### History of the Department

# A BRIEF HISTORY OF THE DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE AT THE UNIVERSITY OF THE SOUTH by W.M. Priestley, continued

In 1989 the Gaston Swindell Bruton Chair in Mathematics was established in his memory by alumni and friends. On this occasion at the invitation of the Mathematics Department, short talks were given in his honor by John Wilson and Thomas Greville. Wilson was then the most recent Sewanee graduate to earn a doctorate in mathematics, and Greville, as noted below, was the first. Since its inception, the successive holders of the Bruton chair have been Stephen Puckette, James Cross, Sherwood Ebey, and William Priestley.

During the early years of Bruton's tenure, Thomas N. E. Greville, Class of 1930, became the first Sewanee graduate to attain a Ph.D. degree in mathematics (University of Michigan in 1933). Over a long career, mainly spent at Wisconsin-Madison, Greville was to write many articles on combinatorics, probability and matrix algebra, most of which were related to population issues connected with actuarial science. Greville played a large role in undertaking the U. S. Census on at least one occasion, and the Greville name is still well known in actuarial circles, being attached to one of the fundamental methods he discovered and defended in connection with the interpretation of data. Greville's selected papers were bound and published in 1989. In 2003, five years after his death, there appeared a second edition of the book he wrote with Adi Ben-Israel on the theory and applications of generalized inverses.

Despite Tom Greville's example from the Class of 1930, no other Sewanee alumnus was to attain a doctorate in mathematics until the Class of 1949, which included Thomas W. Mullikin and Stephen E. Puckette. Mullikin received his Ph.D. degree from Harvard in 1954; Puckette received his from Yale in 1957 after first earning a master's degree in forestry. A perhaps decisive influence during this period was Robert Hooke, a Princeton Ph.D. and a great admirer of Bruton's, who had joined Sewanee's faculty to bring much-needed expertise in modern mathematics. One gathers from a remark made by Tom Greville that Bruton had had no one to “talk shop with” for most of his early teaching career.

It is thus no wonder that the great changes taking place within mathematics in the first half of the twentieth century had been largely overlooked at Sewanee. For example, although we now would find it difficult to believe that a serious modern student of mathematics could be ignorant of groups, fields, and rings, Puckette remarked more than once that when he entered Yale he didn't even know what a ring was.

Unfortunately, Hooke soon left Sewanee to become chief statistician for the Westinghouse Corporation. The costly medical attention needed by a family member had forced him to seek more lucrative employment. Hooke later published a short and witty paperback book entitled How to tell the Liars from the Statisticians, which became widely known.

Despite Hooke's departure, a remarkable upsurge in mathematical activity at Sewanee followed Puckette's return in 1956 to join a department including Bruton, James T. Cross, and Sandy McLeod. A string of seven consecutive graduating classes (1959-1965) produced fourteen Sewanee mathematics majors who eventually received doctorates, during a time when the total enrollment in the college was about six hundred. One of these was Harry Mullikin, the aforementioned Thomas's youngest brother. (The Mullikin brothers were Tom, Dick, and Harry.) Harry taught at Pomona College for many years, served as Chair, and won the Pomona teaching award several times. Of these fourteen alumni, two returned to teach in the Mathematics Department: Laurence R. Alvarez, Class of 1959, after earning a degree at Yale, joined the Sewanee faculty in 1964, retiring in 2005; William M. Priestley, Class of 1962, joined the Sewanee faculty in 1967 and later completed his degree at Princeton in 1972.

We give here only a quick summary of the history of computing at Sewanee because a document describing this in detail is readily available. In the early 1970's the Department of Mathematics had been asked by the administration to shepherd the development of a fledgling program in computer science, eventually resulting in the hiring of a full-time instructor, Clay C. Ross, Jr., in that discipline in 1973. Marcia S. Clarkson began teaching computer science courses in 1975, and Chris Parrish developed several new computer science courses after his arrival in 1987. The Department was re-named the Department of Mathematics and Computer Science in 1988. In 1997 the College approved a major in computer science. David R. Binger, Class of 1985, was the first alumnus to receive a Ph.D. in computer science (University of Illinois at Urbana-Champaign in 1992).

Following Puckette's departure in 1966 to direct the undergraduate program in mathematics at the University of Kentucky, graduate activity in mathematics among alumni continued at a more modest level. Twenty majors in mathematics or in computer science from the classes of 1969 through 2000 have so far attained doctorates, making a grand total of some forty such alumni through the Sewanee Class of 2000. Yale University and the University of Virginia have each awarded four doctorates in mathematics to Sewanee graduates, more than any other university. The alumni section of the departmental web pages attempts to keep current a complete list of Sewanee mathematics and computer science students who have received a Ph.D.

Puckette was soon to return to Sewanee, but as Dean (1969-1979) rather than as a regular instructor in mathematics. His deanship oversaw the advent of coeducation, and Sara Lynne Stokes, Class of 1972, became the first alumna majoring in mathematics to receive a doctorate, earning a Ph.D. in statistics from the University of North Carolina at Chapel Hill. So far, six alumnae majoring in the department have attained doctorates. The first to do so in computer science was Katharina Probst, Class of 2000, who did her graduate work at Carnegie-Mellon University.

From the mid-1960's until 1990 or so, full-time instructors in mathematics included James T. Cross, William M. Priestley, Sherwood F. Ebey, and Frederick H. Croom. Laurence Alvarez became Coordinator of Program Planning and Budgeting in 1972, and later became Associate Provost in 1989. Stephen Puckette returned as a full-time member of the department in 1980, following a Fulbright professorship in the Ivory Coast. Puckette was Section Lecturer of the Southeastern Section of the Mathematical Association of America (MAA) in 1991, and gave invited plenary lectures at two annual meetings of the Section.

