UNIVERSITY OF GEORGIA
DEPARTMENT OF MATHEMATICS
FIVE YEAR PLAN: 2000-2005
Fall 2000

Introduction

The Department of Mathematics faces significant challenges during the next five years. Faculty hired in the late 1960's and early 1970's are likely to retire in increasing num-bers, a phenomenon already beginning with four retirements in 2000. Several strong re-search groups within the department may see their ranks dwindle by half or more. These senior faculty are also the most experienced teachers. New instructional initiatives, in-cluding the major in Mathematics with Computer Science, the Regents' mandates for teacher preparation, and a proposed program in Integrated Genomics, will all increase the number of students being taught each year. The Department will have to devote serious effort to hiring strong young faculty to replace the research and instructional capacity being lost through retirements. Additional lines will need to be acquired and filled to support the new initiatives.

While much progress has been made in the area of faculty salaries, thanks to the efforts of former Governor Zell Miller, over the past five years, the department's median salary is still just at the median for Group II institutions, as defined by the National Academy of Sciences. The Department sees itself at the "rising Group I" level, with a five-year goal of raising median faculty salaries to the Group I level at all ranks. With senior retirements depleting the departmental salary budget and raise pool, it will be exceedingly difficult to adequately compensate deserving faculty.

The graduate program in Mathematics is perhaps the strongest in its history, with seven Ph.D. students finishing in 2000, many of our recent graduates getting postdoctoral or tenure track positions at excellent universities, and the department's reputation getting national attention. Despite this prosperous environment, recruiting excellent graduate students is becoming increasingly difficult. This is partly a result of a national trend to-wards a decreasing applicant pool for the available slots. But it is also due to a lack of competitiveness of our graduate stipends, which compare unfavorably even with other schools in the southeast. Since a strong Ph.D. program is a key ingredient in many as-pects of a mathematics department, including the ability to attract and retain excellent faculty, it is important that we work hard to maintain the momentum that our graduate program has attained.

Physical space is a resource which is in constant short supply. Many mathematics courses are taught in far-flung classrooms across south campus, many of which are barely ade-quate for the teaching of the subject. These remote classrooms have the additional unde-sirable effect of reducing faculty-student interactions, as students are less likely to attend office hours. Over the years, a number of classrooms in Boyd Graduate Studies have been converted to computer laboratories, which only exacerbates the problem. The new Mathematics with Computer Science major may require the creation of yet another un-dergraduate computer lab, although the department has no available space for this pur-pose. We have long wanted to provide a study room for math majors to get together and collaborate on problems, but there is no space for that either. Several instructors who teach large numbers of undergraduates each semester currently occupy offices in Barrow Hall, given to the Department a few years ago in exchange for offices in Boyd. It is im-portant to maintain this office space, or its equivalent. Finding offices for new faculty who will support the various new instructional efforts will be problematic. A long-range solution to the space problem would be the construction of a new Mathematical Sciences Building, complete with state-of-the-art classrooms, computer labs, study, seminar, and conference rooms, and offices for faculty, graduate students, and support staff, to bring together under one roof the departments of Computer Science, Mathematics, Mathemat-ics Education, and Statistics, along with the mathematics collection from the Science Li-brary.

The ensuing sections detail the plans of the Mathematics Department for the next five years in the areas of Hiring Strategy, Faculty Salaries, Graduate Program, Undergraduate Program, Facilities, and Outreach.

Hiring Strategy

In an environment of increased competition for retention of positions, our hiring strategy must address at least two issues: how to choose those candidates who will best help us fulfill the missions of the Department in research, teaching and service; and how to convince the administration of the wisdom of permitting us to hire our preferred choices.

It is imperative in this situation that we choose candidates whose ability to enhance our mission can be clearly demonstrated, and also that we pay attention to what the administration expects from us as a Department. We must choose candidates whose research potential is truly excellent, measured by a national standard, and whose presence will not merely increase the productivity of those of us already here, but contribute to elevating or creating a group which is nationally visible for its excellence. We must insist that every candidate be a committed teacher with at least the potential to become an excellent one. Of obvious importance to the future of our profession and our society, is the need to hire faculty who inspire both undergraduates and graduate students to appreciate and understand mathematics, and who reach out to the general public through the students who study here.

The Department recognizes its important role in helping to prepare teachers at all levels. We are committed to providing excellent courses for this purpose. These courses are often difficult to teach and need the serious involvement of the permanent faculty. We must encourage the contribution of current experienced faculty to these courses, and hire additional faculty who are willing and able to teach them as well.

The ability of a group to recruit and serve a reasonable population of graduate students is important both to us and to our credibility with the administration. Hence we must pay greater attention to the potential of a candidate to interact with and direct graduate students in research.

