Marshall Hall Honored by Ohio State

Madison Scott (left) hoods Marshall Hall as he receives the Doctor of Science degree from President E. H. Jenning (Photo by Lloyd Lemmermann)

Marshall Hall received the honorary Doctor of Science degree from The Ohio State University at the 1988 Autumn Commencement ceremonies. Professor Hall was recognized for his immense contributions to mathematics. His work in group theory and combinatorics has been substantial and influential. He has over 120 research publications which also include work on number theory and projective geometry. He is considered a pioneer in the use of computers in mathematical research. Presently his research includes work in the area of codes and designs and the Burnside Problem of Group Theory.

He was a member of the Department of Mathematics at Ohio State from 1946 through 1959. During that time period he played an important role in the department's growth. His influence and presence at Ohio State attracted quality young faculty. In 1981, he retired as a professor emeritus from the California Institute of Technology. Over his career he has held positions at Yale University, the University of California at Santa Barbara, and conducted research work at Oxford and Cambridge Universities in Great Britain. At present, he is a visiting distinguished professor at Emory University.

Professor Hall has been a major influence on several generations of young mathematicians. He has directed numerous Ph.D. students and collaborated with others at an arly stage of their career. Students and associates in this country and abroad bear the unmistakable imprint of his teachings. He continues to maintain an active association with colleagues here at Ohio State.

We in the Department of Mathematics are proud that the University chose to honor the distinguished mathematical research contributions of Marshall Hall and extend to him our warmest congratulations.

Department Receives Academic Challenge Award

According to the American Mathematical Society, the term "global analysis" refers to the general area of analysis on manifolds, in which the methods of modern algebra, analysis, geometry and topology are blended. Although the beginnings of these ideas can be traced to the 17th century, major contributions in this direction were made by Lie, Riemann and Poincare towards the end of the last century, followed by the work of G. D. Birkoff, E. Cartan, and Morse in the early part of this century. However, it is only in recent years that the subject has attained its present central position in mathematics.

Contemporary science is witnessing an unusual rapprochement between mathematics, physics, and computer science. Fundamentally different from the usual "applications of mathematics to physics and engineering," this new approach comes from: (a) the discovery of unexpected analogies between mathematical theories (developed in topology, operator algebras, algebraic K-theory, algebraic geometry, number theory) and some of the most exciting theories in physics (like gauge theory, quantum field theory, quantum gravity); (b) the discovery in physics of new aspects of symmetry, the so-called supersymmetries; (c) the simultaneous discovery in mathematics and physics (with the help of the computer) of basic patterns for chaotic behavior and turbulence; and (d) the new insights gained into the relationship between computational problems in group theory and global structure of manifolds.

Global Analysis at Ohio State, growing rapidly from roots in the topology research area, presently involves approximately 28 mathematics faculty members and 50 graduate students. Among these faculty members, a large proportion are internationally recognized scholars and regular participants in major research center programs worldwide. Of the students, seven will complete Ph.D. dissertations during 1988-89.

With the resources provided through the Academic Challenge Award, the department plans to appoint one additional faculty member in global analysis and to establish a program of international research workshops under the auspices of Ohio State's developing International Institute for Mathematical Research. These workshops, involving leading mathematicians from a variety of U. S. and foreign institutions, would be from one to three quarters in length and address specific topics of particular timeliness. At the conclusion of each workshop, a short conference or symposium is planned to present the current state of development of the targetted topic.

A four month research workshop in Low Dimensional Topology is in the planning stages for Spring 1990. Walter Neumann and Alan Reid are serving as chief organizers for this effort. The topology of low dimensional manifolds interfaces with diverse areas of mathematics including geometry, geometric methods in group theory, number theory, complex analysis, gauge theory, and operator algebras. Many of the most exciting advances in mathematics over the past 15 years have been in, or closely connected with this area.

