In the fall of 1971 the two-day meeting of the Ohio Section at Ashland College was a "theme meeting", devoted entirely to a series of invited lectures by three prominent differential geometers. The main thrust of the lectures was to bring to the attention of mathematics faculty the nature of modern differential geometry and the desirability of integrating it into the undergraduate curriculum. The extent to which the conference resulted in an increased emphasis on differential geometry in Ohio's colleges and universities is unknown, but the theme meeting turned out to be the spark that ignited a chain of events culminating in a complete innovation in the annals of the Association - the Section Summer Short Course.

In the interim between the fall, 1971, and spring, 1972 meetings the Section's chairman-elect, who was due to assume the chairmanship following the spring meeting, accepted a position outside of Ohio. At the spring meeting Professor Will Hahn (Wittenberg University) was elected to fill the vacancy created by the chairman-elect's move. One of his first discoveries at being thrown into the breach without the usual year's period of training was that his predecessor, Professor Elwood Bohn (Miami University) had, during his incumbency, rejuvenated the various Section committees. (See the chapter on history of committees for details.)

Now the seemingly unrelated events of a meeting on differential geometry and the rejuvenation of committees came together in a strange way. Along with some other Section members, Hahn had been sold by the experts on the importance of differential geometry in the undergraduate curriculum, but he also realized that his own meager knowledge of the subject was a deterrent to his doing anything about it. Hence Problem #1: How could faculty members, particularly those at undergraduate institutions, be helped to extend their knowledge of differential geometry (or more generally, of any area or mathematical topic)? At the same time he was concerned about Problem #2: What constructive things could the newly revived section committees be doing to keep from lapsing into inactivity?

Hahn then reasoned that Problem #2 could be partially solved by getting some committee(s) involved in seeking a solution to Problem #1. In November, 1972, at the Toledo meeting of the Section Executive Committee, he talked about the problem of "faculty retreading" and suggested that the Ohio Section look into ways to help with the continuing education of its membership. After some discussion, the Executive Committee voted to refer the matter to its Committee on Cooperation between Colleges and Universities (COCCU) and charged COCCU to make recommendations at the April, 1973, meeting of the Executive Committee.

From this time on things moved rapidly. COCCU accepted the challenge with enthusiasm and was able to announce to the Executive Committee on April 13, 1973, that Kent State University had already agreed to host a one week summer short course in Numerical Analysis in June, 1974, and that Ohio State University was considering offering a similar course in Combinatorics during the same month. In each case the plan was that the faculty of the host institution would provide the instruction and make housing and other arrangements for participants. There would be no tuition or fees, other than the cost of instructional materials, required of participants. Thus, initially, the Ph.D.-granting institutions were in a real sense offering their expertise and facilities as a service to the Section. Although this point of view has since been abandoned, and other changes have been made in the short course format, it is interesting to note for the record how it all began.

The Executive Committee gave the go-ahead to COCCU to proceed to work out the details of the inaugural short courses with Kent State and Ohio State. On the next day Chairman Hahn gave his chairman's address on the subject "The Retread Problem," in which he directed the attention of the entire membership to the problem and tried to state the case for the Section's becoming involved in its solution.

During the 1973-74 academic year COCCU, Ohio State, and Kent State worked out and publicized details of the initial short courses. The Combinatorics course at Ohio State took place June 10-14, 1974, with a registration of 40 participants. This was followed June 17-21 by the Numerical Analysis course at Kent State University, with a total of 20 registrants.

Every summer since 1974 the Section has sponsored a short course of three to five days' duration. The complete list, with dates, locations, topics, and attendance, is found in Appendix D.

Although the short courses were originally thought of as vehicles for upgrading the competence of Ohio Section members, from the very beginning they have drawn participants from a much wider geographical area. As might be expected, nearby states like Pennsylvania and Michigan are usually represented, but participants have also come from such diverse places as Massachusetts, New York, South Carolina, Puerto Rico, Florida, California, Minnesota, and Canada. On some occasions the out-of-state participants have substantially outnumbered the Ohio Section participants. This seems to indicate that many mathematicians really do want to know what is going on outside of their narrow specialties, and that this desire knows no geographical limitations.

