EPADEL:A Semisesquicentennial History, 1926-2000

The first public notice of the Executive Committee’s express interest in sponsoring a second meeting each year occurred in the section’s February 1976 newsletter. An item titled “Special spring meeting” announced, “Plans are brewing for a special session on the use of mathematical models in undergraduate teaching Saturday, April 10, at Gettysburg College. Carl Leinbach (Gettysburg) is chairman of the planning committee. Other members are Jerry Porter (Penn) and Eugene Klotz (Swarthmore.) Professor Leinbach is willing to organize some special entertainment for families of members. If enough interest is shown, he will plan a bus tour of the battlefield conducted by a member of the Gettysburg College History Department.” Although those plans did not materialize exactly, the idea of holding a spring meeting in addition to the annual fall meeting got off to a good start.

The meeting began with welcoming remarks by Leonard Holder, the dean of the college and former chair of the mathematics department. Next came a panel discussion on the question, “What do we mean by mathematical modeling?” Moderated by Jerry King (Lehigh), the panelists were Fred Roberts (Rutgers) and Gerald Thompson (Carnegie-Mellon). The two panelists delivered invited lectures after that. Before lunch Thompson spoke on “Combinatorial decision – Problem applications and solutions.” After the meal Roberts described “Interval graphs, traffic lights, and ecological phase space”. Samuel Merrill (Wilkes) followed that with a third invited lecture, “Citizen voting power under the Electoral College system.” The day ended with another panel discussion, this one devoted to “Experiences in the teaching of courses on mathematical modeling.” Eugene Klotz (Swarthmore) was the moderator, while Gene D. Chase (Messiah) and Randall King (Gettysburg) were the panelists.

The format of spring meetings began to evolve the next year when the section met at Kutztown. This time the gathering was called a Spring Symposium; the theme was “Structured Programming”. Although the March 1977 newsletter did not announce the program, it did list three sessions to be covered by the program that would run “from 8:00 or 8:30 to 3:00 or 3:30”:

There were four organizers: John Beidler, Ranan R. Bannerji, Wallace Growney, and John Koch. Dalton Hunkins was in charge of local arrangements. The newsletter also carried an editorial whose title asked, “Why should mathematicians be interested in structured programming?” The question was answered by listing three benefits derived from teaching proper programming:

Beginning with the 1978 meeting at Ursinus, and continuing ever since, the new annual gathering was called the Spring Meeting. Its format resembled a typical fall meeting – it began with welcoming remarks and continued with three speakers. However, the speakers delivered their lectures before lunch, which was served at the unusually late time of 1:30. The final speaker, whose talk was scheduled an hour later, was “to be announced – speaker from the area of Computer Science.” The program chairman for the meeting was Leslie K. Arnold of Daniel H. Wagner Associates. Although no general theme for the meeting was stated officially, one can deduce from the topics of the lectures that the theme was applied, or even industrial, mathematics. The three announced speakers, with affiliation and title are:

The meeting at Penn’s David Rittenhouse Labs the next spring, under program chair Gerald J. Porter, was the first one sponsored under the section’s new EPADEL name. The announced theme was computer graphics, with one- hour morning sessions on graphics hardware and graphics software. Next came lunch in the Egyptian Gallery of the University Museum. The two-hour afternoon session was devoted to applications of computer graphics in undergraduate mathematics education.

The 1980 meeting at Cedar Crest College in Allentown was devoted to combinatorics. Two speakers from the AT&T Bell Laboratories in Murray Hill, NJ, addressed this theme in the morning session, Neil Sloane and Jessie MacWilliams. The titles of their presentations were “Hadamard, Hotelling, and Harwitt: A new application of some old mathematics,” and “A survey of coding theory,” respectively.

