What Technology Is Used: 1950 -- Slide rule (you may be hard pressed to even find one today and you definitely will need to describe this to today's students). 2000 -- Graphing calculators and computer algebra systems like Mathematica. 2050 -- "Boxels" will replace pixels to power three-dimensional graphing calculators. Virtual imaging will make it possible for students to walk, drive, or fly above and through any n-dimensional surface.
How Classes Are Delivered: 1950 -- Primarily lecture classes. 2000 -- Classes of different types; some lecture, some discussion, some television and web classes. 2050 -- Online "blackboards" and computer language translators will make international web classes possible with students interacting from remote corners of the world.
What Motivates Teachers: 1950 -- Teachers searched for ways to pass on their love of mathematics to their students. 2000 -- Teachers search for ways to pass on their love of mathematics to their students. 2050 -- Teachers will search for ways to pass on their love of mathematics to their students.
Ray Tennant
Friday Afternoon Short Course: Paul Eakin, University of Kentucky, will present a two-hour short course titled "COMMUNICATING MATHEMATICS: Application of communication technology in the teaching of mathematics." If you are considering using technology to enhance the teaching of your mathematics courses (from algebra and pre-calculus through linear algebra and other upper-level courses) you will want to be sure to attend. There will be hands-on opportunities to work with the materials Dr. Eakin and his colleagues at UK are developing.
Friday Evening Banquet: The banquet will be a fine dinner served in a very elegant dining room at the university. A highlight will be the announcement of the annual KYMAA Teaching Award and the announcement of the high school and middle school winners in Kentucky of the American Mathematics Competitions with presentations.
Friday Evening Invited Address: Walter Mientka, Executive Director of IMO 2001 USA, Inc., will give a presentation titled "The International Mathematical Olympiad: Hong Kong 1994 to USA 2001." Dr. Mientka was for many years the executive director of American Mathematical Competitions and is currently leading the preparation for the USA hosting of the 2001 Olympiads. He will share with us the fascinating story of recent Olympiads and may even try to stump us with a problem or two.
Friday Evening Aftermath: After Dr. Mientka's presentation, we will move to the Grand Reading Room in the library for snacks, conversation and music. The music will be provided by the Madison County Dulcimer Group. This should be a real treat.
Saturday Morning Curriculum Panel: There will be a panel presentation and discussion on the topic "Mathematics and the Mathematical Sciences in 2010: What Should Graduates Know?" The panel discussion is being organized by Dora Cardenas Ahmadi, Morehead State University. Panelists include Harriet Pollatsek, Mount Holyoke College, Peter Hislop, University of Kentucky, John Wilson, Centre College, and Danny Sharp, IBM, Inc. CUPM is currently studying these issues and plans on issues a set of recommendations in the near future. This is your opportunity to give your opinion.
Saturday Morning Invited Address: Harriet Pollatsek, Mount Holyoke College, will give a presentation titled "Quantum Error Correction: Classic Group Theory Meets a Quantum Challenge." Dr. Pollatsek has promised we will all be experts in this exciting new area of coding theory by the end of her talk (at least if we will follow through with the reading assignments). She also is very involved in innovative curriculum initiatives at Mount Holyoke College and will be happy to share their successes with you.
Saturday Afternoon Lunch & Business Meeting: Join your colleagues for a hearty lunch and share in the decisions that will be required to keep KYMAA an important part of mathematics education in Kentucky.
Additionally, there are scheduled 32 contributed papers from faculty, graduate students and undergraduate students. For details, see the program and list of abstracts that follow. Please do not forget the book exhibits. This is a good chance to browse some great new books from the MAA as well as review some new textbooks.
Friday Evening Student Pizza Dinner: On Friday evening there will be a free pizza party for students, planned by the students of the Kappa Mu Epsilon chapter at EKU. Let us know on the registration form if you can join in for pizza and conversation with other students! Afterwards, hear the invited talk by Professor Walter Mientka.