James T. Cross had come to Sewanee with a master's degree from Harvard in applied mathematics, but after his interest turned to pure mathematics he wrote a Ph.D. thesis at the University of Tennessee in number theory. Upon his retirement in 1991 Cross left behind a deftly composed set of notes -- A Do-It-Yourself Course in Number Theory -- that are still used at Sewanee as the sole text in a number theory course taken by advanced undergraduates.

William M. Priestley wrote a textbook, Calculus: An Historical Approach, Springer-Verlag, 1979, that was used for ten years in the two-semester beginning calculus course at Sewanee. After Sewanee's graduation requirements in mathematics were reduced, he wrote a second book, intended for use in a more elementary, one-semester calculus course, emphasizing the place of mathematics within the liberal arts. In 2006 Priestley was given the Distinguished Teaching Award of the Southeastern Section of the MAA.

Sherwood F. Ebey came to Sewanee in 1968 and proved to be an exceptional teacher. Seeing a need for a statistician at Sewanee, Ebey used two sabbatical leaves to re-make himself from an algebraist into a specialist in probability and statistics and even developed a computer science course in analysis of algorithms with appropriate probabilistic underpinnings. In the meantime he had served for two five-year terms as a thoughtful chairman, and he ended his career on the faculty as the first head of the newly developed Center for Teaching. He endowed the annual Ebey Lecture to bring to Sewanee a speaker to give a public talk emphasizing the role of mathematics in current life, together with a second lecture directed to advanced undergraduate majors. A number of prominent speakers have come to Sewanee to give the Ebey lecture, including Gian-Carlo Rota and Paul Halmos.

In 1971 the department was bolstered by the arrival of Frederick Croom, who was to add much-needed strength in topology. Croom published textbooks in algebraic topology and in point-set topology. In 1984 he began serving in the administration, first as Associate Dean and later as Provost, assuming the post originally filled by Gaston Bruton.

Over the years a fair number of mathematics majors have been valedictorians or salutatorians of their graduating classes. One of these, Anne Katherine Jones, who also majored in chemistry, was a 1998 Rhodes Scholar and went on to earn a doctorate in chemistry at Oxford. Sewanee's only other mathematics major to receive a Rhodes Scholarship was Thaddeus G. Holt, Jr., Class of 1951, who read law. On a document furnished by the Dean’s office listing valedictorians and salutatorians since the Class of 1951 there are noted at least 16 students who majored in mathematics. Several of these carried a second major as well, in such subjects as chemistry, economics, English, music, or physics.

The “mathematics requirement” at Sewanee has undergone several modifications over the years. It was perhaps strongest for a time beginning with the class entering in 1957 when all graduating Sewanee students were required to complete two semester-length courses in mathematics. The college catalog then explicitly stated that four years of secondary-school mathematics were generally necessary in order that entering students might expect to fulfill this requirement. It seems safe to say that during this period virtually all graduates would have had at least one semester of calculus, a subject that demands considerable secondary-school preparation. During this time graduating students had to complete as well a foreign language through the third-year level, four semesters of English, two semesters of history, and two semesters of either physics, chemistry, or biology -- not to mention additional requirements in social sciences, philosophy, and religion. Over the years the number of such requirements has diminished in almost all liberal arts colleges, and Sewanee has been no exception. Today, in 2008, one semester-length course in mathematics is required of all graduates.

Since 1965 the department has intermittently offered semester-length "faculty" seminars, which in fact often included advanced senior majors receiving credit for independent study. Various members of the faculty have led seminars for interested faculty and students in such topics as differential forms, graph theory, non-standard analysis, catastrophe theory, mathematical foundations of quantum theory, Fourier analysis, difference equations, fractals, history of mathematics, dynamical systems, probability models for computer science, etc.

Fred Croom led perhaps the most notable faculty seminar, developing notes that resulted in his publishing a textbook, Basic Concepts of Algebraic Topology, Springer-Verlag, 1978. Two other faculty members, Priestley and Ross, have also written textbooks for this Springer undergraduate series.

Another successful program, ongoing now for over thirty consecutive years, has been the annual Sewanee-Rhodes-Hendrix Undergraduate Symposium in Mathematics. This is held in Rhodes College, Memphis, every other year, with meetings every fourth year at Sewanee and at Hendrix College in Conway, Arkansas. Usually, three to six undergraduates from each college give brief talks on their research in mathematics. Robert Eslinger, who moved to Hendrix College to teach after being briefly on the faculty at Sewanee, was the prime mover behind the development of this symposium.

The size of the faculty of the Department of Mathematics and Computer Science and of the female/male ratio within it has grown with the college from a staff of two (Bruton and Jervey) to include in 2008 about an equal number of women and men, comprising in all a faculty of about 9.33 full-time equivalents. Emily Puckette is currently serving as Chair of the Department, following Catherine Cavagnaro's tenure, and Lucia Dale directs the computer science program.

Several members of the department have been able to teach only part-time because they have followed Dr. Bruton's example in assuming administrative tasks. These include Stephen Puckette (Dean), Laurence Alvarez (Coordinator of Program Planning and Budgeting, and later Associate Provost), Marcia Clarkson (Director of Administrative Computing, later Director of University Services, and finally, Personnel Director), Clay Ross (Director of Academic Computing), Frederick Croom (Associate Dean, and later Provost), Linda Lankewicz (Provost), and Joel Cunningham (Vice-Chancellor).

Stephen Puckette and Laurence Alvarez also followed Bruton's lead in a second way. For many years they volunteered to coach the canoe team and the women's volleyball team, respectively, and both actively supported philosophy professor Hugh Caldwell’s founding of the Sewanee Ski and Outing Club, which eventually evolved into the current Sewanee Outing Program.