David Neal's short course promises to be most helpful if you have any plans to integrate technology into your classroom pedagogy. I'm certain that we will be informed, challenged and entertained by Frank Morgan on Friday evening and similarly so by Ed Dubinsky on Saturday. Check out the web site for our meeting. Many thanks to Donald Spickler for this first for our Section.
At this meeting we will decide on future meeting sites. May I ask Department Chairs to consider hosting our Section meeting? If interested, please investigate local arrangements, and inform me if a gathering at your home institution is possible.
I look forward to our gathering at Morehead on March 27th and 28th. In the meantime, "Good teaching."
Most of the motels listed in the January newsletter are right at the exit off of the interstate.
At both the undergraduate and graduate levels, Glenn was considered a master teacher who had gained the admiration of his students and of colleagues throughout the university. In his quiet and friendly way, he demonstrated his commitment to teaching, scholarship, and service every day of his thirty years at Western. He is truly missed.
Remembrances may take the form of contributions to the R. Glenn Powers Memorial Scholarship, College Heights Foundation, Western Kentucky University, 1 Big Red Way, Bowling Green, KY 42101. His family will be notified of your thoughtfulness.
Douglas A. Lapp has conducted research on student perception of technological authority in both computer and graphing calculator environments, and has identified some factors that influence students' willingness to challenge the output of these machines. In addition, he has proposed a theoretical model of the interactions of these factors. Lapp has extensive experience with in-service training that integrates the use of technology at the middle grades, secondary, undergraduate, and graduate levels. In the summer of 1993, at The Ohio State University, Lapp taught a 6-week intensive institute along with Drs. Robert Brown, Joe Ferrar, and Terry Herrera designed to model the inquiry style of teaching with 24 in-service teachers. This institute was a part of Ohio's State Systemic Initiative Project Discovery. Following the institute, he served as part of the leadership team for the Central Region of Project Discovery. Lapp holds a Masters Degree in Mathematics and a Ph.D. in Mathematics Education, both from The Ohio State University. In 1995, Lapp joined the faculty of the mathematics department at Morehead State University. At MSU Lapp has started to develop curricula for teacher education that prepares secondary teachers to implement the Standards and to incorporate the effective use of technology in the teaching of mathematics. He has spoken both nationally and internationally on the issue of technology use and how the classroom environment must change to allow its true integration into the curriculum. Lapp is a member of the National Council of Teachers of Mathematics, Mathematical Association of America, the International Group for the Psychology of Mathematics Education, and the American Educational Research Association. Lapp teaches both mathematics and mathematics education courses for secondary teachers as well as the mathematics content courses for elementary teachers.
J. Lyn Miller
J. Lyn Miller received her Ph.D. in computational commutative algebra in 1994 from the University of Maryland at College Park. Her area of specialty is Grobner bases. Since the fall of 1994, she has been an assistant professor at Western Kentucky University. Miller has taught a variety of service courses, ranging from pre-calculus to the math for elementary teachers sequence. The upper-level courses she has taught are primarily in algebra, but include one on algebra and technology for middle school teachers. For the past two years, she have maintained the Section's web page. Miller was a Project NExT Fellow during the 1995-96 academic year. She is still looking for opportunities to try out some of the ideas she learned during that fabulous learning experience.
On Friday afternoon, David Neal of Western Kentucky University will present a workshop entitled, "Technology Throughout The Curriculum." Dr. Neal will discuss and demonstrate several self-contained projects that can be used to enhance a variety of courses. Topics will include Amortization, Annuities, a Monte Carlo Approximation of Pi, The Quickest Path Principle, The Falling Object Problem With Air Resistance, Cryptography With Matrices, and Gambler's Ruin. He will provide programs for the TI-83 and for Mathematica which simulate the problems and make solutions easily accessible.
Dr. Neal is an associate professor of mathematics at Western Kentucky University, where he has taught since 1989. He received his Ph.D. from the University of Florida in 1988 with work in stochastic integration in Hilbert spaces. He is now interested in applied probability and the simulation of probabilistic techniques using current technology. He has received two PRISM- UG grants to develop technological instructional materials for probability and statistics courses. His homepage is wkuweb1.wku.edu/~neal/neal.html.