Saturday Morning Student Panel: On Saturday morning there will be a special panel discussion for students to learn about interesting summer opportunities involving mathematics. Come hear from students who have done such things as studied in Ireland, participated in special summer programs for women, or been part of an REU (Research Experience for Undergraduates). Ever wondered how you could get involved in such a program? Come hear first-hand from students who have done it!
If you need help finding accommodations for Friday evening, there are some possibilities available for inexpensive student housing on campus. If interested, contact Lisa Elderbrock (elderbrockl@nku.edu) before March 17, 2000.
Hope to see you at the meeting!
Lisa Elderbrock
Holiday Plaza or Hampton Inn: From the north, take exit 87 off I-75. Turn right for Hampton Inn and turn left for Holiday Plaza, which will be on the right, at the second light after turning. From the south, take exit 87 off I-75. Turn left for Hampton Inn and right for Holiday Plaza, which will be on the right, at the second light after turning.
Directions to Campus: From the north, take exit 90A, loop around to Lexington Road (US 25). Proceed to the light and turn right. This turns into West Main Street. After about 2 miles, you will reach Church Corner (a T formed by the Baptist, Christian, and Methodist churches). Continue on West Main to South Second Street, and turn right onto South Second. You will go down a hill to a light, and up a hill to The Colonel’s Corner BP gas station, which will be on your right. Go one more block and make a left at Kit Carson Drive. Proceed through a stoplight and turn left at the next parking sign to the E (employee) portion of the Daniel Boone Parking lot. This lot is available to us from Friday afternoon through Saturday.
From the south, take Exit 87 and make a right onto the EKU By-Pass, Hwy. 876. There are five traffic lights to the junction of the By-Pass and Lancaster Avenue. At the second light past this intersection, turn left onto Kit Carson. The Begley Building will be on your right after you turn. Continue down Kit Carson; go through a stop sign and a stoplight. After the light, the Wallace Building will be on your left. Proceed to the small brick building on your right (the Brewer Building) and turn right and then left into the Daniel Boone Parking Lot.
Parking: The Daniel Boone lot, employee E portion, is open to us on Friday afternoon. Any Employee E lot is OK after 5 PM and on Saturday. If by some chance you do get a ticket, contact Amy C. King.
Meetings: Registration and part of the meetings will be held in the Wallace Building. Other activities, as listed, will be in the J. C. Powell Student Center, and the Crabbe Library. Check the map for their locations.
Eastern Kentucky University March 31-April 1, 2000 Schedule of Events (All times are EST) (F= Faculty; G = Graduate Student; U = Undergraduate Student) Friday, March 31 2:30 – 6:15 Registration Wallace 4th Floor Hall 3:00 – 6:00 Refreshments Wallace 403 3:00 – 5:00 Short Course “COMMUNICATING MATHEMATICS: Application of communications technology in the teaching of mathematics,” Paul Eakin, University of Kentucky. Library 128 4:00 – 6:00 Book Exhibit Gold Room, Wallace 452 3:00 – 3:20 Contributed Papers “Linear Programming: From Steel to Wall Street,” Shannon Purvis, Eastern Kentucky University. Wallace 432 (U) 3:30 – 3:50 Contributed Papers “The Oddball Problem,” Amy Wheeler, Eastern Kentucky University. Wallace 432 (U) 4:00 – 4:20 Contributed Papers “Volume of Truncated Cubes,” Nicole Allen, Kentucky State University. Wallace 432 (U) 4:30 – 4:50 Contributed Papers “On Complex Cobordism Modules mod(p),” Augustine K. Maison, Eastern Kentucky University. Wallace 428 (F) “Groebner Bases,” Christina Piercy, Western Kentucky University. Wallace 432 (U) 5:00 – 5:20 Contributed Papers “Mean Value Theorem Entrapment Sham,” James Barksdale, Western Kentucky University. Wallace 428 (F) “Engle Properties