Ross to Receive MAA Award for Distinguished Service

Arnold E. Ross, professor and chairman emeritus, has been selected by the Board of Governors of the Mathematical Association of America to receive the 1986 Award for Distinguished Service to Mathematics. The award will be presented at the business meeting of the Association, Friday, January 10, 1986, in New Orleans. Ross received his B.S., M.S., and Ph.D. degrees in mathematics from the University of Chicago. His doctoral dissertation was written under the direction of L.E. Dickson in 1931. For two years after completing his degree, he was a National Research Council Fellow at the California Institute of Technology. Returning to Chicago in 1933, he headed the Mathematics Department of People's Junior College, an experimental, cooperative venture by a number of young Ph.D.'s, to benefit those who could not otherwise afford college. In 1935, Ross joined the faculty of St. Louis University where he remained until 1946 when he became professor and chairman of the Mathematics Department at the University of Notre Dame. In 1963, he became chairman of the Department of Mathematics at The Ohio State University, holding that position until his retirement in 1976.

While at Notre Dame, Ross began his remarkably effective summer program for gifted high school students. Ross recognized that elementary number theory was the vehicle most suited for the gifted, but inexperienced, high school student. The program is unique in its emphasis on problems and on its heavy use of returning students serving as role models and counsellors for the younger participants. The program arranges more advanced courses in mathematics for these returning counsellors.

Ross is also responsible for the creation of several other programs. In 1970 he initiated Horizons Unlimited, a Saturday morning mathematics program designed to uncover and develop talent in children of grades 6 through 12 in the inner city schools of Columbus, Ohio. In India in the Spring of 1973, Ross served as a consultant and lecturer for an NSF/UGC sponsored program for mathematically gifted children. After his retirement from OSU, Ross was invited by the Australian National University to take part in a summer talent search modeled on the one he developed here. He remained active in that January summer program until 1983. In between the programs running in the northern and southern hemispheres, he found time in 1978 and 1979 to help initiate in Germany, with Professor Peter Roquette, a similar mathematics program at the University of Heidelberg.

Students who have completed the Ross summer program are now scientists, teachers, and university professors (four are currently on the faculty at OSU), others are researchers in industrial settings. More than six have received Sloan Foundation grants. In recent years, finalists in the Westinghouse Science Talent search have frequently been products of "The Program."

Over the years, Ross has been presented with high university and faculty honors. He has received an Honorary Doctor of Science degree from Denison University, the OSU Alumni Award for Distinguished Teaching, and the Distinguished Service Award from both The Ohio State University and the University of Notre Dame.

The Department of Mathematics and all of his "kids" extend warm congratulations on this most recent recognition of the contributions of Arnold E. Ross to the mathematics community.

Another academic year is well underway with 90 regular faculty, 30 visiting faculty and 254 teaching assistants handling 15,500 under graduates and 160 graduate students. Although enrollment was expected to decrease this year, this did not materialize because the retention rate proved larger than projected. The rise in SAT scores nationwide for the second year in a row, in the mathematics portion, locally resulted in a significant decrease in the percentage of entering freshman poorly prepared in the subject. We also feel that the Early Mathematics Placement Testing Program supervised by Bert Waits and the Articulation Program underway statewide between the schools and universities contributed greatly to the upward swing in the preparation of the incoming students. The honors program is flourishing and receiving increased support from the higher administration. Graduate enrollment has, again risen, split approximately equally between domestic and foreign students.

We were all very thrilled to that the MAA has selected Arnold Ross as the next recipient of the Distinguished Service Award, to be given at the Winter Meeting of the Society in New Orleans January 10, 1986. He is being recognized for his summer program, now in its 27th year. Plans are underway next summer's offering of the program. Professor Antoine Brunel of the University of Paris has already agreed to participate.

The long standing tradition of a mathematician's needs being pencils, paper and a good library must now be modified to include computers. The department, in collaboration with Statistics, has purchased a Pyramid Computer. The machine and a full-time programmer are housed in the basement of Cockins Hall. Faculty members have discovered that the MacIntosh Personal Computer is indeed user friendly and many are acquiring them. The initial attraction is the word processing capability of these machines. However, the development of software may significantly affect the way many courses will be taught in the future.

I would like to thank everyone who has donated both to Arnold's program and to the department's discretionary fund. In the latter case funds will be used to offer scholarships to students applying for admission with outstanding credentials in mathematics.

Alan Woods Chairman

Actuarial Sciences at OSU

(Professor Robert Brown has directed the Actuarial Science major program since its initiation in 1979. In this article he discusses some of the current program activities.)

