Accent on Mathematics

Spring 2000

CHAIR’S THOUGHTS

Dr. Janice Huang

As many of you may know, George Poole, after 13 years of outstanding service to the department, decided to return to full-time teaching this year. As the new Interim Chair for the department, I have had a lot to learn this semester! Although I have been at ETSU since January 1995, there is much about the university and about how things work that I did not know! Fortunately, George has given me much good advice and counsel. I also appreciate the support of the other faculty members who have given their time and effort to make things work as smoothly as they have so far.

Probably the most exciting news we have concerns the new "Internet-Based Classroom" which is now installed in Gilbreath 205. Last spring we received the news that NSF had funded our grant to establish the classroom, which will hold 24 computers networked to a server. This room is being used for computer-based instruction and demonstration and will also allow access from remote environments so that students can get real time help with their questions. Jeff Knisley and Don Hong provided the leadership for developing this classroom. Come by to see it if you are in the area.

This fall we participated in the Alumni Return to the Classroom for the first time. Lyndell Kerley invited Tammy Gillenwater Hubbard, our outstanding mathematics major of 1985, to come and spend the day sharing with students and faculty what she has been doing for the last few years. Tammy works for Lockheed Martin Energy Systems at Oak Ridge as a Computing Specialist. She spoke to us about "A Software Engineering Career Starting with a Foundation from ETSU." It was a very enjoyable experience and all of us learned something about how math majors use their training while working in industry. If you or someone you know would be interested in participating in this program sometime, please let us know!

In other news, Jay Boland is developing an Honors Program for mathematics students. We hope that this will encourage excellent students to apply for our program as they will be given financial support when they are accepted.

Last spring we hosted an External Review Team, which spent several days looking at our undergraduate and graduate programs. Their report was very complimentary, in general, and most of their recommendations were things that we had heard before and over which we have no control – for example, we need a second part-time secretary and the graduate students need more space, etc. For the third time, the review team recommended that the university make MATH 1080: Probability and Statistics a prerequisite for other statistics classes on campus. We are once again pushing this idea and asking the Administration to recognize that the other courses should not just be duplicates of this course! Wish us luck!

I did follow the Review Team’s recommendation to broaden the governance structure in the department and established several standing committees this fall, one to look at the department’s vision and goals, one to adjust workloads for faculty, one to set up priorities for travel funds, and one to look at curriculum issues. The Vision and Goals Committee has produced a Vision Statement which has been forwarded to the Administration and it is currently working on the list of short-range and long-range goals. The Workload Committee has drafted a set of equivalencies to help faculty in constructing their yearly plans. I believe that it will help all of us to realize that what each of us does in the department is important and that all of us have full assignments. The Travel Committee has taken a good look at available travel monies and has suggested a list of priorities which the Chair will adhere to in making hard decisions about who will be able to travel in these times when funds are cut.

There are actually two curriculum committees currently working – one for mathematics and one for statistics. The statistics group is developing a new minor in statistics which we hope will attract students from a variety of fields – from sociology to accounting to biology. They have also developed a new experimental lab course which will be offered in conjunction with MATH 1080 to computer science students this summer. The work for this course will take place in the computer lab and will introduce the students to statistics software such as SAS, Minitab, etc. They have other "irons in the fire" which you will be hearing about later.

The mathematics curriculum committee is looking at revising and updating our major tracks now that we have had them in place for several years. They are also working on improving contacts with our client disciplines and making sure that courses required for other major programs are satisfying the needs of their students.

In addition to the above, we also have a search committee working at selecting a new permanent chair for the department, and a second search committee seeking an individual to fill the tenure track position which we were unable to fill last year. A third search committee is seeking someone to fill a new tenure track position in Kingsport/Bristol.

As you can see, the mathematics faculty are working hard in a variety of areas and building a reputation for excellence in teaching, research, and service. Several of us have had major papers published in the last year and have made presentations and organized sections at professional meetings. A few of us teach large sections of introductory courses, with built-in support systems for students, so that others can have more time for research. Our reputation for good teaching is well known on campus – especially with regard to the MATH 1080 where we now have about 1300 students enrolled each semester and which is masterfully coordinated by Tod Jablonski. I don’t know of any other department which has been as successful in ensuring that the content and quality of a course is consistent across a multitude of sections.

