The Changing Scene in Mathematics Classrooms

Students in M151 work with MathematicaTM         Photo by Terry Swagger

As Autumn Quarter begins, there is a changing scene in some mathematics classrooms at Ohio State. For the first time, all of the sections of precalculus mathematics (Math 148) require the use of a calculator with graphics capability. There is a section of calculus (Math 151) being taught based on'the symbolic manipulation program Mathematica^TM Another one of our calculus courses (Math 117) is using MAPLE. Upper division courses in linear algebra are making use of MATTLAB. Teaching and learning mathematics using available technology is under way!

The curriculum for the precalculus course has been developed over the past several years by Frank Demana and Bert Waits. Their efforts have shown that significant student understanding of mathematical concepts is achieved by a combined instructional approach which fully uses the graphing capabilities of calculators and computers. Classes are taught in specially equipped classrooms which provide instructors with demonstration computers and the necessary projection capability for student viewing. Students are required to use graphing calculators for in-class explorations and out of class problem assignments.

The M151 calculus section using Mathematica^TM, is being taught by Bill Davis, Holly Hirst, and Jim Braselton. The course uses Ohio State modifications of materials developed by H. Porta and J. Uhl at the University of Illinois. Course Iessons are arranged in computer notebooks which students work through, modify, and experiment with in a special computer Laboratory. The software package provides a powerful graphing and symbolic manipulation capability available to students in a very friendly, even conversational, form. We hope that, with this technological assist, the standard calculus course can be upgraded to give deeper insights into the calculus than was previously possible.

A different computer algebra system, Maple, is being used in the one-quarter survey course in calculus for non-science liberal arts majors (MI17). This course touches both differential and integral calculus. The weekly instructional format is traditional for large enrollment classes-three lectures given by a faculty member and two recitations conducted by graduate teaching associates. However, students now spend one of the recitation sessions in a microcomputer lab working on calculus problems using Maple as a "Gaussian pencil" to carry out calculations that allow them to explore different potential avenues for solutions. The availability of Maple to students makes it possible to spend less time drilling on mechanics and more time on exercises that require higher level analytic thinking. Interestingly enough, the instructional support needed to make Maple viable as a teaching tool has been provided by Ohio State graduates, William Bauldry, Joseph Fiedler and Wade Ellis. Ellis is coauthor of a book that introduces the new user to Maple. Bauldry and Fiedler are the authors of the calculus problems book used as part of the microcomputer lab recitations. Bauldry, an Assistant Professor at Appalachian State University, is currently visiting Ohio State and is teaching the course this Autumn Quarter.

The MATLAB system is a software tool used for numerical matrix computations and applications. It can be thought of as an extremely powerful "calculator" which can diagonalize a matrix with a few keystrokes, or as a specialized computer language. MATLAB is powerful enough for serious research projects and simple and intuitive enough to be used in an introductory linear algebra course. Currently at Ohio State, the software is being used in the applied linear algebra sequence for undergraduates (Math 571-572) and in the modeling course (Math 578). It has also been successfully used in several workshops for in-service secondary mathematics teachers. Advanced uses of MATLAB are being discussed in an actuarial science seminar on the Theory of Graduation and in a joint seminar with the Department of Electrical Engineering.

MATLAB differs from Mathematica^TM and Maple in that it is strictly a numerical system, with no symbolic manipulation capabilities. On the other hand, it is much easier to use than these two other packages, and it operates on smaller and cheaper computers. The integration of technology in the teaching and learning of mathematics is finding its way into classrooms at the collegiate level across the country. Ohio State, because of its unique situation in terms of size, is an important contributor to the national scene.

