http://www4.wku.edu/~miller/KYMAA.homepage.html
Check it out. Send comments, criticisms and reasonable suggestions to Lyn at: miller@puslar.cs.wku.edu. In particular, if your school or department has its own home page, please send your URL to Lyn so that we can include a link to it.
John Oppelt
Bob Osserman wrote his Ph.D. thesis on the subject of Riemann surfaces under the direction of Lars V. Ahlfors at Harvard University. He continued to work on geometric function theory and later on differential geometry, combining the two in a new global theory of minimal surfaces. He has also worked on the isoperimetric inequality and related geometric questions. After obtaining his Ph.D., he joined the faculty of Stanford University and has been there ever since, with periods of leave to serve as Head of the Mathematics Branch at the Office of Naval Research, Fulbright Lecturer at the University of Paris and Guggenheim Fellow at the University of Warwick. In 1987, he was named Mellon Professor for Interdisciplinary Studies, and in 1990 he joined MSRI as half-time Deputy Director. In recent years he developed and taught a new course jointly with a physicist and engineer designed to present mathematics, science and technology to a non-technical audience. A portion of the course was elaborated in a new book, entitled, Poetry of the Universe--A Mathematical Exploration of the Cosmos, intended to provide the general public with an introduction to cosmology focusing on a number of mathematical ideas that have played a key role.
Roger Horn
Professor Horn studied mathematics and physics as an undergraduate at Cornell and earned his Ph.D. at Stanford under the direction of Donald Spencer and Charles Loewner. He has been a mathematics faculty member at the University of Santa Clara, The Johns Hopkins University (where he chaired the Department of Mathematical Sciences from1972 to 1979), the University of Maryland-Baltimore County and the University of Utah. His published papers and books reflect research in number theory, differential geometry, probability, health policy analysis, statistics, analysis, complex variables and matrix analysis. He has been an associate editor for the SIAM Journal on Matrix Analysis and Applications. Presently, Dr. Horn is editor-elect of the American Mathematical Monthly.
Short Course: Cooperative Learning in Collegiate Mathematics
In this workshop, strategies and techniques for implementing cooperative learning will be explored. These include forming student groups, creating classroom activities, and assigning and grading group work. Participants will engage in cooperative activities which could be used in various undergraduate mathematics courses.
Barbara Reynolds, SDS, of Cardinal Stritch College and Brown University, is co-author of A Practical Guide to Cooperative Learning in Collegiate Mathematics, published by the MAA.
Bill Fenton, of Bellarmine College, is co-author of Introduction to Discrete Mathematics with ISETL, which features cooperative learning and computer activities.
March 29-30, 1996 Murray State University, Murray Name_______________________________________________ School_______________________________________________ Address_______________________________________________ _______________________________________________ _______________________________________________ Phone_______________________________________________ Check all that apply. ____1. Conference Registration/Dues $13.00 ____2. Short Course (Friday afternoon) No Charge ____3. Friday Banquet $10.00 ____4. Friday Invited Address No Charge ____5. Aftermath (Friday evening) No Charge ____6. Saturday Breakfast $4.95 ____7. Saturday Invited Address No Charge ____8. Saturday Business Luncheon $4.50 TOTAL ENCLOSED $__________ The deadline for submitting this form is Friday, March 15, 1996. 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.____ 5. I will give a talk in the student sessions.____ Mail this form to John Wilson, Centre College, 600 W. Walnut St., Danville, KY 40422. It must be submitted by Friday, March 15, 1996.
Change is hard. Change is especially hard if it involves things in which we believe very deeply, or have believed for a very long time. The way we teach is one of those things. We believe very deeply that when we teach we are doing something good, useful, valuable, even noble. We touch future generations. We make a difference. Furthermore, the method of teaching that we have known and have come to believe in is successful. It must be. After all, look at us--we learned, we prospered.
