WPI Hosts First in Series of SIAM's Regional Math in Industry Workshops

Cleve Moler (left), forthright speaker in a panel discussion of hiring in industry ("we hire relatively few with degrees in math"), talks during a break with WPI mathematics department chair Homer Walker (center) and James Brannan.

Paul Davis

How do interactions between university and industry get started? What forms do those interactions take? What do the participants get out of them? What sorts of problems are considered? What kinds of mathematics are used?

These and a range of related questions were addressed at the first SIAM Regional Workshop on Mathematics in Industry, held at Worcester Polytechnic Institute, May 18-20. Bogdan Vernescu of WPI handled local arrangements for the workshop, which concluded with a visit to the United Technologies Research Center in East Hartford, Connecticut. Robert Kohn of the Courant Institute of Mathematical Sciences and James Phillips of Boeing Computer Services are co-chairs of SIAM's Mathematics in Industry Steering Committee. The workshop was supported by the National Science Foundation.

Variety of Problems
The workshop's three keynote speakers provided an overview of the variety of problems faced by industrial mathematicians, a theme that was continued by former SIAM president Margaret Wright in her banquet address.

William Pulleyblank offered vignettes of a few of the long-term problems being studied at the IBM T.J. Watson Research Center. Those problems include risk assessment in financial models, strategic risk management for casualty insurers, stochastic load forecasting for pricing electricity contracts, and improved mechanisms for Web searching.

For a broader view of mathematics in industry, Pulleyblank paraphrased his predecessor at IBM, Shmuel Winograd: "The strength of the mathematical sciences is that they are pervasive in many applications. The challenge is that they are only a part of each application."

"How then does a university connect with industry?" Pulleyblank asked rhetorically. "By building credibility with industrial partners, similar to the instant credibility IBM Research already has." One approach Pulleyblank recommended was that universities establish visible groups of faculty and students to work on industrial problems.

Peter Castro of Eastman Kodak Company encouraged academic mathematicians interested in industrial problems to think in terms of impact on the bottom line and also in terms of technology transfer. Reinforcing Pulleyblank's theme of credibility-building, Castro suggested that mathematicians begin by taking on small problems. His example of a first problem was the design of a mechanism path in a copier that would minimize wear; in that case, even the suboptimal output of just a few iterations of the mathematicians' optimization process was a big improvement over the design engineers' first try.

Castro then described some of the more complex problems that arise in modeling the manufacturing and processing of color film. He also posed and answered a common question: "What kind of mathematics is useful? Every kind, but at Kodak partial differential equations are useful more often than topology."

Nikan Firoozye of Lehman Brothers reviewed some of the challenges facing those who use stochastic calculus to price options and derivatives. He also cited the rising barriers encountered by mathematicians who seek to enter the financial industry: "Mathematicians need greater expertise, intuition, and flexibility, but such broader knowledge does mean increased demand [in the employment market]."

For her banquet address, Margaret Wright drew on her current experience at Bell Laboratories, Lucent Technologies and on her earlier work at Stanford University to identify important qualities of mathematicians in industry. She cited work on the problem of optimal power flow in an electric network as a setting in which crucial differences in terminology were revealed only when the mathematicians persisted in asking questions to the point of becoming "pesky." Despite the risk of such an accusation, she asserted that, "Mathematicians must come in with a fresh viewpoint."

Other examples, including recalibration of the Stanford Linear Accelerator, protocols for testing the robustness of communications networks, and the design of indoor wireless communication systems, all illustrated the full range of work habits Wright considers important: "Ask thoughtful questions; be persistent; be flexible; be firm; be rigorous; aim for the best; be visionary. And," she concluded, "be active in SIAM!"

Hiring Decisions
The most concrete manifestation of an organization's interest in mathematics is the decision to hire a mathematician. A panel organized by William Browning of Applied Mathematics, Inc., reviewed the primary steps in this critical process. Panelists were Peter Castro, Cleve Moler of The MathWorks, Inc., Ernie Mintel of Pratt & Whitney, and Alfredo Bequillard of Lehman Brothers.