Over Groups and Modular Group Algebras,” Leanne Faulkner, Western Kentucky University. Wallace 430 (F) “Introduction to Dendrominos,” John Scoville, University of Kentucky. Wallace 432 (U) 5:30 – 5:50 Contributed Papers “Attracting Women Into Mathematics,” Dora Cardenas Ahmadi and Joyce Saxon, Morehead State University. Wallace 428 (F) “'Dual'-ing Orthogonalities,” Bruce Kessler, Western Kentucky University. Wallace 430 (F) “Why Commander Riker is Greater than Seven of Nine, and Other Star Trek Conundrums,” Mike LeVan, Transylvania University. Wallace 432 (F) 6:00 – 6:20 Contributed Papers “Web Enhancement: What Worked for Me,” Margaret Yoder, Eastern Kentucky University. Wallace 428 (F) “Jacobian Analysis for Nonlinear Systems of Differential Equations,” Mark P. Robinson, Western Kentucky University. Wallace 430 (F) “On the Existence and Probable Value of Brun's Constant (The Sum of the Reciprocals of the Twin Primes) What is Known for Sure?” Andrew Martin, University of Kentucky. Wallace 432 (F) 6:30 – 7:45 Student Pizza Dinner Location TBA 6:30 – 7:45 Banquet Board of Regent's Dining Room, Powell Building 8:00 – 9:00 Invited Address “ The International Mathematical Olympiad: Hong Kong 1994 to USA 2001,” Walter Mientka, Executive Director, IMO 2001 USA, Inc. Library 108 9:00 – 10:00 Aftermath Grand Reading Room, Crabbe Library Saturday, April 1 7:45 – 11:00 Refreshments Wallace 403 8:00 – 10:00 Registration Wallace 4th Floor Hall 8:30 – 11:20 Book Exhibits Gold Room, Wallace 452 8:00 – 8:50 Curriculum Panel “Mathematics and Mathematical Sciences in 2010: What Should Graduates Know?” Organized by Dora Cardenas Ahmadi, Morehead State University. Wallace 447 8:00 – 8:50 Student Panel “Undergraduate Opportunities in Mathematics,” organized by Lisa Elderbrock, Northern Kentucky University. Wallace 448 8:30 – 8:50 Contributed Papers “Impossibility and Time,” Homer S. White, Georgetown College. Wallace 428 (F) “The Use of Mathematics in Optometry,” K. Renee Fister, Murray State University. Wallace 432 (F) 9:00 – 9:20 Contributed Papers “A Group with Two Operations,” S. S. Abhyankar, Purdue University and Chris Christensen (presenter), Northern Kentucky University. Wallace 428 (F) “Novel Treatment Schedules for Antibiotic Use Confirmed by Mathematical Analysis,” Robert L. Fulton, University of Louisville School of Medicine, Department of Surgery. Wallace 432 (F) “Ideas on Web-Based Learning at the University of Kentucky,” Jody Fast, Mike McCraith, Angela Chappell, University of Kentucky. Wallace 447 (G) “Differential Downcutting,” Melissa Tolene, Murray State University. Wallace 448 (U) 9:30 – 9:50 Contributed Papers “Burnside, Cayley, Frobenius, and Hilbert,” S. S. Abhyankar, Purdue University. Wallace 428 (F) “The Annotated Glossary in Linear Algebra,” William Fenton, Bellarmine College. Wallace 432 (F) “Trigonometric Identities from a Different Angle,” Kim Calender, Murray State University. Wallace 447 (G) “Optimal Control Applied to Immunotherapy,” Thalya Burden, Murray State University. Wallace 448 (U) 10:00 – 10:20 Refreshment Break 10:30 – 10:50 Contributed Papers “From Michelangelo to Japan-the Trail of a Geometric Construction,” Carroll G. Wells, Western Kentucky University and David Lipscomb University. Wallace 432 (F) “A Maple Approach to Representation Theory,” John Eveland, Murray State University. Wallace 447 (U) “From the Interstate to Mathematics,” Mallie McCloud, Murray State University. Wallace 448 (U) 11:00 – 11:20 Contributed Papers “Palindromes by Subtraction,” Claus Ernst, Western Kentucky University. Wallace 428 “The Tenure of Charles Loewner at the University of Louisville,” Richard M. Davitt, University of Louisville. Wallace 432 “The Use of Technology in an ODE Class,” C. Maeve McCarthy, Murray State University. Wallace 447 (F) “Picturing Representations of Lie Algebras,” Marti McClard, Murray State University. Wallace 448 (U) 11:30 – 12:20 Invited Address “Quantum Error Correction: Classic Group Theory Meets a Quantum Challenge,” Harriet Pollatsek, Mount Holyoke College. Wallace 147 12:30 – 1:15 Lunch Board of Regent's Dining Room, Powell Building 1:15 – 2:00 Business Meeting Board of Regent's Dining Room, Powell Building 2:00 – 3:00 Executive Committee Meeting Location TBAReturn to Table of Contents