For my own part, the ghost of William Shanks haunted me for a long time as I began to think more about curriculum reform. William Shanks (1812- 1882) was a nice enough person, and a very dedicated scholar. His most noted accomplishment, and the one that gives life to his ghost, was calculating the digits of pi to over 600 decimal places. He used Machin's formula, pi/4 is approx. 4arctan(1/5) - arctan(1/239), and he spent years working on it. Unfortunately, he made an error in the 528th decimal place, and every single digit after that was wrong. Years of effort, and it was all wrong. Many people note how fortunate Shanks was, to have died before the error was detected (in 1945).
That ghost is still around, and its presence helps me understand colleagues who resist change. People are saying that the lecture method, at least for lower-division courses (and even for upper-, according to some), just isn't a very effective way of getting students to learn mathematics. To accept that seems to call into question much of our life's work! It can't be! Nevertheless, the evidence is accumulating that, in spite of "anecdotal data" of success (such as those who become professors of mathematics), a great many of our students exit our courses retaining far less than we thought they did, far less than they should, and indeed far less than they can. It sometimes is easy to gather such evidence. Ask your students for examples. Ask them why.
Recognizing that change is necessary, even recognizing that what we accomplished before wasn't quite as valuable as we thought it was, doesn't mean that we weren't trying. It doesn't even mean that the time was wasted. We were doing the best we could under the circumstances. And make no mistake, I still strongly believe that teaching is good, useful, valuable and noble. Up until only the fairly recent past, I have read, about as many patients died as result of being under a physician's care as died from their illness or accident. Such was our ignorance of infection, anatomy and spread of disease. That doesn't mean that the earlier physicians made no contributions; we should know, as professionals in mathematics above all, that we all learn from our mistakes. Banish the ghost of William Shanks!
Barry Brunson
"Judging a Contest: A Mathematical Model" by Jeff Belchner, Tracy Blankenship and Ali Seerea, Bellarmine College. -- Judging a large contest is made difficult by funding and time constraints. Such constraints impose limits on the number of judges and the number of papers each judge can evaluate. The challenge is to produce a pool of winners with timely and fair results that reduces the number of papers each judge reads (without compromising fairness).
"Link Energies by Ropes" by Gregory Jason Slone, Western Kentucky University. -- My research stems from an undergraduate seminar course in knot theory. Physical experiments are utilized to determine the energy of each individual link. The links are tied into ropes and the ropes are hung from an apparatus with weight placed on the end. The energy of a given link is equal to the change in length divided by the thickness of the rope used.
"Implementing Great Ideas to Teach Mathematics" by Dora Cardenas Ahmadi, Morehead State University. -- This talk will address the issue of incorporating cooperative learning, the use of technology, reading and writing in the teaching and learning of mathematics.
"Normalized Zero/Flex Polynomials" by James B. Barksdale, Jr., Western Kentucky University. -- This presentation completely characterizes a special class of monic polynomial functions, H = {h_n}, n = 2 to infinity, (indexed by degree), which constitutes a quasi-classical family; furthermore, the inflection point abscissas of each h_n coincide with its zeros.
"An Interactive Approach to College Algebra and Trigonometry" by Barry Brunson and Claus Ernst, Western Kentucky University. -- This presentation will give an overview of a different approach to College Algebra and Trigonometry used in two pilot sections during the Fall of 1995. Students used Mathematica in a computer laboratory working on notebooks written by the presenters. Examples will be shown of the courseware, student homework and student evaluations. Some advantages/ disadvantages of this approach will be pointed out.
"Conceptual Mathematics" by Patricia B. Cerrito, University of Louisville. -- A general education course in College Algebra or Precalculus can be enhanced through the use of conceptual problems. Examples will be presented together with a suggested methodology for facilitating student understanding of problem solving. Students can be encouraged to translate mathematics into English and conversely.