Frank Morgan
On Friday evening, Frank Morgan of Williams College will give a lecture entitled, "Soap Bubbles, 1998," describing new research by undergraduates and will include fun questions, demonstrations, and prizes for students.
Dr. Frank Morgan works in minimal surfaces and studies the behavior and structure of minimizers in various dimensions and settings. His three texts all have new editions: Geometric Measure Theory: A Beginner's Guide (1995), Calculus Lite (1997), and Riemannian Geometry: A Beginner's Guide (1998).
Dr. Morgan went to MIT and Princeton, where his thesis advisor, Fred Almgren, introduced him to minimal surfaces. He then taught for ten years at MIT, where he served for three years as Undergraduate Mathematics Chairman, received the Everett Moore Baker Award for excellence in undergraduate teaching, and held the Cecil and Ida Green Career Development Chair. He spent leave years at Rice, Stanford, and the Institute for Advanced Study. He served on the NSF Math Advisory Committee from 1987-90, on the AMS Council from 1994-97, and as chair of the Hudson River Undergraduate Mathematics Conference in 1997. In January 1993, he received one of the first MAA national awards for distinguished teaching. In 1995 he represented mathematics research at the exhibition for Congress by the Coalition for National Science Funding. He received the Allen High School Distinguished Alumni Award and an honorary doctorate from Cedar Crest College.
For several years Dr. Morgan served at Williams as Mathematics Department Chair and founding director of an NSF undergraduate research project. Work of his undergraduate Geometry Group is featured in the 1994 AMS publication, What's Happening in the Mathematical Sciences. He has recently been selected as Dennis Meenan '54 Third Century Professor of Mathematics.
Dr. Morgan has a weekly live call-in Math Chat on local cable TV, featured in Ivars Peterson's column MathLand, and a biweekly Math Chat column in The Christian Science Monitor, both available via his web page at www.williams.edu/Mathematics/fmorgan. For 1997-98 he holds the new Visiting Professorship for Distinguished Teaching at Princeton University.
Ed Dubinsky
On Saturday, Ed Dubinsky of Georgia State University will address the assemblage with a lecture entitled, "Bridging the Gap Between Education Research and Teaching Practice." Dr. Dubinsky will discuss how the field of research in undergraduate mathematics education (RUME) is growing and how much of the activity is being done by members of the MAA. He will address the question that arises concerning what applications can be made of this research by the college teacher of mathematics. He will illustrate these applications by examples from his work and work from various collaborators.
After receiving his Ph.D. from the University of Michigan, Dr. Dubinsky spent two years in Africa teaching at the University College of Sierra Leone and the University of Ghana. Subsequently, he has taught at Tulane, the Polish Academy of Sciences (Warsaw), Clarkson, Purdue University, and Georgia State University. He is the winner of several awards for teaching, including the Charles B. Murphy Award for Outstanding Teacher at Purdue University in 1991. In 1996, he was awarded a Certificate of Appreciation by the MAA for his contributions in mathematics education.
The author of numerous articles and books in mathematics, computer science, mathematics education, Dr. Dubinsky's most recent text is Introduction to Discrete Mathematics with ISETL (with W.E. Fenton), Springer, 1996.
Dr. Dubinsky's current interests include the extension of Piagetian and related theories of learning to the acquisition of abstract concepts in mathematics and also new approaches to teaching calculus and abstract algebra based on research in learning and using computers, cooperative learning and alternatives to lecturing. He is involved with others on the continued development of a community of Researchers in Undergraduate Mathematics Education. Recently, he was elected Second Vice-President of the MAA.
