AMS Department Brochure (1992)

The Applied Mathematics Department shares the Math Tower with the Mathematics Department and the Institute for Theoretical Physics, which is headed by Nobel Laureate C.N. Yang. The building contains a small conference center in addition to offices for faculty and graduate students, attractive seminar rooms and lounges, and a microcomputer lab.

There is a large Mathematics-Physics library in the Physics building which is joined on four levels to the Math Tower. The library contains a broad range of textbooks and journals: 22,000 mathematical sciences books and 11,000 bound journal volumes. The library currently subscribes to 350 mathematical sciences journals. In 1991, the Department acquired a 32-node Hypercube iPSC/860 parallel supercomputer with computing power comparable to a Cray Y-MP. A second, more powerful 56-node Intel Paragon parallel supercomputer arrived in 1993. The department has a network of 30 SUN SPARCstations plus numerous terminals and microcomputers.

INSTITUTE FOR MATHEMATICAL MODELING

The Institute for Mathematical Modeling houses the department's major research initiatives and computing equipment, including two parallel supercomputers and a cluster of the student SUN workstations see Facilities below.

The Center for the Mathematics of Nonlinear Systems at Stony Brook is part of the U.S. Army's Mathematical Sciences Institute other centers are located at Cornell. Current projects include nonlinear wave interactions, elastic plastics , robust control theory , computational methods for electromagnetic scattering, and parallel computing. Last year , the Center sponsored conferences in hyperbolic laws, computational geometry and biomathematics.

The Department is a member of the U.S. Dept. of Energy' s Partners in Computational Science Consortium for high-performance computing and applications to groundwater flow, porous media, and environmental clean-up. Stony Brook's effort in the Consortium focuses on parallel computing algorithms to analyze moving boundaries in fluid flow and to study flow dispersion properties of the stochastic differential equations which describe heterogeneous geologies. Activities of the Consortium encourage interaction with students and faculty at other sites eight universities and three government laboratories.

RESEARCH OVERVIEW

In 1988 the University at Stony Brook launched a major initiative to strengthen Applied mathematics at Stony Brook with the addition of four new faculty positions, the creation of a research institute, and the recruitment of a distinguished mathematical scientist to lead the department and new institute. New chair James Glimm has made fundamental contributions to nonlinear equations in pure mathematics, to quantum field theory in physics, and most recently, to computational fluid dynamics. Subsequent new appointments have strengthened all areas of the department. Three junior faculty are NSF Presidential Young Investigators. A parallel effort was undertaken at the same time to enhance the Mathematics Department; John Milnor, one of the giants of modern mathematics, was recruited to head a new Institute for Mathematics.

The Applied Mathematics Department has highly regarded faculty in numerical analysis, computational fluid dynamics and applied analysis; in stochastic models, computational geometry, combinatorial optimization and game theory; in mathematical and applied statistics; and in biomathematics.

A strength of the department is its focus on problem-driven research, arising from collaboration between Applied Mathematics faculty and dozens of diverse scientific groups on campus and in industrial and national laboratories. Applied Mathematics faculty have written scientific papers with researchers in two dozen different disciplines. Frequent interaction with other disciplines permeates all aspects of the applied and theoretical training of doctoral students, from motivating examples in first-year courses through dissertation research.

The department is an active player in the current initiative in manufacturing of the College of Engineering and Applied Sciences. Applied Mathematics faculty and graduate students are working on problems in facility location, computer-aided design, process control, production management, and quality control. Manufacturing problems have been the main subject of recent talks in the department's industrial mathematics seminar, where industrial scientists talk about their current research.

The department has an industrial advisory board, composed of leading mathematical scientists at companies such as IBM and Eastman Kodak, to help guide the department's research programs.

In the past ten years, Applied Mathematics faculty and graduate students collaborated in research projects with faculty in the Engineering departments, Computer Science, Physics, Chemistry, Geology, Economics, the Manage- ment School, Marine Science, numerous Medical School departments, Psychology, Sociology on campus and several groups at nearby Brookhaven National Laboratory. Faculty have also collaborated with researchers at Harvard, Cornell and Duke Medical Schools, Columbia School of Social Work, Los Alamos, Oak Ridge and Livermore National Laboratories, Bell Labs, Chevron, Grumman, Boeing, Hughes Aerospace.

The computational applied mathematics area of the department has grown recently with the appointment of James Glimm and the faculty he has brought to Stony Brook. This area includes computational fluid dynamics, numerical analysis, and applied analysis. At the Master's level, the computational applied mathematics track requires the following courses: applied linear algebra, foundations of applied mathematics, applied complex analysis, numerical analysis two courses, and differential equations. Doctoral students in this area have a wide array of advanced courses and seminars to choose from all graduate courses are listed on page 21 of this booklet. Most computational applied mathematics students aspire to earn a Ph.D. There is also a strong employment market for Master's graduates in this area.

COMPUTATIONAL FLUID DYNAMICS : James Glimm's computational fluid dynamics group, which moved to Stony Brook from the Courant Institute, includes Brent Lindquist, John Grove, and Qiang Zhang. Brad Plohr was recruited from Wisconsin and Yuefan Deng from Columbia to join this group, while Dan Marchesin frequently visits from Brazil. Later additions to this group are: XiaoLin Li (from Indiana), David Saltz and Folkert Tangerman. Six post-docs, supported by research grants, also play an important role in the group. Much of the research effort in this area centers on the interaction of nonlinear waves that occur in solutions to systems of hyperbolic conservation laws. These waves correspond to a variety of physical processes, including diffraction of shock waves through material surfaces, the chaotic mixing of fluids, nonlinear waves in an elastic material, and enhanced recovery of oil. This research is unified by the mathematical theory of elementary wave interactions known as Riemann problems.

Much effort is currently directed at gaining a mathematical understanding of Riemann solutions for more highly nonlinear systems, as well as interactions in two or more space dimensions. In contrast to the classical example of compressible ideal gas flow, these systems exhibit a variety of complex composite waves, shock breaking, and even loss of hyperbolicity. An additional effort is devoted to the study of stochastic partial differential equations, with applications to fluid mixing and chaos, and to dispersion of pollutants at environmental clean-up sites. The results of this analysis are being incorporated into a numerical front tracking algorithm to gain better resolution in computations.

