attracting more domestic students into the mathematical sciences and giving those students proper foundations for their future careers.

A positive outlook that serves the interests of the profession and the country can be translated into actions intended to achieve the following two broad objectives:

• All students, including the majority who will spend their careers in teaching, government laboratories, business, and industry rather than in academic research, should be well prepared by their doctoral and postdoctoral experience for their careers.

• Larger percentages of domestic students, and, in particular, women and underrepresented minorities, should be attracted to the study of and careers in the mathematical sciences.

In this report, a “successful” program is understood to be one that accomplishes these two objectives. The needed renewal of the profession, as pointed out in the “David I” report (NRC, 1984), A Challenge of Numbers (NRC, 1990b), and the “David II” report (NRC, 1990c), requires larger percentages of domestic students. Although statistics invariably oversimplify the situation, the following two “completion rate” statistics concerning percentages of domestic students are useful in judging a program's success: (1) the percentage of students who entered the program five years earlier and who have received their doctorates, and (2) the percentage of students who completed their second year of graduate study four years earlier and who have received their doctorates. The first of these two types of completion rate is an appropriate measure of the success of highly selective programs, while the second is appropriate for less selective programs. The committee observed a number of programs for which both rates were well above 50 percent.

The charge to the committee was to determine what makes certain doctoral and postdoctoral programs in the mathematical sciences successful in producing large numbers of domestic PhDs, including women and underrepresented minorities, with sufficient professional experience and versatility to meet the research, teaching, business, and industrial needs of our technology-based society. The mathematical sciences are considered to be pure mathematics, applied mathematics, statistics and probability, operations research, and scientific computing. Computer science, a separate discipline, is not included among the mathematical sciences.

The doctoral period considered in this report extends from the first year of graduate study through completion of the thesis, regardless of whether or not the student obtains a