We also need to be concerned about those who aren't (yet) inclined to become involved with our Section. We are part of the primary national organization dedicated to the teaching and learning of collegiate mathematics. We need to reach out more to those faculty, such as at KSU, UK, and many smaller schools, who are underrepresented at our meetings. That might lead to self-examination to see if there are things we should be doing that we aren't.
I regret that I did not do more to address these needs myself.
Barry Brunson
My first revelation came with Freedman, Pisani, and Purves' Statistics. That was the first text I had seen that openly claimed that (1) students generally don't learn very much from traditional statistics survey courses, other than to poorly push around formulas whose significance they don't understand (and I don't mean "statistical significance", which has its own burden of misuse to bear), but (2) students generally are capable of understanding the concepts of statistics.
My second, and even more heartening revelation was Toward a Lean and Lively Calculus. With it, I discovered how widespread was the view of the "calculus industry" as somehow dysfunctional, but that it really didn't have to be that way. My professional life has not been the same since.
More people are realizing that the "Domino Theory" as applied to calculus reform, really is true: it is not possible to reform just calculus. If calculus changes, so must courses before, after, and beside it. However, not everyone agrees about how to achieve curriculum reform, and some remain unconvinced of the need to do it at all. The 7 February issue of The Chronicle of Higher Education, on its front page touted "A Backlash Against 'Reform Calculus'", with subtext of "Efforts to make the subject more relevant to students have produced a disaster, many mathematicians charge."
I am glad to see the whole mathematics community get so much publicity! Open debate is far better than hidden grumbling, on either side. Since I already am delinquent with getting this to our long-suffering Newsletter Editor, I will make only one small point here. In the Chronicle article, we are told that critics allege "By relying on calculators and computers ... students may never learn to perform difficult calculations." The missing hypothesis here is that students ever did learn such things! A few did; from among those who did came most mathematics professors. But most did not, even in the "golden age" that never really existed. Quite by accident the other day, I came across a 1951 article in The Mathematics Teacher, "Mathematical Understandings and Judgments Retained by College Freshmen" (by Ben A. Sueltz, vol. 44, p. 13 - 19). One quote is too good to resist: "Schools tend to place too much dependence upon 'paper and pencil' work. Many high school and college students set down figures and compute without doing any critical thinking."
Teaching a "reformed" course generally takes more time and more effort on the part of the faculty member. Of course, one of the goals is to get the students to expend more time and effort. I know that most of us work much harder, even on traditional courses, than the public, our state government, or our local administrations give us credit for. I also know that a few of our colleagues don't. For those few, the traditional way of doing things is better, not because they really think the students learn more, but just because it is comfortable.
So I'm convinced that I must be stupid. I wore myself ragged in reformed sections of calculus and algebra, and have tried incremental improvements in other courses. Even now, teaching a traditional calculus course again, I am unable to resist the temptation to really strive for, and construct examples, exercises, and tests that probe for, real understanding on the part of the students. External rewards are meager at best, and it certainly doesn't make life very comfortable; but the occasional sense of fulfillment still makes it all worthwhile. If you don't grade any homework, if you don't give quizzes, if all you do is lecture (using the same notes and examples from years ago), and give a few exams, being a professor can be a relatively cushy job. A few people want to cling to such a job, and they view moves to change it as inherently stupid. That shouldn't dissuade the rest of us from doing the very best we can. Dare to be stupid!
(Credit where credit is due: I learned about musician "Weird Al" Yankovic and his remarkably clever parodies from my kids. His delightful song "Dare to Be Stupid" includes a litany of "stupid things" one is encouraged to do, such as "Burn your candle at both ends. Look a gift horse in the mouth. ... Bite the hand that feeds you. Bite off more than you can chew." I also must admit (proudly) that I wanted to check the lyrics instead of possibly misquoting them. In a matter of minutes, and without leaving my office, I found them on the Web, at: http://crist1.see.plym.ac.uk/dfsmith/index.html.)