NUMERICAL ANALYSIS : This group consists of Y.M. Chen, Ram Srivastav, and Reginald Tewarson, plus members of the computational fluid dynamics group. A strong program in parallel computing, led by James Glimm and Yuefan Deng, is linked to the department's recent acquisition of two parallel supercomputers. Reginald Tewarson works on numerical analysis of sparse matrices and large systems of nonlinear equations. For the past dozen years, much of his research has been motivated by work with physiologists to model renal function. Y.M. Chen leads a group of postdoctoral fellows and graduate research assistants studying the numerical solution of inverse problems. He works on reconstructing images from remote sensing devices, such as infrared sensors on satellites to determine the presence of cloud layers at many different attitudes, radar, and seismic signals. Ram Srivastav's research concerns numerical solutions of singular integral equations and associated problems in fracture mechanics.

APPLIED ANALYSIS : Ed Beltrami works on nonlinear optimization and diverse uses of mathematical modeling. He is currently collaborating with marine scientists on models for the growth of "brown tide algae", which has caused great economic losses in Long Island's bays in recent years. Dan Dicker works in theoretical civil and mechanical engineering problems with current interests in flow in porous media. Vaclav Dolezal's research concerns monotone operators, nonlinear systems theory, and control theory. W. J. Kim studies the theory of ordinary differential equations, with emphasis on oscillation and disconjugacy.

Brad Plohr does 'applied differential geometry' using geometric methods to solve Riemann problems. James Glimm's research interests include nonlinear systems and chaos, quantum field theory, and hyperbolic conservation laws.

FACULTY IN COMPUTATIONAL APPLIED MATHEMATICS

The operations research graduate curriculum is a joint venture with faculty in the Harriman School of Management and Policy. This cooperation is reflected in the joint appointment of Professor Matthew Sobel in the School of Management and Department of Applied Mathematics, as well as affiliated appointments for four operations research faculty in the School of Management. The program also draws on faculty in the Computer Science and Economics Departments. Most graduate courses in operations research are cross-listed in Applied Mathematics and the School of Management.

The OR area divides into four basic groups: stochastic models, computational geometry, mathematical programming/combinatorial optimization, and game theory. The game theory area is a joint effort of Applied Mathematics, Economics, the School of Management, and the Institute for Decision Sciences. The program produces 2 or 3 O.R. Ph.D.'s a year. The operations research Master's track requires the following courses: applied linear algebra, applied probability, linear programming, stochastic models, simulation, and applied statistics. Students are encouraged to take courses in Computer Science and the School of Management.

STOCHASTIC MODELS: Hussein Badr works on the simulation and performance evaluation of distributed computing networks. Michael Taksar works on the theory of optimal control of diffusion processes and their application to manufacturing processes. Matthew Sobel's current research interests include Markov decision problems, production management, and natural resource management. Eugene Feinberg works on a variety of problems in stochastic models and applied probability.

COMPUTATIONAL GEOMETRY: Esther Arkin, Joe Mitchell, and Steven Skiena work on efficient algorithms to recognize and characterize geometric objects or collections of objects. These algorithms are applied to problems such as routing robots around obstacles and efficiently cutting parts out of rolls of metal or cloth.

An interesting new line of research, funded jointly by Boeing and NSF, involves the use of virtual reality in designing complex products. For example, an engineer might put on a virtual reality helmet to 'see' inside the wing of a jetliner under design to optimize the placement of various pipes and wires.

MATHEMATICAL PROGRAMMING AND COMBINATORIAL OPTIMIZATION: Alan Tucker, Robert Frey, and Darko Skorin-Kapov work on graph theory and related graph algorithms for optimizing facility placement, scheduling, and routing. Ellis Johnson, a member of the National Academy of Engineering, works on polyhedral and group- theoretic methods in integer programming. Jadranka Skorin-Kapov works in integer programming and production management. Esther Arkin works on network flows and scheduling problems.

GAME THEORY: Research in game theory is centered in the Institute for Decision Sciences, which grew out of a decision sciences initiative in Applied Mathematics in the mid-1980's when two eminent game theorists, Pradeep Dubey and Abraham Neyman, were recruited from the University of Illinois. Their appointments are divided among this Institute, Applied Mathematics, and Economics. Matt Sobel, who came from Georgia Tech as part of the decision sciences effort, also has research interests in game theory.

With the addition of Robert Aumann a member of the National Academy of Sciences, J.P. Mertens, and Yair Taumann, Stony Brook is now widely considered to have the strongest game theory group in the country the Economics Department is the primary home for this group. Their research interests span all areas of game theory: stochastic games, repeated games, infinite games, strategic stability, non-atomic markets, and more.

FACULTY IN OPERATIONS RESEARCH

Esther Arkin, Associate Professor , computational geometry, combinatorial optimization.
Hussein Badr , Associate Professor in Computer Science , network simulation, distributed computing.
Pradeep Dubey , Leading Professor , joint with Economics and Institute for Decision Sciences, game theory, mathematical economics.
Eugene Feinberg , Full Professor in School of Management , applied probability.
Robert Frey , Adjunct Professor Renaissance Technologies Inc., mathematical programming.
Jean-Pierre Mertens , Leading Professor , joint with Economics and Institute for Decision Sciences, game theory, mathematical economics.
Joseph Mitchell , Professor , computational geometry, combinatorial optimization.
Abraham Neyman , Leading Professor , joint with Economics and Institute for Decision Sciences, game theory, mathematical economics.
Steven Skiena , Associate Professor in Computer Science , analysis of algorithms, computational geometry.
Jadranka Skorin - Kapov , Associate Professor in School of Management , mathematical programming, production management.
Matthew Sobel , Leading Professor , joint with School of Management and Institute for Decision Sciences, stochastic models, operations management, game theory.
Michael Taksar , Professor , stochastic processes, stochastic control.
Alan Tucker , Distinguished Teaching Professor and Associate Chair , graph theory, combinatorial algorithms.

The Stony Brook Statistics faculty have a wide range of methodological interests, from probability theory to statistical decision theory to industrial statistics and applied statistical studies in foster care.