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Friday Invited Address “The International Mathematical Olympiad: Hong Kong 1994 to USA 2001,” Walter Mientka, Executive Director IMO 2001 USA, Inc. The USA will host the 42nd International Mathematical Olympiad (IMO) in the year 2001 in Washington DC. The IMO is the premier international mathematics competition for high school students and it will bring to the USA more than 500 of the most talented high school age mathematicians from more than 80 countries. The American mathematics community will use this opportunity to promote the importance of mathematics for all students and to celebrate the accomplishments of our best and brightest students. We believe that the IMO 2001 event offers a unique opportunity to pursue corporate marketing, workforce development, and community support objectives. Visibility at this event, would offer a special opportunity to help nurture top-notch student talent and to make the case for a career in mathematics, statistics, science, and engineering fields.
Panel on Curriculum “Mathematics and Mathematical Sciences in 2010: What Should Graduates Know?” Organized by Dora Cardenas Ahmadi, Morehead State University. The third millennium confronts us with the need to prepare our students for new challenges. Identifying these challenges will guide mathematics departments in setting, addressing, and meeting goals. A broad look at the undergraduate curriculum is particularly timely after a decade of innovation and debate about content and pedagogy in specific courses. The panelists will discuss what majors should know, successful programs, preparation for the workplace, post-bachelor studies, and other issues related to preparation of undergraduates in the mathematical sciences. Audience reaction is invited. Panelists include: Harriet Pollatsek, Mount Holyoke College; Peter Hislop, University of Kentucky; John Wilson, Centre College; and Danny Sharp, IBM Inc.
Saturday Invited Address “Quantum Error Correction: Classic Group Theory meets a Quantum Challenge”, Harriet Pollatsek, Mount Holyoke College. Quantum computers are massively parallel and hence extremely efficient. But quantum information is more vulnerable to errors than classical information, and errors are trickier to detect and correct. Quantum error correcting codes are thus essential. The geometry associated with a certain family of groups of order a power of 2 (called extraspecial 2-groups) provides the setting for a lovely construction of "good" quantum error correcting codes due to Calderbank, Rains, Shor and Sloane. We will offer a self-contained description of these ideas. We'll begin with a brief introduction to some necessary notions in quantum computing, describe qubit errors and the error group they generate, construct codes via the extraspecial error group, and conclude with some suggestions for further reading.
“Optimal Control Applied to Immunotherapy,” Thalya Burden, Murray State University. We consider an ordinary differential equation system of activated immune system, tumor and interleukin-2 cells. Interleukin-2 cells are cytokines that enhance immunity and have been shown to increase tumor cell kill. Our goal is to control the external source of the activated immune cells so that we maximize the normal cells and minimize the tumor cells. Our preliminary results provide a characterization of an optimal control and the optimality system, which is the state system coupled with the adjoint system.
“Trigonometric Identities from a Different Angle,” Kim Calender, Murray State University. Establishing trigonometric and hyperbolic trigonometric identities using ordinary differential equations.