| 2:30-6:15 | Registration Entrance to Lappin Hall |
| 3:00-5:00 | Short Course "Technology Throughout The Curriculum," David Neal, Western Kentucky University. Lappin 107 |
| 4:00-5:00 | Presentation for Students "Maintaining a Math Club or MAA Student Chapter," David Housman, Jason Hasbrouck, Allegheny College. Lappin 241 |
| 4:30-4:50 | Contributed Papers |
| "Experiencing Calculus Reform," Dora Cardenas Ahmadi, Morehead State University. Lappin 101 | |
| "Using Technology in Algebra and Calculus," Claus Ernst, Western Kentucky University. Lappin 108 | |
| "Will an Early College Mathematics Placement Program Reduce the Number of Students Required to Enroll in Remedial Mathematics Courses?" Gail Wells, Northern Kentucky University. Lappin 113 | |
| 5:00-5:20 | Contributed Papers |
| "Another Look at Sine and Cosine Formulas," James Barksdale, Jr., Western Kentucky University. Lappin 101 | |
| "Computer Power for Your Statistics Calculator," Bill Johnston, Centre College. Lappin 108 | |
| "Finding Extreme Values," Steven Wilkinson, Northern Kentucky University. Lappin 113 | |
| 5:30-5:50 | Contributed Papers |
| "One Algorithm Fits All," Neil Eklund, Centre College. Lappin 101 | |
| "Concrete Models in Abstract Algebra," Ray Tennant, Eastern Kentucky University. Lappin 107 | |
| "Numerical Approximation of Improper Integrals," Mark Robinson, Western Kentucky University. Lappin 108 | |
| 6:00-7:30 | Student Dinner Lappin 113 |
| 6:30-7:45 | Banquet The Commonwealth Room in the Adron Doran University Center |
| 8:00-9:00 | Invited Address "Soap Bubbles, 1998," Frank Morgan, Williams College. Claypool-Young Art Building, Room 111 |
| 9:00-10:00 | Aftermath Claypool-Young Art Gallery |
| 9:30-10:30 | Student Movie Lappin 241 |
| 7:30-8:20 | Breakfast The Eagle Dining Room in the Adron Doran University Center |
| 8:00-10:00 | Registration Entrance to Lappin Hall |
| 8:30-11:20 | Book Exhibits Lappin 203 |
| 8:30-10:00 | Minicourse "Using Minitab for Windows in the Teaching of Elementary Statistics," Lloyd Jaisingh, Morehead State University. Lappin 241 |
| 8:30-8:50 | Contributed Papers |
| "Software and Lab Activities for a Course in Abstract Algebra," Vivian Flora Cyrus and Tabitha Mingus, Morehead State University. Lappin 101 | |
| "A Historical Tour of Transcendental Numbers," Lisa Elderbrock, Northern Kentucky University. Lappin 107 | |
| "Modeling One-Dimensional Chaotically Forced Turbulent Flows," Lee Gibson, University of Kentucky. Lappin 108 | |
| "Evaluation of Input Devices for Use in Functional Neuromuscular Stimulation," Jason Neiser, Centre College. Lappin 113 | |
| 9:00-9:20 | Contributed Papers |
| "Painting Gabriel's Horn," Barry Brunson, Western Kentucky University. Lappin 101 | |
| "I've Still Got a Secret: Zero Knowledge Proofs," Lynne Brosius, Eastern Kentucky University. Lappin 107 | |
| "Randomized Treeforms," Susan Conarroe, Centre College. Lappin 108 | |
| "The Theology of Several Famous Mathematicians," Richard Davitt, University of Louisville. Lappin 113 | |
| 9:30-9:50 | Contributed Papers |
| "Model for Oblique Angles without Distortion in the MRI," Robert Bern, Melanie Hash and Anna Berzovfskaya, Bellarmine College. Lappin 101 | |
| "A Geometric Approach to Linear Algebra in an Analytical World," Tabitha Mingus, Morehead State University. Lappin 107 | |
| "Conjugacy in Braid Groups," Margaret Yoder, Eastern Kentucky University. Lappin 108 | |
| "Evaluation of NKATE Intermediate Algebra Project," Darrell Abney, Maysville Community College, and Lillie Crowley, Lexington Community College. Lappin 113 | |
| "Constructing Intersections of Lines and Conics," Don Coleman, University of Kentucky. Lappin 129 | |
| 9:55-10:25 | Coffee Break |
| 10:30-11:20 | Internet Demonstration "Internet Resources for the Teaching of Mathematics," Larry Husch, University of Tennessee at Knoxville. Lappin 108 |
| 10:30-10:50 | Contributed Papers |
| "Problems and Concepts that Deserve More Attention," Reza Akhlaghi, Prestonsburg Community College. Lappin 101 | |