While several statistics faculty have a primary focus on theory and developing new methodology, much of the research of all statistics faculty involves applied studies. Two statistics faculty have adjunct appointments in the Biostatistics group in the Medical School, while four faculty in biomedical sciences and Sociology have adjunct appointments in Applied Mathematics. These four include Robert Sokal of the Department of Ecology and Evolutionary Biology, one of the country's leading biometricians and a member of the National Academy of Sciences, and Judith Tanur of the Department of Sociology, an eminent applied statistician who has held many senior editorial and committee positions in the American Statistical Association. Several statistics graduate students work on research projects in epidemiology and medicine: one recent major project involving Applied Mathematics students was an epidemiological study of eye diseases.

The statistics Master's track is the most structured track in the department, with eight required courses in theory and applied techniques. Doctoral research builds on the Master's program and focuses on specific research projects. The required Master's courses are data analysis, probability theory, estimation, regression, analysis of variance, applied linear algebra, foundations of applied mathematics, and data lab. All applied courses in statistics include data analysis projects. The capstone course in the Master's track is the data laboratory, in which each student serves as a statistical consultant, under faculty supervision, on a research project normally outside the Applied Mathematics department. Several data lab projects have led to jointly published papers.

Applied statistics is the primary interest of Professors Steven Finch, and Nancy Mendell. They have collaborated with dozens of researchers on and off campus in the last decade, in genetics, psychiatry, orthopedics, immunology, ecology, economics, energy modeling, environmental health, psychology, politics, discrimination suits, nuclear safeguards, geology, and material science. Professor Finch's main work in recent years has involved collaboration with Dave Fanshel of the Columbia University School of Social Work on studies of foster care. This work led to testimony before a congressional subcommittee. His theoretical interests include the robustness of tests.

Professor Mendell originally worked as a biostatistician specializing in statistical genetics. She has served on a national advisory panel to determine directions for immunogenetic research in areas such as immunological matching for organ transplants. Recently she has also been collaborating with faculty in political science and psychology.

FACULTY IN STATISTICS

Hongshik Ahn , Assistant Professor
Stephen Finch , Associate Professor , adjunct appointment in Preventive Medicine, applied statistics.
Roger Grimson , Associate Professor in Preventive Medicine , biostatistics.
Nancy Mendell , Associate Professor , adjunct appointment in Preventive Medicine, applied statistics, statistical genetics.
James Rohlf , Professor in Ecology and Evolutionary Biology , biometrics, numerical taxonomy.
Robert Sokal , Leading Professor in Ecology and Evolutionary Biology , biometrics, theory of systematics.
Judith Tanur , Professor in Sociology , applied statistics, survey methodology.
Henry Thode , Assistant Professor in Preventive Medicine , biostatistics.
Wei Zhu, Assistant Professor

BIOMATHEMATICS

Several Applied Mathematics faculty and graduate students are currently undertaking research projects in biomathematics. The department has federal support for annual conferences at Stony Brook in biomathematics. A recent Conference on Biomathematics and related research in the department were featured in a major article in the New York Times.

Reginald Tewarson is one of the country's leading mathematical modelers in physiology. Working with renal physiologists at Cornell Medical School and the National Institutes of Health, he has refined over the past twelve years a detailed mathematical model of the biochemistry of kidney function using a large system of partial differential equations. He is also currently working with Stony Brook physiologists to model aspects of the chemistry of the brain. A dozen Ph.D. dissertations have resulted from mathematical questions arising from these models.

Ed Beltrami has been collaborating for several years with Stony Brook marine biologist Elizabeth Cosper to build a model for predicting outbreaks of \'brown tide', an explosive phytoplankton bloom that mysteriously appeared in Long Island bays in the mid-1980's, killing much marine life. His nonlinear dynamic model, evolving in response to experimental data, attempts to relate brown tide growth rates to water temperature, salinity and related parameters. Beltrami is also working with hematologists on blood clotting dynamics.

Biostatistics is a major area of activity within the department. Professor Nancy Mendell was trained as a biostatistician. She and Stephen Finch are involved in a variety of biomedical research projects with researchers in the Stony Brook Health Sciences Center. Mendell is a principal investigator on a large project at the Harvard Medical School concerning the genetic aspects of mental health. Professor Qiqing Yu is working with researchers at Mt. Sinai Medical Center in New York City on several biostatistical studies. He is also collaborating with researchers at Cold Spring Harbor Laboratory on statistical problems in the Human Genome Initiative and with Stony Brook pharmacologists on protein folding studies. A large proportion of the Master's and Ph.D. graduates go on to positions in biotechnology or pharmaceutical firms. The development of biostatistical skills is therefore an important priority in most graduate statistics courses.

Affiliated faculty member Lev Ginzberg of Ecology and Evolutionary Biology adds to the department's strength in biomathematics. Ginzberg uses diffusion theory to model evolutionary change and does extensive consulting on environmental impact studies.

JAMES GLIMM

Department Chair and Distinguished Professor, had a childhood ambition to be an astronomer. Later interests in chemistry, physics and electronics led to his undergraduate major in Electrical Engineering at Columbia University. By graduation, the future was beckoning in mathematical terms and he enrolled in the graduate math program at Columbia, earning a Ph.D. in 1959. Discussing the evolution of his interests from theory to applications, Glimm says, I used to view mathematics as a fantastic, fascinating puzzle. Then I considered it a formal structure of great depth and beauty. Later I came to see it as a tremendously powerful tool for understanding the universe. Of course, all three views are valid. He notes that the use of computers has completely altered the role of mathematics within the sciences and within society, giving it a much more central position. Computers change the questions we ask in mathematics. Answers tend to be more precise and quantitative. Theories an now attack the deeply nonlinear problems that used to be intractable.

Glimm is well known for changing research fields. Why do mountain climbers keep choosing new peaks to climb? It keeps life interesting. He's noted for contributions to C*-algebras, quantum field theory, partial differential equations, fluid dynamics, scientific computing, and the modeling of petroleum reservoirs.

What does a mathematical career offer today's students? Glimm mentions the challenges, the important problems waiting to be solved. This is an exhilarating time to work in the subject. Computing opens doors into whole new realms. Who should be mathematical scientists? People who are creative, analytical, individualistic and determined.

Jim Glimm has previously been a professor at M.I.T., the Rockefeller University, and the Courant Institute of New York University. He holds numerous leadership positions in professional societies and is an editor of several journals. He thinks his work is fun. He also enjoys mountain hiking, and at lower altitudes, jogging and attending the opera.