The Actuarial Science Program beginning its seventh year. From the initial class of four students, it has grown today to enroll nearly forty. Actuarial Science continues to be an excellent field for persons who are keen on applying their quantitative analytical skills in a business setting. Career prospects learn are better than ever, both in availability of jobs and in salaries. Inquiries about students for permanent positions are received from both local and national companies. So far this year nine of our students have graduated and begun their careers. Another four students are currently employed in part-time or co-op actuarial positions with Columbus based companies.

Our recent graduates bring to about forty the number of actuaries who can trace their actuarial education to our program. Our congratulations and warmest best wishes for continued success go to Anne DeFrancis, Linda Gifford, Sid Richard, Steve Sorrentino, and Dave Zimmer, graduates who are now Associates of the Society of Actuaries.

During the past two years the variety of actuarial activity at OSU has increased. Two exam review courses have been added to the curriculum. These courses have been taught by our esteemed frien and colleague, Raj Arockiaswamy, an actuary with William M. MercerMeidinger, Inc., Columbus. Professor Brown is serving on a task force of the Society of Actuaries which is concerned with the application of modern technology to the education of actuaries. Miss Jihan Tewfik will join our staff as a lecturer. She has been teaching actuarial science in Canadian universities and will do much of the actuarial instruction during 1985-86. The program will sponsor the first actuarial seminar at OSU. The subject of the seminar will be risk, valuation, and surplus, a subject of intense theoretical and practical interest in the actuarial community. The seminar will run throughout the year. In October, 1986 The Ohio State University will host the 21st Annual Actuarial Research Conference. The conference is being organized by Professor Brown and Professor Hank Waits.

A Note From the Editor

This is the fourth issue of Math Matrix. The mailing list currently numbers close to 2000 but we have not had responses from nearly that many individuals. I'm afraid a lot of you tell yourselves "well, I don't have any real news" and decide not to reply (maybe some of you simply procrastinate). But we all like to keep up with the activities of our friends and this newsletter can be the instrument for that. After you finish reading this issue, don't delay, sit down and send a note to the editor about your current activity or how you feel about the newsletter. Suggestions for future articles would be especially welcome.

Responses from alumni keep coming in. Please take a minute, complete the form, and send it along to us.

Deborah A. Bayer B.Sc. '72, currently pursuing an MBA in finance and management at Lindenwood College, St. Louis, and serving as an o research analyst, helicopter program manager office, AMCCOM.

Carol Provci Cico B.Sc. '64, M.Sc. '66, currently instructor of mathematics at the Western Ohio Branch Campus of Wright State University in Celina, Ohio.

Frederick J. Dickey B.Sc. '64, M.Sc. '75 and software researcher with Boeing Aerospace Company, Bellevue, Washington.

Win Emmons M.Sc. 70, currently Vice-President and Actuary with Home Life Insurance Company in New York.

Kerry Gunn B.Sc., 71, M.Sc. '80 from University of California, irvine, currently operations research analyst for the Naval Surface Weapons Center in Silver Spring, Maryland.

Robert A. Hovis Ph.D. 72, currently holds the Mary Reichelderfer Chair of Mathematics and Computer Science at Ohio Northern University, Ada, Ohio. Prior to that he served as chair of the

William R. Klinger M.Sc. '67, Ph.D. 73 in Mathematics Education, currently Academic Dean at Marion College. The College is a liberal arts school of about 1100 students situated in Marion, Indiana.

Michael McGinnis B.Sc. '80, Ph.D. '85 in Political Science from University of Minnesota, currently an Assistant Professor of Political Science at Indiana University, Bloomington. His area of specialization is formal (mathematical) models of international conflict and cooperation. His dissertation developed and tested a policies of regional powers in the Third World.

John F. Oprea Ph.D. '83, currently an Assistant Professor of Mathematics, Cleveland State University.

Janeal Mika Oprea M.Sc. '80, Ph.D. '84 (Mathematics Education), currently a visiting assistant professor and computer education coordinator for the College of Arts and Sciences at Cleveland State University.

Gary M. Rectenwald B.Sc. 71, M.Sc. 72 (Computer Science), M.B.A. 78, currently marketing manager for IBM in East Lansing, Michigan.

Alum Profile

(Nancy Augsburger graduated with a B.Sc. degree in mathematics in 1980.)

As I packed my belongings for the move east, I wondered what my mathematics degree would do for me. I had been hired as a mathematician for a private research and development company, a government contractor with 90-95% of its work coming from the Navy. Because of my previous army communications experience, I was hired for communications work with my customer being the Naval Electronics System Command (NAVELEX). While in this position I worked on several projects. I built a computer model to test the idea for a new submarine laser communications system.

Incorporated in this system were mathematical equations that dealt with such factors as compensation for the curvature of the earth, clouds in the sky, bioluminescence of fish, and torpidity of the water The system also had to take into account the angle of refraction, message coding for maximum use of time and allowance for cryptography.