| "MathExcel and EKU and UK," Amy King, Eastern Kentucky University, and Mike Freeman, University of Kentucky. Lappin 107 | |
| "Common Approximation Techniques and Image Compression," Bruce Kessler, Western Kentucky University. Lappin 108 | |
| "From Lattice Paths to Three-Dimensional Constructions of Stuff," Joseph Sweeney and Gregory Hicks, Morehead State University. Lappin 113 | |
| 11:00-11:20 | Contributed Papers |
| "Extending Java to Support Shared Resource Protection and Deadlock Detection in Threads Programming," Michael Bradshaw, Centre College. Lappin 101 | |
| "Kentucky Lottery Games," Carolee Chumley & Donna Moore (mentor: Lloyd Jaisingh), Morehead State University. Lappin 107 | |
| "Reinventing the Wheel," John Maki, University of Kentucky. Lappin 108 | |
| "Ill-Posedness of an Orbit Model," Kristie Pfabe and Maria Falbo-Kenkel, Northern Kentucky University. Lappin 113 | |
| 11:30-12:30
| Invited Address "Bridging the Gap Between Education Research and Teaching Practice," Ed Dubinsky, Georgia State University. Claypool-Young Art Building, Room 111 |
| 12:30-1:15 | Lunch The Commonwealth Room in the Adron Doran University Center |
| 1:15-2:15 | Business Meeting The Commonwealth Room in the Adron Doran University Center |
This is one of the problems from the MAA modeling competition held this February. The problem was to develop a model that would illuminate the restrictions for finding oblique cross-sections in the MRI, while minimizing the amount of distortion. Our model used the Multiple Intersection Method. After defining the oblique angle in a predetermined grid in the MRI, we used the ability of the MRI to use planes that were perpendicular to the three axes to intersect the oblique plane. Each intersection line (set of pixels) is then put into a matrix position that has a specific place on the CRT. This allows us any possible angle without a loss of distortion.
"Extending Java to Support Shared Resource Protection and Deadlock Detection in Threads Programming," Michael Bradshaw, Centre College.
Java threads enable programmers to write parallel programs very easily and conveniently. However, the current Java specification does not adequately provide for the protection of shared resources or for deadlock detection, two of the most common problems arising from parallel programs. The ability to solve these problems is crucial for real Java concurrent programming. I'll introduce and implement a model that provides various levels of protection for shared resources and the ability to detect deadlock. This model can be used to write parallel programs which protect shared resources and are able to detect when deadlock occurs.
This work was done as a REU at Hope College with Anita J. Van Engen, Nathan Oostendorp, and Dr. Mike Jipping.
"I've Still Got a Secret: Zero Knowledge Proofs," Lynne Brosius, Eastern Kentucky University.
"I know something you don't know!" taunted Sally. "Oh yeah?" said Jeff. "Prove it!" Now Sally is in a predicament. If she tells Jeff her secret, it won't be a secret anymore, and she can no longer tease him. However, there is no way that he will believe that the secret even exists without proof. In this presentation, we look at ways to handle situations similar to Sally's. Zero- knowledge proofs take the form of interactive protocols designed to convince a verifier that a prover does indeed possess the knowledge that he or she claims to. This is done without disclosing the knowledge itself or even giving substantial clues that could lead to discovery. Examples from number theory and graph theory are used to model the process.
"Kentucky Lottery Games," Carolee Chumley & Donna Moore (mentor: Lloyd Jaisingh), Morehead State University.
This presentation will analyze the Kentucky lottery games from a statistical stand point. Analysis will be done on the fairness of the games from a graphical stand point as well as from an expected value stand point. The analysis will reveal which of the "scratch" games has the highest expected return.
"Randomized Treeforms," Susan Conarroe, Centre College.