ALAN TUCKER

Associate Chair and Distinguished Teaching Professor, comes from a clan of mathematics professors. His father, a well-known mathematician at Princeton, communicated to Alan a love of teaching and working with students. I wanted to become a mathematics professor for as long as I can remember. My mother and my uncle encouraged this strongly; they said all the smartest students in college were math majors. But my father thought it would put too much pressure on me, that I might be under his shadow. He wanted me to try another field: if I looked at a weather map for 5 minutes, he would tell me what an exciting field meteorology was.

He went to college and became a math major. He actually did poorly in early math courses, but believed from his mother being a math major would make him smart. In graduate school at Stanford, I finally was turned on to mathematics, in particular, graph theory. As a child I used to spend hours looking at road maps and memorizing railroad schedules. My father was afraid to tell me there was a mathematics of networks-- graph theory. After a postdoctoral research year at Wisconsin, he came in 1970 to Stony Brook, where he has been ever since.

Prof. Tucker quickly became the guiding force behind a new Applied Math major that had just been established at Stony Brook. In his research, he was making important contributions in chromatic graph theory and combinatorial algorithms. He has advised or co-advised 8 dissertations. He was Department Chairman from 1978 to 1989 and has held numerous leadership positions in the University Senate.

For many years, he has been very active in the Mathematical Association of America. He currently chairs the MAA Education Council and serves on 10 other MAA committees. In the late 1980's, he was elected MAA First ice-President. He has served as a consultant or reviewer to over 40 mathematics departments. His text "Applied Combinatorics" has been called a path-breaking monograph that helped define the discipline of combinatorics at the undergraduate level.

His hobbies are tennis, squash, bridge, and classical music.

BRENT LINDQUIST

Associate Professor, was born in Fort Frances, Ontario, Canada, but grew up in Manitoba, all over the province. His father worked with the railroad and we always lived with railroad tracks in the backyard. At the University of Manitoba, Lindquist took only one non- science course his first year. "I always knew I'd go into science and I couldn't stand to write another essay", he says. I chose physics during my first year after hearing a lecture on neutrinos. I approached the Physics Department chair and said, 'Sign me up!' I was intrigued by all those particles passing through the earth without interaction. He graduated with an honors degree in physics and gold medals in both science and physics.

At Cornell, Lindquist earned a Ph.D. in particle physics with a de\336nitive calculation in Quantum ElectroDynamics for the magnetic moment of the electron. From Cornell he went to the Courant Institute at New York University as a post-doc of James Glimm and later became a research faculty member. He joined the Stony Brook faculty in 1989.

Professor Lindquist's current research interests are the mathematical equations describing flow in porous media, numerical computations and methods to solve those equations, and using them as tools to understand the physical processes involved. "I like doing computation because I'm good at it", he says, "and we're studying important problems". Our work can ultimately contribute to extracting more petroleum from depleted oil reservoirs and a better understanding of the dispersion of contaminants in polluted groundwater, for example. Numerical computation is a tool that holds wonderful promise but needs more than is available now. I'm doing what I can to push it toward that goal.

Brent is a very popular teacher. Even his specialized "service" course in numerical hydrology for geology graduate students draws a crowd of Applied Mathematics graduate students.

For fun, Lindquist plays the piano, works on his house, and dabbles in tennis.

NANCY MENDELL

Associate Professor, has known since high school that she wanted to be a biostatistician. Her knowledge of this field was acquired during summers, rather than the school year. A high school mathematics teacher encouraged her to apply to an NSF-sponsored summer program after her junior year which involved an epidemiology project at the Boston University Medical School. The following summer she was accepted into a similar NSF program at the Jackson Laboratory in Bar Harbor, Maine where she participated on a project in statistical genetics.

At Smith College she was a mathematics major and also followed a pre-med program. Her initial summer positions were at Jackson Laboratory. Later she worked for two summers as a biostatistician at the Harvard Medical School: "The minute they heard I was a math major and knew some epidemiology, they were eager to give me their data to analyze."

Following graduation from Smith, she went to the Harvard School of Public Health to study biostatistics. After two years and an M.S. degree, she switched to the Biostatistics Department at the University of North Carolina, the country's leading biostatistics center. After receiving her Ph.D. in 1972, she joined the faculty of the Division of Immunology at the Duke Medical School. Among her many achievements during this period were appointments to national and international advisory committees to study immunological criteria for determining matches in organ transplantation. Professor Mendell moved to Stony Brook in 1980, initially in the faculty of Community and Preventive Medicine in the Stony Brook Medical School. In 1981 she became a faculty member in Applied Mathematics and Statistics.

She has broadened her research interests since joining the Applied Mathematics Department and has been collaborating with political scientists, psychologists and biometricians as well as other Applied Mathematics statisticians. She currently is involved in half a dozen research projects outside the department. The two she is most involved in are the genetics of schizophrenia and health psychology.

ESTHER M. ARKIN , Assistant Professor , and
JOSEPH MITCHELL , Associate Professor

are a wife and husband research team whose paths converged in the Stanford Operations Research Department after under graduate careers at Tel Aviv University Arkin and Carnegie-Mellon Mitchell. After earning their Ph.D's at Stanford in 1986, they both accepted faculty positions at the Cornell University Department of Operations Research and Industrial Engineering. In 1991, they moved to Stony Brook.

Professor Arkin loved mathematics starting from first grade. In high school, the proofs in geometry and power of algebraic methods seemed really neat. At Tel Aviv University, an operation research course taught by a dynamic professor led her to see O.R. as a field where one can do fun mathematics in a concrete and often geometric setting. She soon discovered that combinatorial optimization was where she wanted to be. Recent interests include computational geometry and approximation algorithms. Besides collaborating with Mitchell It's convenient, Arkin collaborates with researchers at Tel Aviv University.

Professor Mitchell's original interests were pure mathematics and mathematics applicable to physics. After getting my B.S. and M.S., I thought I'd work in industry. I had forgotten that I'd applied for the Howard Hughes Doctoral Fellowship and, when I won it, I was entitled to an attractive job at Hughes as well as support for obtaining a Ph.D. This opportunity to combine industry and academics kept me in school. I went back and forth between summers at the Hughes Research Lab in Malibu, CA and the school year at Stanford. I loved my job at Hughes and there I got involved in mobile robotics. A typical problem is to compute a shortest path for a mobile robot to get from point A to point B. This problem was the catalyst for much of what I do today in computational geometry and its applications to manufacturing, cartography and computer vision.