The department is presently pursuing other potential funding sources in its attempts to broaden the focus of the research workshop program beyond the area of Global Analysis to encompass all research strengths present in mathematics at Ohio State.

Comments from the Chair

My favorite target, aside from strengthening and broadening of the undergraduate major, is the proposed establishment of an International Institute for Mathematical Research at Ohio State. Partially funded by an Academic Challenge Award recently granted to the Department, this Institute will bring the world's most distinguished mathematicians for extended stays on campus to share their ideas with our students and faculty members. What a sense of excitement and innovation this will add to all our programs! Hopefully we will be able to build in some activities with appeal to our more venturesome alumni. Have you any special ideas as to how we might accomplish this? I'd be happy to hear your views!

The Ohio State University Calculator and Computer Precalculus Project

The Ohio State University Calculator and Computer Precalulus Project (C2PC) is a curriculum revision project designed to improve the mathematics preparation of students intending to take college level calculus. The project is a cooperative effort of the Department of Mathematics and the Department of Educational Theory and Practice. Many other colleges, universities, and high schools throughout the United States are also participating through their involvement in the field test of these technologically enhanced precalculus materials.

Textbooks and computer graphing software, written by Frank Demana and Bert Waits have been developed for high school and college use. The new textbooks (available through Addison-Wesley Publishing Co.) put strong emphasis on applications and graphing as a tool to build geometric intuition. The computers and graphing calculators available to students at all times enable them to produce accurate graphs of functions, conic equations, polar equations, parametric equations, and surfaces very quickly. Computer graphing is used as a tool to solve equations, inequalities, and various types of max - min problems. This highly geometric approach to problem solving and precalculus mathematics is designed to strengthen students' understanding of mathematics and to effectively foreshadow the study of calculus. Instructors' Manuals for use in teaching the materials were developed by Alan Osborne and Greg Foley.

At present the materials are being tested in 86 high schools and 40 colleges throughout the country. Inservice training and various workshops were held for the many teachers involved in this aspect of the project. In the next phase, research evaluating the graphing instructional approach used in the materials will be conducted. The evaluation materials will include precalculus items from the Second International Mathematics Study and the Ohio Early College Mathematics Placement Testing Program's calculus readiness test. Preliminary results are extremely positive.

The department's Undergraduate Committee has approved requiring all precalculus students at Ohio State to purchase a graphing calculator and the use of the C2PC materials for all College Algebra and Trigonometry classes at Ohio State beginning in Autumn Quarte 1989.

For more information on this project, write to Frank Demana or Bert Waits in the Department of Mathematics.

Sucheston Receives Humboldt Award

Louis Sucheston has received the Senior Distinguished Scientist Award of the Alexander von Humboldt Foundation. This prestigious award is granted to outstanding United States scientists in recognition of past research accomplishments in order to promote scientific cooperation between institutions in the Federal Republic of Germany and the United States. This special program was inaugurated by the Chancellor of the Federal Republic of Germany in 1972. Its purpose is to honor American scientists who have gained an international reputation and thereby to promote the interchange of ideas in specific fields. Nominations for the award are initiated solely by leading German researchers and research institutions. American scientists are not permitted to submit applications for this award. After the U.S. scientist is nominated, the selection of the award winner is the responsibility of the general election committee of the Humboldt Foundation.

Professor Sucheston's general research area is Ergodic Theory and Probability. His special areas of expertise are Limit Theorems and Optimal Stopping. While in Germany he will stay primarily at the University of Göttingen. Additional visits to the Universities of Erlangen-Nurnberg and Bonn are also planned.

Recognitions for Graduate Associates

The department relies heavily on its core of graduate students to carry out much of its teaching obligations. The 192 graduate students in the various graduate programs offered by the department meet their teaching assignments, for the most part, in a professionally competent way. Each year undergraduate students nominate several of our graduate students for the honor of the Graduate Student Teaching Award. This year we are pleased to recognize Bela Bajnok, Amy Lee, Darrell Minor, Akihiro Munemasa, and Tamila Wickham who were so honored by their students. We extend particular hearty congratulations to Tamila Wickham who was selected by the Graduate School to be one of this year's winners. The University grants only 10 such awards each year. Tammy graduates with a MA degree at the end of Spring Quarter.