Another project involved building and maintaining a data base of message elements and format type for the Navy System under the Naval Command and Control System (NCCS). Each system had own method of naming elements and formating them. Most of my time was spent analyzing each system, its needs, storage space, and formating; and then suggesting ways to standardize between systems. It was at my suggestion that software be developed to convert messages from one system to another. After this was done, my database was no longer used for this project but because of its design and ease of use it is being used for analysis of other types.

A third project was a cartography feasibility study. The Defense Mapping Agency stores maps of the world on magnetic tape. Hundreds of tapes are required. Our job was to develop an algorithm that could reduce the storage space needed yet still give a usable map for targeting and navigation. We designed an algorithm that reduced storage space by 96% and remained within the navy's tolerace of +-1 nautical mile (the standard given to us for this study).

While working on these projects I was promoted to Section Leader. We were the Software Engineering and Data Management Section. I worked with engineers, programmers, and physicists (several with Ph.D.'s). My mathematics degree provided an excellent base for this position. I was the "Jack-of-all-trades" and they were the "masters." I had to function as the team leader getting the best to shine and tying them all together. I was the customer liaison as well. The best way to describe myself here was as an interpreter. If my physicists couldn't seem to get the programmer's to understand what they needed, it was up to me to talk physics to the physicists and then translate it to computerese for the programmers and vice-versa. Since my customer was not as technically educated, I had to do a translation for them on every paper or program we wrote. During the last couple months, I was asked to analyze the test procedures for software developed to run the new coast guard cutters.This involved technically analyzing the test after it was run to correct any problems that were found. Editing was needed to make sure all commands and entries were in the right format and sequencing.

Without my math degree I would never have been able to have that experience. It was not the case that I used every bit of content I learned in my degree program. What opened these opportunities for me were the skills in analyzing a problem, the logical organization of communicating results, and the ability to think at an abstract level. All these qualities come from the undergraduate mathematics program experience. My base has been strong and I am now able to build and grow in any direction I choose. My current plans are to pursue a degree in biomedical engineering.

Problem Corner

(Material for this column is prepared by Gerry Edgar.)

Another chance to try your problem solving skills! Send your solutions to the Editor. The best (or most interesting) solutions will be included in the next issue of Math Matrix. You are encouraged to submit problems for inclusion in this corner. Problems with an applied flavor are especially welcome.

Problem 5. Which is larger? 1986! or 662¹⁹⁸⁶

Problem 6. What will happen if I try to get my computer to sum the harmonic series

Solutions to previous problems

n->

n->

Solutions were received from:
Joachim Domstra and Peter Imkeller, Paul Nevai, Boris Pittel (all at OSU), and Brian R. Scalley (Mayfield Heights, Ohio). Here is Nevai's solution:

Let v_n = .   Then v_n>=0, v₁ = =1/2 and

n->

n->

Problem 3. Does e^x/x have an indefinite integral of the form A(x)e^B(x)/x, where A(x) and B(x) are rational functions?

Two solutions were received from Brian R. Scalley (Mayfield Heights, Ohio).

We will write A=A(x), etc. and A' for the derivative. If (Ae^B)' = e^x/x, then (A'+AB')e^B = e^x/x, so x(A'+AB')=e^x-B.

By considering what happens as x-->, we see that x(A'+AB')=1=e^x-B, so B=x and A'+AB'=1/x. Suppose A=P/Q, where P and Q are polynomials with no common factor.

Then

Therefore x divides Q², so x divides Q. Say Q=x^kR, k>=1 and R is a polynomial not divisible by x. So

So the assumption that (Ae^B)' = e^x/x is not true.

Problem 4. A square cake with icing on the top and on the four sides is to be divided into seven pieces. Each piece should have same volume of cake and the same area of icing. Is this possible?

A solution (and generalization) was received from Brian R. Scalley (Mayfield Heights, Ohio).

We assume that the thickness of the cake's icing is zero (a good approximation at some bakeries). The top of the cake is a square S of sides m and center C. Divide the perimeter of S into 7 parts of length 4m/7 with points P₁, P₂,..., P₇. Make vertical planar cuts through the cake from C to each P_i. Seven pieces result, with either a triangular cross section of area A_i = (1/2)(4m/7)(m/2) - m²/7, or a quadrilateral cross section of area

Nevai Receives Fullbright Award

Paul Nevai, professor of mathematics, has been selected to receive a Fulbright award. Established in 1946 under congressional legislation introduced by former Senator J. William Fulbright of Arkansas, the program is designed "to increase mutual understanding between the people of the United States and the people of other countries." Individuals receiving the award are selected on the basis of their academic and professional qualifications. Professor Nevai's area of research is orthogonal polynomials and other special functions. He will spend 6 months in Hungary visiting the University of Szeged (where he received his Ph.D.) and the Mathematics Institute of the Hungarian Academy of Sciences. In 1983 he was recognized by The Ohio State University through its Alumni Distinguished Research Awards program.