Applicants "need attitude, a desire to solve real-world problems, to get information that wasn't available before," Castro argued. Because of the "continuous communication" involved in industrial mathematics, he also looks for a "team player." "Stand-out applications are articulate, targeted at my business, show breadth as well as depth, demonstrate real interest in applications, and indicate flexibility," Castro said. "Prior industrial experience demonstrates interest in applications," he added, and a project program like that run by WPI's "Center for Industrial Mathematics and Statistics is an outstanding source of such experience."

Mintel hires mostly BS and MS graduates who can support the simulation and geometric design needed to achieve Pratt & Whitney's corporate goal of "virtual overnight simulation of engine design to evaluate proposed engines before we cut metal."

Moler echoed Castro's call for teamwork and communication skills in potential employees. Among MathWorks's 500 employees are approximately 40 PhDs, "most in engineering with strong math backgrounds. We hire relatively few with degrees in math," Moler explained, "because math graduates don't know much about software." MathWorks hires BS graduates for entry-level positions, such as technical support via telephone or e-mail. Those new hires usually have some knowledge of the MathWorks products Matlab or Simulink.

As desirable mathematical background, Moler listed ordinary differential equations, linear algebra, numerical analysis, and probability and statistics. The mathematics should be linked to applications in such areas as control, signal processing, image processing, or financial engineering, a connection that might come through courses in either engineering or physics. Emphasizing the need for knowledge of software, Moler said, "I would rather see an applicant who knew about make [the Unix command] instead of group theory, RCS [Revision Control System] instead of topology, HTML and Java instead of Besov spaces."

Bequillard outlined the two halves of the investment business, the sell side and the buy side. On the former, the mathematician's ultimate job is to incorporate stochastic models of market behavior into computer programs that will price financial products, given the necessary parameter values. One way in which advanced mathematics is useful, he said, is in covering all angles in attempts to resolve "why a model does not match the market."

Bequillard explained that Lehman hires through several approaches: associates programs, in which PhDs and MBAs rotate through different parts of the organization until they find a good fit; summer hires; and permanent hires, mainly through contacts at conferences.

A typical interview at Lehman Brothers will have two stages. In the first, a trader might ask for a brief description of how to hedge a particular product. In the second, longer phase, Bequillard explained that "other scientists and engineers ask questions based on the applicant's paper work to see if the individual is still as impressive in person."

Browning's firm of 12 employees---about half physicists and half mathematicians, a third of them hired as new bachelor's graduates---applies mathematics to submarine and search problems. He described the working environment as "fast-paced, confidential, team-oriented, having an external focus, involving close supervision (if you are working by yourself, you aren't working on an important problem!), and requiring significant client interaction.

"Mathematical preparation must include a solid foundation in mathematics with applications-oriented courses in areas like probability and statistics, optimization, and numerical analysis. We also expect study in a field that uses mathematics---physics, engineering, and so on---as well as computational skills, typically using C or C++ and various kinds of applications software."

William Browning of Applied Mathematics, Inc. (third from left), organizer of a panel on hiring decisions in industry, meets with panel members (left to right) Ernie Mintel of Pratt & Whitney, Alfredo Bequillard of Lehman Brothers, and Peter Castro of Eastman Kodak.

Browning hires throughout the year. A typical interview visit lasts one to three days, and a hiring decision follows within a few weeks.

Much of the discussion following the panelists' presentations emphasized the importance of industrial work experience for students, through co-op employment, summer experience, or industrial project work. Such experience, according to Mintel, "is a big discriminator among applicants." "We look for talent and interest," Browning added. "Co-op shows you know what the environment is like." None of the panelists could describe more than limited opportunities for faculty consulting.

University-Industry Interactions
There seem to be nearly as many ways to begin an industrial interaction as there are pairs of collaborators!

• Ferdinand Hendriks of IBM and Thomas Witelski of the Massachusetts Institute of Technology began their joint work on the thin-film fluid dynamics of IBM's Tango class of hard disk read-write heads after Hendriks's presentation at one of Rensselaer Polytechnic Institute's annual Workshops on Mathematical Problems in Industry.