Graphing calculators are integrally used in M148

Photo by Terry Swagger

Comments from the Chair

Back to school! Autumn Quarter has begun with 50,000 plus students having once again descended on our campus, spilling over sidewalks and sunning on the Oval. There is good news in that the quality of entering students is on the rise (this year the average ACT score for entering freshmen may exceed 22.5). Our highest level freshmen honors mathematics course has an enrollment of over 100 students. Last year, that course enrollment was 46. Moreover, student retention rates are much improved. A few years ago, 8000 freshmen entered Ohio State each year. This year the entering class will be only 6200, yet overall enrollment remains the same. With improved student quality has come a modest surge in enrollment in the mathematics major program and a quantum leap in the Actuarial Science major. This latter is attributable in large part to a highly publicized study touting Actuarial Science as the most desirable occupation ("mathematician" came in fourth in that study -- not bad!). Awaiting new majors is a revised mathematics curriculum, formulated in the context of a university-wide curriculum review. The revised program is designed to emphasize the underlying logical structure of mathematics while increasing the breadth of exposure to a variety of mathematical subdisciplines. Playing the key role in implementing the curriculum is a faculty grown this year to number 100, augmented by several visiting mathematicians. As we faculty gear up for another year (and try to shake off the dispiriting effects of past encounters with the all too numerous students whose principal intellectual query seemed to be "Is it on the exam?"), a little encouragement from our graduates can go a long way. I was most pleased a few weeks ago to get a telephone call at home from a graduate who studied algebra with me for a few quarters in the early 70's. In town on business, he took the opportunity to say thanks for the time and energy I had spent on his, and others', behalf. A brief encounter, but one that encourages me to renew my commitment to students this year. Surely each of you recalls one faculty member (or more) who was particularly helpful in smoothing your academic way at Ohio State. Why not drop a line (or phone, or stop by if you are in Columbus) to say thanks? It would be a valuable contribution in building the enthusiasm level necessary to sustain an outstanding mathematics program at Ohio State.

AMS/MAA Joint Summer Meetings

The joint Summer Meetings of the American Mathematical Society and the Mathematical Association of America will be held on Ohio State campus August 8 - 11, 1990. The meetings will celebrate the 75th Amniversary of the founding of the Mathematical Association of America with a special day of activity on Wednesday, August 8. The Association was founded, and held its first meetings, on Ohio State's campus December 30-31, 1915. Commemorative plaques will be dedicated at Page Hall and the Department of Mathematics. All alumni of Ohio State are encouraged to make a special effort to attend these meetings for a grand reunion.

Cleary, Patricia, M.A. '87, currently on the staff at Shippensburg University, Shippensburg, Pennsylvania.

Dachner, David, B.A. '69, J. D. '72 (College of Law), currently an attorney in Columbus, Ohio.

Donaldson, William, B.Sc- '85, MAS '87 (Statistics), currently employed by U. S. Department of Agriculture, Washington, DC.

Ficocella, Mary Ellen, B.A. '64, B.Sc. '66, M.A. '71, presently serving as a substitute teacher in secondary mathematics and science.

Kisielewski, Karen A., M.Sc. '85, M.Sc. '86 (Computer Science) and Brian R. Link, M.Sc. '84, M.Sc. '85 (Computer Science), married aad currently employed as Principal Members of Technical Staff of Siemens Public Switching Systems in Boca Raton, Florida.

Lifshin, Syd, M. Sc. '78, M.Sc. '79 (Computer Science), currently a Technical Support Manager with IBM, Columbus.

Lipp, David A., B. Sc. '65, M.B.A. '67, currently President, Market Horizons, Inc. Jacksonville, Florida.

Mahoney, Carolyn, PhD '83, currently on the faculty at Denison University, has accepted a full professorship on the "founding faculty" of the newly established California State University at San Marcos.

Nord, John and Gail, both received the M.A. in '85, celebrating the birth of a daughter Katie Marie, on July 7, 1989.

Showalter, Carolyn Dalsey, B.Sc. '72, M.A '82, currently an Assistant Professor of Mathematics at Ocean County Community College, Toms River, New Jersey.