Given the administration's expectation that an excellent research program will generate revenue, we must not ignore this aspect of a candidate's potential, although it should not be primary and should never substitute for mathematical excellence. We must also persist in making the difficult but valid argument that research faculty are inherently better qualified for our teaching mission, which is ultimately our greatest generator of revenue and goodwill for the University.

Recent experience suggests that it will be increasingly difficult to hire our top candidates in the next few years. The number of jobs available at universities of a stature similar to UGA is increasing while at the same time the pool of high quality new graduate students is decreasing. Evidence for this impression comes both from professional studies by groups such as the American Mathematical Society, and from anecdotal evidence. For that reason it will be vital that offers to our top job candidates be set at a high level matching or surpassing those of our competition. In addition, we should seriously consider alternative hiring strategies such as hiring at the associate or full professor level. Such a scheme might give us the chance to tap into a pool of candidates for whom the competition is not so strong.

Some observations on the current makeup of the Department suggest specific strategies for hiring. The algebra group, although small, has a high profile and serves a graduate population. It may be wise to add an outstanding member to this group while it is at the height of its stature. The Department has not hired a topologist in over ten years. The analysis and applied mathematics/numerical analysis groups, although they are among the largest here and have received four hires in the past 8 years, have the largest proportion of full professors among almost all groups. It seems prudent to consider adding additional excellent junior faculty to these groups over the next five years with a view to the long term vigorous presence of these essential disciplines. We must remain aware, however, whether building new groups or strengthening existing ones, that creating potential for fruitful interaction between personnel is more important than maintaining nominal representation of traditional areas. A group may be strengthened more by adding someone who bridges it to another group, than by someone who falls strictly within the specialty of its current members.

In summary, within the scope of our departmental mission, we must recruit and hire the best-qualified people available, excellent in both teaching and research, with potential to attract undergraduates to mathematics and to recruit and train excellent graduate students. We must be aware of the advantages that accrue to the Department from excellent high profile groups. With regard to groups that have attained exceptional stature, we must maintain their strength, along with their ability to generate revenue and to attract and serve an excellent graduate population. We must strive to create an atmosphere wherein successful hires will flourish and wish to stay permanently in the Department. In particular, the Department should maintain favorable teaching loads for "on track" junior faculty and exceptional research faculty. At the same time, we must maintain a willingness to add more members to a newly-created or -strengthened group, until it reaches a "critical mass" where its members are able to support and sustain each other by cooperative seminars and research, and to begin to attract personnel and resources. It is crucial to maintain the successful postdoctoral program, including support of faculty who advise in it, and to provide teaching mentoring for postdocs. We should give serious attention to the needs of the teacher preparation initiative. Finally, we should be open to cooperation with other departments in joint efforts to obtain resources for projects which promise to strengthen mathematics and the Mathematics Department.

Faculty Salaries

There is a natural correlation between a department's faculty quality and faculty salaries. The goal of the UGA Mathematics Department is to assemble a faculty which will raise the Department to the public doctoral granting Group I level as defined by the National Academy of Sciences. In order to achieve this goal, UGA must be prepared to pay Group I salaries. The combination of the sacrifice of a retired line and former Governor Zell Miller's education initiative has enabled the Mathematics Department median salaries to rise to the Group II median salary level. At the same time there are still considerable gaps between departmental averages and Group I salary averages. The main 5-year goal concerning salaries should be to raise median mathematics faculty salaries into the Group I level at all ranks.

The impending retirements of many senior faculty during the next 5 years will greatly reduce the total salary budget of the Mathematics Department. The policy of returning faculty lines to a department at the base assistant professor level will only exacerbate the decline in the salary portfolio of the Department. The reduction of the total salary budget will be accompanied by a decline in the merit raise pool. This will make it more difficult to adequately compensate deserving faculty. In order to accomplish the primary goal as stated above, the department should attempt to negotiate an agreement on retired positions with the administration.

Graduate Program

Maintaining a strong and vital Ph.D. program may be one of the biggest challenges facing the Department over the next five years. On the one hand, the program is quite strong now, with many of our Ph.D.s from the past two years landing excellent postdoctoral and tenure-track positions. On the other hand, recruitment seems especially tough in the 2000 season, due to a sharp drop in the number of qualified applicants. Clearly the Department will have to work hard to "get out the message" and attract more good graduate student applicants, especially in view of the administration's desire to increase overall graduate enrollment at the University.

One of the first (and perhaps only) points of contact between a prospective applicant and the Department is likely to be through the Web. We must make certain that our graduate web page is informative, enticing, up-to-date, and useful. It should include statistics indicating our strength and reputation in various areas of mathematics, as well as our success in placing recent Ph.D.s. Ideally, the Graduate Secretary should regularly review and update material on the web page. Faculty should be encouraged to post preprints on their personal web pages, along with a description of their research which is accessible to undergraduates.

