if you plan on eating with us. Questions concerning local arrangements should be directed to Dick Davitt at (502) 852-6826 or rmdavi01@athena.louisville.edu

...for our invited speakers, Peter Winkler and Dan Kalman, appear in our Winter newsletter.

University of Louisville March 26-27, 1999

2:30 - 6:15 Registration Natural Science (NS) Building, First Floor Hallway

4:00 - 5:30 Problem Solving Workshop for Students NS 108

4:00 - 6:00 Short Course "History of Mathematics," Dan Curtin, Northern Kentucky University, and Dick Davitt, University of Louisville.

NS 112

4:00 - 6:30 Book Exhibit NS 128 and 130

5:00 - 5:20 Contributed Papers

"Mean Traps," James Barksdale Jr., Western Kentucky University.

NS 110

"Even Pairs," Matt Scobee, University of Louisville. NS 212 C

"Extensions of Flett's Mean Value Theorem," Thomas Riedel, University of Louisville. NS 212 E

5:30 - 5:50 Contributed Papers

"Differential Graded Modules over Differential Graded Algebras,"

Stephen Tempest Aldrich, University of Kentucky. NS 110 (S)

"Chebyshev Polynomial and Binomial Expansion," Gregory Babushkin, Kentucky State University. NS 212 C (S)

"Two Elementary Techniques in Edge Detection," Bruce Kessler, Western Kentucky University. NS 212 E

6:00 - 6:20 Contributed Papers

"Chaotic Behavior in Numerical Solutions to Differential Equations," Kenny Palmer, Western Kentucky University. NS 110

(S)

"Discrete Least Squares Approximation With Non-Polynomial Models," Mark P. Robinson, Western Kentucky University. NS 212 C

"The Changing Concept of Change," Jennifer Phillips, University of Kentucky. NS 212 E (S)

6:30 - 7:30 Student Pizza Dinner Student Activities Center W 303 E

6:30 - 7:45 Banquet Atrium of the Business School

8:00 - 9:00 Invited Address "Probability and Intuition," Peter Winkler, Bell Labs. Middleton Auditorium - Strickler Hall 101

9:00 - 10:00 Aftermath Foyer of Middleton Auditorium - Strickler Hall

7:30 - 8:20 Breakfast Holiday Inn Louisville-Downtown

8:00 - 10:00 Registration Natural Science Building - First Floor Hallway

8:30 - 11:20 Book Exhibits and Complimentary Coffee & Donuts

NS 128 and 130

8:30 - 10:15 Calculator Workshop "The TI-83 in Elementary Statistics,"

Lloyd Jaisingh, Morehead State University. NS 112

8:30 - 8:50 Contributed Papers

"Opening Communication in the Classroom: Classroom Assessment Techniques for Mathematics," Lee R. Gibson, University of Louisville. NS 110 (S)

"Computational Anomalies in Analysis," Tom Richmond, Western Kentucky University. NS 212 C

"Ramanujan, the Man Who Knew Infinity," Ray Tennant, Eastern Kentucky University. NS 212 E

9:00 - 9:20 Contributed Papers

"Nash Equilibrium of an n-Sumgame," Heather Anderson, Murray State University. NS 110 (S)

"Methodologies for Tessellation Study in the Hyperbolic Plane,"

Brandy Smith, Eastern Kentucky University. NS 212 C (S)

"The Steady-State Distribution of Some Classes of Birth-Death- Immigration-Emigration Processes," Randall Swift, Western Kentucky University. NS 212 E

9:30 - 9:50 Contributed Papers

"Women in Mathematics," Dora Cardenas Ahmadi, Morehead State University. NS 110

"A Stochastic Richardson's Arms Race Model," John Fricks, Western Kentucky University. NS 212 C (S)

"Mathematics Does Need New Axioms," Andy Martin, Eastern Kentucky University. NS 212 E

9:55 - 10:25 Coffee Break NS 130

10:30 - 10:50 Contributed Papers

"The Structure of Infinity: An Introduction to Penrose Diagrams,"

John Pearson, University of Kentucky. NS 110 (S)

"A Taste of Automated Theorem-Proving," J. Lyn Miller, Western Kentucky University. NS 212 C

"Bounds on Sum-Free Sets," Margaret Yoder, Eastern Kentucky University. NS 212 E

11:00 - 11:20 Contributed Papers

"The Moore Determinant," Chris Christensen, Northern Kentucky University. NS 110

"The Degree Function for Euclidean Domains," Bettina Richmond, Western Kentucky University. NS 212 C