Both are excellent teachers. In 1990 Cornell students voted Mitchell the best teacher among the 300 Engineering faculty. Professor Arkin plays bridge for relaxation, while Professor Mitchell enjoys woodworking. Together they enjoy their two daughters, aged three and five.

REGINALD TEWARSON,

Leading Professor, was born in a small Indian town in the Himalaya mountains near Nepal. His scientific career can be traced back to old issues of Popular Mechanics. A missionary donated them to my school. I pored over them and became fascinated with how things work and with America. Tewarson says his choice of an academic career was also influenced by his father, a professor of business several of his brothers became professors, one is now a college president. I enjoyed physics from high school on and wanted to be a physicist or mathematician. In high school I did electrical experiments. I even made a little radio set-- this was illegal but the man who should have enforced the law came to listen instead.

After earning a Bachelor's degree from Lucknow University, he taught there for a few years. A graduate fellowship in mathematics took him to Boston University in 1957. He was fascinated with the then young field of numerical analysis, and wrote his dissertation on the numerical solution of differential equations. After his Ph.D., he took a position in the research department at Honeywell Computers, where he worked in numerical linear algebra and also helped design Honeywell's linear programming software.

Professor Tewarson joined Stony Brook's Applied Math Department in 1964. He was one of the early pioneers in the study of sparse matrices and wrote the first book ever on the subject. The Russian translation was a best seller with over 20,000 copies sold. Tewarson now uses that subject to model physiological connectivity in his current work on mathematical models of kidney function. The kidney is one of the most complex parts of the body. The models are still evolving and new numerical procedures are needed all the time because the equations in the models are so hairy. He collaborates with several physicians at Stony Brook and Cornell Medical Schools on this research.

Tewarson has guided the dissertations of 24 students and has 90 research papers to his credit. When not doing research or teaching, he enjoys gourmet cooking, hiking, biking, carpentry since Popular Mechanics, I can fix anything and theatergoing in New York City.

GRADUATE PROGRAM

While most major universities have graduate programs in applied mathematics, operations research, and statistics in different departments, the faculty and graduate students at Stony Brook find many advantages to a unified mathematical sciences department. Many incoming graduate students are not ready to make a definite choice to specialize in one of the mathematical sciences, and in any case benefit from the broader education which the unified Stony Brook program offers. A unified department is able to offer courses and nurture research programs that have limited appeal in any one discipline alone.

There exists extensive interaction today among the mathematical sciences and other disciplines, both in academic and industrial research. All students in the department acquire a deep awareness of this interaction in courses and research projects, and simply by living with fellow students and faculty specializing in related mathematical science disciplines. Because of the increasing overlap among these disciplines, doctoral students are given considerable flexibility in selecting courses and Ph.D. qualifying exams students choose two out of six exam areas, plus a required exam in linear algebra and analysis. To serve the needs of professionally oriented Master's students, the department offers Master's level tracks in Statistics, in Operations Research, and in Computational Applied Mathematics, with specific course requirements.

The Master's programs are viewed as professional programs, similar to an engineering or M.B.A. degree. The programs train students in modes of analysis and computational skills that they will need on a daily basis as statisticians, or operations researchers, or numerical analysts. Five years ago, a combined five-year B.S./M.S. program was started in response to growing student interest in such a program.

The department's new actuarial training program includes courses preparing students for the first seven exams of the Society of Actuaries plus review sessions for the beginning exams.

The doctoral program trains students to do independent research and to advance the frontiers of knowledge. Most doctoral students first complete the course work of one of the Master's tracks so that their research will be based on a sound practical foundation. To help students learn to do individual research, the department encourages doctoral students to learn on their own, by forming small groups to study a topic together with faculty guidance and by participating in faculty seminars. As a result, virtually all doctoral students complete their Ph.D. in five years, many in four years. The dropout rate for those who have passed the Ph.D. qualifying examination taken in the second year is very low.

COURSES OF STUDY

FRST YEAR:

In the first semester, most Master's and doctoral students enroll in Foundations of Applied Mathematics and Applied Linear Algebra, plus one or two courses in their chosen track. Students with TA duties normally take three courses plus Teaching Practicum. In the second semester, M.S. and Ph.D. students take three or four courses. Some core courses are required for M.S. students and some electives.

SECOND YEAR:

Master's students usually complete their degree requirements in the third semester. Doctoral students take part or all of the Ph.D. qualifying examinations in the fall. The exams are offered twice a year and students have two chances on each part. Doctoral students normally take two or three courses a semester in the second year. After passing the qualifying exam, students start working closely with one or two faculty members, doing directed reading to become knowledgeable about a research topic that could lead to a dissertation.

THIRD YEAR :

Students take one or two courses a semester, participate in seminars, and normally meet at least once a week with their advisor as they begin to develop their doctoral research. Towards the end of the third year, students take a Preliminary Oral examination to demonstrate their readiness for independent research.

FOURTH /FIFTH YEAR :

Students complete their doctoral research and write their dissertation. Finally, they defend their dissertation orally. At the same time, students begin applying for positions in industry and/or academia. The faculty assist students in finding suitable employment.

Typical First Year Programs

Computational Mathematics Ph.D.

Fall:

AMS 504 Foundations of Applied Math
AMS 505 Applied Linear Algebra
AMS 526 Numerical Analysis I
AMS 698 Teaching Practicum

Spring:

AMS 501 Boundary Value Problems I
AMS 503 Applied Complex Analysis
AMS 527 Numerical Analysis II
AMS 528 Computational Methods in PDEs

Operations Research M.S.

Fall:

AMS 505 Applied Linear Algebra
AMS 507 Applied Probability
AMS 540 Linear Programming
AMS 547 Discrete Mathematics

Spring:

AMS 546 Graphs and Networks
AMS 550 Stochastic Models
AMS 556 Dynamic Programming
AMS 599 Masters Research

Statistics Ph.D.

Fall:

AMS 504 Foundations of Applied Math
AMS 505 Applied Linear Algebra
AMS 572 Data Analysis
AMS 698 Teaching Practicum

Spring:

AMS 550 Stochastic Models
AMS 569 Probability Theory I
AMS 573 Categorical Data
AMS 698 Teaching Practicum

GRADUATE COURSES

Additional courses are offered on an irregular basis.