Barry Brunson
In addition, seesions of contributed papers will produce good mathematics served in a variety of packages, including interesting results, technology to support our teaching, approaches to our craft, and some thoughtful comments on our profession. For students, Friday afternoon will include a talk on applications of mathematics, and Saturday will feature a double session of contributed papers. Students are encouraged to attend at little or no cost, thanks to the generosity of the Section, Exxon and our hosts.
The success of the meeting is guaranteed by the enthusiasm of our hosts. The gathering should be challenging to the mind and relaxing to the body. Most of all, we will be provided with opportunities to renew old mathematical acquaintances and to make new ones.
John Oppelt
His research interests include commutative harmonic analysis, especially where it has a probabilistic flavor. His most recent work has been on Markov chains and random walks on finite groups and other algebraic systems. He has published (with E. Hewitt) Abstract Harmonic Analysis I and II; Elementary Analysis: The Theory of Calculus (now in its 8th printing); and Discrete Mathematics (with C. Wright).
He spent post-doctoral years at the University of Zurich with B. L. van der Waerden and at the University of Bonn with Jacques Tits. Since returning to the faculty of Notre Dame in 1972, he has had visiting positions at the University of California- Santa Barbara and at the University of Innsbruck.
Dr. Hahn has published a number of papers in his field of algebraic number theory on the classical groups, on orthogonal groups and on integral linear groups. His books include The Classical Groups and K-Theory (with O. T. O'Meara), Learning Basic Calculus: From Archimedes to Newton to its Role in Modern Science and Quadratic Algebras, Clifford Algebras and Arithmetic Witt Groups. He is the recipient of Notre Dame's Madden Award for Excellence in Teaching Freshmen (1995).
Prior to studying mathematics, Ray spent several years working as a stoneware potter. He continues to be a productive artist as well as a professor of mathematics at Eastern Kentucky University.
March 28-29, 1997 Western Kentucky University, Bowling Green Name _______________________________________________ School _______________________________________________ Address _______________________________________________ _______________________________________________ _______________________________________________ Phone _______________________________________________ Check all that apply. ____ 1. Conference Registration/Dues $13.00 ____ 2. Short Course (Friday afternoon) No Charge ____ 3. Friday Banquet $11.00 ____ 4. Friday Invited Address No Charge ____ 5. Aftermath (Friday evening) No Charge ____ 6. Saturday Breakfast $5.50 ____ 7. Saturday Invited Address No Charge ____ 8. Saturday Business Luncheon $6.00 ---------------------- TOTAL ENCLOSED $__________Deadline for advance registration is Friday, March 14, 1997. 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 29-30, 1996 Murray State University, Murray Name _______________________________________________ School _______________________________________________ Classification (circle one): Fr So Jr Sr Check all that apply. 1. Count on me for the free pizza dinner Friday evening. ____ 2. I would like a place to sleep in the dorm, if available. I will bring a sleeping bag. ____ 3. I will attend the MAA breakfast on Saturday morning, and am enclosing $4.95 payable to the KY Section MAA. ____ 4. I will attend the MAA business lunch on Saturday afternoon, and am enclosing $4.50 payable to the KY Section MAA. ____Mail this form to John Wilson, Centre College, 600 W. Walnut St., Danville, KY 40422. It must be submitted by Friday, March 15, 1996.