Thiel, David W., B.Sc. '80, currently a First Officer, DC-8, with the Flying Tigers.

Weber, Robert L, B.A. '68, retired as a Statistician III from the Ohio Bureau of Employment Services, Division of Research and Statistics (having compiled a record by working for 5 different departments in the State of Ohio by age 31), formerly taught Business Statistics st Central Wyoming College (Riverton).

White, Donald, B.Sc. '80, M.Sc. '82, PhD '86 (Yale), formerly a visiting Assistant Professor at the University of Illinois at Chicago, currently an Assistant Professor of Mathematics at Kent State University.

Send Me Your Ideas!

Mathematics Awareness Week, national focus on mathematics organized by the Joint Policy Board on Mathematics, is scheduled for the period April 22-28, 1990. This year the theme is Communicating Mathematics. Many of you, the department's alumni, are in positions where communicating mathematics to other publics is an important ingredient. Share some of your experiences with me so we can make our current undergraduates more aware. Send your contributions to Jim Leitzel, Editor, Math Matrix, Department of Mathematics, 231 West 18th Ave., Columbus, Ohio 43210-1174.

The Rasor-Bareis-Gordon Competitions in Mathematics

The Department of Mathematics at Ohio State sponsors three contests with monetary awards: the Rasor Contest for Freshmen, the Bareis Contest for Sophomores and the Gordon Contest for Juniors and Seniors. The examination taken by a student is determined by what mathematics courses that student has taken.

The Rasor Scholarship Examination was first given in 1947. Professor Samuel Eugene Rasor (1873-1950) received his B.S. in 1898 and M.A. in 1902 at Ohio State, and earned an M.S. in 1906 at the University of Chicago. He also studied at the University of Berlin in 1910-11. He continued his career of teaching and service at Ohio State for nearly fifty years, being promoted to Professor in 1912 and Professor Emeritus in 1943. He was immediately recalled to teach mathematics to the large number of army trainees on campus. Professor Rasor was an active member of the AMS and the MAA and was the author of three textbooks in mathematics. In 1943 Professor and Mrs. Rasor established the Rasor Scholarship in mathematics with a gift of $1000. In 1946 they made an additional gift to the University to provide a scholarship of $60 to be awarded each year on the basis of a competitive written examination among freshmen students.

The Grace M. Bareis Mathematical Prize was first given in 1949. Grace Marie Bareis (1875- 1962) received her A. B. from Heidelberg College (in Tiffin, Ohio) in 1897, did graduate work at Bryn Mawr College and Columbia University. She came to Ohio State in 1906 and earned a doctorate in mathematics in 1909. She was an Assistant Professor in 1908 and became an Associate Professor Emeritus in 1946. She continued to teach for two years after retirement because of the shortage of mathematics instructors to teach the returning veterans. In 1948, Dr. Bareis gave $2000 to the University for a fund to award prizes on the basis of written contests open to sophomores at Ohio State. The first of these contests was held in 1949.

The Kate Deterly Gordon Fund was established in 1972 with a contribution made by Ruth Gordon in memory of her mother. Income from the fund was designated for the higher education of individuals, especially those talented in mathematics. Because of high interest rates in the 1970's, a surplus of money accumulated in the Gordon Fund, and in 1980 the department instituted the Gordon Prize Exam for upper division students, to parallel the Rasor-Bareis examinations.

There have been mathematics competitions every year since 1947, except for 1970 when the University was closed. The total amounts of the awards continued at $60 for the Rasor Scholarship and $120 for the Bareis Prize until 1971 when the amounts began to increase each year. In 1989, over $1500 in prize awards was distributed, with $250 awarded for first prize, $150 for second prize and $100 for third prize in each of the three contests.

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 13. In a certain multiple- choice test, one of the questions was illegible, but the choice of answers was clearly printed. Determine the true answer(s), if the choice was:

(a) All of the below.

(b) None of the below.