Sparked by an article on treaps, this is a comparative study of tree algorithms, including basic, self-adjusting, and treap. The approach taken is empirical, with the basic algorithms coded in Java for testing purposes. The study focuses on efficiency with respect to lookup time and height. A non-tree alternative is also discussed: skip lists.
"Modeling One-Dimensional Chaotically Forced Turbulent Flows," Lee Gibson, University of Kentucky.
Turbulence has sometimes been referred to as the last great unsolved problem of classical physics. Due to the incredible amounts of required arithmetic, few direct numerical solutions can be obtained to difficult problems in fluid dynamics. These results are governed by the 3-D nonlinear partial differential equations known as the Navier-Stokes Equations. Since direct solutions are difficult, one goal of a great deal of present research is to properly model, and thus predict (statistically) the behavior of turbulent flows. This project qualitatively tests one such model on the one dimensional level, where direct results are available for comparison.
"Reinventing the Wheel," John Maki, University of Kentucky.
How should you construct a "roadbed" which will allow a square wheel to roll smoothly, keeping the axle moving in a straight line and at a constant velocity? A simple analysis shows that the required supporting curve is a certain inverted catenary. We also treat the case in which the “wheel” is an equilateral triangle or any regular polygon. Other related questions are considered.
"Evaluation of Input Devices for Use in Functional Neuromuscular Stimulation," Jason Neiser, Centre College.
A mouse, rate-controlled joystick, and handheld trackball were evaluated in a target acquisition task and a figure eight tracking task to determine the best device to use with an FNS control system. For half of the trials, the device input was mapped to cursor position by a time-discrete second order difference equation to simulate the actual response of the musculoskeletal system to electrical stimulation. The performance of the trackball and joystick did not change significantly when the mapping function was applied, suggesting those devices perform nearly independent of the muscle mapping function.
"From Lattice Paths to Three-Dimensional Constructions of Stuff," Joseph Sweeney and Gregory Hicks, Morehead State University.
Consider a point in the plane that is given by (m,n) where m and n are integers. Such a point is called a lattice point. A path consisting of horizontal and vertical line segments of unit length that connects lattice points is known as a lattice path. If one contemplates the lattice paths of minimum length beginning at the origin and terminating in the non-negative portion of the x-y plane, many combinatorial identities and trends in Pascal's triangle can be explained and proven. Now, after examining the logic in the construction of such paths, it becomes obvious that the same situation and the identities arise from thence can be generalized to 3-space and even n-space. In the course of formalizing such a resolution, it can be seen that there is indeed a Pascal-like tetrahedron and other Pascal-like number comber constructions that can be forged. The talk will focus on the Pascal-like tetrahedron and some of the patterns and identities that lurk within its construction.
The NKATE Project implemented experimental intermediate algebra classes in several community colleges during the last three years. Evaluation results show a significant improvement in college algebra success rates for students in those experimental classes. Project materials were written in the spirit of the AMATYC standards for problem solving, modeling, connecting with other disciplines, and technology. Course materials rely heavily on collaborative activities and hands-on experiments. The graphics calculator is used for numerical and graphical explorations. Topics are motivated by student activities and Calculator-Based Laboratory (CBL) experiments to generate data describing real world situations.
"Experiencing Calculus Reform," Dora Cardenas Ahmadi, Morehead State University.
This talk will briefly review research relevant to calculus reform. It will discuss the main ingredients of calculus reform and it will share classroom experiences in the implementation of a reform calculus program using the textbook by Ostebee and Zorn.
"Problems and Concepts that Deserve More Attention," Reza Akhlaghi, Prestonsburg Community College.
During my long teaching experience, I have found that students make repeated mistakes which require more attention and patience. We will focus on these mistakes, problems and concepts.
"Another Look at Sine and Cosine Formulas," James Barksdale, Jr., Western Kentucky University.
This presentation illustrates the application of innovative pedagogy which offers: (a) alternative approaches to conventional presentations, (b) fresh, crisp, and lucid demonstrations, and (c) uncommon awareness of relationships linking formulas and laws of the sine and cosine functions.
"Painting Gabriel's Horn," Barry Brunson, Western Kentucky University.