SCHEDULE OF EVENTS (All times are CST) Friday, March 28 2:30-6:15 Registration Lobby, Thompson Complex Central Wing (TCCW) 3:00-5:00 Short Course "Visual Mathematics: Understanding Abstract Mathematics with the Aid of Visual Themes, or, Do You See What I'm Saying?" Ray Tennant, Eastern Kentucky University. 4:00-5:00 Presentation for Students "Manufacturing Math Problems," Frank Plano, James River Corporation. 4:30-4:50 Contributed Papers "On Models of Plane Geometry," Robert C. Powers, University of Louisville. TCCW 302 "A Cursory Exploration of the Psi-Function," James Barksdale, Western Kentucky University. TCCW 304 "Flett's Mean Value Theorem for Holomorphic Functions," Prasanna Sahoo, University of Louisville. TCCW 305 5:00-5:20 Contributed Papers "Interchange of Limits for Random Walk Areas," David K. Neal, Western Kentucky University. TCCW 302 "New Proofs for a Continued Fraction of Ramanujan," Robert Lamphere, Elizabeth Community College. TCCW 304 "Some Generalizations of Flett's Mean Value Theorem," Thomas Reidel, University of Louisville. TCCW 305 5:30-5:50 Contributed Papers "When Should a Second Checkout Counter Be Opened?" Randall Swift, Western Kentucky University. TCCW 302 "Clustering and Dispersion in Spatial Competition," John P. Boardman and Timothy C. Pitts, Morehead State University. TCCW 304 "How to Recognize a Power Function," Tom Richmond, Western Kentucky University. TCCW 305 6:00-7:30 Student Dinner Location to be announced 6:30-7:45 Banquet Faculty Log House (The Log House is adjacent to the Garrett Conference Center) 8:00-9:00 Invited Address "The Mathematics of Card Shuffling," Kenneth Ross, President, Mathematical Association of America. Garrett Conference Center Auditorium (103) 9:00-10:00 Aftermath Garrett Conference Center Lobby Saturday, March 29 7:30-8:20 Breakfast Faculty Log House 8:00-10:00 Registration Lobby, TCCW 8:30-11:20 Book Exhibits TCCW 303 8:30-8:50 Contributed Papers "One-Dimensional Random Walks with Negative Binomial Stopping Times," Mark W. Rodgers, Western Kentucky University TCCW 301 "A 'Pump' or a 'Filter': Is Technology Making a Difference?" Joyce H. Saxon, Morehead State University. TCCW 302 "Multivariable Newton's Method: Theory and Practice," Mark P. Robinson, Western Kentucky University. TCCW 304 "Patterns in Decimals," Wiley Williams, University of Louisville. TCCW 305 "The Hypercube and Other Regular Polytopes in Four Dimensions," Michael Haney, University of Kentucky. TCCW 309 9:00-9:20 Contributed Papers "Modelling 2- and 3-Dimensional Aperiodic Tilings," Aaron Zerhusen, University of Kentucky. TCCW 301 "Positive Profit in a Predator-Prey Parabolic System," K. Renee Fister, Murray State University. TCCW 302 "Group Projects in College Algebra and Trigonometry," Claus Ernst, Western Kentucky University. TCCW 304 "Linear Algebra and Indiana's Interstates," William Fenton, Bellarmine College. TCCW 305 "Modelling of Airflow in Mammoth Cave," Jonathan Jernigan, Western Kentucky University. TCCW 309 "Continuous Almost Everywhere...Well, Almost," John S. Spraker, Western Kentucky University. TCCW 369 9:30-9:50 Contributed Papers "The Freshman Summer Program at the University of Kentucky," Colin Starr, University of Kentucky. TCCW 301 "The Smiling Face Equation," Andy Martin, Morehead State University. TCCW 302 "PRISM-SMI Update," Vivian Cyrus and Ben Flora, Morehead State University. TCCW 304 "The Power of Experiential Learning--Absorbing the History of Mathematics and Science on Site in England," Dick Davitt, University of Louisville. TCCW 305 "Arithmetic Dice Sums," Brian Fowler, Western Kentucky University. TCCW 309 9:55-10:25 Coffee Break 10:30-10:50 Contributed Papers "Elementary Transforms," Kenny Palmer, Western Kentucky University. TCCW 301 "Metric Spaces in Which All Triangle are Degenerate," Bettina Richmond, Western Kentucky University. TCCW 302 "Teaching Calculus with the TI-92," Dora Ahmadi and Bob Lindahl, Morehead State University. TCCW 304 "Real Even Symmetric Forms," William R. Harris, Georgetown College. TCCW 305 "Knot Theory and Group Representations," Lee Gibson, University of Kentucky. TCCW 309 11:00-11:20 Contributed Papers "Round-off Rules: Science of Folklore?" Andy Martin, Morehead State University. TCCW 302 "Experiencing Geometry," Nancy Rodgers, Hanover College. TCCW 304 "What Our Students Think About Us and Why It Matters," Thomas J. Klein, Morehead State University. TCCW 305 "Fundamental Solutions and Green's Functions," Greg Slone, Western Kentucky University. TCCW 309 "Ways to Encourage Student Reading in Math Courses," J. Lyn Miller, Western Kentucky University. TCCW 369 11:30-12:30 Invited Address "Learning Calculus from the Masters," Alexander J. Hahn, Chairman, Department of Mathematics, University of Notre Dame. Garrett Conference Center Auditorium (103) 12:30-1:15 Lunch Faculty Log House 1:15-2:15 Business Meeting Faculty Log House
"Knot Theory and Group Representations" by Lee Gibson, University of Kentucky. We will discuss some of the invariants of knot theory, particularly group representations of knots. This presentation springs from independent study during the summer of 1996 under the direction of Dr. David Johnson at the University of Kentucky.