“A Maple Approach to Representation Theory,” John Eveland, Murray State University. This talk will be preliminary report on a project that aims to concretely produce certain combinatorial objects related to the representation theory of Lie algebras. A representation of a Lie algebra can be though of as a collection of square matrices satisfying a set of relations. The goal is to use Maple to completely determine the spectrum of "supporting graphs" associated to a given particular representation of a simple Lie algebra. A "supporting graph" is a directed graph of colored edges, and it is known that there is only a finite number of these graphs associated to a given representation.
“Ideas on Web-Based Learning at the University of Kentucky,” Jody Fast, Mike McCraith, Angela Chappell, University of Kentucky. The math department at the University of Kentucky has been implementing a Web-based course in several Business Calculus sections. This is an effort to adapt a Long-Distance Learning environment to a local level. At the same time we are working to improve our understanding of how technology can best be used to aid learning in an LDL setting. In the two semesters of our involvement with the program, we have used two separate approaches, each with its own advantages and disadvantages. Our main focus will be the comparison of these two styles, as well as a discussion of the benefits of Web-based learning. A demonstration will be given if time permits.
“Picturing Representations of Lie Algebras,” Marti McClard, Murray State University. This talk is a report on a project investigating interactions between combinatorics and certain algebraic structures, namely representations of Lie algebras. A Lie algebra is a vector space endowed with a certain non-associative multiplication. A representation of a Lie algebra is a realization of the Lie algebra as a collection of linear transformations (or matrices) on a given finite dimensional vector space. We are looking for "nice" partially ordered sets that can be used to explicitly construct representations of several special Lie algebras (the "rank two" simple Lie algebras).
“From the Interstate to Mathematics,” Mallie McCloud, Murray State University. This problem examines the conditions under which a tractor-trailer will jackknife, and the conditions under which a tractor-trailer will remain unjackknifed. Computer-generated graphs will be used in order to visualize the problem and solutions.
“Groebner Bases,” Christina Piercy, Western Kentucky University. A short introduction to Groebner Bases and their computation will be discussed.
“Linear Programming: From Steel to Wall Street,” Shannon Purvis, Eastern Kentucky University. Linear Programming is a highly effective problem solving technique that has developed in the past century. Often overlooked in the classroom setting, it has many applications in business and industry. This talk will look at the history of Linear Programming, where it is now, and where it is going.
“Introduction to Dendrominos,” John Scoville, University of Kentucky. A special class of polyominos, which we call dendrominos, have some interesting properties. A polyomino is a collection of squares arranged with incident sides. Dendrominos may be intuitively defined as chains of lattice elements, such as squares, hexagons, tetrahedra, cubes, etc. Some of these chains are terminal - no lattice elements may be added to them to create another legal dendromino in n-space, and examine existence conditions for terminal dendrominos.
“Differential Downcutting,” Melissa Tolene, Murray State University. The purpose of this paper is to use a simple differential equation model to describe downcutting in a river. Downcutting is a process where the water flowing through a river channel carries sediment and by doing so widens and deepens the river. This model is applied to real data from the Kentucky Lakes area.
“The Oddball Problem,” Amy Wheeler, Eastern Kentucky University. The Oddball Problem, also known as the "12-Coins Problem" or the "Counterfeit Coin Problem" is this: "There are 12 coins, all identical in appearance, and all identical in weight except for one, which is either heavier or lighter than the remaining 11 coins. Devise a procedure to identify the counterfeit coin in only 3 weighings with a balance." In this talk we will present several solutions to this problem. These solutions are generalized to obtain solutions to Oddball Problems of larger sizes.
“Burnside, Cayley, Frobenius, and Hilbert,” S.S. Abhyankar, Purdue University. I shall discuss a versatile theorem of Burnside and its relationship to theorems of Cayley and Frobenius and a problem of Hilbert. This theorem of Burnside appeared in the first 1895 edition of his famous book on groups of finite order. It says that a doubly transitive permutation group has a unique minimal normal subgroup which is either elementary abelian or simple.
