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A. Executive summary
A.1 Current status
The most central academic unit on campus The School of Mathematics is arguably the most central academic unit on campus. Like many Math departments, we provide a large number of en- abling courses—in fact, every year nearly half of all Georgia Tech students take a course in the School! What is even more striking at Georgia Tech is the amount of high level teaching provided to non-majors. Advanced courses such as real analysis, abstract algebra, probability, and dynamical systems attract large numbers of non-majors. Indeed, at the 3000 level, non-majors outnumber majors more than 10 to 1, and at the 4000 level, undergraduate Mathematics ma- jors are only 1/3 of the total student population. Even advanced graduate courses have large enrollments from other departments. It is fair to say that a Georgia Tech education would simply not be possible without the courses o↵ered by the School of Mathematics. Con- tinuing to o↵er all the necessary courses and meet the needs of our majors and graduate students will require a highly qualified sta↵ of research-active mathematicians. A highly successful research unit The School of Mathematics is a highly successful research unit. Faculty in the School carry out world-class research in a variety of core and applied areas of mathematics. Our group in Discrete Mathematics is routinely ranked in the top 10 nationally, and our group in Applied and Compu- tational Mathematics is in the top 15. Interdisciplinary projects abound. Plenary lectures at international conferences by School faculty are common- place. About 78% of the faculty have external research support and new awards are coming in at an average rate of over $3M per year. Over half of the faculty serve on editorial boards, several of them in editor-in-chief roles. 3
A. EXECUTIVE SUMMARY 4
Rapidly increasing quality and reputation During the last two decades we have experienced rapidly increasing quality and reputation. As one measure, we consider NRC research ratings. In the 1982 rankings, Georgia Tech Mathematics was 71st of 102. A decade later, the 1995 ratings placed us 44th of 140. Using the middle of the research activity range, the most recent NRC study places the Georgia Tech School of Mathematics at 33rd of 127, i.e., in the 26th percentile. R-ranking and S-ranking numbers are similarly high. As another measure, we consider awards to junior faculty. Since the last external review, School faculty have received five CAREER awards, three Sloan Research Fellowships, and one PECASE award, in addition to numerous NSF, NSA, and NIH grants. The quality of our recruiting since the last external evaluation has been excellent and we have every reason to hope that, with adequate support, we will be able to continue our rise in quality and national rankings.
A.2 Ingredients for continued success
Budget to fill available lines The School holds 59 tenure/tenure-track faculty lines. In recent years sev- eral of these lines have been held open to meet budget cuts. (With antici- pated retirements and hiring, we expect to have four open lines in 2012-13.) A good-faith estimate of the gap between our current budget and what would be needed to fill all lines and carry out current operations leads to a “structural deficit” of approximately $450K. A sum of similar magnitude was discussed in negotiations between the current chair and the dean in 2008, but the financial crisis has so far precluded action on this point. The School has pressing research needs and an ever-increasing load of classroom teaching, research and mentoring duties supporting undergrad- uates and graduates, and outreach. Long-term there is a strong case for additional faculty. In the immediate future, we are requesting an increase in budget to bring our faculty back up to full strength. A post-doctoral program The career path in mathematics leading to a tenured position at Research I institution often passes through a named post-doctoral position. (“Named” because the positions are often named after a distinguished former faculty
B. Overview
B.1 Our role, status, and ambitions
Role The School of Mathematics plays a central role in the Institute’s mission. Our contributions range from service teaching and undergraduate degree programs, through graduate education, disciplinary and interdisciplinary research, and on to service and outreach. Our enabling courses form the foundation of most degrees at Tech. Ev- ery major on campus requires mastery of at least second-semester calculus; most require three or four semesters of mathematics, and many require significant amounts of higher-level math. Even our most advanced un- dergraduate and graduate courses often have large enrollments from other departments in science and engineering. In any given year, fully 47% of the Tech undergraduate population takes at least one course taught by the School of Mathematics. Another important aspect of our role is the formation of mathematical professionals through our degree programs. The School is sole proprietor of bachelor’s degrees in Applied Mathematics and Discrete Mathematics, and Master’s of Science and PhD degrees in Mathematics. These degrees are the nominal focus of this review. We also collaborate with several other units on campus to o↵er Master’s degrees in Computational Science and Engineering (CSE), Quantitative and Computational Finance (QCF), and Statistics, as well as doctoral degrees in Algorithms, Combinatorics, and Optimization (ACO), Bioinformatics, and Computational Science and Engineering. Our status in the mathematical community is based on our disciplinary and interdisciplinary research. We have strong groups in about a dozen areas of mathematics and its applications, ranging from fundamental ar- eas such as analysis, geometry-topology, and algebra, through interdisci- plinary and applicable areas such as discrete mathematics, dynamical sys- tems, PDEs, numerical analysis, probability and statistics, mathematical physics, and mathematical biology. These are not rigid divisions and there 6