Although the 1981 meeting was ostensibly devoted to computational geometry, the lectures reveal a much broader theme. Initially Philip J. Davis was scheduled to open the meeting with a talk on computer graphics but due to unforeseen circumstances he was replaced by Sandra Fillebrown, who spoke about cryptography. Next, Drexel’s William J. Gordon spoke about “Computer graphics as an aid to problem solving in science and engineering”. His colleague, Oleh J. Tretiak, from the Department of Biomedical Engineering, followed lunch with a talk on tomography, a field whose role in CAT scans was only beginning to surface at the time. In the final presentation, cleverly titled, “Is \(\mu\)-math the \(\nu\)- math?” Penn’s Albert Nijenhuis demonstrated “a symbolic manipulative program capable of performing symbolic differentiation, integration, and other feats on a digital computer.”

The program at the 1982 meeting reflected the advantage of the flexible format over the traditional fare at fall meetings. The theme was curricular interfaces, a term that was defined in the first talk of the day, when Anthony Ralston (SUNY-Buffalo) proposed replacing calculus as the first course in the standard curriculum for mathematics majors by a course in discrete mathematics. Next, James P. Crawford (Lafayette) provided a 15-minute rebuttal by raising some concerns about such a radical change. Following that came a 30-minute “Audience discussion” moderated by Carl Leinbach (Gettysburg). The final part of the morning session featured a lecture by Eugene M. Luks (Bucknell) titled, “Recent advances in graph isomorphic testing: An application of group theory in computer science”. Like the morning session, the afternoon did not adhere to the usual format of two one-hour talks. Instead, there was a “Microcomputer medley” of five 30-minute presentations on “the use of microcomputers and intelligent terminals in the teaching of undergraduate mathematics.” Table 8.3.1 lists the five speakers, their affiliations, and the titles of their presentations. Some presentations were conducted concurrently so the audience could view the demonstrations up close and gain hands-on experience with the materials; some were also repeated.

The morning and afternoon formats did not present the only variations from the usual program. Instead of the book display, the Gettysburg duo of David Flesner and Carl Leinbach conducted an information exchange concerning computer science and mathematics programs.

The next two meetings were conducted in a manner similar to the standard format at fall meetings. The theme of the 1983 meeting, “Mathematics and artificial intelligence”, was addressed in two lectures in the morning and two in the afternoon. Only three of the talks were announced, however – Aravind Joshi (Penn), “Grammatical representations in natural language processing: Some mathematical results,” Jack Minker (Maryland), “Logic and its uses in artificial intelligence and databases,” and Casimir Kulikowski (Rutgers), “Expert systems”.

The theme for the 1984 meeting was “Mathematics and communication theory”. The morning session began after a welcome by the host institution’s Dean of the Graduate School, Jerry King. The two invited lectures were Chester Salwach (Lafayette), “Codes that detect and correct errors,” and Andrew Odlyzko (Bell Telephone Laboratories), “Public key cryptography.” A demonstration of a Hewlett-Packard processing system occurred between these two lectures. The afternoon session featured two lectures, Walter Hiver (Hewlett- Packard Corp.), “Computer system performance evaluation,” and Jack Wolf (UMass), “Mu Hiaccess communications.”

The 1985 meeting took advantage of the flexible format in several ways. For one, a social hour was held at the historic Hotel Magee in Bloomsburg on Friday night. For another, Garrett Birkhoff reminisced publicly about his life in mathematics over lunch on Saturday. But the largest deviation was the four-hour workshop on “Discrete algorithmic mathematics” taught by Swarthmore’s Steven Maurer. The four hours were divided evenly into morning and afternoon sessions.

The format of the 1986 meeting was also different. The first lecturer, M. Zuhair Nashed (Delaware), reflected the day’s theme on numerical linear algebra in his talk, “Computational methods for linear least squares problems”. However, the rest of the morning session and the entire afternoon session consisted of workshops run by three EPADEL presidents. Drexel’s Howard Anton presented a 21⁄2-hour workshop on the linear-algebra software package he developed, LINEAR-KIT. Two other one-hour workshops ran concurrently – David Hill (Temple), “An introduction to PC-MATLAB”, and Bernard Kolman (Drexel), “Matrix algebra for the Macintosh”.