"The Hypercube and Other Regular Polytopes in Four Dimensions" by Michael Haney, University of Kentucky. This talk will discuss the regular polytopes which can be constructed in four dimensions. It will include some of their basic properties, including the determination of the coordinates of their vertices. The central focus will be on visualization of these polytopes through the construction of 2- and 3-dimensional projection models and computer-generated images.
"Modelling of Airflow in Mammoth Cave" by Jonathan Jernigan, Western Kentucky University. One hundred and seventy-five years ago, modifications were made to the natural entrance of Mammoth Cave. These changes were made to make the cave more accessible to visitors. Unfortunately, this has brought about a major ecological change in the cave. In this talk, we will present multilinear regression analysis for the physical effects of air temperature, cave wall temperature and barometric pressure on air flux. The talk requires some basic knowledge of regression analysis.
"Elementary Transforms" by Kenny Palmer, Western Kentucky University. Definitions of the Laplace and Fourier transforms will be presented, along with some of their properties and connections between the two. A few applications will be presented.
"One-Dimensional Random Walks with Negative Binomial Stopping Times" by Mark W. Rogers, Western Kentucky University. We consider a negative binomial distribution created by a one-dimensional random walk stopped at the kth downward step. We will outline the derivation of formulas for the average height, arc length and area under the path. Analogous results for other stopping criteria will be discussed.
"Fundamental Solutions and Green's Functions" by Greg Slone, Western Kentucky University. Definitions of distributions, fundamental solution, and Green's functions will be presented, along with the calculation of at least one fundamental solution of Green's function associated with a particular differential equation.
"The Freshman Summer Program at the University of Kentucky" by Colin Starr, University of Kentucky. Since 1985, the Department of Minority Affairs at the University of Kentucky has hosted the Freshman Summer Program, a program designed to accustom incoming minority freshmen to college life. During the six-week term, participating students take a full complement of courses, including a math class and a math workshop in the collaborative learning style. I will discuss the Freshman Summer Program, focussing on my experiences in the math workshops.
"Modelling 2- and 3-Dimensional Aperiodic Tilings" by Aaron Zerhusen, University of Kentucky. An expository talk on the nature of aperiodic tiles and quasicrystals, focussing on Danzer's tetrahedral tiling of 3-space, modelling this tiling using Zometool and computer models. This is a result of an independent study with Dr. Carl Lee.
"A Cursory Exploration of the Psi-Function" by James Barksdale, Western Kentucky University. The purpose of the presentation is to describe some of the interesting aspects of a classical, special function known as the Psi-Function. This exploration will present some historical references together with a few of the more prominent, technical details and features regarding some of the elementary properties and applications of this function.
"Clustering and Dispersion in Spatial Competition" John P. Boardman and Timothy C. Pitts, Morehead State University. The location that two sellers will choose in a linear market has long been of interest. It is well-accepted that firms will tend to cluster in the center of the market as long as demand for the product is inelastic. This paper uses elementary calculus to explore clustering in spatial duopoly as elastic demand is allowed.
