Although the United States is considered a world leader in mathematical sciences research and in doctoral and postdoctoral education, concern is growing about whether the needs of the profession and of an increasingly technological society are being met. Many doctoral students are not prepared to meet undergraduate teaching needs, establish productive research careers, or apply what they have learned in business and industry. This inadequate preparation, continuing high attrition, and the declining interest of domestic students, the inadequate interest of women students, and the near-absent interest of students from underrepresented minorities in doctoral study are problems that transcend the current difficult job market.

The charge to the Committee on Doctoral and Postdoctoral Study in the United States was to determine what makes certain programs successful in producing large numbers of domestic Ph.D.s, including women and underrepresented minorities, with sufficient professional experience and versatility to meet the research, teaching, and industrial needs of our technology-based society. The committee based its findings on site visits to a diverse set of programs in 10 universities carried out in late 1990 and early 1991. These programs were in both small and large, and in both public and private, universities. They were also geographically diverse. They were all in the "top 100" and included four departments in the "top 20."

The audience to which the report speaks is all U.S. doctoral and postdoctoral programs in the mathematical sciences, and, in particular, those programs that have limited human and financial resources. The report suggests that even with limited resources success can be achieved if, among other things, a program focuses its energies rather than trying to implement a "standard" or traditional program that covers too many areas of the mathematical sciences. It also notes that departments with the best faculty do not necessarily have the most successful doctoral and postdoctoral programs. A quality faculty is necessary for a good program, but of equal importance are students and researchers that can benefit from the program.

In this report, a "successful" program is understood to be one that accomplishes the following two 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 its site visits, the Committee on Doctoral and Postdoctoral Study in the United States looked for features that were present in successful programs as well as for elements that were detrimental to quality education. The committee noted that successful programs possessed, in addition to the sine qua non of a quality faculty, the following three characteristics:

1. A focused, realistic mission
2. A positive learning environment
3. Relevant professional development

A positive learning environment is an environment that provides the assistance, encouragement, nurturing, and feedback necessary to attract and retain students and to give them an education appropriate for their future careers.

The findings of the committee are as follows:

• There are several different models (missions) for programs, including
• the standard model, which supports research in a broad range of areas, offers depth in each one, and has as its goal preparation for careers at research universities, and
• specialized models, such as the subdisciplinary model, the interdisciplinary model, the problem-based model, and the college-teachers model, which were seen to alleviate two large human resource problems, recruitment and placement, and to be conducive to clustering of faculty, postdoctoral associates, and students, a practice that helps create a positive learning environment and promote relevant professional development.

• Both standard and specialized programs can be successful. However, programs that do not have the human or financial resources to run a successful standard program should consider whether a specialized model might better fit their needs.
• New Ph.D.s with a broad academic background and communication skills appropriate for their future careers are better able to find jobs.
• Active recruiting increases the pool of quality students. It does not just reapportion the pool. It also increases the number of women and underrepresented minorities. Students with strong mathematical backgrounds have a choice of studying mathematical sciences, physical sciences, engineering, law, medicine, and other areas. More of them can be attracted to the mathematical sciences.
• Clustering faculty, postdoctoral associates, and doctoral students together in research areas is a major factor in creating a positive learning environment.
• A positive learning environment is important to all doctoral students but is crucial for women and underrepresented minorities.

• All departments, including those characterized as elite and selective, need to provide a supportive learning environment.
• Doctoral students and postdoctoral fellows should receive broad academic preparation appropriate for their future careers in research universities, teaching universities, government laboratories, business, and industry.
• Doctoral students and postdoctoral fellows should learn teaching skills and other communication skills appropriate for their future careers.
• The number of postdoctoral fellowships in the mathematical sciences should be greatly increased so that such positions can be viewed as the logical next step after completion of the doctorate for the good student, not as a highly competitive prize for a select few. More postdoctoral fellowships should have applied, interdisciplinary, or pedagogical components.

Changing the American doctoral and postdoctoral system in the mathematical sciences so that it responds better to the needs of the profession, students, and the society is a task that requires the cooperative efforts of faculty, departments, professional societies, and federal agencies. The departments at research universities have a special responsibility to raise the level and increase the knowledge of talented but underprepared entering American doctoral students. Federal agencies should continue their programs and also increase their awareness of the impact of their programs on the doctoral and postdoctoral system. Professional societies should be involved in monitoring change in the universities, the agencies, and the community. But action, if it starts at all, will start from the faculty. The faculty should be aware that creating and maintaining a successful doctoral/postdoctoral program will require additional effort and time. The long-term benefits to the department, the students, and the society are clearly worth the effort.