Consider the graph of y = 1/x for x > 1. If we revolve this around the x-axis, we generate an object, sometimes called "Gabriel's Horn" having finite volume but infinite surface area. Such objects have amused and sometimes perplexed generations of calculus students, due to the following apparent paradox: In order to change the color of the horn, we would seem to require an infinite amount of paint. We could, however (so the story goes), just tilt it and fill up the interior with a finite amount of the very same paint. We take a closer look, using realistic estimates of paint coverage and the size of paint molecules. Consistent with tradition, the presentation remains lighthearted, but with undertones of legitimate mathematics.
"Constructing Intersections of Lines and Conics," Don Coleman, University of Kentucky.
The following two problems will be discussed and illustrated using Geometer's Sketchpad: (1) given a conic and a point, construct the line passing through the point and tangent to the conic; (2) given a conic and a line, construct the points of intersection of the conic and the line.
"Software and Lab Activities for a Course in Abstract Algebra," Vivian Flora Cyrus and Tabitha Mingus, Morehead State University.
The resenters will be sharing their experiences using the software "Exploring Small Groups" developed by Ladnor D. Geissinger and the manual "Laboratory Experience in Group Theory" by Ellen Maycock Parker designed to go along with the software.
"The Theology of Several Famous Mathematicians," Richard Davitt, University of Louisville.
The speaker will take a look at the personal theologies of a number of renowned personages in the history of mathematics. Special attention will be given to the tenets of each of the chosen mathematicians concerning the existence of a God or gods and how such deeply held convictions influenced her/his outlook on and work in mathematics.
"A Historical Tour of Transcendental Numbers," Lisa Elderbrock, Northern Kentucky University.
A number which is the root of a non-zero polynomial with integer coefficients is said to be algebraic. A transcendental number is any number which is not algebraic. It is fairly easy to come up with a list of algebraic numbers: Ö2, i, and all rational numbers are algebraic. Coming up with numbers which are not algebraic is much more difficult, yet, in 1874, Cantor showed that the set of transcendental numbers is actually larger than the set of algebraic numbers! In this talk, we will explore some of the history of identifying transcendental numbers; by the time we finish, you should be able to list a lot of them.
"One Algorithm Fits All," Neil Eklund, Centre College.
One algorithm using recursive sequences is used by manufacturers of hand-held calculators to do almost all computations. The algorithm will be presented and the constraints will be discussed. This algorithm will apply to all functions between products and the hyperbolic functions.
"Using Technology in Algebra and Calculus," Claus Ernst, Western Kentucky University.
Last semester I gave a TI-92 (owned by the department) to each student in a section of Technical Calculus II. In this talk I would like to report about my experiences teaching with the TI-92. In particular I will concentrate on the graphing and integration capabilities of the TI-92.
"Internet Resources for the Teaching of Mathematics," Larry Husch, University of Tennessee at Knoxville.
The presenter will give a guided tour of major internet sites which provide materials which can be used in the teaching of mathematics. The demonstration will start with a general overview and finish up with the best of the current sites which demonstrate how the World Wide Web is being used in the teaching of mathematics.
"Using Minitab for Windows in the Teaching of Elementary Statistics," Lloyd Jaisingh, Morehead State University.
The presentation will provide participants with hands-on experience in integrating the MINITAB for Windows software in the teaching of elementary statistics concepts. The presentation will focus on the discovery through simulations and real data. Techniques will be presented in such a way to help students have a better understanding of the concepts they are taught in any basic statistics course. Participants will be provided with fifteen already prepared explorations that they can use in their classes. Also, the level of presentation will assume no prior knowledge of the software but the presentation will not be a tutorial for the software.
"Computer Power for Your Statistics Calculator," Bill Johnston, Centre College.
With some simple concepts usually taught in a calculus-based probability class, some short programs generate probabilities for normal, student-t, chi-square, and F distributions. Some classroom demonstrations are easy to use on an overhead display for, say, the TI-85. Students and faculty can share programs using the Texas Instrument link-up feature. And they like the programs because it's actually easier to use (and gives more information) than statistical tables.
"Common Approximation Techniques and Image Compression," Bruce Kessler, Western Kentucky University.
