The University of Florida
Center for Applied Mathematics

History and Mission
Spring 1996




Co-Directors:
Ulrich Kurzweg, Aerospace,
Zoran Pop-Stojanovic, Mathematics, and
David C. Wilson, Mathematics

History

The Center for Applied Mathematics (CAM) was formed in 1974 through a cooperative effort of Professors A. R. Bednarek and Knox Millsaps. Letters of support for the formation of the center were provided by a number of prominent University of Florida individuals including E. T. York, Linton E. Grinter, and Harry Sisler. Dean Grinter wrote an extensive white paper delineating the structure, goals, and aspirations of the center. In addition, in a letter to Dean Harold Hanson he made the following remarks.
My thought, expressed in the white paper attached, is that an opportunity exists to train applied mathematicians here at several levels by using courtesy appointments of qualified faculty to a Center for Applied Mathematics. This Center would require a half-time Program Director and a Coordinating Committee to establish degree standards. Hence costs would be minimal. Nevertheless, the effect in the South, and therefore upon Washington sponsors, might be quite significant because comparable degrees seem limited to Rice, Georgia Tech and North Carolina State.

Chancellor Robert Mautz set in motion the formal mechanism for the creation of the center in a letter dated 6 February 1974, when he wrote:

I note that establishment of the proposed interdisciplinary Center for Applied Mathematics will aid in the training of students at both the undergraduate and graduate levels in various aspects of applied mathematics. While I encourage the interdisciplinary approach and optimization of campus resources in mathematics which this center may engender, establishment of the Center should not be interpreted as encouragement to plan any additional degree programs in the mathematical sciences at this time.

The University of Florida is hereby authorized to proceed with the establishment of an interdisciplinary Center for Applied Mathematics. No further action is necessary.

The Center was started at The University of Florida because of the presence of a strong group of internationally recognized applied mathematicians including the late Stanislas Ulam, late Karl Pohlhausen, M. Popov, and M. Longuet-Higgins. Soon this impressive group was joined by another internationally recognized authority, the late L. Cesari, who was instrumental in organizing a Symposium on Dynamical Systems, held at UF during 24 - 26 March 1976. The funding for this symposium came from the State of Florida's Quality Improvement Program. Five years later, during 25 - 28 February 1981, the CAM held the second Symposium on Dynamical Systems (under the same source of funding as the first). The central theme of the symposium was the relation of dynamical systems to current research on ordinary and functional differential equations, partial differential equations, stability theory, and optimal control. The Proceedings of the symposium was published by Academic Press. Also, during 1981 the CAM organized a Seminar on Stochastic Processes with funding from the Division of Sponsored Research. The proceedings from this conference were published by Birkhaauser. The CAM organized three more Seminars on Stochastic Processes, the last held in 1995. Funding for all these seminars came from the Division of Sponsored Research and the College of Liberal Arts and Sciences. The Center also sponsored the Sir Jeffrey Taylor memorial lecture series, which featured many distinguished speakers including Stan Ulam, Mark Kac, Felix Browder, G. Carrier, and M. Longuet-Higgins.

Administrative Structure

In his letter to Vice President Bryan dated 17 January 1974, Dean Harry Sisler proposed the following structure for the Center.

The original council consisted of Associate Vice President Robert A. Bryan, Dean Wayne H. Chen, Dean Harry Sisler, and Dean C. A. VanderWerf. The Council has now been replaced by Professor Karen Holbrook, Vice President for Research and Graduate Education. The original External Scientific Advisory Board consisted of J. P. LaSalle, C. C. Lin, J. B. Rosser, G. C. Rota, and S. Ulam. The original administrative structure consisted of Co-Directors A. R. Bednarek and Knox Millsaps. The original faculty in the Center included individuals from the following academic disciplines.


Purpose and Goals

The goal of the Center for Applied Mathematics is to create and support programs that provide students and faculty the opportunity to be involved with the exciting mathematical, scientific, and technological challenges of the 21st century. These challenges arise from fields as diverse as engineering, computer science, medicine, biology, and finance. The role of the center is to initiate contacts with knowledgeable individuals from the corporate as well as the academic sector to: establish collaborative projects, generate required funding, and produce research that is at the cutting edge. Thus, service, training (particularly at the graduate level), and research are at the core of the activities of the Center.