"PRISM-SMI Update" by Vivian Cyrus and Ben Flora, Morehead State University. One of the initiatives included under the PRISM $10,000,000 grant to the State is the Secondary Mathematics Initiative reported on two years ago at Transylvania. This talk will provide a status report to those interested in this state-wide effort, which will be completing its final phase of operation this summer.
"The Power of Experiential Learning: Absorbing the History of Mathematics/Science on Site in England" by Dick Davitt, University of Louisville. During the Winter Break of the 1996-97 academic year the speaker had the extraordinary opportunity to teach a course in The History of Mathematics: British Influences in and around London, England. The course was taught under the aegis of the Cooperative Center for Study Abroad, a consortium of more than 20 universities with headquarters at Northern Kentucky University. Besides describing some the course's modi operandi and detailing some of the important venues visited, the talk will center on the spontaneous, lasting learning experiences of the instructor and his seven students. To a person, everyone in the group was impressed with the fact that learning something in context is not only easier than, say, reading or being told about it, but that experientially acquired information automatically and unconsciously becomes part of that person's knowledge base.
"Group Projects in College Algebra and Trigonometry" by Claus Ernst, Western Kentucky University. During the last couple of years, I have assigned group projects in each College Algebra and Trigonometry course I have taught, worth 10% of the final grade. Some beautiful projects were produced by the students. Students used Mathematica for their work and were required to turn in their final version in the form of a science paper. In this talk, I will share examples of these projects.
"Positive Profit in a Predator-Prey Parabolic System" by K. Renee Fister, Murray State University. Optimal control of a parabolic system, in which solutions are population densities of the prey and predator species, represent harvesting a proportion of these populations. The payoff functional is maximized over the class of admissible controls which are characterized in terms of the optimality system. The optimality system is the state system coupled with the adjoint system. To analyze the positivity of the payoff functional, conditions are formulated on the bounds of the admissible control pair. In order to accomplish this, parabolic maximum principles for weakly coupled systems are utilized.
"Linear Algebra and Indiana's Interstates" by William Fenton, Bellarmine College. For many years, the completion of I-69 between Indianapolis and Evansville has been a political battle. One question is the economic impact on cities in the southwest region of the state. A student, Tracy Blankenship, and I investigated this question using linear algebra and Maple IV. The highway system in Indiana can be pictured as a weighted network. When this network is represented by a weighted adjacency matrix, the principal eigenvector produces a relative ranking of the nodes (cities). The rationale for this interpretation of the eigenvector will be briefly reviewed. Our model allowed us to "build" the missing portion of I-69 and predict some surprising changes in the rankings for these cities.
"Real Even Symmetric Forms" by William R. Harris, Georgetown College. Let S(n,m) denote the set of all real even symmetric forms of even degree m in n variables. Let PS(n,m) and SS(n,m) denote the cones of positive semidefinite elements and sums of squares elements of S(n,m), respectively. We shall present an easily-checked, necessary and sufficient condition for an even symmetric n-ary octic p to be in PS(n,8). We also will show that PS(n,8) = SS(n,8), a companion result to Hilbert's theorem that a positive semidefinite ternary quartic is a sum of squares of quadratic forms.
"What Our Students Think About Us and Why it Matters" by Thomas J. Klein, Morehead State University. Some mathematics professors believe that student feedback is unimportant and irrelevant in determining their teaching effectiveness. Others consider this feedback valuable and use it to improve their mathematics instruction. This presentation addresses various interesting results from research on the use of student course evaluation forms and how these results could be helpful to mathematics faculty.
"New Proofs for a Continued Fraction of Ramanujan" by Robert Lamphere, Elizabethtown Community College. Two new proofs are given for G(1/4 (x + n + 1)) G(1/4 (x - n + 1)) = 4 n2 - 12 n2 - 32 n2 - 52 G(1/4 (x + n + 3)) G(1/4 (x - n + 3)) x- 2x- 2x- 2x- .