The main part of the program for the 1987 meeting consisted of three lectures and a panel discussion on the theme of actuarial mathematics, with all participants hailing from the EPADEL area. The first speaker was Roy G. Shrum, an actuary and a vice-president of the Pennsylvania National Casualty Insurance Company, who had passed two actuarial examinations while still an undergraduate student at Penn State. Shrum had, in fact, passed all ten exams before delivering his presentation, “A day in the life of an actuary”. The next two speakers represented emerging academic programs at local universities. Bonnie Averbach, the director of the program in Actuarial Science at Temple, spoke about “Life contingencies”. She was followed by Neil Vance, from Penn’s Department of Insurance, a specialist on the use of Fourier analysis in insurance problems, whose lecture was titled “Approximating total claims of a life insurance company”. The panel discussion aimed to answer the question, “How do you prepare to become an actuary?” Moderated by Brian Hearsey, the director of Lebanon Valley’s acclaimed actuarial program, the panel consisted of recent graduates from liberal arts colleges who had pursued careers in actuarial science. While the format of the program at the spring 1987 meeting might have been fairly standard, the day did not end that way. The last item on the agenda treated attendees to a reception at Moravian’s Payne Gallery where they could view an exhibit titled “A mathematician views M. C. Escher,” hosted by our section’s Escher specialist, Doris Schattschneider.

The program for the 1988 meeting consisted of four lectures on the theme of the day, operations research. Shippensburg’s Fred Nordal, the recipient of a Virginia Tech Ph.D. in operations research, began the day with a talk titled, “Origin, history and some applications of operations research”. He was followed by George Freestone, the manager of operations research for chemical systems development and services at Air Products and Chemicals, Inc. His talk on “Logistics planning for chemicals at Air Products” dealt with the application of linear programming to customer sourcing and product mix problems in the chemicals business. Next, Jeffrey Lagarias of AT&T Bell Laboratories provided EPADEL members with an updating on very recent developments in his lecture titled, “Karmarkar’s linear programming algorithm and nonlinear programming”. The final speaker, Temple’s Leon Steinberg, spoke on “Simulation and the Monte Carlo method”. He based his remarks on the history and application of Monte Carlo methods from his vast years of experience as a mathematical consultant.

Like the 1987 spring meeting, the 1989 version, whose theme was “Computer algebra systems”, consisted of three invited lectures and a panel discussion, this one devoted to “An introduction to computer algebra systems and their use in undergraduate mathematics education”. In the first talk, “Computer algebra using the HP28S,” John Kenelly described his department’s use of Hewlett Packard hand-held calculators, emphasizing the fact that these very powerful calculators placed symbolic calculation in the palms of his Clemson students. Next, Paul Zorn (St. Olaf) emphasized mathematical content and pedagogy rather than technical matters in his lecture titled, “Mathematica in undergraduate mathematics”. Zorn stated, “Although it seems obvious that computing should be a powerful force for change, so far that force has proved eminently resistible. Elementary calculus courses, for example, have hardly changed after 20 years of experiments with numerical computing. Symbolic computer systems, such as Mathematica, will be harder to ignore.” The purpose of the day’s remaining talk, “Computer algebra systems: Issues and inquiries,” by Warren Page (NY City Technical College) was “to initiate dialog and raise awareness of the many critical issues related to the introduction of CASs into the mathematics curriculum.”

In his president’s message introducing the 1990 spring meeting, David Hill noted that the national MAA was about to embark on a series of new programs at the same time it looked to the past to celebrate the Association’s semisesquicentennial anniversary. He wrote, “Within EPADEL we hope to follow suit ... the spring meeting offers an opportunity for you to bring students and high school math teachers. The morning program on GEOMETRY should be especially appealing to a wide audience.” While that morning session was indeed appealing, in retrospect its introduction of the Visual Geometry Project was historic. The Project, under the direction of Eugene Klotz (Swarthmore) and Doris Schattschneider (Moravian), had been created in response to the widespread concern for the lack of 3-dimensional geometry in the schools. The former section presidents wrote, “Our multi-media approach seems of much broader applicability than our target high-school geometry population, and in particular some of our materials should be of use in a variety of college courses. In our presentation we will demonstrate some of the materials we have under development, including a videotape, some 3-dimensional models, and a computer program.”