"The NKATE Algebra Reform Project" by Lillie F. Crowley, Lexington Community College. -- The curriculum group of the NKATE (National Science Foundation Kentucky Advanced Technological Education) project has piloted two semesters of a reform Intermediate Algebra Project. The project incorporates the AMATYC Crossroads as well as NCTM Standards and MAA Guidelines for mathematics courses. It relies heavily on collaborative learning activities, and uses real-life, real-time applications or data collection activities to motivate topics. The project also incorporates technology in the form of TI-82 graphics calculator applications, without letting them dominate the course or determine the curriculum. This presentation will discuss various aspects of the project along with its results to date, and will present examples of activities involved.
"Rafael Bombelli of Bologna: Renaissance Algebraist" by Daniel J. Curtin, Northern Kentucky University. -- Following the work of Tartaglia, Cardano and others in solving equations of the third and fourth degree, Rafael Bombelli wrote a treatise _l'Algebra_ (published 1572 and 1576). In this work is the first systematic treatment of what we now call complex numbers, which arise in the Cardano formulas for the solution of cubic equations, even in cases where all three roots are real numbers. The work also gives a good system of notation for roots and algebraic expressions, as well as detailed treatment of the processes for working with them. The talk will give a brief overview of this fascinating book. A copy of the book resides at American University, and I was able to use it during last summer's NSF Institute for the History of Mathematics.
"MAMS: Parallels in Mathematics, Art, Music and Science" by Richard Davitt, University of Louisville. -- We as mathematics teachers often miss the boat when it comes to telling our students (at all levels) about what a wonderful intellectual creation mathematics is. This story can be well told if we reveal to our classes the strong parallels which exist in the historical developments of mathematics, art and science, fields which many have at least some exposure to. Specific instances (besides Godel, Escher, Bach!) of such parallel developments will be delineated in this talk.
"Understanding Math Anxiety" by Thomas J. Klein, Morehead State University. -- College students affected by math anxiety avoid math courses and, as a result, also avoid careers that require quantitative skills. This presentation will survey research on what causes math anxiety, who is most susceptible to it and what has been done to help math anxious students.
"Enumeration in the Fibonacci Lattices" by Darla Kremer, Murray State University. -- In a 1988 paper, R. Stanley introduced a class of partially ordered sets, called differential posets, defined independently by S. Fomin, who called them Y-graphs. The prototypical example of a differential poset is Young's lattice, the lattice of all partitions of positive integers ordered by inclusion of their Young diagrams. Another important example is given by the Fibonacci differential poset, Z. Many of the enumerative results related to these posets were originally consequences of representation theory and the theory of symmetric functions, but now can be shown to depend only on simple structural properties of the poset. In an earlier paper, Stanley defined the Fibonacci lattice, Fib, which is not a differential poset, but has many enumerative properties in common with Z. In this talk, I will define the lattices Z and Fib and give a combinatorial explanation for some of their similarities.
"Triptychs: Group Activities for the Short of Time" by J. Lyn Miller, Western Kentucky University. -- In a 1995 Project NExT lecture, Sr. Barbara Reynolds inspired me to experiment with quick group learning activities that I call "Triptychs." I will outline the general format of these 5-minute activities and present several examples of Triptychs that I have used successfully in calculus and precalculus classes.
"Project NExT: A Panel Discussion" by J. Lyn Miller, Western Kentucky University. -- Project NExT is an MAA-sponsored program for newly hired Ph.D.s; its purpose is to help such individuals explore the issues of implementing new curricula and teaching techniques in light of current interests in improving the teaching and learning of mathematics.
"Modified Moore Methods at the Undergraduate Level: An Open-Panel Discussion" by Kay Moneyhun and Ed Thome, Murray State University. -- A panel discussion with input from the audience, concerning the use of a modified Moore Method for upper level undergraduate mathematics classes. Issues we will consider: 1) size of class; 2) level(s) of ability of students; 3) math maturity of students.
"Attractors and Nonlinear Wave Equations" by Ken Nelson, Eastern Kentucky University. -- One facet of the study of a dynamical system concerns the existence of attractors of the system. The talk will present a way of showing the existence of attractors. Further, we demonstrate that the properties of the attractor are much nicer than the properties of the equation's solutions.