B. OVERVIEW 7
is a great deal of cross-fertilization between areas. We are also deeply in- volved in interdisciplinary research with collaborations involving the Schools of Physics, Biology, Computer Science, Industrial Engineering, Biomedical Engineering, and others. The School of Mathematics also contributes to the larger community through several outreach and service e↵orts. We inspire future scientists and engineers through the High School Mathematics Competition and through Distance Calculus. We participate in the formation and reinvigoration of teachers through the Georgia Tech’s Center for Education Integrating Sci- ence, Mathematics, and Computing (CEISMC). We o↵er continuing ed- ucation through video courses and we o↵er foundational courses at Tech’s campuses in Lorraine and Shanghai. And we engage our alumni and friends through quality publications and periodic social, mentoring, and scientific events. Status We have achieved a certain level of national prominence. National Research Council ratings have placed us in the Research I group of Math departments since 1995. The most recent NRC study ranks the School’s research activi- ties at about #33 of 127. (This is the average of the 5th percentile and 95th percentile rankings of 16 and 50 respectively.) There is a clear increasing trend: in 1982, we were 71st of 102 and in 1995, we were 44th of 140. The latest US News ranking of mathematics graduate programs places us at #30, up from #36 two years ago. Also, two subspecialties are highly ranked by US News—Discrete Mathematics at #8 and Applied Mathe- matics at #12. Georgia Tech as a whole is a highly regarded educational institution, consistently ranking in the top 10 among public universities in the US. Shanghai Jiao Tong University’s “Academic Ranking of World Univer- sities” placed Mathematics at Georgia Tech #20 world-wide. (This is an entirely data-based ranking of the Institute as a whole, about which we will say more in Section C.2 below.) A large proportion (currently 78%) of our faculty receives research sup- port from external agencies such as NSF, NSA, NIH, DoD, DARPA, etc. Since the last review, five of our junior faculty members have been awarded CAREER grants, three have received Sloan Research Fellowships, and one has received the PECASE award. Several senior faculty have led Focussed Research Group projects, and several have five-year, “high-impact” awards
B. OVERVIEW 9
distinct students. This is more than 10% of the total credit hours taught at the Institute and more than 1/3 of the total in the College of Sciences. Each year almost half of the undergraduate population takes a course from Mathematics! At the graduate level, last year we taught about 4350 credit hours with about 27% of them taken by students whose home school is Mathematics. We have about 200 undergraduate students in the two majors and about 140 graduate students divided among several MS and PhD programs. We also serve a large number of students through various outreach pro- grams. Almost 300 Georgia high school students take calculus at Tech through the distance calculus program. About 500 middle school and high school students participated in the last High School Mathematics Compe- tition. In 2011, over 100 students took courses taught by Mathematics faculty in Lorraine and Shanghai. And during this last summer we hosted 13 students doing undergraduate research projects. Faculty The school currently has 59 faculty lines. At the end of 2011-2012, 53 of these will be occupied (55 will be occupied if expected hires occur this spring). Four faculty members (one assistant, two associates, and one full professor) are on leave exploring other opportunities. There are four adjunct professors associated with the School (Cook and Nemirovski from Industrial Engineering, Randall from the College of Com- puting, and Tannenbaum from Electrical Engineering). Two more are un- der consideration. (At Georgia Tech, “adjunct” means “prestigious associ- ated faculty” not “temporary teaching faculty.”) There is one Professor of the Practice associated with the School, Richard Milman, the Director of CEISMC. We have three academic professionals (all with PhDs in Math or Physics) and two instructors, all on long-term contracts. The academic professionals handle computing infrastructure, advising for our majors, and scheduling and evaluation of transfer credit. The permanent instructors play a key role in mentoring our undergraduate and graduate teaching assistants. (One of them is a full-time English as a second language expert dedicated to supporting our graduate students. We may be the only program in the country with such a position.) We have one additional temporary instructor (a former tenured faculty member) teaching specialized courses related to the QCF graduate program.