In addition to being hardworking and successful students and teachers, many of our graduate students participate in other activities for relaxation and exercise. From time to time these students are featured in the local press for their accomplishments. A few who have been so featured recently include: Brian Jones, Tom Reischman, and Ralph Tippins for their juggling ability; Griff Elder for his inclusion in the Midwest Senior Select Side Rugby Team; and Andy Herr, Tony Pryzbylski, Paul Larick, and David Stroh for their participation in the Banc One Marathon. This Spring, both of the department's softball teams, the MathMAddicts and the Cauchy-Schwarzstops, will be playing in the Intermurals championships.

Problem Corner

(material for this column is prepared by Gerald Edgar)

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

Problem 10. (corrected). Let the function f(x) be defined by

Problem 11. How many different ways are there to make change for a dollar, using only coins worth 1, 5, 10, and 25 cents?

We received solutions from Joe Damico (B. A. '72), who enumerated the cases by hand, and Andrew Lingler (M. Sc. '73), who used a computer program. Here is Lingler's solution:

Undergraduate Recognition Program

In conjunction with the celebration of "Mathematics Awareness Week," the department hosted a reception to recognize the academic achievements of undergraduates participating in its various programs. The list of activities and accomplishments is quite impressive, and we especially congratulate these young people who have found that Ohio State provides a challenge and an opportunity to study a subject in depth, work closely with faculty members, and gain personal satisfaction in a job well done. Many of the students are active members of the department's chapter of Pi Mu Epsilon and the newly formed Student Chapter of the Mathematical Association of America.

It is difficult, in a limited space, to adequately summarize the full academic achievements of students who range from freshmen through graduating senior status. Thus, the list that follows only includes the participation and recognitions received by these students during the current academic year.

Rasor-Bareis-Gordon Mathematics Competition: Michael Booth, Jonathan Caudill, Daishi Harada, Chris Haase, Patrick Hayes, William Kalies, Keith Kingsley, Roger Kumpf, Tony Maric, Ramzi Nahhas, Matthew Norby, Andrew Racevskis, David Sujudi, Minh Tranh and Donald Zeigler (a winner in each of his four years at Ohio State).

Putnam Exam Team: Daniel Dynin, Patrick Hayes, Tienchin Ho, William Kalies, Tony Maric, and Michael Titko.

Joyce Scholars: Daniel Elwell, Ruth Jackson, and Patrick Pauken.

Modeling Contest Winners: Derek Gerlach, Chris Haase, and Charles Martin. (See related article elsewhere in this issue.)

William Kalies and Michael Titko were also recipients of 3 year National Science Foundation Fellowships for graduate study. Additional recognitions included that Daniel Dynin, Ruth Jackson, William Kalies, and Michael Titko were elected to Phi Beta Kappa; Daniel Dynin, Chris Haase, Ruth Jackson, William Kalies, Carrie Stroud, Michael Titko, and Lori Waugh received the College of Mathematical and Physical Sciences Excellence in Scholarship Award; Diane Evans received a National Alpha Lambda Delta Scholarship; and Athena Yiamouyiannis, a student athlete in cross country and track, served as President of Ohio State's Undergraduate Student Government.

Monetary and scholarship awards given by the department to these students for their academic achievements come, in part, from your contributions as alumni to the Department of Mathematics. These special funds enable us to recognize the outstanding performance of our most capable undergraduates. We encourage you to participate in these activities by making a donation.

You may send your check, made payable to The Ohio State Development Fund, to the Editor, Math Matrix, The Department of Mathematics, 231 West 18th Ave., Columbus, Ohio 43210.