"Philosophy, Theology, and Georg Cantor's Transfinite Set," Aaron Zerhusen, University of Kentucky. NS 212 E (S)

11:30 - 12:30 Invited Address "Viewing Polynomial Roots With Matrix Eyes -- Linear Algebra Methods Applied to some Classic Polynomial

Problems," Dan Kalman, American University. NS 112

12:30 - 1:15 Lunch Ground Floor Cafeteria - Miller Instructional Technology Building

1:15 - 2:15 Business Meeting Ground Floor Cafeteria - Miller IT

(S) denotes student talk.

Remember, the KYMAA Section Newsletter is now available via email! If you would prefer to receive your newsletter this way, send email to William Harris, KYMAA Newsletter Editor (wharris@georgetowncollege.edu). Please follow these guidelines:

1. Your message should be entitled, "Electronic Newsletter."

2. Include the email address at which you wish to receive the newsletter in the body of your message.

3. You need to indicate the format you wish to receive. Current options are:

a) Plain text;

b) Microsoft Word 6.0 attachment;

c) Corel Word Perfect 5.x attachment.

If you choose to receive the electronic version of the newsletter, you will no longer receive the "hard" version through regular mail. Reply today!

We will discuss the varying notions of projectivity and injectivity in the category of differential graded modules over a differential graded algebra (over a commutative ring with identity). Specifically, we will describe when the d.g. algebra itself is projective and injective.

Game theory is a mathematical theory that deals with the basic characteristics of competitive situations by examining the decision-making process of adversaries. John Nash was awarded the Nobel Prize in Economics for 1994 for the work contained in his Ph.D. thesis in mathematics. The main result of his thesis was that every general sum game has a "Nash equilibrium," which is a collection of strategies by various players such that no one player can improve his outcome by changing his own strategy. In this presentation, the history of game theory and some of its applications will be examined. Attention will be focused on the proof of Nash’s result.

This presentation will introduce the arms race model originally devised by Lewis F. Richardson. Variations on the model will be considered. A stochastic analogue will then be developed and explored, using the framework of a birth-death stochastic process.

Classroom Assessment Techniques (CATs) are a simple and time-economic way to open teacher-student dialogue regarding student learning. Many teachers have experienced significant improvements in student learning over surprisingly short periods of time as a result of the use of these techniques. This presentation will describe several CATs specifically adapted for the mathematics classroom, as well as some first-hand results of their use in an undergraduate course in finite mathematics.

When some simple looking initial value problems are solved numerically, they give rise to bifurcation diagrams, which are similar to that of the logistic map. This behavior is the result of the numerical method and not of the exact solution. The characteristics of such initial value problems and their exact solutions as well as the reasons why these bifurcation patterns take place will be investigated, and comparisons will be made with other dynamical systems.

Penrose diagrams are a common tool used to represent the manifolds which appear as solutions to general relativity. These diagrams allow physicists to study the causal structure of various spacetimes by facilitating the treatment of infinity as a normal point. Basic diagrams will be constructed which demonstrate such essential

features as event horizons, singularities, and wormholes.

I plan to present a conception of mathematical history first presented by Dr. Judith Grabiner in her article in Mathematics Magazine entitled, "The Changing Concept of Change: The Derivative from Fermat to Weierstrass." She asserts that mathematical knowledge is attained first by use without theoretical knowledge, then by discovery of its theoretical validity, then further exploitation, and finally by rigorous definition. This conception has implications for both mathematics education and for the philosophy of science. My presentation will focus on the mathematical history and education aspects and then briefly posit some side notes on its relation to the philosophy of science.

Although similar to Euclidean geometry, the hyperbolic plane encompasses a greater number of polygons. The fact that a polygon's angle measures must sum to less than the sum of their Euclidean counterparts accounts for this. We will consider one particular tiling style in the hyperbolic plane: tiling quadrilaterals by triangles. The

author illustrates methods used in determining these tilings of size k, the number of triangles composing a quadrilateral.

I will discuss Cantor's philosophical and theological motivations for developing his theories of transfinite sets and ordinals, and possibly some of the

impact. This is a result of work done on a thesis for the Gaines Fellowship, an undergraduate humanities fellowship at the University of Kentucky.