B. OVERVIEW 10
Staff The School operates with a very small sta↵: two in finance/accounting, two full-time and one half-time in academic support, three (one being hired) in faculty support, an o ce manager, and a receptionist. We also have a small computing sta↵ including one academic profes- sional, two full-time sta↵ members, and several student workers. The overall level of sta↵ professionalism and e ciency is remarkable.
B.3 Academic and administrative structures
Faculty committees Roughly a dozen faculty committees set policy for the school. In total there are about 50 positions on these committees and the vast majority of faculty members not on leave serve on at least one School committee. Academic policy is set by the Undergraduate and Graduate committees; these are entirely elected and have administrators as ex-o cio members. Appointment, promotion and tenure, and salary recommendations are made by four committees: Hiring, Junior P&T, Senior P&T, and Salary & Awards. These committees have both elected and appointed members. In response to a previous review, the size of the hiring committee was increased in 2008 in order to have greater faculty input. An entirely elected Faculty Advisory Committee receives input from faculty members on all matters of concern and advises the chair on appro- priate courses of action. It has representation from all ranks of the faculty. This committee calls faculty meetings and sets the agenda for these meet- ings. An entirely elected Elections and Nominations committee organizes elections for all School committees. Appointed committees for the Colloquium, Computing, and the Library orchestrate the School’s activities in these domains. The School currently has three members elected to the General Faculty Assembly. Administration The School’s administrative team consists of the chair, an associate chair, undergraduate and graduate coordinators, and a director of teaching e↵ec- tiveness (DOTE). It also includes a team of administrators and academic professionals who handle scheduling, and permits and overloads.
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College at the start of the current chair’s appointment, and it will e↵ectively give us several new positions. This should help alleviate the strains asso- ciated with increasing student populations and increasing commitments to the rest of the Institute (such as joint degrees and interdisciplinary research programs). Budget Our main state budget is currently approximately $8.8M. The major cate- gories of spending are as follows: Tenure/tenure-track faculty: 68% Contract faculty and sta↵: 11% Graduate program: 15% Visitors and research support: 6% Over the last five years, our main budget was cut by approximately $800,000, or roughly 10%. About half of this cut has been met by holding open faculty lines. The majority of the rest was met by drastically reducing our program of matched post-docs and visitors. Smaller sums were saved by eliminating a sta↵ position and reducing the number of teaching assistants and graders. Additionally, all faculty and sta↵ su↵ered furloughs in 2009- on a sliding scale of up to six days (which amounted to a pay cut of about 3%). There are two other important streams of revenue to the School. The first comes from start-up commitments made with new faculty appoint- ments. Funds are allocated to new faculty members for travel, equipment, students, etc., as at most other universities. These funds are controlled by the faculty member, not by the School. However, and in the background, a second commitment of funds is made to the School to be used for computing equipment. As discussed on the following page, our computing environment is managed centrally and this stream of start-up commitments is the critical resource that allows us to build and maintain a quality environment. Last year there was some resistance from the Provost’s o ce to this model and we view this as a significant threat to the long-term health of our computing environment. The second stream of revenue mentioned above consists of funds from the Georgia Tech Research Corporation (GTRC), the Georgia Tech Foundation (GTF), and our friends and alumni. These are the only funds that can be