We must intensify our efforts to recruit good graduate students from regional colleges. Encouraging faculty to give colloquia at such schools is one way to do this. But we must also be able to make attractive offers to the best graduate students. At the regional level our stipends compare unfavorably with those offered by Georgia Tech and Emory. We definitely lack competitive edge with these and other schools in the southeast. We need continually to seek additional sources of fellowships for entering graduate students. Since it seems unlikely that new funding will be forthcoming from within the University, we should continue to apply for external funding, including the VIGRE grant.

We must focus on getting a diversified student body. We need to put out the word that our Department is a friendly place for good minority graduate students. The Department has had success in recruiting students from Africa, and those efforts should continue. One impediment to admitting such students is financial, specifically, the fees for the GRE and TOEFL tests, and for applying to UGA. An arrangement should be negotiated with the Graduate School whereby the application fee could be waived or at least deferred, and perhaps the standardized testing also deferred, under special circumstances.

We must enlarge and strengthen our M.A. and M.A.M.S. programs. There has been a significant decline in the number of Ph.D.s produced by Group I schools. This decline in quality doctorates is occurring in virtually all scientific areas. There is at the same time a vigorous interest in masters degrees. We can provide a real service to the State by training at the masters level more individuals for careers in industry and teaching. Undergraduate advisers should encourage their better advisees to continue at UGA and obtain a masters degree.

Finally, faculty should be encouraged to work with graduate students. Faculty who advise large numbers of graduate students should receive a reduced teaching load or similar compensation.

Undergraduate Program

Three new teaching initiatives will require additional permanent faculty as well as shifts of emphasis in the teaching mission of the department. These initiatives are: the major in Mathematics with Computer Science; the Regents' mandates for teacher preparation; and a proposed program in Integrated Genomics. It is necessary for the success of these programs that junior faculty get more involved.

The major in Mathematics with Computer Science is currently awaiting final Regents' approval, and is expected to be put in place in Fall 2001. This will not be a joint major with the Computer Science Department, but instead it will be a new mathematics major. The development of the major involves the introduction of new courses at the 3000- and 4000-levels. We have already received one new faculty line to support this program, but more lines are needed for the full development of the major. One concern which has been raised recently is that we may need an additional undergraduate computer lab for the students in this major.

The Regents' Teacher Preparation Initiative calls for a substantial increase in the number of mathematics courses taken by undergraduates in the College of Education. These courses are explicitly defined by the Regents as being taught by faculty in the College of Arts and Sciences. The increases in mathematics training for teachers which have been approved will result in significant increased teaching by the Mathematics Department. Two additional mathematics courses for elementary school teachers will be added in Spring 2001 and Fall 2001, and an additional mathematics course for middle school teachers will be added in Fall 2001. One new faculty line in mathematics to cover these new courses has been approved, and more lines will be needed. The Regents state that secondary education mathematics teachers should have a major in mathematics. Mathematics Education majors do take a significant number of our upper level mathematics courses, and they should actually be considered to be joint majors. The growth of the Mathematics Education program at the undergraduate and graduate level will continue to increase enrollments in our courses at the 3000-7000 levels.

The proposed program in Integrated Genomics includes a new 2000-level course in Discrete Mathematics and Computational Biology. The enrollment in such a course is projected to be up to several hundred students a year. The Mathematics Department would support such a program only if we obtain the additional faculty necessary to develop and teach this new course. In preparation for that eventuality, a pilot course in discrete mathematics for biologists will be taught in Spring 2001.

The teaching of Mathematical Modeling (MATH 1101) in large sections 3 days a week, with no breakout sections, is not optimal for the students. The Department will move towards converting the teaching of at least some sections of this Core Area A course to small (35 student) sections. Recent experience shows that this format is much more effective for the teaching of fundamental "word problem" skills.

We are committed to computer testing in Precalculus (MATH 1113). The testing system is now running smoothly. It's also being used by Academic Assistance. The instructors in this course like computer testing; they say that it enables them to teach large numbers of students with efficiency.

We will continue to use part-time instructors for the foreseeable future. We employed 17 part-time instructors last year, teaching 117 sections, and we do not expect these numbers to change significantly in the near future. We do not have enough full time faculty to teach all of our service courses. The Department and University derive great benefit from the success of our core of hardworking long-term instructors; the temporary instructor pool on the other hand should not be allowed to grow at the expense of regular faculty, and we will strive to hire as temporary instructors only candidates with Ph.D.s whenever possible.