(c) All of the above.

(d) One of the'above.

(e) None of the above.

(f) None of the above.

Problem 14. Disect the hexagon ABCDEF pictured into three pieces which can be reassembled to form a square. (From the Pi Mu Epsilon Journal.)

SOLUTIONS TO PREVIOUS PROBLEMS

PROBLEM 10. Let the function f(x) be defined by f(x)=log₁₀(log₁₀(exp(exp x))). Using a scientific calculator, it seems that if we start with any number and apply the function f over and over, the results converge to a number -0.64029. Evaluate this limit in closed form.

Solution by Brian R. Scalley (Mayfield Heights, Ohio). Use the identity log₁₀(x)=ln(x)/In(IO) to show that f(x) - A x + B, where

Department News

New faculty in the department this Autumn Quarter include: Anthony Bloch (PhD,Harvard), applied mathematics; Randall Dougherty (PhD, Berkeley), logic; Roy Joshua (PhD, Northwestern), algebraic geometry; Akos Seress (PhD, Ohio State), combinatorics. Saleh Tanveer (PhD, Caltech), applied mathematics; and at the Marion Regional Campus, Yong Kang Huang (PhD, Ohio University), functional differential equations and boundary value problems.

Bryan Johnson and Julie Shalack, two new entering graduate students, are recipients of University Fellowship Awards. Bryan did his undergraduate work at the College of Wooster and Julie did hers at Rutgers University. In July and August, members of the department have received grants and awards totalling $458,395. Most of the support funds came from the National Science Foundation.

One of the exciting new ventures in the department this year is the Graduate Student Seminars. They began late in Spring Quarter, continued through the summer, and are scheduled for the rest of this year. These seminars are designed to acquaint graduate students (as well as undergraduates and the faculty) with current research topics in mathematics and the dissertation results of students close to graduation. They are planned, organized, and implemented by the graduate students. Taking leadership in this enterprise are John Blanchard, James Braselton, and Karen Reinhold-Larsson.

Frank Carroll has been appointed to the University Excellence Committee. This 15 member committee was established by President E. H. Jennings to address ways that Ohio State's quality and leadership in public higher education can be better communicated to various publics.

Frank Demana, Joan Leitzel, Jim Leitzl, and Bert Waits were invited participants and speakers the Sixth International Congress of Mathematics Education held in Budapest, Hungary, August, 1988. James Schultz is on leave this year and has spent part of the time at the University of Georgia. In addition, he has travelled to and given several presentations in England, Scotland, Holland, and Germany.

Ulrich Gerlach was among the 10 finalists for the 1988 Outstanding Teaching Awaid given by the Colleges of the Arts and Sciences.

Arnold Ross, emeritus professor and former chair of the department continues active in developing programs for gifted students. In January, he gave a special session the Winter Meetings of the AMS-MAA in Phoenix, AZ and then went on to give a presentation, Creativity in the Mathematical Sciences, at the Annual Meeting of the American Association for the Advancement of Science in San Francisco.

Yuji Kodama, Boris Mityagin, and Ted Scheick, faculty members in Applied Mathematics, have been involved in discussions with engineers from the Electrical Research Section and the System Planning and Information Systems Department of American Electric Power to explore the possibilities of mutual collaboration on common problems of interest.

Dijen Ray-Chaudhuri served as the organizer for the Design and Coding Theory Section of the Applied Combinatorics Year at the Institute for Mathematics and its Applications. He is presently editing the Proceedings of the more than 50 presentations given in the workshops. More than 100 mathematicians and statisticians participated in the program.

Karl Rubin gave an invited addres and served as coorganizer of a Special Session on L-functions and arithmetic at the AMS Regional Meeting held at the College of the Holy Cross in Worcester, MA in April 1989.