• Paul Kornfeld, now with EBF & Associates, and Neil Chriss, currently director of the master's program in financial mathematics at the Courant Institute and a vice president at Goldman Sachs Asset Management, were brought together during Kornfeld's internship as a master's student in financial mathematics at the University of Chicago (see SIAM News, March 1998, page 1).

• The collaboration of Richard Braun of the University of Delaware and Dow Corning Corporation chemist Steven Snow began at a fluid mechanics meeting, where Braun was intentionally seeking industrial contacts (see SIAM News, March 1997, page 1).

• Steven Shreve of Carnegie Mellon University and Joseph Langsam of Morgan Stanley Dean Witter & Co. cooperated in developing the master's and PhD programs in computational finance at CMU. (See sidebar for Langsam's views of the variety of ways in which universities can work with the financial industry.)

• Arthur Heinricher of WPI and Richard Welch of The Premier Insurance Company met at a church social and went on to develop undergraduate student projects that gave Welsh "a fresh look at old problems I couldn't study internally," as well as offering him "interaction with knowledgeable university faculty."

• Natalia Sternberg of Clark University also met her collaborator, experimental physicist Valery Godyak of OSRAM Sylvania, Inc., at a party. Their work has greatly improved the understanding of industrial plasma processing. "The collaboration also changed my life as a teacher," Sternberg reported. "I learned how to talk to people who don't understand mathematics. My once-mediocre course evaluations have sky-rocketed."

• Folkert Tangerman of SUNY Stony Brook and Mike Brazao of Storage Computer Corporation are cooperating in the construction of a PC-based supercomputer at Stony Brook. Stony Brook is acquiring a relatively low-cost parallel computer, and Storage Computer has a test bed for its proprietary technology.

• As a doctoral student at WPI, Ani Velo attacked a problem of ripple instabilities in film manufacturing at Kodak to complete a required extramural project in applied mathematics. Thesis connections have also facilitated industrial interactions for Anna Gilbert, who is developing wavelet models of computer network traffic at Lucent Technologies with the support of an NSF postdoctoral appointment, and for Lucia Kimball of Bentley College, whose collaboration with the Brattle Group, a utility consulting firm, on economic dispatch problems in the electric power industry arose from her doctoral thesis work at WPI.

University Programs
University programs with an industrial focus come in as many flavors as Ben & Jerry's ice cream; consult the URLs for a more substantial taste!

• James Glimm called the broad Stony Brook program "basic research that happens to have a partner," on campus or off. See http://www.ams.sunysb.edu/department/research.html.

• Because it offers industrial work to its students at all levels---BS, MS, and PhD---Bogdan Vernescu described WPI's program as "vertically integrated industrial mathematics." See http://www.wpi.edu/Academics/Depts/Math/CIMS/.
  
• The master's program in computational finance at Carnegie Mellon is offered jointly by four departments: mathematical sciences, the business school, statistics, and computer science. Steven Shreve directs both the master's program and the doctoral program in mathematical finance; for the latter, see http://www.math.cmu.edu.

• Rensselaer's industrial programs have several facets, the most unusual of which is its Oxford-style Workshop on Mathematical Problems in Industry, which is organized by Don Schwendeman. See http://www.math.rpi.edu.

• According to Peter Monk, Delaware's program in industrial and applied mathematics uses its NSF Group Infrastructure Grant (GIG) in part to support paid industrial and government internships for graduate students. See http://www.math.udel.edu/~braun/imath.html and SIAM News, March 1997.

• George Knightly explained that the heart of the two-year master's degree program in applied mathematics at the University of Massachusetts is a group project. See http://www.math.umass.edu/Progs_Events/Grad_Program/new_applmath.html.

No Single Prescription
The range of industrial problems, university programs, and personal experiences presented during the workshop is persuasive evidence that there is no single prescription for successful interaction between academic mathematicians and industry.

Paul Davis is a professor in the Department of Mathematical Sciences at Worcester Polytechnic Institute.

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