The Curriculum Committee has been evaluating the Calculus sequence (MATH 2200/ 2200L, MATH 2210/2210L). They have met with faculty from the Business School, and with members of other client departments (Computer Science, Statistics, Chemistry, Biological Sciences, Psychology, and Biological and Agricultural Engineering), to get their input. These clients seem happy with the calculus courses as they are, but we still see room for improvement. The Department is committed to continuing the calculus labs. The key to the success of these labs is that they should be taught by faculty and by graduate students who have actually taught calculus. It is now apparent that we cannot put all of these labs in the hands of graduate student TAs. We are also concerned about standardization of the calculus sequence, and to this end we have instituted, on a volunteer basis, uniform examinations in pilot sections of Differential Calculus.

The Department will continue actively to recruit mathematics majors from all of our courses, especially at the freshman level. We will continue to develop our web site and to promote the fact that the mathematics major is sought after by many employers in business and industry, with many opportunities in the Atlanta area. The new major in Mathematics with Computer Science should play into this growing market for graduates with analytical and technical skills. We will continue to keep in touch with our graduates and to keep informed about the jobs they get.

Facilities

One of the perennial problems facing the Mathematics Department is acquiring and keeping physical space. Current needs in this area fall into three main categories: classrooms, undergraduate labs, and faculty offices.

The vast majority of mathematics sections are taught in classrooms dispersed throughout south campus. Many of these older classrooms were not designed for mathematics instruction, and are barely adequate for the teaching of mathematics, in terms of blackboard and seat configuration, visibility, lighting, and use of modern technology. Given that most mathematics is best learned and taught in small (at most 35 student) classes, and in light of the University's stated policy that students must be given room to "spread out" when taking tests and exams, a high priority for the Department should be to secure many small classrooms of approximately 50 seats, to facilitate the proper teaching and learning of the subject.

Presently the Department has five rooms in the Boyd Building dedicated to computer laboratories: one for graduate students, two for calculus labs, and two for core course testing. A sixth lab needs to be added and equipped for the new Mathematics with Computer Science degree. It is unfortunate that providing such space probably means that the Department will have to dedicate another classroom to this laboratory (as it has for some of its existing labs). This will only exacerbate the problem with shortage of classrooms.

A number of the mathematics majors and other students taking mathematics courses form study groups, and several faculty do not have enough space in their offices to hold the students that attend office hours. For many years, the Department has needed a study room or "math lab" for these purposes. Perhaps now is the time for the Department to provide an undergraduate study room, although it currently has no space in which to accommodate one.

Four instructors who teach large numbers of lower-division students each semester currently share two offices in Barrow Hall. These rooms were provided to the Mathematics Department in exchange for faculty offices in the Boyd Building appropriated by the Office of the Vice-President for Research. Given the expected growth in mathematics faculty to support the three new teaching initiatives, it is imperative that the Department either retain the offices in Barrow Hall, or acquire new space in Boyd to replace them. Indeed, even such a steady state in faculty offices will likely create a space deficit in the coming years.

Departmental computer systems support staff are increasingly preoccupied with the day-to-day maintenance of our computer labs, classroom computer systems, as well as fac-ulty, staff, and graduate student computers. An additional staff position is needed for routine maintenance so that the current staff can devote more time to upgrading our net-work and computer facilities.

Finally, upgrading and replacing obsolete computers constitutes an ongoing need. Pres-ently, the lab fee card provides sufficient funds to replace the laboratory computers as needed; however, if this is not allowed in the future, then sufficient funds from elsewhere (such as the new student technology fee) must be obtained. The Department should en-courage the College to continue startup money for new hires; in addition, there should be some sort of budget line for replacement of faculty computers on a regular basis. Too of-ten these purchases are made in a last minute rush to beat the end of the fiscal year.

Outreach

The Department is beginning to become involved with fundraising, having set up a web page from which alumni can make contributions to various funds. Future fundraising ef-forts should include periodic advertisements in the Alumni magazine (especially targeting former students of popular teachers) and reminders in the annual departmental newslet-ters.

The Department will continue to make contact with mathematics students at all levels in the state of Georgia, both with an increased presence on the web and with more "on site" visits to schools. We should make the Mathematics Olympiad an annual occurrence, cul-minating in a final event at UGA to cap off the high school mathematics activity for the year. We should explore the possibility of increased contact with programs such as the Governors Honors Program. In addition, there should be greater involvement with the development of in-service teachers, particularly at the secondary level. For instance, we could hold an intensive, 3-4 week summer enrichment institute for high school teachers on an "advanced" topic such as advanced calculus, number theory, or Euclidean geome-try. Such a course would carry professional development credit for the teachers, and would be taught by one of our faculty members. Our faculty could be encouraged to seek federal funding for such an institute, or it could be run on an in-service basis.