Distinguished Visiting Professor: J. P. Bourguignon

The Department, Graduate School, and the University were pleased to host Jean-Pierre Bourguignon as a University Distinguished Visiting Professor during Spring Quarter, 1989. Professor Bourguignon is Professor of Mathematics at École Polytechnique and Directeur de Recherche at the Centre National de la Recherche Scientifique in Paris. His mathematical training includes degrees from the École Polytechnique and the University of Paris. His research deals with systems of non-linear Partial Differential Equations occurring in Differential Geometry and the connections between Geometry and Theoretical Physics. In particular, his current work centers on efforts to understand more fully recent developments in Quantum Field Theories and their relationship to Geometry. He describes these interests as falling under the general heading of "Global Analysis." In addition to actively participating in various aspects of department life during his visit, he presented a lecture titled "Drumatic Mathematics" in the Graduate School's Spring Quarter Lecture Series.

NATO Advanced Study Institute Held at Ohio State

More than 150 mathematicians, physicists, and graduate students in these areas from around the world gathered at Ohio State from May 22 to June 3 to attend a North Atlantic Treaty Organization advanced study instute. The conference topic was Orthogonal Polynomials and their Applications. Paul Nevai, professor at Ohio State, served as Director. NATO advanced study institutes are designed to disseminate advanced knowledge not yet part of the curriculum and foster international scientific contacts. Nevai notes that, while more than 50 such seminars are conducted each year, it is rare that NATO sponsors such a seminar in the United States. Few of the seminars address mathematical topics. The subject of orthogonal polynomials was regarded as a mathematical subject of primary importance and Ohio State's mathematics department was recognized as a prominent place to organize and host the event. Principal speakers included participants from Belgium, France, Germany, Hungary, and the Netherlands. There were panels and discussion sessions on a variety of topics such as the History of Orthogonal Polynomials, Applications of Orthogonal Polynomials in Coding Theory, Communications Engineering, Difference and Differential Equations, Signal Processing, Solid State Physics, and Symbolic Computer Algebra. Fifteen faculty and ten graduate students from the department were actively involved in the conference proceedings.

Workshop for College Faculty

In mid-August, Ohio State hosted 70 mathematicians from 59 colleges and universities at a three day workshop for college faculty. The participants represented 32 states and one foreign country. This was the second annual such summer workshop on the effective use of technology in the teaching of calculus and precalculus mathematics. It was co-sponsored by the Department of Mathematics and the Addison-Wesley Publishing Company. The co-organizers of the event were Frank Demana, Bert Waits, and Tom Ralley. Principal activities during the three days were workshops and demonstrations on how to use graphing calculators and computers to enhance the teaching and learning of mathematics. The content focus of the sessions was provided by the technology intensive precalculus textbook College Algebra and Trigonometry, A Graphing Approach by Demana and Waits. Computer software instruction included Master Grapher, MATLAB, and Mathematica^TM.

The third annual Workshop on Using Technology to Enhance the Teaching of Calculus and Precalculus Mathematics will be held at Ohio State, August 12-13, 1990. This is immediately following the AMS/MAA Summer Meetings' to be held at Ohio State (see related article in this issue). The deadline for applications for the Workshop is June 1, 1990. For application forms or additional information, contact Bert Waits and Frank Demana, Department of Mathematics, The Ohio State University, 231 West 18th Ave., Columbus, Ohio 43210-1174.

Spring Quarter Picnic Just prior to the opening of Summer Quarter, the departmen hosted a picnic for all new and returning graduate students, staff, faculty and their families. More than 200 people enjoyed good food and fellowship along the banks of the Olentangy River at Drake Union shelter house.	Jim Leitzel (left) and Joe Ferrar do the grilling while Tim O'Neill arranges his plate and Kai Deng waits for service.
Kim Washington (left) and Sharon Rivers work at mixing the punch.	Kevin Maxwell (left), Darrell DeLoach, and Sheryl Stitt, second year graduate students, work on their name tags.
Photos by Karen E. Stein

[0]