Do let us hear from you! We hope that things are going well and that you will come by to visit with us when you are in East Tennessee.

Interim Chair: huangj@etsu.edu

Undergraduate Coordinator: kerleylm@etsu.edu

Graduate Coordinator: knisleyd@etsu.edu

You should also visit the Mathematics Department’s home page at:

http://www.etsu.edu/math/math.htm

UNDERGRADUATE RESEARCH

Four of our undergraduate students have been participating in undergraduate research projects-

Susan Hosler, Ken Proffitt, Jason Osborne, and Scott LaVoie.

These students were advised by Drs. Edith Seir, Jeff Knisley, and Bob Gardner.

Susan Hosler conducted a time series analysis of data related to the state of Tennessee under the guidance of faculty advisor, Dr. Edith Seir, during the summer of 1999 as a part of the Ronald McNair Postbaccalaureate Achievement Program. A description of her project is now described.

A univariate time series consists of a sequence of observations to a single variable over time. The purpose of this applied research was to identify and fit the most appropriate models to represent the behavior of demographic and economic variables in the state of Tennessee. The models were used to quantify the historical changes and to forecast future values. The demographic variables considered were population counts, number of occupied housing units, and percentages of crowded and severely crowded housing units as indicators of poverty. Non-linear models were used for the demographic variables and models of the same nature were fitted to the data corresponding to the whole country in order to make comparisons. The economic variables considered were monthly unemployment rates and average hourly earnings of Tennessee workers in the durable and nondurable goods sectors. ARIMA-type models were fitted to the economic series and the existence of cycles and seasonal behavior was analyzed using periodograms based on the fast Fourier transform.

During the 98-99 academic year, Jason Osborne pursued undergraduate research in Lie Algebras and Lie Groups under the direction of Dr. Jeff Knisley. This effort resulted in a paper entitled "A Lie algebra of Integrals of Keplerian Motion Restricted to the Plane," as well as a presentation on the same topic at the Southeastern Section of the MAA’s annual meeting held in Memphis, Tennessee, in March of 1999. Jason went on to pursue an NSF-sponsored Research Experience for Undergraduates at Northern Arizona University during the summer of 1999.

Sponsored by support from the Ronald McNair Program, Ken Proffitt investigated alternative methods for finding solutions to Pell’s equation. This undergraduate research, under the direction of Dr. Jeff Knisley, resulted in a presentation at the Southeastern Section of the MAA’s annual meeting held in Memphis, Tennessee, in March of 1999. In addition, Ken presented his work at the MAA Mathfest in Toronto, Canada, in the summer of 1998 and placed third in the Southeast for a presentation of his work at a conference for Ronald McNair participants.

Ken Proffitt completed a second project of "Decomposing, Packing and Covering the Complete Graph with Osculating 4-Cycles" with funding provided by the Ronald McNair Program. The research was conducted under the direction of Dr. Robert Gardner.

Scott LaVoie is studying "A 4-Cycle Covering of the Complete Graph with a Hole" under an ETSU Honors Program grant. Dr. Robert Gardner is directing the research.

ANNUAL ALUMNI RETURN TO THE CLASSROOM

Mrs. Tammy Hubbard participated in the Alumni Return to the Classroom program during the fall semester. She received the Outstanding Mathematics Award in 1985 and worked at Beecham Labs in Bristol, Tenn., in a statistical capacity before joining the staff at Lockheed Martin Energy Systems. She spoke to our undergraduate mathematics majors and our mathematics faculty. The title of her presentation was "A Software Engineering Career Starting with a Foundation from ETSU."

MATHEMATICS COMPUTER LABORATORY

Dr. Jeff Knisley, Director

The mathematics department added a new, state-of-the-art computer laboratory at the beginning of the spring semester 2000. The lab is configured as a classroom and is located in room 205 of Gilbreath Hall. It is carpeted and contains a white board for teaching. The lab contains 25 Dell Optiplex GX1 computers with Pentium III processors running at 500 mhz. Each computer has 128 MB RAM, a 9 Gb hard drive, a 100 MB zip drive, and a 21" flat-screen monitor. In addition, the computer-based classroom is to have its own Internet server and two high-volume printers.

Currently, three math courses and two computer science courses are using the lab. The students have access to

Maple, PC-Matlab, and Sigma-Plot for Windows. If you visit the campus, be sure to visit this state-of-the-art facility.