The presentation by Klotz and Schattschneider was followed by a computer- animated video by Eiji Hirai from Swarthmore College, and two lectures, the first by Cynthia Schmatzried on “The relationship of pre-college math to college mathematics: What should we be teaching secondary teachers?” and the second by Ann Fetter and Cynthia Schmatzried on “Hands-on models”. The final part of the morning session was a demonstration of The Geometer’s Sketchpad by its developers, Nicholas Jackiw and Eugene Klotz. The Geometer’s Sketchpad has been highly successful and is currently available commercially from Key Curriculum Press. (Incidentally, Key Curriculum’s president, Steven Rasmussen, holds two Temple degrees, a B.A. in mathematics in 1976 and a masters degree in mathematics education in 1978.)

The afternoon session at the 1990 meeting consisted of two lectures – Paul Kumpel (SUNY - Stony Brook), “Untangling a bicycle chair”, and Andrew Hume (AT&T Bell Laboratories), “Folding polyhedra and other computer databases”.

The following year president Hill wrote, “The theme of this year’s spring meeting is Decision Sciences ... While there is significant movement to reform our calculus instruction format, there is ample reason to believe that a similar effort in elementary statistics instruction should be initiated at a variety of levels.” William E. Rosenthal addressed the same issue in his opening lecture, “No more sadistics [sic], no more sadists, no more victims”, in which he called for a radical reconstruction of the standard college-level elementary statistics course. Besides being a member of the mathematics department at Ursinus, Rosenthal was the co-coordinator of the College’s women’s studies program. In the final talk of the day, Temple statistician Janos Galambos, who had lectured on all continents except Antarctica, spoke on his specialty in a lecture titled, “Bonferroni-type inequalities: Fatigue failure of metals and the twin-prime conjecture”. The two lectures between Rosenthal and Galambos were by James M. Landwehr (AT&T Bell Laboratories), “What should be in an introductory statistics course?” and Fred S. Roberts, “Meaningless statements”.

The 1991 meeting also featured a new element at spring meetings, student paper sessions. Deborah Frantz (Kutztown) moderated two one-hour sessions that ran parallel to lectures given in the morning and the afternoon. The following year Lamarr Widmer (Messiah) ran a 21⁄2-hour session of student papers in the morning session. The theme of that year’s meeting, “Mathematical modeling”, was a reprise of the section’s inaugural spring meeting held at Gettysburg 15 years earlier. Jefferson S. Hartzler (Penn State Harrisburg) began the day with an address whose title was congruent to the day’s theme. His lecture described, inter alia, a junior/senior modeling course developed for Messiah College and his own campus of Penn State. Next David (“Chris”) Arney (United States Military Academy) described the modeling course that formed the core of the four mathematics courses required of all cadets at West Point. After a discussion by Joseph H. Discenza (Daniel Wagner Associates) on modeling aspects of search problems about target a priori location, Ben A. Fusaro ended the day with a lecture on his specialty, environmental modeling. Fusaro included an outline of a six-week module appropriate for a general-education or liberal arts course.

At the 1993 spring meeting, four lecturers described projects related to the day’s theme, “Improving mathematics learning”. All four talks reflected the change in perspective that was taking place in the mathematics community at the time – from an emphasis on instructors and teaching to an emphasis on students and learning. Two of the presentations described projects developed in classrooms in the EPADEL area. One was a joint presentation by Gerald J. Porter (Penn) and David R. Hill (Temple). Former EPADEL governor Porter began by describing an interactive linear algebra text the two speakers had written; he then related experiences in using it at Penn in what he called “Linear algebra AS a laboratory course”. Former EPADEL president Hill then described a similar course at Temple and contrasted it with Porter’s course. The distinction between the two can seen in the title Hill adopted, “Linear algebra WITH a laboratory course”. The other EPADEL speaker, Nancy Baxter (Dickinson), discussed design and implementation issues that arose when she adopted a lab-based, collaborative, constructivist approach to teaching functions, in her lecture “Teaching mathematics without learning”.