B. OVERVIEW 13
used for entertainment, faculty and graduate student recruiting meals, and other purposes not allowed with state funds. Our GTRC allocation in the last two years has been $17,000, which is roughly half of what it was in earlier years. Our Foundation accounts are small—currently slightly less than $100,000, and most of these accounts have restricted uses. We are working diligently to build relationships with friends and donors with a view toward future donations. See “Alumni and Friends” below for more on these e↵orts. Computing environment The School’s computing environment is managed centrally so that all com- puting resources are shared and form a coherent system. The environment and support thereof are often commented on positively by visitors and fac- ulty candidates. It is our main laboratory and is becoming increasingly important both directly for our faculty and students, and as we deepen our collaborations with other Schools, notably the School of Computational Science and Engineering. Here are more details of this resource: The School’s computing environ- ment consists of a high-speed, Gigabit switched network connecting several hundred workstations, printers, servers, and other network devices. We support a variety of desktop and laptop hardware. We have over 175 computers in o ces and computing labs. The PCs mostly run Linux and are typically at least 2.4-GHz, quad core CPUs with 8 Gb of RAM. All of them have 64-bit processors and most have a reasonable quality discrete video card. All user data, including large research datasets, are stored on a se- cure central file server. The storage capacity is several terabytes of hot- swappable disks in a RAID configuration. All user data (files, email, etc.) and critical system configuration data is backed up nightly. We support two computer labs for graduate and undergraduate students with a total of 26 seats. Note that, since 2009, all Georgia Tech students are required to have a laptop. The lab systems mostly run Linux, but we also have Windows 7 and Mac OS X systems available there, as well as scanners and printers. The School of Math has a small cluster of servers for high performance code that can take advantage of a parallel and/or distributed computing architecture. This includes a server with NVIDIA TESLA C2070 video card for GPU processing. In addition, our faculty and students have access to a
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B.5 Notable achievements
Faculty milestones Faculty in the School have received significant awards of several types since the last departmental review in 2007. In 2010 Robin Thomas was appointed Regents’ Professor, bringing to two the number of Regents’ Professors in the School. Maria Westdickenberg received a PECASE award (the Presidential Early Career Award in Science and Engineering, “the highest honor bestowed by the United States government on science and engineering professionals in the early stages of their independent research careers”) in 2011. Sloan Research fellowships were awarded to Silas Alben in 2011, Maria Westdickenberg in 2010, and to Dan Margalit in 2009. NSF CAREER awards were made to Maria Westdickenberg in 2010, Dan Margalit in 2010, Brett Wick in 2009, Yuri Bakhtin in 2008, and Haomin Zhou in 2007. Rafael de la Llave was appointed a fellow of the Institute of Physics in
- Klara Grodzinsky received the Institute-wide CETL Undergraduate Educator award in 2011. Je↵ Geronimo was appointed to a C´atedra de Ex- celencia chair in Madrid in 2011. Matt Baker won the University System of Georgia Regents’ Teaching award in 2010. Robin Thomas was a co- recipient of the Fulkerson Prize, for the second time, in 2009. Liang Peng was appointed fellow of the IMS in 2009. Prasad Tetali was appointed a fellow of SIAM in 2009. Tom Trotter won the College of Sciences’ Gret- zinger Award for his e↵orts toward faculty diversity in 2009. Brett Wick received a Humboldt Research fellowship in 2009. Michael Lacey received a Fulbright fellowship in 2008. Several faculty members (Professors Alben, Bunimovich, Loss, Peng, Yu, and Zhou) have collaborative, multi-institutional projects with NSF support. Christine Heitsch was PI (with co-PIs in Biology and Computer Science) on an NIH R01 grant of $1.3M awarded in 2007. Major training grants Both our undergraduate and our graduate programs are currently supported by major training grants. PI Michael Lacey made a Mentoring through Critical Transition Points (MCTP) proposal to NSF which was awarded $730,000 in 2008. This grant supports our undergraduates through schol- arships for high performing majors, the High School Mathematics Compe-