Are women in your classes asking what they can do with a degree in mathematics? Come and listen to this talk. The presenter will examine mathematical contributions by yesterday's women mathematicians, today's careers taken by women with degrees in mathematics, as well as intervention programs designed to recruit women into mathematics.

Determining the mean of a data set by hastily leaping to a typical calculation choice may seem to select both the natural and appropriate choice of procedure--until, perhaps, a surprising result prompts a closer examination of the data, or the calculation process. This presentation illustrates how even careful thinkers could be impulsively drawn into a mean trap calculation. Also presented is a generalized formula which embodies various mean calculation formulas including the arithmetic, geometric, harmonic, root-mean square and the general p-power mean.

This talk will illustrate the mathematics behind two simple edge detection techniques. The first will use some basic linear algebra ideas and the second will use a multiresolution (wavelet) approach. Examples will be given to show the effectiveness of each technique.

This talk responds to the question presented by Solomon Feferman in the title of his February 1999 Monthly article. I will take the "old axioms" to be ZFC, the Zermelo-Fraenkel set theory axioms, with the Axiom of Choice. Along with the article, I will discuss Peter Aczel’s non-well-founded set theory.

Don't get too excited that you're going to see a computer spit out the proof for your favorite senior-level result. The purpose of this talk is to demonstrate the basic mechanics of one type of "automated" theorem-proving: we'll convert the hypotheses of a typical geometry problem to polynomials, then see how computational abstract algebra can be used to determine whether the conclusion follows. If you never thought abstract algebra could be "applied" to anything, you may be surprised! Students are invited to attend.

D being an Euclidean domain guarantees the existence of a degree function d from the nonzero elements of D to the set of nonnegative integers satisfying certain conditions. We discuss general properties of d-functions and give examples of different d-functions on Z, the ring of integers. In particular, we exhibit a minimal d-function on Z and prove the existence of a unique minimal d-function for any Euclidean domain.

What is the difference between Abs[n^2 x] and n^2 Abs[x] ? In some calculations illustrating the uniform convergence of the convolutions f * g_n(x) to f(x) for a nice function f(x) and an appropriate sequence of weight functions {g_n (x)}, Mathematica responded quite differently to these expressions. A graphical presentation of the ideas of a proof of the Weierstrass Approximation Theorem will be used to demonstrate this and other similar anomalies.

Flett's mean value theorem goes as follows: If f is differentiable on the real interval [a,b] and the derivatives of f at a and at b are equal, then there is a point c between a and b such that a line through (a,f(a)) is tangent to the graph of f at (c,f(c)). The endpoint condition makes this theorem an analogue of Rolle's Theorem, rather than the Mean Value Theorem. We present two ways of "getting rid" of the endpoint conditions as well as a higher-dimensional version of this theorem. Finally, we show some interesting consequences of the location of the point c relative to a and b.

Discrete least squares approximation is known best through its application with polynomial models, in particular the least squares linear model or "line of best fit." In many cases, however, polynomial models are not appropriate for the given data. In this talk, least squares approximation using non-polynomial models, such as exponential and rational models, is considered.

A pair of vertices of a graph is called an even pair if every chordless path between them has an even number of edges. A graph is minimally even pair free if it is not a clique, contains no even pair, but every proper induced subgraph either contains an even pair or is a clique. In this talk I will discuss results concerning which graphs areminimally even pair free. (This is a joint work with André Kezdy.)

In this talk we will consider the steady-state distribution of the birth-death-immigration-emigration process and the birth-death-immigration-emigration process with total catastrophes. The distributions are obtained in terms of hypergeometric functions.

On a recent trip to India, I spent some time at the Ramanujan Institute

for the Study of Advanced Mathematics at the University of Madras and had the opportunity to speak with several mathematicians who are involved with preserving the memory of India’s greatest mathematician, Srinivasa Ramanujan. I will talk about the life of this extraordinary mathematician and discuss several of his remarkable formulas.

After a definition of sum-free sets we will look at bounds on the number of sets needed. We will construct several sets and look at various open problems.