“Attracting Women Into Mathematics,” Dora Cardenas Ahmadi and Joyce Saxon, Morehead State University. The presenters will discuss important aspects of model programs that attract and guide college women to enter successful careers in mathematics and mathematics related areas. Of special interest will be the beginning stages of these programs and the impact they have played on departments and universities. Also of interest will be the different aspects of these programs such as orientation, mentoring, study groups, supplemental instruction, faculty training, and other aspects of support programs.
“Mean Value Theorem Entrapment Sham,” James Barksdale, Western Kentucky University. The intention of this presentation is to illustrate how easily even alert thinkers, who are usually cleverly aware of subtle and technical menaces, can still fall victim to intellectual entrapment. An instance of such entrapment is illustrated by a cursory review of certain circumstances followed by a fraudulent application of the Mean Value Theorem.
“The Tenure of Charles Loewner at the University of Louisville,” Richard M. Davitt, University of Louisville. In his Editor's Introduction to the Collected Works of Charles Loewner, Lipman Bers provides a brief but fascinating mini-biography of this renowned Czech mathematician. As a 46-year-old Jewish refugee with an already established reputation as a research mathematician, Loewner spent five years at U of L that Bers describes as "hard," before moving on to Brown, Syracuse, and finally Stanford Universities. The talk will present salient details of Loewner's brilliant career (he merits 2 full pages in the Dictionary of Scientific Biography.) concentrating especially on his stay in Louisville.
“Palindromes by Subtraction,” Claus Ernst, Western Kentucky University. A palindrome is an integer that does not change under digit reversal, such as 1234321. For any positive integer x define x' to be the integer obtained from x by reversing the digits of x. (For example if x=123 then x'=321.) Let x0 be a positive integer and define a sequence by x1=xi-1+x'i-1 for i>0. An old and open question is the following: Will every sequence contain a palindrome? In this talk we will define a different sequence: Let x0 be a positive integer and define a sequence by x0 = x, xi = (xi-1-x'i-1( for i>0. Will every sequence contain a palindrome? The answer is no, since such a sequence can contain cycles. The talk will concentrate on what kind of palindromes and cycles are generated in such sequences.
“Engle Properties Over Groups and Modular Group Algebras,” Leanne Faulkner, Western Kentucky University. This talk will cover some of the history of the Engel condition. Let G be a group. Then for any f, g in G, (x,y) the group commutator. The complex commutator (x,y,n) is defined by the rules (x,y,0)=x,(x,y,1)=(x,y), and (x,y,n)=((x,y,n-1),y) for all x,y in G. The group, G is said to satisfy the Engel condition if for all x,y in G, there exits an integer n such that (x,y,n)=1. This condition is also studied over Group Rings considered as Lie algebras, with the appropriate commutators. Connections between the Upper Central Series and an "Engel" Series will be developed.
“The Annotated Glossary in Linear Algebra,” William Fenton, Bellarmine College. Mathematics has its own peculiar, and sometimes mystifying, vocabulary. In Linear Algebra the host of new terms can become a serious impediment to learning. To encourage better understanding of terminology, I required my Linear Algebra students in Spring 1999 to compile a glossary which went beyond the definitions to include some context for the terms. I will present the specific assignment, samples of student work, and will discuss students' reactions to the assignment.
“The Use of Mathematics in Optometry,” K. Renee Fister, Murray State University. This project stems from a question from a local optometrist. He needed to know the correct combination of lenses for a person with astigmatism. This problem was presented in a calculus course. Under a simplifying assumption, we determine a framework to find the correct prescription.