The two outside speakers are well known for their involvement in undergraduate mathematics education. Cornell’s Beverly H. West described the interactive computer graphics she developed for use in calculus, linear algebra, and differential equations courses in a lecture titled “Integrating friendly graphics technology into the calculus curriculum”. In the remaining lecture, “Mathematics as a thinking subject,” Robert B. Davis (Rutgers) presented data obtained from school mathematics and innovative calculus courses that helped students learn mathematics in a reflective and analytical way.

Once again the flexible format of the spring meeting allowed the organizers to insert yet another element into the mix. During the day William Hawkins (MAA) ran a two-hour SUMMA workshop on proposal preparation, and Deborah A. Frantz moderated two one-hour student-paper sessions. (SUMMA is the MAA program Strengthening Underrepresented Minority Mathematics Achievement.)

The 1994 spring meeting was run in conjunction with PSMATYC, the Pennsylvania State Mathematical Association of Two-Year Colleges. President Walter Stromquist invited EPADEL members to “hear from Roseanne Hofmann and Stan Clemens on the use of graphing calculators, and from David A. Smith and Andy Gleason on their projects in calculus reform.” Stromquist then noted, “There will be parallel sessions of student presentations, including (a new emphasis) student papers on the teaching of mathematics.” Table 8.3.2 lists information about the four EPADEL presentations. Table 8.3.3 lists workshops offered under the aegis of PSMATYC.

In announcing the theme for the 1995 meeting, Walter Stromquist wrote, “Printed texts might be near the end of their run ... they may hang on for a while, but students can now demand electronic tutorials ... fortunately for EPADEL, much of the leadership in meeting this demand is coming from within our region. Hence the attraction of the spring meeting, whose focus on interactive texts will give us the best glimpse we are likely to get of the future of this technology.” To begin the day, William J. Davis (Ohio State) described the interactive calculus text called Calculus&Mathematica. Then James E. White (UNC, Institute for Academic Technology) described some of the design implications for computer- based teaching and learning environments that were then emerging from computational styles that included object orientation, graphical user interfaces, and hypertext.

But it was the afternoon session that fulfilled Stromquist’s promise. He wrote, “We are experimenting with a somewhat different format, in order to allow attendees to sit at the keyboards and work directly with several of the most promising interactive systems.” Four 20-minute presentations demonstrated the systems Stromquist mentioned: Charles E. Hofmann (LaSalle) and Roseanne S. Hofmann (Montgomery CCC), “Explorations in mathematics using MathKit,” Jack R. Stodghill and Barry A. Tesman (both from Dickinson), “Mathematica- based labs for calculus I, II, and III,” David R. Hill (Temple) and Gerald J. Porter (Penn), “Interactive linear algebra in MathCAD,” and Charles E. Ashley (Villanova), “Maple projects for differential equations and linear algebra”. Two types of parallel sessions were conducted during these presentations – a 90- minute student-paper session organized by Linda C. Thiel (Ursinus), and a series of interactive demonstrations on MathKit, Mathematica, MathCAD, and Maple.

The 1996 meeting, devoted to active learning, returned to the theme from the 1993 meeting, improving mathematics learning. President Louise Berard wrote beforehand, “Active learning at first may sound redundant because all learning IS active. However, traditional classroom techniques often allow students to be more passive than we would like regarding their educational experience. Our invited speakers will share with us some important suggestions for engaging students more actively in the learning process.”

Two of the four speakers came from the EPADEL section, with Louise’s husband, Anthony D. Berard, Jr. (King’s College), leading off the program. His lecture, “Applying logic/designing small axiom systems”, described a course in which students worked in small groups in class to develop proofs together. He ended his talk by supplying an example of an axiom system designed by first- semester students. In the final talk of the day Nancy L. Hagelgans (Ursinus), the former section president who was then the section’s governor, discussed “Cooperative learning in discrete mathematics”. This talk described a sophomore-level course in which students solved problems in three different settings – using a computer algebra system by participating in groups during class, in the computer laboratory, and outside scheduled hours. In the remaining two lectures, E. Jacquelin Dietz (North Carolina State) presented two hands-on activities that were developed to teach the concept of sampling distribution, while Richard W. Decker (Hamilton College) described an introductory survey course in computer science in his presentation “A suite of hands-on laboratory exercises”.