"Shape Preserving Operators" by Michael Prophet, Murray State University. -- Shape-preserving approximation has been a topic of much study. The majority of the work has been done in the context of the (in general) non- linear best approximation operator. This talk will discuss the existence and uniqueness of shape-preserving linear operators. Specifically, fix Banach space X, finite dimensional subspace V, non-singular matrix A, and 'shape' S. We will give theorems and conjectures concerning the characterization of those linear operators from X onto V, with representation A when restricted to V, which preserve the 'shape' of their arguments.
"On the Order of ab" by Bettina Richmond, Western Kentucky University. -- Let a and b be two commuting group elements of finite order. We give upper and lower bounds on the order of the product ab, depending on the order of the intersection of the cyclic groups generated by a and b.
"Global Behavior in Functional Iteration Problems" by Mark P. Robinson, Western Kentucky University. -- Functional iteration--the process of forming a sequence x_0, x_1 = f(x_0), x_2 = f(x_1) = f(f(x_0)) = f^2(x0), .... by repeated application of a function f--is fundamental to the approximation of solutions to nonlinear equations and plays an important role in the study of nonlinear dynamics and chaos theory. In this talk, we examine another aspect of functional iteration: the global behavior of the sequence f, f^2, f^3, . . . f^n, . . . of composite functions as n increases without bound. Computer graphics are helpful in enabling one to make conjectures about such behavior, and these conjectures can then be investigated theoretically.
"Mathematical Symmetry: A Mathematics Course of the Imagination" by Ray Tennant, Eastern Kentucky University. -- The perspective of the talk holds that students have strong visual senses and that they may be introduced more easily to complex ideas by appealing to their geometric intuition. A liberal arts course, titled "Mathematical Symmetry: Connections Between Mathematics and Art," designed and taught by the author over the past seven years, is described. Included in this description are several design projects as well as a writing project involving the imagination.
"Parametrizing Implicitly Defined Curves: A Tale of ODE" by Steven Wilkinson, Northern Kentucky University. -- An implicitly defined planar curve is given as the locus of points (x,y) satisfying some relation, F(x,y) = 0. For many purposes, it is easier to study a curve if it is represented by parametric equations, (x(t),y(t)). How can one parametrize a curve that is given implicitly? The problem can be solved by setting up a system of first-order ordinary differential equations. Complications arise in solving this system where the gradient of the implicit relation is zero. Studying the problem at these points gives graphic examples of the existence and uniqueness theorem for ODE, as well as an introduction to the technique of prolongation.
Governor Christine Shannon 600 West Walnut St. Centre College Danville, KY 40422 (606) 238-5406 shannon@centre.edu Chair Barry Brunson Department of Mathematics Western Kentucky University Bowling Green, KY 42101 (502) 745-6221 bbrunson@wku.edu Chair Elect John A. Oppelt Department of Mathematics Bellarmine College Newburg Road Louisville, KY 40205-0671 (502) 452-8237 johnaopp@iglou.com Vice-Chair David K. Neal Department of Mathematics Western Kentucky University Bowling Green, KY 42101 (502) 745-6213 nealdk@wkuvx1.wku.edu Secretary/Treasurer Karin Chess Department of Mathematics Owensboro Community College 4800 New Hartford Road Owensboro, KY 42303 (502) 686-4473 kchess@occ.uky.edu Newsletter Editor William Harris Dept. of Math, Physics & Comp. Sci. Georgetown College Box 234 400 E. College St. Georgetown, KY 40324 (502) 863-7921 wharris@gtc.georgetown.ky.us AHSME Coordinator David Shannon Department of Mathematics Transylvania University Lexington, KY 40508-1797 (606) 233-8185 dshannon@music.transy.edu Student Chapters Coordinator John Wilson 600 West Walnut St. Centre College Danville, KY 40422 (606) 238-5409 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.eduReturn to Table of Contents
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