Another bit of evidence of this "desire to know" is seen in the fact that at least a dozen other MAA sections have followed Ohio's example by setting up short courses of their own, and others are in varying stages of planning such workshops. In this activity Ohio has unquestioned priority, but it is glad that the idea has been appropriated by others.

Even though the short course program has been in existence for a relatively brief time, it is interesting to observe the wide range of subject matter that has been addressed. It is also clear that, intentionally or not, it has been predominantly those branches of mathematics that have crept (or "stormed") into the curriculum more recently that have been studied. One might pose the hypothesis that, if short courses continue for another few decades, the fashions in undergraduate mathematics curricula may well be traceable by an examination of the titles to Ohio's summer short courses!

Following the success of its first ten short courses, in 1983 the Ohio Section inaugurated a bold variant of the previous one-week courses. This was a sequence of three annual three-week courses designed to qualify mathematicians to teach the first few courses in a modern computer science curriculum at the undergraduate level. The 1983 course was on Data Structures. In spite of some initial concern about whether the length of the course and its substantially larger cost for participants would be problems, the maximum planned enrollment of 30 - necessitated by space and equipment limitations - was quickly exceeded, and a number of applicants had to be turned away. Concurrently with the first week of this three-week course at Denison University, a traditional short course on Introduction to Factoring and Primality Testing at Kent State University enrolled 46 participants.

The Data Structures short course was followed in 1984 by a course in Systems Programming, also held at Denison. In 1985 the third course of the sequence, Operating Systems, was held at Bowling Green State University, while a second round of the sequence began with Data Structures again at Denison. It was during these same years that the Institute for Retraining in Computer Science (IFRICS) was in full swing, with 9-week courses at Clarkson University and, later, Kent State. Unfortunately, about the same time as the computer science retraining movement peaked, nationwide enrollments in computer science fell off drastically. As a result, the second round of Ohio Section computer science retraining courses was not completed.

In the late 1980's national attention was focused on the state of elementary and secondary school mathematics. The Ohio Section, in cooperation with the Ohio Council of Teachers of Mathematics, decided to sponsor short courses for secondary school mathematics teachers. The first of these was held the last week of June, 1988, at Muskingum College, under the leadership of James Smith and Janet Roll. The following summer Richard Little directed a two-week "Math Camp for Teachers" at Baldwin-Wallace College. Topics covered in these short courses included geometry, discrete mathematics, and graphing with hand-held calculators and computers. Fifteen teachers were enrolled in 1988 and thirty in 1989. In 1990 a short course, focusing on the NCTM Curriculum and Evaluation Standards for School Mathematics was offered at Muskingum College, with fourteen middle school teachers in attendance.

Short courses were not planned as money making ventures, and costs to participants have always been kept low. Nevertheless the short courses have turned out to be profitable for the Ohio Section, because registration has usually exceeded the minimum number needed to break even. Also, a grant from GTE helped to fund some of the computer science retraining courses, and the short courses for school teachers received partial funding from the Ohio Board of Regents.

Two of the short courses have resulted in publications as MAA Notes. Volume 4 in that series, Notes on Primality Testing and Factoring, is based on the 1983 short course taught by Carl Pomerance. Using History in Teaching Calculus, by V. Frederick Rickey, is due to appear soon. This latter monograph is an outcome of the 1986 Ohio Section short course, which has also been offered in the popular MAA minicourse series at national meetings.

The success of short courses has spawned another phenomenon, the micro-course, at Ohio Section meetings. Modesty prevents us from claiming this as an Ohio innovation, for several other sections had implemented micro-courses before 1985. The duration of a micro-course is typically about two hours, and it precedes or follows the regular program of a fall or spring Section meeting. Topics have spanned the old and new, including computer simulation, computer algebra systems, graphing calculators, NSF grant preparation, and calculus. Attendance usually ranges from 20 to 40, reinforcing once more the notion of a "desire to know" on the part of Ohio mathematicians.

Copyright 1990, The Ohio Section, MAA, All rights reserved.