1. Service

By service we mean those activities, which enhance the teaching and research of applied mathematics. While the scope of the classical areas of pure mathematics tend to be somewhat limited, the activities included in applied mathematics encompass a diverse collection of disciplines reaching across campus as well as outside to government, business, and industry. This complexity makes it difficult for students to know what mathematics courses to take, for departments to know what programs and courses to offer, and for researchers to build alliances for common projects.


One main aspect of service is to educate and advise individuals about opportunities in applied mathematics. This advising should include descriptions of courses for students both inside and outside mathematics. These descriptions (in the form of handouts) are most helpful if they not only describe the material in the course, but also what group of students might be interested. Since applied mathematics students typically take courses from outside the mathematics department, descriptions of key courses from agriculture, business, computer science, ecology, engineering, finance, and statistics should also be assembled and made readily available to both currently enrolled as well as prospective students. To facilitate this process lists of advisors and graduate coordinators as well as other interested faculty across campus should be compiled. The week before registration these people can then be contacted and informed of what courses will be available during the next term. Information seminars can also be organized so that faculty can present a short description of the course materials, the historical background of the subject, as well as employment possibilities.


Since granting agencies (eg, the Department of Defense, ARPA, NSF, and NIH) develop large initiatives, where mathematics is but one small component, it is impossible for a single researcher to respond unless he/she is networked to other research groups across campus with similar interests. Thus, networking of research groups with similar interests is of fundamental importance so they can focus their energies on projects of common interest.


Since many of the most interesting mathematical questions originate from problems arising from computer science, engineering, medicine, statistics as well as business and industry, a third objective is to network with groups in business and industry. While this effort can be conducted on an individual basis, it is far more efficient to form an Applied Mathematics Consulting Laboratory. The purpose of this laboratory is to provide support to those individuals or groups from the outside world in need of insight or solutions to computational problems. Members of the Laboratory might work individually with a particular company or as part of a consortium to go forward together in search of funding from the federal government.


The final effort would be to take a more aggressive approach in recruitment of students. A primary way to achieve this task is to increase the visibility of our program by conducting sessions at regional AMS, SIAM, and MAA meetings. A second way is to hold conferences at UF on specialized research topics. A third way is to begin offering short courses in the NSF Chautauqua program. These courses would create visibility for the program with other teachers around the state. The goal would be to eventually develop short courses targeted for business and industry. If developed properly, these short courses could have the added benefit of returning resources back to the department.

2. Teaching

Effective teaching of applied mathematics requires the classroom be properly equipped for computation and display. The students would find it much easier to grasp concepts such as instability, ill-conditioned, and ill-posed if the faculty member could log into his/her account, run, and immediately display the results in the classroom. By graphing the output for various input parameters, the students could visualize the changes in the results immediately. A ``guest" account could also be set up so that faculty could share each others programs, particularly if they are written using standard software packages such as matlab, maple, and mathematica.


A popular and well regarded textbook is an excellent way for a faculty member and his/her department to achieve recognition. However, in most areas of classical mathematics the material included has been standardized for a long time. In addition, writing a textbook is a long, grueling, and boring process with typically little financial reward. If the pain could be spread across the shoulders of several faculty members, more such projects might be initiated. Since applied mathematics encompasses such a diverse collection of disciplines, the opportunities in this area abound. If faculty (together with the help an editorial assistant) were to begin typing up notes for their courses, then a permanent record would have been created. These notes could then be passed on (by e-mail) to the next faculty member in charge of a particular course. Graduate students could also be involved in this process-- particularly those interested in writing a dissertation. After a number of revisions, short pamphlets or modules that could provide useful teaching materials for others. Eventually, a textbook would be the result.

3. Research

The primary research goal is to encourage the formation and development of groups to investigate problems of interest to business, industry, and government. This development can be enhanced by providing a working environment with ample computer hardware and software support. While it may be the case in pure mathematics that a single faculty member can work effectively in isolation, in applied mathematics the amount of coding, debugging, and testing of algorithms can sometimes be overwhelming. (It is no accident that faculty members in Chemistry, Physics, and Computer Science frequently have large teams of graduate students and post-docs working for them.) Creating such a talent pool requires extensive financial resources. Thus, a second goal of the Center is to facilitate the efforts to obtain external funding. This can be done by developing a mechanism to aid faculty and groups of faculty to write grant proposals to business, state, and federal agencies on a regular basis. Support staff should be trained and a database of previous proposals made available.

Governance

An advisory committee will be formed to provide input to the directors of the Center. This committee will be comprised of those faculty actively contributing to its success. The directors of the center will consult with these faculty on financial matters as well as research priorities.