AMS 500 Mathematical Modeling, Spring.
AMS 501 Differential Equations & Boundary Value Problems I, Spring.
AMS 502 Differential Equations & Boundary Value Problems II, Fall.
AMS 503 Applications of Complex Analysis, Spring.
AMS 504 Foundations of Applied Mathematics, Fall.
AMS 505 Applied Linear Algebra, Fall.
AMS 506 Finite Structures, Spring.
AMS 507 Applied Probability, Spring & Fall.
AMS 508 Mathematical Physics I, Fall.
AMS 509 Mathematical Physics II, Spring.
AMS 517 Ordinary Differential Equations, alternate Springs.
AMS 521 Mathematical Models in Physiology, alternate Springs.
AMS 523 Control Theory, alternate Falls.
AMS 524 Approximation Theory, alternate Falls.
AMS 526 Numerical Analysis I, Fall.
AMS 527 Numerical Analysis II, Spring.
AMS 528 Computational Methods in Partial Differential Equations, Spring.
AMS 531 Generalized Inverses & Sparse Matrices, alternate Springs.
AMS 540 Linear Programming, Fall.
AMS 542 Analysis of Algorithms, Fall.
AMS 543 Theory of Interest, Fall
AMS 544 Integer Programming, alternate Falls.
AMS 545 Computational Geometry, Spring.
AMS 546 Network Flows and Graph Theory, Spring.
AMS 547 Discrete Mathematics, Fall.
AMS 548 Nonlinear Programming, alternate Falls.
AMS 550 Stochastic Models, Spring.
AMS 552 Game Theory, Fall.
AMS 553 Simulation and Modeling, Fall.
AMS 554 Queuing Theory, Fall.
AMS 556 Dynamic Programming, Spring.
AMS 557 Inventory Theory, Spring.
AMS 558 Stochastic Processes, Spring.
AMS 559 Modeling Laboratory, Fall.
AMS 562 Numerical Hydrology, alternate Falls.
AMS 565 Hyperbolic Waves, Spring.
AMS 566 Compressible Fluid Dynamics, Fall.
AMS 569 Probability Theory I, Spring.
AMS 570 Mathematical Statistics I: Estimation, Fall.
AMS 571 Mathematical Statistics II: Hypothesis Tests, Spring.
AMS 572 Data Analysis, Fall.
AMS 573 Analysis of Categorical Data, Spring.
AMS 575 Data Analysis Laboratory, Fall and Spring.
AMS 576 Statistical Methods for Social Scientists, Summer.
AMS 577 Multivariate Statistics, alternate Fall.
AMS 578 Regression Theory, Spring.
AMS 580 Reliability Theory, alternate Falls.
AMS 582 Design of Experiments, Fall.
AMS 584 Survival Analysis, alternate Springs.
AMS 587 Nonparametric Statistics, alternate Springs.
AMS 588 Biostatistics, alternate Springs.
AMS 611 Theory of Partial Differential Equations, alternate Falls.
AMS 627 Integral Equations, alternate Springs.
AMS 628 Applied Functional Analysis, alternate Springs.
AMS 691 Topics in Applied Mathematics, several sections on varying topics each semester.

UNDERGRADUATE PROGRAM

Probably the most successful overall undergraduate mathematical department in the country, is how the Stony Brook Department of Applied Mathematics and Statistics was characterized by a chairman of the Mathematical Association of America's curriculum committee. In recent years, the department has averaged about 105 B.S.'s a year, 6% of Stony Brook Bachelor's degrees. In addition, the Mathematics Department graduates about 30 majors a year, giving Stony Brook the highest percentage of mathematics Bachelor's graduates of any American public university.

From its beginning in 1971, the Applied mathematics major has been a national innovator in curriculum. Widely used innovative courses, textbooks, and supplementary materials have been developed here. Stony Brook Applied Mathematics faculty have been invited to run dozens of workshops across the country to show other college mathematics faculty new approaches to teaching linear algebra, statistics, combinatorial mathematics, and mathematical modeling.

Alan Tucker, Distinguished Teaching Professor, who guided the development of the undergraduate major, is a national leader in collegiate mathematics curriculum. He is currently leading two Mathematical Association of America curriculum studies, one assessing the impact of calculus reform efforts and the other on model undergraduate mathematics programs.

Most Applied Mathematics majors enter the program after taking one or two Applied Mathematics courses as part of another major. This delayed interest in applied mathematics is probably explained by the fact that current high school mathematics fails to communicate to students the essential uses made of mathematics in today's world. The department likes to believe that the quality of its teaching is also a significant factor in influencing students to major in Applied Mathematics.

While the Applied Mathematics major is one of the university's largest undergraduate programs, the department offers only 14 courses for its majors: four in probability and statistics, two each in combinatorics, numerical analysis, nd operations research, and one each in applied linear algebra, differential equations, game theory, and mathematical models in the social sciences. The largest upper-level Applied Mathematics course, with an enrollment of 300 students a year, is the applied combinatorics course developed by Prof. Tucker.

The department believes that after taking six to eight Applied Mathematics courses, students should turn to courses in related departments such as Mathematics, Computer Science, Economics, as well as engineering and physical sciences. Several Applied Mathematics courses are cross-listed with courses in other departments. About 50% of the Applied Mathematics majors have a double major, most often with Computer Science or Economics. The Applied Mathematics Department participates with the Mathematics Department in offering a state-certified secondary school mathematics teacher preparation program.

In 1992, the department was awarded a $1,000,000 federal grant to increase the number of minority students at Stony Brook preparing for graduate study in the mathematical sciences.

The department and university try in many ways to help make the lives of graduate students enjoyable outside the classroom. Extensive orientation programs and social events are provided for new students. The department staff tries to assist graduate students with university and personal problems. The staff and faculty tend to become good friends with most graduate students, and often correspond for years after the students leave Stony Brook.

Much of the social life grows out of friendships made in the department. Applied Mathematics graduate students organize Tuesday afternoon get-togethers in the department, plus other social events at off- campus establishments. They also plan several larger social events, including a barbecue the Friday before classes start followed a few weeks later by a welcoming buffet party at the chairman's house and an international buffet for which foreign students prepare specialty dishes from their native lands and Americans bring favorite hometown dishes. Graduate students and faculty enjoy sports, such as tennis and volleyball, together and form teams to play other departments.