In Memoriam

Cynthia Yang, M.Sc. '66, died in November 1988. She was an active member of: the MAA-Ohio Section and the Two year college organization. She taught on the Middletown campus of Miami University.

Leslie Miller, professor emeritus, died February 18, 1989. He was an early worker in the field of computer graphics and employed his geometric research skills in that field as well as in his hobby of gourd carving.

Mahoney Elected to Ohio Women's Hall of Fame

Carolyn Mahoney (Ph. D. '83) was recently inducted into the Ohio Women's Hall of Fame. The Ohio Women's Hall of Fame was created in 1978 to honor Ohio women who have attained outstanding achievements in their field of endeavor. Professor Mahoney was one of 16 women inducted this year. The selection was based on the scope and impact of their achievements and on the extent to which these achievements provide example and inspiration for other women. At the time she received her degree, Professor Mahoney was the 25th black woman in the history of the United States to earn a Ph. D. in mathematics. She has dedicated her life to researching, developing and teaching programs which significantly improve the quantitative skills of women and minority students. For the past two years she has been visiting the department, on leave from Denison University. While at Ohio State she has been intensely active and effective at all levels of the University in trying to reverse the traditional underrepresentation of blacks in mathematics and science.

Divis Selected for Professional Development Program

Zita Divis has been selected to participate in Ohio State's 1989-90 University Internship Program. This special program is part of the University sponsored Professional Development Program for faculty. During the term of her appointment, Professor Divis will be working with Donald W. Good, Secretary for the Colleges of the Arts and Sciences and Curriculum Coordinator. Her activities will center around the various aspects of course development and approval processes needed to institute the new General Education Curriculum at Ohio State, expected to be implemented in Autumn, 1990. She will meet and work with the Curriculum Committees of all five colleges that constitute the Colleges of the Arts and Sciences.

Ohio State Team Wins Modeling Competition

Chris Haase (left), Derek Gerlach, and Chuck Martin (seated), the winners in the modeling competition

Derek Gerlach, Chris Haase, and Charles Martin were a winning team in the Fifth Annual Mathematics Contest in Modeling. The contest is sponsored through the Consortium for Mathematics and Its Applications. Their winning solution will be published in the COMAP Journal. The competition is particularly intense. The team gets the problems (they choose one of two possible) on a Friday and must have the solution mailed no later than the following Monday. The team chose the following problem:

A common procedure at airports is to assign aircraft (A/C) to runways on a first come-first serve basis. That is, as soon as an A/C is ready to leave the gate ("push back"), the pilot calls ground control and is added to the queue.

Suppose that a control tower has access to a fast, on-line data base with the following information for each A/C:

1. The time it is scheduled for push back;
2. The time it actually pushes back;
3. The number of passengers on board;
4. The number of passengers who are scheduled to make a connection at the next stop, as well as the time to make that connection;
5. The scheduled time of arrival at its next stop.

Assume that there are seven types of A/C with passenger carrying capacities varying from 100 to 400 in steps of 50.

Develop and analyze a mathematical will meet and work with the model that takes into account both travelers' and airlines satisfaction.

Thomas Ralley serves as the team advisor. He noted that the team's solution was not only accurate but well presented. That was a factor in its being selected for publication. The team's diversity of background probably was a positive factor in their ability to provide a creative solution. Haase is a senior mathematics major. Gerlach is a junior majoring in electrical engineering. Martin is a junior carrying a double major in mathematics and chemistry. All three are also active members in Ohio State's chapter of Pi Mu Epsilon.

Ohio State Host to NEH Seminar

This past summer, the National Endowment for the Humanities sponsored a 5-week seminar titled "The Great Theorems of Mathematics in Historical Context" on the Ohio State campus. William Dunham, visiting associate professor of mathematics, served as the seminar's director, and Penny Dunham was administrative assistant.