"The Smiley Face Equation" by Andy Martin, Morehead State University. Let us say an equation in x and y is "simple" if it only involves polynomials, rational functions and root functions (with their natural domains). A challenging yet amusing problem in precalculus is to find simple equations whose graphs meet some interesting conditions. For example, what is a simple equation whose graph looks like these three vertices of a triangle?
. . .Can one simple equation have a graph which is the entire triangle? How about the ubiquitous Smiley Face?
"Round-off Rules: Science or Folklore?" by Andy Martin, Morehead State University. Many mathematics textbooks give rules for rounding off the results of computations involving approximate numbers (see, for example, Introductory Technical Mathematics by J. Christopher, 2nd ed., chapter 2). As will be shown in this talk, the rules as stated in the above book are inconsistent, although they are quite common rules in our texts. In some cases the application of these rules give results which implicitly boast of a reliability which is in fact incorrect. Where did these rules come from? Are they used outside our classrooms? Are there better rules? Should we teach them instead?
"Ways to Encourage Student Reading in Math Courses" by J. Lyn Miller, Western Kentucky University. I will address three techniques that I have used to encourage students to read their texts in a meaningful way. These techniques come from a precalculus course, an elementary education major course and an abstract algebra course.
"Interchange of Limits for Random Walk Areas" by David K. Neal, Western Kentucky University. We consider the Boundary Problem for a one-dimensional random walk which begins at height j on the y-axis and moves along the x-axis. We consider the "signed area under the curve" that is created when stopping upon reaching either height m or height n, for m < j < n. We show that as n ® ¥ (or as m ® -¥) the limit of the average area is the average of the limit of the areas.
"On Models of Plane Geometry" by Robert C. Powers, University of Louisville. In the American Mathematical Monthly, volume 97 (1990) pp. 839-846, Grunbaum and Mycielski propose several different models of plane geometry and suggest that these models are nice examples for students who take a geometry-for- teachers course. We discuss these models and present some related results.
"Metric Spaces in Which All Triangles are Degenerate" by Bettina Richmond, Western Kentucky University. Clearly, any subspace of the real line with the Euclidean metric is a metric space in which all triangles are degenerate. Are there other metric spaces in which all triangles are degenerate? Is the usual topology on the plane generated by any metric in which all triangles are degenerate? Is the usual topology on the real line generated by any metric which has no degenerate triangles with more than two distinct vertices? These questions will be addressed in this talk.
"How to Recognize a Power Function" by Tom Richmond, Western Kentucky University. Consider a positive multiple of a power function with positive power f(x) = k xn over [0,r]. Revolving this curve around the y-axis gives a "bowl" of volume V1(r). Let V2(r) be the "volume under the bowl." We will show that the ratio of the volumes V1(r) and V2(r) is constant, and that this property can be used to characterize these power functions.
"Some Generalizations of Flett's Mean Value Theorem" by Thomas Riedel, University of Louisville. T. M. Flett's mean value theorem states that if a differentiable function f has the same derivative at the endpoints of the interval [a,b], then there is a point c in [a,b] such that the line starting at (a,f(a)) is tangent to the graph of f at (c,f(c)) in a formula: f(c) - f(a) = f'(c) (c - a). Using ideas from calculus, we generalize this result to the case where there are no conditions on the derivative at the endpoints and also take a look at a higher dimensional version of this theorem. We conclude with some interesting questions.
"Multivariable Newton's Method: Theory and Practice" by Mark P. Robinson, Western Kentucky University. Newton's method, probably the most popular numerical technique for approximating zeros of nonlinear functions, is introduced in most first-semester calculus courses. The multivariable version of Newton's method, used for solving nonlinear systems of equations, is frequently employed in scientific computing. The formulation of this method, some of its convergence properties and several applications are discussed.