“Novel Treatment Schedules for Antibiotic Use Confirmed by Mathematical Analysis,” Robert L. Fulton, M.D., University of Louisville School of Medicine, Department of Surgery. Clinical and bench research in our department has suggested that traditional antibiotic administration (cyclic/low-dose) is not the best regimen to eradicate infection. These experiments can be modeled with differential equations (DE's): B'(t) = (B(t)-f(a) A(t) B(t), where B(t) is a function of bacterial growth and A(t) is the method of antibiotic delivery. The function f(a) incorporates drug sensitivity and killing rates, and exponential growth solutions to the DE's are explicit. The ratio of (/f(a) is critical for cyclic treatment plans to be effective. Continuous administration (A'(t) = A(1-A/K) where K is the maximum tissue level is the best method of antibiotic administration. Development of resistance (mutation) is modeled by incorporation of the unit step function. When B'(t) is B(1-B/J) and J is the carrying capacity, systems of DE's with numerical solutions were employed. The solutions have confirmed the experiments, changed our use of antibiotics and may stimulate interest in calculus for "bio-med" students.
“'Dual'-ing Orthogonalities,” Bruce Kessler, Western Kentucky University. Most people are familiar with the concept of orthogonality in some setting. I will introduce the concept of biorthogonality, and show how it is similar to orthogonality, with some interesting advantages. Methods for constructing biorthogonal bases will be provided, as well as demonstrations and examples of their usefulness in solving standard approximation problems and in signal processing applications.
“Why Commander Riker is Greater than Seven of Nine, and Other Star Trek Conundrums,” Mike LeVan, Transylvania University. This talk shall introduce to the audience questions that every starship captain will have to face at some time. We shall boldly answer these questions with our main tool being some basic graph theoretical concepts.
“On Complex Cobordism Modules mod(p),” Augustine K. Maison, Ph.D., Eastern Kentucky University. Let ( = (((, where ( is the category of CW – complexes of finite type, and ( is the Steenrod category of compactly generated spaces ([2]). Let also Lp = MU*(pt, Zp). In this paper the Lp – module structure of MU*(X,Zp), is completely determined for X ( ( . Let A* be a free Lp – module on even dimensional generators. Let A*p-1 be a free Lp – module on p-1 even dimensional generators. Let Bp* be an Lp – module with even dimensional generators of degree greater than or equal to p such that Bp* has EMBED Equation.DSMT4 – torsion ([1]). Then we have the following theorem.
Theorem 1. MU*(X, Zp) ( EMBED Equation.DSMT4 [1] A.K. Maison “On the homology of a certain algebra over Lazard’s universal ring mod(p)”. Africa Mathematica, 1985, pp. 1-15. [2] N.E. Steenrod “A Convenient Category of Topological Spaces”. Topology, 1968. “On the Existence and Probable Value of Brun's Constant (The Sum of the Reciprocals of the Twin Primes) What is Known for Sure?” Andrew Martin, University of Kentucky.
Euler proved that the series of the reciprocal prime numbers is divergent (yielding yet another proof that the primes are infinite in number). Recall that a TWIN PRIME is a prime number p such that either p+2 or p-2 is also prime. The problem of whether there are infinitely many twin primes is unsolved. But amazingly, in 1919 Viggo Brun proved that the series of reciprocal twin primes converges. His proof was an existence proof. References such as Ribenboim's New Book of Prime Number Records (Springer-Verlag 1996) and Mathsoft (mathsoft.cpm/asolve/constant/brun/brun.html) list Brun's constant as being about 1.9021605778 +/- 2.1e-9, but do not make clear that this interval is a 68% confidence interval, and that not even one digit of Brun's constant is known for sure. This talk discusses the meaning of the error bound, and to what extent the value of Brun's constant is absolutely known.
“The Use of Technology in an ODE Class,” C. Maeve McCarthy, Murray State University. The importance of modeling in an ODE class can be emphasized through the use of appropriate technological tools, such as ODE Architect. With this in mind, students in our sophomore differential equations class were assigned lab projects every other week. These projects culminated in a term project which the students worked on in teams. In the term project, students were asked to analyze the heating and cooling of the main classroom building on campus with a view to discussing the efficiency of the present system. The project involved the adaptation of Newton's law for heating and cooling sources and non-constant ambient temperatures. These adaptations were based on information given to them by the Facilities department and also on weather data provided by the Midwestern Climate Center.