UNDERGRADUATE RESEARCH PRESENTATIONS AT AMS AND MAA IN WASHINGTON, D. C.

In January of 2000, three math students - Rachel DeHart, Jason Osborne, and B. J. Smith presented posters at an undergraduate research session of the joint meetings of the American Mathematics Society (AMS) and the Mathematics Association of America (MAA) in Washington, D. C. Each was presenting research that they had conducted during the fall of 1999. Rachel’s poster used continued fractions as a nonstandard method for perturbing Kepler’s problem. Jason’s poster described his efforts in using geometric quantization to map a Lie algebra of classical integrals to a Lie algebra of quantum observables. B. J.’s poster detailed his investigation of rocket-powered flight in an inverse square field.

GRADUATE PROGRAM NEWS

Dr. Debra Knisley- Graduate coordinator

The ETSU mathematics graduate program is continuing to flourish. The department received a grant from the National Science Foundation for a new computer laboratory. As part of that grant a new graduate assistantship was acquired, bringing the total of assistantships and tuition waivers to 17. All 17 positions are currently filled. We also have several part-time students.

Several of the graduate students attended the joint meetings of the AMS, MAA and SIAM held in Washington D.C., in January 2000. Ken Proffitt, one of our graduate students, presented his work at the MAA Graduate Student Paper Session.

This year we welcomed the following new students.

New Students:

There are six returning students:

Now for some news regarding recent graduate students -

Recent graduates:

Six students recently received their master’s degrees in mathematics.

HONORS

Scott Wilson (1999) and Susan Hosler (2000) are the outstanding graduating mathematics seniors with the highest grade point average and have been or will be recognized at Honor’s Day at the university. Scott is presently enrolled in the Quillen College of Medicine at East Tennessee State University. Susan will attend graduate school at ETSU.

Donny Belcher (1999), Jason Osborne (2000), and Justin Christian (2000) have been recognized by the Department of Mathematics as the outstanding students in mathematics. Donny is a graduate student in mathematics at ETSU; Jason has been offered an assistantship in mathematics at N.C. State University; and Justin has been offered an assistantship in mathematics at the University of Wyoming.

SCHOLARSHIP INFORMATION

A new scholarship, the Jeff Hightower Scholarship, has recently been endowed by his widow Mrs. Tammy Hubbard. Jeff was our outstanding senior mathematics major in 1986 and completed an M.S. at Clemson University prior to his employment at Lockheed in Oak Ridge, Tenn. Mrs. Tammy Hubbard, outstanding senior mathematics major of 1985, established the scholarship in memory of her husband. She is associated with Lockheed Martin Energy Systems in Oak Ridge, Tenn., and was formerly with Beecham Laboratories in Bristol, Tenn., in a statistical capacity.

The Faber-Neal Scholarship, which is designed to cover annual tuition costs to sophomore mathematics majors, was awarded to Ree’l Street of Erwin, Tenn., Jason Robert Lewis of Johnson City, Tenn., and Jamie Marie Howard of Louisburg, North Carolina. One week before his death (1995), Dr. Larry Neal, a distinguished professor of mathematics at East Tennessee State University, established a scholarship fund, the Faber-Neal Scholarship, to honor his very dear friend, Joe Faber, professor emeritus of East Tennessee State University.

The Wilson-Hartsell Scholarship, which serves to help aspiring mathematics teachers, was awarded to Travis Chambers of Roan Mountain, Tenn. The Wilson-Hartsell Scholarship was initiated in 1987 and named in honor of two former department chairs with long-term commitments to ETSU: Mr. Charles Wilson (retired, '86) and Dr. Lester Hartsell (retired, '87).

The Depew Scholarship, which is designed to be awarded to students planning to major in mathematics, was awarded to mathematics senior Jason Osborne of Jonesborough, Tenn. Mrs. Rex Depew (Sara Margaret) established an endowed scholarship, the Depew Scholarship, in memory of her husband, who graduated from ETSU in 1940, having majored in mathematics. Dr. Depew (Ph.D. in mathematics at Vanderbilt University in 1963) served with the Air Force, taught at both Everett High School and North Alabama State University, and provided mathematics support and analysis for NASA Space Systems as an employee at the IBM Corporation. Mrs. Margaret Depew continues to reside in Maryville.