Department News

Joseph Ferrar recently spent six weeks at Utrecht University, Utrecht, Netherlands as a Visiting Professor (guiding the work of a Ph.D. candidate). While there, he participated in the Netherlands American Seminar on "Representations of Semisimple Lie Groups and D-Modules." He also attended a conference on Jordan Algebras at Oberwolfach where he gave a talk on homomorphisms of Moufang-Veldkamp planes.

Dijen Ray-Chaudhuri has been appointed to a three year term as a member of the Board of Governors of the NSF supported Institute for Mathematics and its Applications at the University of Minnesota. The principal duty of the IMA Board of Governors is to oversee the scientific programming at the institute.

Joan Leitzel has been named to membership on the Board of Mathematical Sciences Education. The Board is a newly created unit of the National Research Council and will address national issues in mathematics education at all levels.

Jessie Engle retired as Associate Professor Emeritus July 1, 1985. Beginning January 1, 1986 she has one year contract with ITM/MUCIA in Shah Alam, Selangor, Malay The Institut Teknologi MARA / Midwest University Consortium for International Activities, Inc. program in Malaysia is administered by Indiana University. The Shah Alam center of ITM is a two-year institution which opened in June. At the center, Malaysian students study the first two years of university work aiming toward majors in engineering, business, and computer science. They will then complete their undergraduate work in the United States. Shah Alam is near the capital, Kula Lumpur, and is about 200 miles from Singapore.

Leslie Miller, professor emeritus and nationally recognized pioneer in computer graphics, will serve as 1985-86 artist-in-residence in the Department of Visual Arts at Otterbein College. In 1978, he was recognized for his pioneerin in computer graphics by the National Computer Conference. While at Ohio State, Miller worked as an associate of Charles Csuri, internationally recognized for his work in computer animation. At Otterbein, Miller will share his expertise in extending computer usage to both the visual arts and theater programs.

Bert Waits has been commended by the Ohio Board of Regents for his efforts with the Early Mathematics Placement Testing Program. That program was also awarded a bronze medal in the category of High School/College Paurtnerships by the Council for Advancement and Support of Education.

A Distinguished Past, A Dynamic Future

The Ohio State University has launched a national campaign to raise $350 million over the next five years. The fund raising drive is the largest ever attempted by a public university. According to President Edward Jennings, the dollar figure represents only the means by which we will achieve the real goal of the campaign--the acquisition of significant additional resources to enable the University to fulfill its potential as one of the leading institutions of higher education in the world.

Of the projected total to be raised, $227 million will be directed toward enhancing the academic core of the University through endowments for faculty chairs and professorships, research endowments, support for the Cancer Research Institute, construction of a Center for the Visu,al Arts and similar projects to support the basic instructional -and research mission of the University. Another $78 million will be dedicated to student initiatives, primarily increased undergraduate scholarships and graduate fellowships. The remaining $45 million in funds will be allocated to strengthening Ohio State's athletic programs through improved facilities.

Planning for the campaign was constituency based. Deans, faculty, and program directors in all nineteen colleges were consulted for their priority needs. Contributions from alumni and supporters of these specific colleges and programs will be used to fund those identified priority needs.

The College of Mathematical and Physical Sciences is seeking $5.25 million for five endowed chairs. Two of these will be in Chemistry and one in each of the departments of Geodetic Science and Surveying, Physics and Mathematics. For mathematics, the funds requested are needed to establish the chair in Scientific Computation. To attract and retain highly qualified students in the College, the fund goal includes $2 million for undergraduate student scholarships and $5 million for graduate student fellowships

You who are recognized recipients of Ohio State's distinguished past now have the opportunity to shape its dynamic future. Through your support the department can make the necessary strides to preserve and enhance its excellence. Your contribution (tax deductible) toward a specific project or toward the greatest need will be most welcome.

The MAA and OSU

In 1915 the Council of the American Mathematical Society recommended that a separate organization be formed to deal specifically with activities related to the improvement of collegiate mathematics. At a meeting held at The Ohio State University on December 30 and 31, 1915 the new organization, the Mathematical Association of America, was formed. K.D. Swartzel, a member of the faculty of Ohio State at that time, was one of twelve persons on the original executive council.

The Ohio Section of The Mathematical Association of America was the first Section organized. To commemorate the 75th anniversary of the founding of both the Association and the Section, a history is currently being prepared for distribution five years from now. If you have old programs or other documents that give some information of the early years of the Section, or if you have anecdotes or personal recollections you would be willing to share, please drop a note to
James R.C. Leitzel, Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, Ohio 43210.