"The Great Theorems" offering was part of NEH's "Summer Seminars for School Teachers" (SSST) program, intended to enrich teacher's appreciation of classic works in the humanities. Following these guidelines, the seminar examined a selection of historically important and logically brilliant "great theorems," spanning over 2300 years and including results from Archimedes, Newton, Euler, Gauss, and others. The theorems were supplemented by biographical information and placed in historical context, but the major focus was on the genius of great mathematicians doing great mathematics. As such, this was the first mathematics seminar ever funded by the National Endowment for Humanities as part of its SSST program.

This approach to mathematics produced a healthy response from U.S. teachers. The seminar had 482 inquiries and 151 completed applications for its 15 available slots. The chosen participants were a very select, eclectic, and talented group of teachers, coming from 13 different states and holding degrees in disciplines as diverse as mathematics, political science, French, engineering, English, and theatre. Besides studying such classics as Euclid's Elements (c.300 B.C.) and Cardano's Ars Magna (1545), the participants explored the mathematics collection in Ohio State's Rare Book Room; welcomed historian of mathematics V. Frederick Rickey from Bowling Green State University as a guest lecturer; and prepared synopses of original papers of Newton and Euler from the collected works of these mathematical giants of the 17th and 18th Centuries.

"Running a seminar for participants of such talent," said Professor Dunham, "turned out to be a very demanding project for Penny and me. Fortunately, it also turned out to be the most stimulating and rewarding thing we have ever done." Encouraged by the response to the 1988 seminar, he hopes to offer "The Great Theorems again during a future summer at Ohio State."

(William Dunham (Ph.D. '74) is visiting the Department of Mathematics this year. He is on leave from Hanover College, Hanover, Indiana. During his time at Ohio State he has been actively involved in the teaching mission of the department. He has taught honors undergraduate and graduate courses on this theme of "great theorems from mathematics." In April, he was invited to present a mini-course on this topic during the MAA-Texas Section Meeting at Texas Lutheran College, Seguin, Texas. He was also invited to give the address at the initiation banquet of the Lake Forest College chapter of the Society of the Sigma Xi.)

ALUMNEWS

Burns, M. Timothy, M.A. '87, currently a Systems analyst with Ohio State and engaged to be married to Beth Dean, M.A. '87.

Carleton, Julie K., B. Sc. '87, currently a student at Harvard Law School.

Chapman, John, M.Sc. '84, currently employed by the National Security Agency located at Fort George G. Meade, Maryland.

Gaeuman, William, M. Sc. '88, currently is serving two years with the Peace Corps teaching mathematics in Papua, New Guinea.

Gong, Mery, B.A. '54, and Dickson Call, M Sc. '58, recently retired from service at the University's Instructional Research and Computing Center. Mery retired after 34 years of service and Dickson has 31 years 0 service to his credit.

Lifshin, Syd, M. Sc., 78, M.Sc. '79 (Computer Science), currently systems engineering manager with IBM in Clevelan(

Oprea, John, Ph. D. '82, currently an Associate Professor with tenure at Cleveland State University, Cleveland, Ohio.

Quillen, Roger K., B.A., B.Sc. '75, M.Sc. 77 from Purdue University, J. D. '80, Ohio State, currently a partner in the law firm of Fisher and Phillips, Atlanta, Georgia.

Richard, Sidney A., M. Sc. 79, became a Fellow of the Society of Actuaries in 1987 and is currently Actuary with Mennonite Mutual Aid in Goshen, Indiana.

St. Andre, Richard J. Ph.D. 71, currently Head of the Department of Mathematical Sciences and Computer Science at Florida Institute of Technology, Melbourne, Florida.

Stranges, Joseph F., III, B. Sc. '72, currently manger in Performance Management at Banc One Information Services.

Weaver, Robert, Ph. D. '86, has joined the faculty of mathematics and computer sciencE at Indiana State University. He was formerly on the staff at Drew University, Madison, New Jersey.