The majority of graduate students live in student housing on campus. While apartments in the area tend to be expensive, some students form groups to rent houses near campus. There are shops at the edge of campus and a 120-store shopping mall three miles from campus.

The university Fine Arts Center offers concerts and plays several times a week. A broad array of interest groups exist on campus: crafts, athletics, music, martial arts, religion, games. A large, new field house opened in 1990. The university has a private beach, although most students prefer the many fine public beaches.

While the village of Stony Brook is wooded suburbia, there are night spots for socializing in the town and along the harbor of Port Jefferson, three miles east. For a fuller range of social and cultural activities, students go to New York City, 50 miles away a station on the edge of campus has frequent trains to the city. New York City is a surprisingly inexpensive place to visit if one does not stay overnight with many museums, excellent low-priced restaurants and off- Broadway entertainment.

The Graduate Student Organization has successfully pressed for improved health insurance for students and day-care for students' children, and in general is a strong lobby for the rights of graduate students on campus.

Many employment opportunities exist for spouses of students in nearby colleges, businesses, and industrial research parks.

FELLOWSHIPS AND ASSISTANTSHIPS

FELLOWSHIPS :

Twelve graduate students a year The university has a limited number of Graduate Council fellowships for exceptional applicants and for students from under-represented minorities. The department also has a small number of industrially supported fellowships.

RESEARCH ASSISTANTS IN APPLIED MATHEMATICS:

Over 20 students a year are supported as research assistants on grants of Applied Mathematics faculty, mostly in the computational fluid dynamics group. The duties of research assistants typically involve reading papers and undertaking research that is both part of the student's dissertation and part of the advisor's overall research program. Often the work includes writing pieces of software for a large computation program which may, for example, model the behavior of shock waves or numerically invert integral equations.

RESEARCH ASSISTANTS IN OTHER DEPARTMENTS :

Some Applied Mathematics research assistants work for faculty in other departments. They have participated in a wide range of interesting projects in computer science, statistical mechanics, physical chemistry, and other 'hard' sciences. Other students have worked on biomedical projects, involving such problems as simulating stresses on bones attached by artificial joints, analyzing epidemiological data for various diseases, deconvoluting neurophysiological stimuli of muscle fibers, and statistical analysis of data at the Sex Therapy Clinic. Students have been supported on research projects at nearby Brookhaven National Laboratory.

TEACHING ASSISTANTS:

Half the department's teaching assistants teach a three- hour elementary course under the supervision of a faculty member. The other half run problem- solving recitation sessions and grade homework. Faculty give TA's teaching for the first time extensive individual preparation for their teaching assignments. The courses taught by teaching assistants are finite mathematics, elementary statistics, and applied linear algebra. The latter two courses use innovative approaches developed at Stony Brook. TA duties require about 8 to 12 hours a week.

Although teaching experience would seem to be important only for students planning a career in academia, it is also highly valued by industrial employers. Industrial mathematicians must explain their work to other scientists and make presentations to laymen.

In 1992, the department started a seminar on collegiate curriculum in the mathematical sciences for advanced teaching assistants interested in academic careers. The Stony Brook Applied Mathematics Department has been a national leader in applied mathematics curriculum. This informal seminar, run jointly with the Mathematics Department, seeks to share with future faculty ideas for revitalizing undergraduate teaching strategies and curriculum in the mathematical sciences.

This is an exciting time to be a mathematical scientist. Every major corporate research effort in the country now employs applied mathematicians with advanced degrees. The demand for applied mathematics Ph.D.'s in academia is also strong.

Because students in the mathematical sciences are poorly informed about the diverse careers open to them, the Applied Mathematics Department invites former students and industrial project leaders to give talks to students about their work and the interesting uses it makes of mathematical sciences. Also, in the department's industrial mathematics seminar, students learn more about industrial mathematics research from leading industry scientists.

Most major corporations today, such as AT&T, American Airlines, Exxon, Ford, Hughes Aircraft, IBM, Merrill Lynch, and Nabisco, have large groups of research mathematicians. All have hired Stony Brook applied mathematics Ph.D.'s and M.S.'s. Bell Laboratories of AT&T alone hired a dozen Stony Brook Applied Mathematics Ph.D.'s and twenty M.S.'s in the 1980's. Stony Brook mathematical scientists have been employed in market research, product testing at Consumer Reports, environmental health, and commodities forecasting. Many work for computer hardware and software companies in Silicon Valley and along Route 128. A good number of M.S. graduates pursue the well-established career path of an actuary. Biomedical centers and drug companies need mathematical scientists for modeling biological systems and statistical analysis.

The federal government employs mathematical scientists some from Stony Brook in technology-oriented agencies like NASA and the Defense Department and also 'non-scientific' agencies like the Departments of Transportation and Commerce to improve operations and do statistical analyses. National laboratories, such as Los Alamos, employ mathematical sciences Ph.D.'s for basic mathematical research and diverse applications such as fusion simulation, air pollution modeling, and nonlinear PDE models of the spread of AIDS they hired six Stony Brook Applied Math Ph.D.s in the 1980's. The National Security Agency employs 1000 mathematicians and is currently hiring 100 more a year.

Two recent Stony Brook Applied Mathematics graduates oversee statistical testing of products at Consumers Union publisher of Consumer Report; another runs the national polls at CBS News. A 1986 Applied Mathematics Ph.D. led a $20,000,000 project funded by the Air Force to develop an artificial intelligence procedure for identifying and diagnosing equipment failures. The Air Force adopted the system as the basis for design specifications for its new Advanced Tactical Fighter.

About one-half of the Stony Brook Applied Mathematics Ph.D.'s have pursued academic careers. Recent Ph.D.'s have accepted faculty appointments at major research universities such as NYU, Penn State, Purdue, Rutgers, University of Massachusetts, and Northwestern in departments of mathematics, computer science, operations research, statistics, and business.

Others have accepted positions at leading liberal- arts colleges such as Bowdoin and Franklin & Marshall. Several M.S. graduates have become junior college teachers.