An often asked question by people unfamiliar with image compression is why are such complicated schemes needed when simpler ideas could be used. This talk will compare several simple techniques, including a Fourier and wavelet decomposition, to JPEG, the current industry standard.
"MathExcel and EKU and UK," Amy King, Eastern Kentucky University, and Mike Freeman, University of Kentucky.
Amy King and a panel of EKU students will briefly discuss their experiences with MathExcel. Mike Freeman from UK will present results which have been obtained there.
"A Geometric Approach to Linear Algebra in An Analytical World," Tabitha Mingus, Morehead State University.
The content of the first linear algebra course includes topics that range from solving systems of equations to finding the basis of a subspace. While the approach to the content of linear algebra in textbooks is generally analytic, these concepts lend themselves naturally to a geometric approach. The Cartesian plane and 3-space provide excellent "playing fields" in which students can investigate the geometric interpretation of concepts, they then have a visual image and intuition on which to build further understanding. Specific examples of how topics can be introduced and enhanced using geometries of 2-space and 3-space will be discussed.
"Ill-Posedness of an Orbit Model," Kristie Pfabe and Maria Falbo-Kenkel, Northern Kentucky University.
The motion of the earth in orbit about the sun can be modeled by a boundary value problem (BVP). One can approximate the solution to this BVP by constructing a sequence of iterates which should converge to a physically reasonable function. But, the iterates are solutions of ill-posed BVP's. In light of this, we suggest a different model, and construct iterates which are solutions to well-posed initial value problems. We prove that these iterates converge, and demonstrate both the ill-posedness and well-posedness numerically.
"Numerical Approximation of Improper Integrals," Mark Robinson, Western Kentucky University.
In many introductory calculus courses, students are introduced to the basic principles of numerical integration, including commonly-used methods such as the trapezoidal rule and Simpson's rule. Discussion of numerical integration in such courses is typically limited to its use for approximating the definite integral of a continuous function over a closed and bounded interval. In this talk, we present a survey of various methods for obtaining reliably accurate numerical approximations for improper integrals which involve infinite discontinuities in the interval of integration or unbounded intervals of integration.
"Concrete Models in Abstract Algebra," Ray Tennant, Eastern Kentucky University.
Historically, the symmetric group on four letters and the alternating groups on four and five letters were referred to as the octahedral, tetrahedral, and icosahedral groups, respectively. These Platonic models and some planar designs will be used to discuss methods for developing concepts in abstract algebra. Topics include subgroups, cosets, group actions, Sylow subgroups, and semidirect products.
"Will an Early College Mathematics Placement Program Reduce the Number of Students Required to Enroll in Remedial Mathematics Courses?" Gail Wells, Northern Kentucky University.
The purpose of this session is to start a state-wide discussion of an Early College Mathematics Placement Testing Program. This program will involve administering a college placement test to high school juniors. The purpose of administering the test is to address the problem of mathematics remediation at the college level by providing students who are high school juniors with an accurate appraisal of their mathematical competency while they still have another year of high school to schedule an appropriate college preparatory mathematics course. The intended use of the test is to encourage students to take a mathematics course during their senior year to maintain or to improve their mathematical knowledge. Therefore the test should be taken and results returned before they schedule courses for their senior year. A pilot program is being administered in the Northern Kentucky school districts this spring.
"Finding Extreme Values," Steven Wilkinson, Northern Kentucky University.
Every calculus student sees the extreme value theorem that guarantees a real- valued function has both a minimum value and a maximum value on a closed and bounded interval. Also, the student works with Fermat's theorem that says local extrema occur at critical points of the function. This leads to a simple but powerful technique for finding extreme values for functions that are continuous on a closed and bounded interval. It will be shown how this technique can be extended to apply to functions that have at most a finite number of discontinuities on any type of interval. Moreover, first semester calculus students will be familiar with the tools used in this extended technique.
"Conjugacy in Braid Groups," Margaret Yoder, Eastern Kentucky University.
In nonabelian groups, the conjagacy equivalence classes are one way to analyze the group. We look at examples in the braid groups.
Return to the KYMAA Home Page.