The 1997 meeting duplicated the theme of that year’s Mathematics Awareness Week – “Mathematics and the Internet”. The local highlight was Eugene Klotz’s presentation with the fetching title, “How the WWW is taking over all of mathematics and what you can do about it”. In the talk the former EPADEL president surveyed old and new developments in the study of symmetry from algebraic and geometric viewpoints. By the time of his lecture Klotz was known internationally for his role in developing the highly successful Math Forum Web site. Three other talks completed the program – Frank Wattenberg (Montana State), “Using the WWW, Netscape, and Helper applications to create a learning environment exploiting hands-on equipment, a CAS, Java, and the Internet to study mathematics across the curriculum”, David Cerone (Union College), “Mathematics on the Web: Looking back and looking forward”, and Frank Beatrous (Pittsburgh), “The use of network resources in calculus instruction”.

The game theoretic theme for 1998 was addressed by three invited lectures. Fan Chung Graham (Penn) discussed a variety of graph pebbling problems, described some classic results, and mentioned several unsolved problems in her talk titled, “Pebbling on graphs”. In the day’s opening address, Alan D. Taylor (Union College) focused on game-theoretic approaches to the question of whether honesty is the best policy in his lecture, “Strategic aspects of fair division”. The third lecture, “Puzzles and paradoxes in game theory” by Ed Packel (Lake Forest College), discussed four problems from game theory. The remaining hour was comprised of contributed papers.

The 1999 meeting at Villanova was cosponsored by the Middle Atlantic Consortium for Mathematics and Its Applications Throughout the Curriculum (MACMATC), so the day’s theme – mathematical applications throughout the curriculum – is not surprising. The morning session offered 11 workshops, four of which were offered by key members of our section: Annalisa Crannell (F & M), “The mathematics behind depth in drawings”; Joanne Darken (CCP), “Precalculus in the here and now: Payoffs the same semester”; Linda Thiel (Ursinus), “Life’s a risk!”; Dennis DeTurck and Larry Gladney (Penn), “Moments of inertia – Integrated first-year calculus and physics”. The afternoon session featured two keynote addresses – “Comparison with disclosure” by Peter Winkler (Bell Labs) and “Slime molds, tiger bush, and bamboo” by Ben Bolker (Princeton).

The first EPADEL meeting of the third millennium (or the last meeting of the second millennium, depending on your viewpoint) was devoted to statistics. Hence it was not by chance that two of the four speakers were graduates of the host institution, Messiah College. Mark Heise B.A. 1986) spoke on “Statistics and the drug development process”. As senior statistician at SmithKline Beecham Pharmaceuticals, and formerly a statistician at Procter & Gamble Pharmaceuticals, Heise was particularly suited to discuss this topic. Tonya Sharpe King (B.A. 1992) spoke on “The role of the statistician in the academic research hospital setting”. Like Heise, her employment record certainly made her well suited for the task because, after obtaining her Ph.D. in biostatistics, she accepted an assistant professorship in biostatistics at Penn State’s College of Medicine at the Hershey Medical Center.

President Douglas Ensley promised that the 2000 meeting would extend beyond local success stories. He wrote, “The meeting features speakers known nationally through the MAA.” One of the renowned speakers was Laurie Snell, known primarily for his 1950s pioneering work in developing (with John G. Kemeny and Gerald Thompson) the now-standard finite mathematics course and writing the first book on the subject. In his talk Snell discussed his more recent interest, Chance News, an electronic newsletter dealing with current news based on probability and statistics. In the remaining talk, “Applications of MAPLE in the instruction of probability and statistics”, Elliot A. Tanis (Hope College) discussed ways to integrate the Computer Algebra System MAPLE into the instruction of probability and statistics. He also illustrated some procedures that helped to complete the statistical package in MAPLE.