B. OVERVIEW 16
tition, a teaching seminar to train Undergraduate Teaching Assistants, and the distance learning program to teach Calculus 2 and 3 in high schools. PI Luca Dieci made a proposal to the Scholarships in Science, Tech- nology, Engineering, and Mathematics (S-STEM) program at NSF which was funded with $600,000. The grant supports graduate students, mostly through fellowships. Staff awards Sta↵ awards: Justin Filoseta received an Institute-wide Outstanding Sta↵ award in 2010. Sharon McDowell received the same award in 2009. School advancement During the academic year 2009-10, the School discussed, wrote and voted in a strategic hiring plan. The process, which was arguably at least as valuable as the final product, included vigorous debate about future directions for the school and tactics to achieve our goals. Further discussion and revision, to take into account progress in the preceding two years, took place in Fall
- The 2009 document and its revisions are available on the APR web site. Since the academic year 2008-09, a team led by Michael Loss has pro- duced a very high-quality glossy annual newsletter called ProofReader. This publication has made a remarkable impression on our alumni and friends and is a great ambassador for the School. (The review team is highly en- couraged to have a look.) Publication has continued at a pace of once per year. Making sure that this e↵ort continues in the long-term should be a priority for the School. As discussed in B.4 above, the School has formalized the group “Friends of the School of Mathematics” (FoSoM) for friends and alumni of the School. We are working to develop this group into a significant resource for the School and its students.
C. VISION AND STRATEGIC DIRECTION 18
to be acquainted with the latest thinking in science education. At the pro- posed scale, the program would allow us to reduce average class size in lower division (1000- and 2000-level) courses from the current 120 students to 80 students. Given the large fraction of Tech students who take Math courses every year, the impact on the undergraduate experience would be huge. Secondary but still very important e↵ects would occur at the upper- division level. Under the proposed conditions and scale, we would be able to o↵er eight additional advanced undergraduate courses and eight additional graduate courses per year. It is also very likely that many of the post- doctoral appointees would become involved in undergraduate research and other one-to-one mentoring activities. They would also be an excellent resource for graduate students. These additional resources will have a large positive impact on our undergraduate and graduate degree programs. Technology and a scientific approach to teaching As detailed in Section E.1, we are just beginning to explore new technolo- gies and learning strategies: personal response systems (“clickers”), on-line homework, and on-line learning platforms such as MUMIE have all been the subject of experiments in the School over the last few years. These experiments have generally been positive and there is interest in spreading some of these innovations more widely in the curriculum. Our vision is that the School will be open to experimentation, that we will take a scientific approach to evaluating the results, and that we will be serious about im- plementing innovations with potential positive impact more widely in the curriculum. It is worth pointing out here that resource constraints may be a limiting factor in some of these e↵orts. For example, there is interest in programs such as SCALE-UP, but lack of enough suitable spaces is an obstacle to widespread implementation.