“Jacobian Analysis for Nonlinear Systems of Differential Equations,” Mark P. Robinson, Western Kentucky University. The analysis of the behavior of solutions to a nonlinear system of the form dx/dt = f(x, y), dy/dt = g(x, y) is considered. Investigation of such a system in the neighborhood of a fixed point may be pursued using linearization of the system and subsequent Jacobian analysis. Illustration of this approach, in addition to phase-plane analysis, will be provided for examples including a predator-prey population model.
“From Michelangelo to Japan-the Trail of a Geometric Construction,” Carroll G. Wells, Western Kentucky University and David Lipscomb University. The "double wedding ring", a geometric construction with circles, is used in art, quilting, and packaging. Examples will be given and discussed.
“Impossibility and Time,” Homer S. White, Georgetown College. It is desirable for mathematics majors to encounter the same basic idea in several distinct guises during their undergraduate experience. A simple "impossibility" principal concerning the orbit of an element under a group action on a set provides numerous convenient points of encounter. We will look at instances of this principal in logic, combinatorial game theory, differential equations and abstract algebra.
“Web Enhancement: What Worked for Me,” Margaret Yoder, Eastern Kentucky University. This session will present ideas that worked, ideas that didn't work, and suggestions for future use. This is not a talk about providing a course on the web, but on using the web to supplement your course. Topics will include planning ahead, finding resources, and issues specific to Eduprise and Blackboard. The material will overlap with the short course as little as possible.
Don Bennett
Eastern Kentucky University, Richmond
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____ 1. ConferenceRegistration/Dues $13.00
____ 2. Short Course (Friday afternoon) No Charge
____ 3. Friday Banquet Option I (Vegetarian) $10.50
____ 4. Friday Banquet Option II $12.00
____ 5. Friday Invited Address No Charge
____ 6. Aftermath (Friday evening) No Charge
____ 7. Saturday Invited Address No Charge
____ 8. Saturday Bus. Luncheon Option I (Vegetarian)$8.50
____ 9. Saturday Bus. Luncheon Option II $9.00
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Deadline for advance registration is Friday, March 17, 2000. 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.
Eastern Kentucky University, Richmond
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 would like to give a talk on Friday afternoon. ____ 4. I would like to give a talk on Saturday morning. ____ 5. I will attend the MAA business luncheon on Saturday afternoon, and am enclosing $8.50 (Option I - Vegetarian) or $9.00 (Option II) payable to the KY Section MAA. ____ Circle your lunch choice: Option I Option II
Please direct any questions you have to Lisa Elderbrock (elderbrockl@nku.edu). 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 17, 2000.
Governor (1999-2002) Chair (1999-2001) Donald Bennett Ray Tennant Dept. of Math. & Statistics Dept. of Math., Stat. & Comp. Sci P.O. Box 9 Eastern Kentucky University Murray State University Richmond, KY 40475 Murray, KY 42071 tennant@acs.eku.edu dbennett@mursuky.edu Chair Elect (1999-2001) and AHSME Coordinator(1997-2000) Vice-Chair (1998-2001) David Shannon J. Lyn Miller Dept. of Mathematics Department of Mathematics Transylvania University Western Kentucky University Lexington, KY 40508-1797 Bowling Green, KY 42101 dshannon@transy.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 karin.chess@kctcs.net wharris@georgetowncollege.edu Stud. Chapters Coord. (1998-2001) 2000 Meeting Coordinator Lisa Elderbrock Amy C. King Dept. of Math. and Comp. Sci. 1228 Tates Creek Road Northern Kentucky University Lexington, KY 40502 Highland Heights, KY 41099 amyking@lex.infi.net elderbrockl@nku.edu