Applied Mathematics graduate students represent a diverse set of backgrounds. They vary in age, undergraduate major, and nationality they come from five continents. Five years ago foreign students were a majority, especially among doctoral students, but recently most incoming students have been U.S. nationals. Of the 27 new graduate students entering with financial aid in the last two years, 22 were U.S. nationals. They came from major research universities such as Cornell, Harvard, UCLA, University of Illinois, and of course SUNY-Stony Brook, smaller research universities, such as Brandeis and RPI, and a diverse range of colleges, such as Beloit College and Western Maryland College. About half of these new supported students were women.

The department is working hard to increase the number of Blacks and other underrepresented minorities in the mathematical sciences. Special university and U.S. Department of Education fellowships are available to support them. The department recently received a large federal grant to increase the number of minority students at Stony Brook preparing for graduate study in the mathematical sciences. The department currently has two Black and two Hispanic doctoral students.

While most of our entering American graduate students and all foreign students have performed well in mathematics and other subjects throughout high school and college and enter graduate school straight from college, a few American students have had some misstarts or periods of weak grades; others have worked one or more years before enrolling in graduate school. The department tries to be especially sensitive to the strengths and deficiencies of these students; some excellent dissertations in recent years have been written by such students.

The following are profiles of three graduate students. Sue Monroe is writing a thesis in resource management, Bill Thistleton in computational fluid dynamics, and Elizabeth Wang in computational chemistry.

SUSAN MONROE

is a doctoral student in operations research. Her interest in mathematics was sparked by her mother, who began college as a math major, and by a dynamic AP calculus teacher in high school. At Colgate, she was a math major who planned to become a secondary school teacher.

Upon graduation, Sue accepted a position as a mathematics teacher at a private coed boarding school where she also served as a dorm mother and assistant softball and basketball coach. During my second year, I decided being a college teacher would be more to my liking. At Colgate, the math course she liked most was a survey course in applied mathematics, taught by Tom Tucker, brother of Stony Brook Applied Math Professor Alan Tucker. When she called Professor Tom Tucker for recommendations for graduate schools, he suggested Stony rook and called his brother Alan to put in a good word for Sue.

At Stony Brook, she chose to enter the operations research doctoral program, passing her qualifying exams in her second year. With a long-standing interest in environmental issues, Sue began doing directed reading in natural resource management with Professor Matthew Sobel. Under Professor Sobel, she is writing a dissertation on strategies for simultaneously managing the water discharge for agricultural and other uses and hydroelectric power generation in a river basin with multiple dams. For her teaching assistantship, she has been teaching a freshman finite mathematics course each semester and enjoying it very much.

In the summer of 1992, Sue worked at Pacific Gas and Electric in San Francisco, evaluating the usefulness of a large general-purpose water resource management computer package in solving the water management problems that PG&E faced shaped by local environmental regulations, Sierra Nevada rainfall patterns, etc.. This job made me start thinking that working on water management problems might be as satisfying as being a college mathematics professor.

Sue's hobbies are mountain biking and pottery.

BILL THISTLETON

received his undergraduate degree in Electrical Engineering from Clarkson University in Potsdam, N.Y. He then entered the Peace Corps and was sent to Cameroon to teach science and mathematics. He lived in the town of Limbe, the site where Tarzan movies were filmed.

Two years later, he returned to Potsdam to relax and do a lot of canoeing. He got a part-time job in a cafeteria and enrolled in two courses in the Mathematics Master's program at SUNY-Potsdam because the Math building was right beside my favorite canoeing stream. One of his professors was Dr. Clarence Stephens, an inspiring teacher who made SUNY-Potsdam a nationally famous mathematics factory, turning out about 200 Math B.S. and M.S. degrees a year out of a total of 1200 Potsdam graduates. Stephens offered Bill a Teaching Assistantship after one semester, provided he would become a full-time graduate student.

After Bill completed his Master's degree, he came to Stony Brook for doctoral work in applied mathematics. He passed his Ph.D. qualifying exams in his third semester. He was soon pursuing two possible thesis topics, one on geochemical diffusion equations that describe oxygen depletion in oceans, with a Marine Sciences professor, and the other in computational fluid dynamics with Professor Lindquist. Eventually, he choose a fluid dynamics topic with an environmental focus, the study of equations describing the dispersion of contaminants in groundwater and strategies for their biomediation. Bill wants to be a mathematics professor. Besides teaching a section of the Applied Mathematics elementary applied linear algebra course, Bill has taught during summers in the C-STEP Program which helps prepare minority students for scientific careers. He is also a volunteer counselor in the university's RESPONSE program, a crisis hotline. His hobbies are playing the guitar and singing, ceramics, and weight-lifting.

For application forms and further information about the graduate programs in the Department of Applied Mathematics and Statistics, please write:

Graduate Program Director
Department of Applied Mathematics and Statistics
State University of New York at Stony Brook
Stony Brook, New York 11794-3600 USA

or call at 516 632-8360, International callers our country code is 1.

Interested students are encouraged to visit the campus to meet with faculty and graduate students. Visits during vacation periods and weekends can be arranged. Visitors can stay overnight with a graduate student. A limited fund is available to subsidize visits by highly qualified students and underrepresented minorities.

Foreign student deadlines are January 15th for Fall admission and October 1st for Spring admission. There are no formal deadlines for American and Permanent Resident applicants.

All students (Foreign, American and Permanent Residents) wishing to be considered for financial support must complete their application by January 15th for Fall admission and October 1st for Spring admission.

The University at Stony Brook is an equal opportunity/affirmative action educator and employer.

VISITING STONY BROOK

BY CAR :

Take the Long Island Expressway Route 495 to Exit 62; follow Nicolls Road County Road 97 north for nine miles.

Ferry Connection: Connecticut car ferry runs from Bridgeport to Port Jefferson 516-473-0286; call for schedules and reservations. Follow Route 25A four miles west to campus at Nicolls Road.

BY RAILROAD:

Take the Long Island Railroad's Port Jefferson line from Penn. Station Manhattan to Stony Brook station, at the edge of campus.

BY AIRPLANE:

Land at New York City's Kennedy or LaGuardia Airport, 50 miles west of campus, or at Long Island MacArthur Airport, 10 miles south of campus served by American and US Air. Limousine service to campus is available from all three airports.

BY BUS: Call Suffolk Transit 516-360-5700 for schedules and routes of buses to campus from many local towns.