This hands-on workshop will focus on how the TI-83 calculator can be assimilated into any introductory statistics course as an instructional and educational tool for learning. Classroom-ready activities designed to help students construct their own understanding of concepts will be utilized. Instructors of elementary statistics with little or no knowledge of the calculator will benefit significantly from this course. This presentation will provide participants with hands-on experience in integrating the

TI-83 calculator in the teaching of elementary statistics concepts. The presentation will focus on explorations that aid in the discovery of concepts through simulations and real data. Techniques will be presented in such a way to help participants aid

their students in constructing their understanding of the concepts they are taught in any basic statistics course. Participants will be provided with fifteen classroom-ready explorations that they can use in their classes to supplement their instruction. The level of presentation will assume little or no prior knowledge of the calculator but the presentation will not be a tutorial for the calculator. The workshop will involve hands-on discovery methods utilizing the interactive use of technology (TI-83 calculator). Participants may work in groups or individually during the course presentation. The presenter has taught mostly statistics during his fourteen years at Morehead State University and has extensively integrated technology into the classroom. He has co-authored a lab manual with explorations using the MINITAB software and is currently working on a book entitled, "Exploration Statistics with Data & the TI-83."

March 26-27, 1999

University of Louisville, Louisville

Name _______________________________________________

School _______________________________________________

Address _______________________________________________

_______________________________________________

_______________________________________________

Phone _______________________________________________

E-mail _______________________________________________

Check all that apply.

____ 1. ConferenceRegistration/Dues $13.00

____ 2. Short Course (Friday afternoon) No Charge

____ 3. Friday Banquet $14.00

____ 4. Friday Invited Address No Charge

____ 5. Aftermath (Friday evening) No Charge

____ 6. Saturday Breakfast $7.00

____ 7. Saturday Invited Address No Charge

____ 8. Saturday Business Luncheon $7.00

----------------------

TOTAL ENCLOSED $__________

Deadline for advance registration is Friday, March 12, 1999. Make checks payable to KY Section -- MAA and remit to: Karin Chess, Department of Mathematics, Owensboro Community College, 4800 New Hartford Road, Owensboro, KY 42303.

March 26-27, 1999

University of Louisville, Louisville

Name _______________________________________________

School _______________________________________________

E-mail _______________________________________________

Classification (circle one): Fr So Jr Sr Gr

Check all that apply.

1. I would like to join the group for dinner on Friday evening. ____

2. I could use some help finding a place to sleep ____

3. I will attend the MAA breakfast on Saturday morning, and am

enclosing $7.00 payable to the KY Section MAA. ____

4. I will attend the MAA business lunch on Saturday afternoon, and

am enclosing $7.00 payable to the KY Section MAA. ____

5. I will give a talk on Saturday morning. ____

Mail this form to Lisa Elderbrock, Department of Mathematics and Computer Science, Northern Kentucky University, Highland Heights, KY 41099. It must be submitted by Friday, March 12, 1999. You may contact her with questions via email at: elderbrockl@nku.edu .

Governor (1996-99) Chair (1997-99)

Peter Moore John A. Oppelt

Dept. of Math & Comp. Sci. Department of Mathematics

Northern Kentucky University Bellarmine College

Highland Heights, KY 41099 Newburg Road

(606) 572-5331 Louisville, KY 40205-0671

moorep@nku.edu (502) 452-8237

joppelt@bellarmine.edu

Chair Elect (1997-99) Vice-Chair (1998-2001)

Ray Tennant J. Lyn Miller

Dept. of Math., Stat. and Comp Sci. Department of Mathematics

Eastern Kentucky University Western Kentucky University

Richmond, KY 40475-3133 Bowling Green, KY 42101

(606) 622-3150 (502) 745-6227

tennant@acs.eku.edu lyn.miller@wku.edu

Secretary/Treasurer (1997-2000) Newsletter Editor (1997-2000)

Karin Chess William Harris

Department of Mathematics Dept. of Math, Physics & Comp. Sci.

Owensboro Community College Georgetown College Box 234

4800 New Hartford Road 400 E. College St.

Owensboro, KY 42303 Georgetown, KY 40324

(502) 686-4473 (502) 863-7921

occkec@pop.uky.edu wharris@georgetowncollege.edu

David Shannon Lisa Elderbrock

Department of Mathematics Dept. of Math. and Comp. Sci.

Transylvania University Northern Kentucky University

Lexington, KY 40508-1797 Highland Heights, KY 41099

(606) 233-8185 (606) 572-6452

dshannon@transy.edu elderbrockl@nku.edu

Richard Davitt

Department of Mathematics

University of Louisville

Louisville, KY 40292

(502) 852-6826

rmdavi01@athena.louisville.edu