The Edward Stanley Scholarship is awarded to promising mathematics students planning to major in mathematics. Reggie Tiller of Davenport, Va., was the recipient. The Edward Stanley Scholarship was endowed in 1986 from a generous gift from a former student, Dr. Ed Stanley, who completed an illustrious career teaching mathematics at Clemson University.

FACULTY PROFESSIONAL ACTIVITIES

Drs. James Boland and Don Hong visited China last summer. They delivered colloquium talks and a series of lectures on such topics as "Recent Progress on Sum Graphs and Mod Sum Graphs," "Scattered Data Representation and Approximation by Using Multivariate Splines,"and "Recent Progress on Wavelets, Multiwavelets and Applications," at Beijing Polytech University, the University of Petroleum- China, and North China University of Technology.

Drs. Jay Boland and Linda Lawson have had the following paper accepted:  "i-connectivity in a Generalized Hypercube" (with Richard Ringeisen) in Journal of Combinatorial Mathematics and Combinatorial Computing.

"The Rook's Pivoting Strategy," an article by Dr. George Poole and the late Dr. Larry Neal, has been accepted for publication in a special edition of the Journal of Computational and Applied Mathematics, recognizing advancements in numerical linear algebra for the last decade of the 20th century.

Dr. Teresa Haynes has had the following papers accepted or published.

On perfect neighborhood sets in graphs, Discrete Mathematics 199 (1999) 221-225 (with Gerd Fricke, Sandra Hedetniemi, Stephen Hedetniemi, and Michael Henning).

Nordhaus-Gaddum type results for the domatic number of a graph, Combinatorics, Graph Theory, and Algorithms, John Riley & Sons, Inc. Vol.1 (1999) 303-312 (with Jean Dunbar and Michael Henning).

Independence, domination, and uniform maximum degree, to appear in Combinatorics, Graph Theory, and Algorithms, John Riley & Sons, Inc. Vol.1 (1999) 291-302 (with Jean Dunbar, Lisa Markus, Gayla Domke, and Debra Knisley).

3-domination critical graphs with arbitrary independent domination numbers, Bulletin of the Institute of Combinatorics and its Applications 27(1999) 85-88 ( with Lucas van der Merwe and C.M. Mynhardt).

A generalization of domination critical graphs, to appear in Utilitas Mathematica (with Ben Phillips).

Extremal graphs for inequalities involving domination parameters, to appear in Discrete Mathematics (with Xu Baogen, Ernie Cockayne, Stephen Hedetniemi, and Zhou Shangchao).

Extremal domination insensitive graphs, to appear in Journal of Combinatorial Mathematics and Combinatorial Computing.

Domination and total domination critical trees with respect to relative complements, to appear in Ars Combinatoria (with Michael Henning and Lucas van der Merwe).

Generalized Maximum degree, to appear in Utilitas Mathematica (with Lisa Markus).

Stratified claw domination in prisms, to appear in Journal of Combinatorial Mathematics and Combinatorial Computing (with Gary Chartrand, Michael Henning, Ping Zhang).

Path-free domination, to appear in Journal of Combinatorial Mathematics and Combinatorial Computing (with Michael Henning).

Strong equality of upper domination and independence in trees, to appear in Utilitas Mathematica (with Michael Henning and Peter Slater).

Distance-k independent domination sequences, to appear in Journal of Combinatorial Mathematics and Combinatorial Computing (with Odile Favaron and Michael Henning).

Dr. Haynes was also elected to a three-year term on the Council of the Institute of Combinatorics and its Applications (ICA). She has been invited to be a speaker at the Twelfth Cumberland Conference, May 2000. She has also been invited to be a principal speaker at the Ninth Quadrennial International Conference on Graph Theory, Combinatorics, and Applications, June 2000.

Dr. Robert Gardner published a paper: "Triple Systems from Mixed Graphs" in Bulletin of the Institute of Combinatorics and Its Applications, 27, (1999), 95-100. Dr. Gardner gave a presentation on "Visualizing the big Bang: An Introduction to Topology and 3-Manifolds for Undergraduates" at the 194th meeting of the American Astronomical Society in Chicago during June 1999.

Professor Lutai Guan, associate dean of the College of Mathematics and Computing Sciences at Zhongshan University, China, visited ETSU during fall ‘99 and worked with Don Hong on a research project "Splines, Wavelets and Applications."