C.2 Research directions
Excellence in a limited number of areas The School’s strategy has been to focus on a limited number of areas where real excellence can be achieved. This strategy has served us well and we plan to continue it. That said, the set of areas we strive to excel in is not static and will evolve over time. Significant energy was put into developing a
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strategic hiring plan that names specific areas where we will build strength. These are discussed in the sections that follow. Renewal in applied and computational mathematics Applied and computational mathematics, in various guises, has been a strength in the School for as long as it has had research ambitions. Clearly this makes sense in our institutional context and is a tradition that should be built upon. The strategic hiring plan makes a case that the School could profit from exploiting developments on campus in this area (strategic initia- tives, hiring in other units, new degrees), and it calls for targeting faculty in applied and computational mathematics more aggressively. Algebra, broadly construed The strategic hiring plan calls for aggressive e↵orts to build strength in algebra, here defined to include algebra, number theory, algebraic geometry, and algebraic combinatorics, as well as their applications. Partly this is due to the large place this area has in contemporary mathematics, partly it is because strength in the area will support interactions with Industrial Engineering, Electrical Engineering, Computer Science, Biology, Statistics, and other areas. There is also a need for sta↵ to teach advanced courses in this area. Significant progress has been made in the two years since the plan was written (with the hires of Josephine Yu and Greg Blekherman), but there is more to be done and possible departures may increase needs in this area. Mathematical biology Biology is the focus of a major strategic thrust at Georgia Tech and math- ematical biology is an area where the School has a small but excellent core group. The strategic hiring plan notes that we are well-positioned to become leaders in the field. For example, a recent $16M proposal for a center ranked second in the nation, and proximity to CDC and Emory gives us resources not available to others. The plan’s recommendation is to hire faculty in mathematical biology with a particular focus on systems biology/dynamical systems on networks, mathematical immunology, and computational methods in biology. Probability and Statistics This is another area where we currently have a small but strong group with an excellent record in training graduate students. There is large demand
C. VISION AND STRATEGIC DIRECTION 21
is that most of them have” a program of instructors. After explaining how these positions work, he notes: “From my own point of view, one of the most important perks of being a member of one of the elite departments is this never-ending supply of young mathematicians.” The Georgia Tech Mathematics brand We mentioned above that Georgia Tech is rated number 20 in mathematics world-wide by Shanghai Jiao Tong’s “Academic Ranking of World Univer- sities.” This ranking is based entirely on objective data (publications, cita- tions, prizes) and has no reputational component. It places Georgia Tech substantially higher than the NRC or US News ratings. We believe that this is because the Shanghai rankings take into account the mathematical output of the Institute as a whole. Clearly there is a great deal of math- ematics produced on campus outside the School of Mathematics (e.g., in Industrial Engineering, Computer Science, Electrical Engineering, ...) and this very rich mathematical environment is an advantage for the School. It is worth exploring whether there are structures or modes of cooperation that could further take advantage of this resource.
C.3 Challenges
Budget cuts As noted above, the School’s budget has been cut by about $800,000 over the last five years. These cuts have been met with (i) drastic reductions in the number of visitors and post-docs; (ii) elimination of sta↵ positions; (iii) faculty lines being left open. It is imperative to eliminate (iii) and reduce the e↵ects in (ii) and (i). Quality space As mentioned is Section B.4, the Skiles building is ill-suited to its current uses. In the long run, a total renovation or even a new building will be required. In the short run, continued infrastructure issues are certain to arise. Beyond Skiles, there is a lack of certain kinds of classroom space, for example very large lecture halls. Moreover, we have little access to small classrooms outfitted for non-traditional teaching, e.g., in the SCALE-UP model. Also, the technology available in classroom is of very uneven quality
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and the number of rooms suitable for distance learning and video courses is quite limited. Lack of suitable classroom space spills over into scheduling—with not enough rooms available at popular times, courses are pushed into more marginal slots and there is strong competition for seats in prime-time sec- tions. Retention Excellent recruitment has brought strong retention challenges. One cause is that there is marked salary inversion in the ranks of associate professors (where there is a negative correlation between time since PhD and salary, even after removing outliers). At the senior levels, salaries are beginning to lag. Also, the lack of endowed chairs or other positions higher than full professor has been a challenge both for recruitment and retention. Diversity The School has made significant progress in recruiting and promoting ex- cellent female faculty. Indeed, after last year’s promotions, we quadrupled the number of tenured female faculty, from one to four. We also have one excellent female assistant professor. Unfortunately, as with all excellent faculty, retention is a challenge and we may lose one of the four tenured female professors. Moreover, there is definitely room for more progress. Given that some critical mass has been achieved, we are hopeful for the future, but attention must be paid to this issue. Recruitment of minority faculty has been extremely challenging. Leave policies A substantial fraction of NSF resources for research in mathematics is de- voted to supporting research institutes (IPAM, MSRI, IAS, IMA, etc.). This underscores the importance of this type of activity for research in mathematics. On the other hand, the University System of Georgia has quite restric- tive policies regarding absence from campus. So far we have been able to organize research visits and semesters away for junior faculty while staying within the letter (and spirit) of the law, but this has relied on the cooper- ation and understanding of the upper administration.