"Experiencing Geometry" by Nancy Rodgers, Hanover College. This talk will highlight my experience in using an innovative text, called Experiencing Geometry by David Henderson. Last summer, I attended Dr. Henderson's NSF workshop at Cornell, which was designed to help teachers use his text successfully. The emphasis of the problems in his text (e.g., "What is straight on a cone?") is on experiencing the meaning of a concept. Through this personal experience in other spaces where right angles may not be congruent or straight lines may intersect more than once, students (and teachers) gain a deeper understanding of the geometry of the plane. The open-ended nature of the problems levels the playing field and makes it highly likely that the teacher will also learn from the students. Some of the questions may never be fully answered, but deep learning occurs through a process of small group discussions, writing, responses to writing and rewriting. It can be a bit nerve-wracking going out on a limb and experimenting with this type of teaching, but what bigger thrill tan to hear one of your junior secondary math majors say, "At last, I know how it feels to be a mathematician!"
"Flett's Mean Value Theorem for Holomorphic Functions" by Prasanna Sahoo, University of Lousiville. In 1958, T. M. Flett proved that if f: R ® R (the set of reals) is differentiable and satisfies f'(a) = f'(b) for distinct a and b in R, then there exists a mean value n in [a, b] such that f(n) - f(a) = (n - a) f'(n). This result is known as Flett's mean value theorem. This result does not extend to the complex plane without any changes. In this talk, we present a theorem analogous to Flett's mean value theorem for holomorphic functions.
"A 'Pump' or a 'Filter': Is Technology Making a Difference?" by Joyce H. Saxon, Morehead State University. Teaching and learning with technology presents new challenges for students and teachers. Are these challenges worth it? How does using technology affect understanding, attrition, attitudes and grades in introductory mathematics courses? This presenter will share information gathered during the last four years on the effect of using technology in the classroom.
"Continuous Almost Everywhere... Well, Almost!" by John S. Spraker, Western Kentucky University. Three definitions of an almost everywhere continuous function will be presented along with interrelationships among them. This is joint work with Dr. Daniel Biles.
"When Should a Second Checkout Counter Be Opened?" by Randall Swift, Western Kentucky University. A popular strategy for reducing a customer's waiting time in line at a supermarket checkout counter is to open a second checkout when there are three or more people in line. In this talk, we will show that opening the second checkout counter when there are three people waiting is optimal for reducing average waiting time. The essential theory of the single server queue will be presented along with simulation results for the queue under varying workload conditions. The level of the talk requires some elements of basic probability theory.
"Patterns in Decimals" by Wiley Williams, University of Louisville. We will investigate the problem of predicting and justifying various patterns in the decimal representation of a fraction a/b, including when the decimal is repeating, how many decimal places lie between the decimal point and the start of the repetend, and the length and structure of the repetend (if there is one). In the latter question there are often nice cyclic patterns whose investigation requires an algorithm for generating as many decimal places as needed. Justifying conjectures about these patterns is a nice use of elementary number theory. Finally, we discuss the use of these ideas as the basis for exploratory problems for preservice teachers.
Governor Chair Christine Shannon Barry Brunson 600 West Walnut St. Department of Mathematics Centre College Western Kentucky University Danville, KY 40422 Bowling Green, KY 42101 (606) 238-5406 (502) 745-6221 shannon@centre.edu bbrunson@wku.edu Chair Elect Vice-Chair John A. Oppelt David K. Neal Department of Mathematics Department of Mathematics Bellarmine College Western Kentucky University Newburg Road Bowling Green, KY 42101 Louisville, KY 40205-0671 (502) 745-6213 (502) 452-8237 nealdk@wkuvx1.wku.edu johnaopp@iglou.com Secretary/Treasurer Newsletter Editor 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 kchess@occ.uky.edu wharris@gtc.georgetown.ky.us AHSME Coordinator Student Chapters Coordinator David Shannon John Wilson Department of Mathematics 600 West Walnut St. Transylvania University Centre College Lexington, KY 40508-1797 Danville, KY 40422 (606) 233-8185 (606) 238-5409 dshannon@music.transy.edu wilson@centre.edu 1996 Meeting Coordinator Donald Bennett Murray State University Dept. of Mathematics and Statistics Murray, KY 42071 (502) 762-2311 a30411f@msumusik.mursuky.edu