Dr. Don Hong and Michael Prophet from the University of Northern Iowa organized a special session on "Wavelets and Approximation Theory" for the American Mathematical Society Meeting #948 during Oct. 8-10, 1999, at Austin, Texas. They were invited to be guest editors for a special issue of the Journal of Computational Analysis and Applications for publishing the papers presented at the special session. Dr Hong also served as a supervisor of the Society of Actuary Exams at ETSU, November 1999.

Dr. Hong has also had the following papers recently accepted for publication:

"On construction of minimum supported piecewise linear prewavelets over triangulation," co-authored by former ETSU graduate student Yuchun Anna Mu, in "Wavelet Analysis and Multiresolution Methods," Lecture Notes for Pure and Applied Mathematics, Marcel Decker Pub., New York, 2000, pp. 181-201.

"Bivariate C1 Cubic Spline Spaces Over Even Stratified Triangulations," co-authored by H.W. Liu of the University of Wollongong, Australia, in Journal of Computational Analysis and Applications, to appear.

Don Hong and Aidi Wu, "Multiwavelets with multiplicity four," International Journal of Computers and Mathematics with Applications, to appear.

"On scattered Data Representations Using Bivariate Splines," in Handbook on Analytic-Computational Methods in Applied Mathematics, Chapter 22 (30 pages), CRC Press, Boca Raton, FL, (2000).

Dr. Janice Huang, interim chair, was project director of a week-long summer workshop for teachers, "Enhancing Concept Development in Algebra I: The Challenge of the New Tennessee Frameworks."

Dr. Robert Price had a paper "Estimating the Ratio of Two Poisson Rates," co-authored by D.G. Bonett of Iowa State University, accepted for publication in the journal Computational Statistics and Data Analysis.

Dr. Rick Norwood has had the following papers published or accepted for publication.

"A Star to Guide Us," Mathematics Teacher, Vol. 92, No. 2, p. 100-101, February 1999. An article on the history of the multiplication sign.

"The Test of Time," Mathematics Teacher, to appear. A major article written for the special focus issue on the history of mathematics.

"Turning Double Torus Links Inside Out," Journal of Knot Theory and Its Ramifications, to appear.

Dr. Debra Knisley published the following papers:

Neighborhood Unions, Generalized Degrees and Graphical Properties, (With L. Lesniak), Graph Theory, Combinatorics, Algorithms and Applications, Vol. II, 555-565, (1999).

Independence, Domination and Uniform Maximum Degree, (with G. Domke, J. Dunbar, T. Haynes, L. Markus), Graph Theory, Combinatorics, Algorithms and Applications, Vol. 1, 291-301 (1999).

GRANTS

Drs. James Boland and Don Hong received an Instructional Development Grant of amount $2,160 from ETSU to enhance actuarial mathematics program and also mathematics graduate students skills in professional typesetting and web page design. They also received a grant from the Office of International Programs to support their travel to China last summer.

Drs. Robert Gardner and Joe Falcone received an Instructional Development Grant of amount $3,100 from ETSU to update ETSU planetarium. See http://www.etsu.edu/physics/planetar/planetar.htm for details!

Drs. Jeff Knisley, Don Hong, and Janice Huang received a grant of amount $65,298 from National Sciences Foundation (NSF) plus matching funds from ETSU to establish a computer lab for the Department of Mathematics.

Dr. Don Hong received a Research Development Grant of amount $4,130 from ETSU for a research project on "Splines, Wavelets and Applications."

 

ACTUARIAL PROGRAM

Dr. Don Hong and Dr. Jay Boland – Directors

Congratulations to the following students who passed SOA Exam 100 in November, 1999:

Lesley Baker, Renee Gaunt, Janeice George, and Joby Kauffman.

An actuarial mathematics program has been developed in the Department of Mathematics. By emphasizing the mathematical topics of interest to Actuaries, this program will prepare students for careers in industries that use business modeling skills such as insurance companies, financial institutions, pension funds, governmental agencies, and consulting firms.

