Appendix: MII Study Methodology

The MII study was initiated by SIAM in 1993 to examine the role of mathematics and mathematicians in nonacademic environments. The focus of the study was on recent graduates of mathematics departments—departments with American Mathematical Society (AMS) classification codes I--III and IVa, including applied mathematics departments—working in industry. By "industry" we mean generically employment outside education and academia; we thus include business, industry, and government (including federal and national laboratories). Excluded from our definition are research institutes associated with universities.

The MII study was performed in four stages: focus groups of mathematicians from industry and government; a telephone survey of Ph.D. and master's graduates of mathematical sciences departments working in industry; a follow-up survey of a set of their supervisors; and visits to industry and government sites conducted by members of the MII steering committee. Overall, we spoke with approximately 500 mathematicians, scientists, and engineers in industry, including more than 175 managers, covering a range of experience levels.

A.1. Focus Groups

In the first stage, we held a series of exploratory focus groups with 40 mathematical and computational scientists working in industry and government. Focus group members had a variety of experience, from new hires to managers, and were employed by a wide array of companies. We also visited several industry sites to speak with mathematicians. The results of this preliminary stage are reported in [Davis91].

A.2. Telephone Survey of Recent Graduates

The second stage of the study involved a telephone survey of Ph.D. and master's graduates of U.S. mathematical sciences departments from 1988--1992 who currently held jobs in industry or government in the United States. Graduates of statistics and operations research departments were not included in the telephone survey, although graduates of mathematics departments working in statistics and operations research were included.

The MII database of recent graduates working in industry was developed as follows. An initial database of Ph.D. graduates was obtained from data collected by the AMS-MAA Data Committee for its annual surveys of graduates in 1988--1992. We then wrote to 210 mathematical sciences departments: 135 Ph.D.-granting departments, chosen as a representative sample using AMS classification codes; and 75 departments granting only master's degrees. Our letter asked for contact information about graduates from 1988--1992 working outside academia. Eighty percent of the departments responded, either providing some of the requested information or giving a negative response (that there were no graduates in industry or that the information was not available). Twenty-five percent of the responding departments were able to supply current information on master's graduates. The Ph.D. information received from departments was then checked against the AMS-MAA Data Committee records, and new or updated records were merged into the database.

As a result, a database was created of 335 Ph.D. and 271 master's graduates working in nonacademic positions. From this database, two samples—101 Ph.D.'s and 102 master's graduates—were selected for telephone interviews. The samples were structured to be representative by both type of department and employer, using the AMS classification codes for departments and an employer code based on the Standard Industry Classification (SIC) codes of the U.S. Office of Management and Budget. Government employers, including government and national laboratories, were assigned employer code 1. The remaining employer codes correspond to the first two digits of the SIC codes: code 2 for engineering research and computer services, including software (87xx and 73xx); code 3 for financial, communication, and transportation services (40xx and 60xx); code 4 for manufacturing, including electronic, computer, aerospace, and transportation equipment (35--38xx); code 5 for manufacturing, including chemical and allied products, petroleum, and petroleum extraction (28xx, 29xx, 13xx); and code 6 for all other codes and cases in which no code could be determined.

Table 16 gives an indication of the numbers of graduates in various categories. Note that the total number of Ph.D.'s is based on the AMS--MAA surveys of Ph.D.'s, 1988--1992, and excludes graduates from departments of statistics and operations research, whereas the total number of master's graduates is taken from [SEI93, page 280,], and includes graduates from departments of statistics and operations research. (No sources of data were available to provide consistent values for these numbers.) The estimates of the numbers of graduates working in industry—25% of Ph.D.'s and 44% of master's graduates—are based respectively on [SEI93, page 283,] and [SEI91, page 283,].

Table 16: Ph.D. and master's graduates, 1988--1992.
Category Ph.D. Master's
Total number of graduates 3,701 17,780
Estimated number of graduates in industry 925 7,823
Entries in MII database 335 271
Telephone interviews 101 102

The MII Ph.D. sample is reasonably large relative to the estimated number of mathematics Ph.D.'s working in industry, while the master's sample is much smaller relative to the estimated population. This reflects the great difficulty of obtaining current information about master's graduates working in industry.

A questionnaire was designed by members of the MII steering committee and tested in a pilot telephone survey of 15 graduates. The full telephone survey of graduates was conducted by Business Science International (BSI) in December 1994.

A.3. Telephone Survey of Managers

Following the telephone survey of graduates, 75 managers representing a good sample of industry classification codes were selected from the "immediate supervisors" of the mathematicians interviewed in the telephone survey. These managers were then interviewed by telephone by BSI.

The telephone questionnaire for managers was intended to obtain further details about the organizations in which the graduates were employed, confirm some of the information obtained from the graduates, and solicit opinions about graduate education in the mathematical sciences.

A.4. Site Visits

The final stage of the MII study consisted of visits by steering committee members to 19 sites in industry and government that employ a significant number of mathematical scientists. During these site visits we spoke with 175 mathematicians, engineers, scientists, and other professionals, of whom 100 were managers at the level of group leader or above. At twelve sites we spoke to managers at the level of director and above; at four sites we spoke to vice-presidents of research. The sites were selected to cover the range of industry codes. We visited five government sites, including four laboratories; five engineering, consulting, or software companies; one financial services company; five aerospace, transportation, or electronics companies; and three companies in chemical and allied products, including one pharmaceutical company. In addition to these site visits, we conducted a special focus group consisting of three managers from small companies (one consulting and two software firms).

Although site visits focused primarily on mathematical and computational scientists, we also spoke with nonmathematicians, particularly managers, who were familiar with the uses of mathematics and computing at the site and in the company at large, as well as with the contributions of mathematical and computational scientists.

Before the site visits, interviewees were sent an overview of the study and its goals, along with a list of detailed questions. In conducting the site visit discussions, we tried to address six general areas: background information on the site, the role of mathematics, the role of mathematicians, factors for success in the company for a mathematician, interaction with academia and government in conducting business, and opinions about academic programs in mathematics. Detailed notes on each visit were taken by members of the site team (typically two to three members), and a report was prepared by one member of the visiting team.

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