Two courses, "Theory of Interest" and "Actuarial Mathematics I," have been developed and taught in 1997-98. A test center for exams of the Society of Actuaries has been arranged at ETSU since May 1998 and the exam center has been approved as a permanent one by the Society of Actuaries. Since the actuarial math program began in the fall of 1997, four students have received five job offers with an average annual salary of $38,000. The academic council of ETSU has approved the following courses to be the permanent ones for the actuarial math program:

MATH-4377/5377: Theory of Interest

MATH-4387/5387: Actuarial Math I

MATH-4397/5397: Actuarial Math II

The Actuarial Student Association (ASA) at ETSU has meetings on the first Monday of each month at Warf-Pickel 308 from 5:30 p.m. - 7 p.m. The current president of ASA-ETSU is Renee Gaunt (zbrg5@etsu.edu).

For more information or recent activities of ETSU actuarial math program, please visit the web site .

http://www.etsu.edu/math/actuary

KAPPA MU EPSILON MATHEMATICS HONOR SOCIETY

Dr. Lyndell Kerley-Faculty Sponsor

Kappa Mu Epsilon (KME) Mathematics Honor Society recently initiated the following eight new members during the spring 1999:

Sarah Dailey, Andrew Finnell, Elizabeth Hyder, Kim Jennings, Jonathan Oakley, Bert Smith, Mark Taylor, Gabriel Zimmer

The 1999-2000 officers are:

B. J. Smith President, Mark C. Taylor Vice President, Susan Hosler Secretary, and Tabitha Taylor Treasurer

 

EAST TENNESSEE STATE UNIVERSITY STUDENT CHAPTER OF THE

MATHEMATICS ASSOCIATION OF AMERICA

Dr. Robert Price - Faculty Sponsor

The chapter attended the Mathematical Association of America in March 1999 in Memphis, Tennessee. Jason Osborne and Ken Proffitt gave presentations on their research. This January several members attended the joint mathematics meeting in Washington, D. C., of the MAA, AMS, and SIAM. Poster sessions were given by Ken Proffitt, Jason Osborne, and B. J. Smith.

Jason Osborne received a summer research grant in 1999 at the University of Arizona.

Ken Proffitt President, Angela Harris Vice President, Renee’ Gaunt Secretary, Tabitha Taylor Treasurer

WE NEED YOU NOW!

Please consider sending a contribution to the Mathematics Foundation Account so we might send an issue to each of you. We also need additional dollars to cover expenses not normally covered by state revenues. In the past these monies have been used to purchase special research equipment, provide faculty release time to complete special departmental projects, and provide expenses for out-of-town speakers.

PLEASE SHARE

If you are an ETSU graduate with a major or minor in mathematics, please share with us your current type of work. More importantly, because we would like to improve our undergraduate and graduate programs, please share with us some things you liked about your experiences at ETSU and some things you would like to see changed. Please indicate your degree and the year you graduated from ETSU. See the form provided on page seven of this newsletter or communicate electronically with Interim Chairman. Janice Huang Department of Mathematics, (Huangj@etsu.edu).

Currently our plans are to distribute a newsletter each year. Please send information on your status to Dr. Janice Huang, Department of Mathematics, East Tennessee State University, Box 70663, Johnson City, TN 37614-0663.

Name                                                                                                                                                                                              

What are you doing now?                                                                                                                                                          

                                                                                                                                                                                                        

Year Graduated Degree Obtained                                                                                                                                              

Name(s):                                                                                                                                                                                        

Preferred Mailing Address:                                                                                                                                                       

City:                                                                                                                                                                                               

State: Zip:                                                                                                                                                                                     


I would like to contribute to the ETSU Department of Mathematics as follows:

Candidates for scholarships apply to the chair, Department of Mathematics.

Mathematics Foundation For covering expenses not normally covered by state revenues, e.g., speakers, research equipment, etc.

Jeff Hightower Scholarship For students majoring in mathematics.

Edward L. Stanley Scholarship For meritorious students planning to major in mathematics. First-year students must have a minimum high school GPA of 3.2 and ACT composite of 25.

Wilson-Hartsell Scholarship For students majoring in mathematics.

Faber-Neal Scholarship For sophomores majoring in mathematics.

Depew Scholarship For students majoring in mathematics.

Amy Weems Memorial Math Graduate Student Fund For ETSU graduate students.

Please make check or money order payable to:

Mathematics Foundation Account

East Tennessee State University Foundation

Box 70732

Johnson City, TN 37614-0732