Chapter 2 gives a brief historical perspective of the mathematical sciences in America, with emphasis on doctoral and postdoctoral training.

Chapter 3 describes how some programs in the present system achieve success. Three characteristics of successful programs—a focused and realistic mission, a positive learning environment, and relevant professional development—are introduced in this chapter. The issue of having a high-quality faculty—a sine qua non of a successful program—is acknowledged but not discussed in detail in this report.

The heart of the report is Chapters 4–7, which treat the three characteristics of successful programs and human resource issues that must be taken into account. Chapter 4 discusses human resource issues; in particular, those related to domestic students, women, and underrepresented minorities are examined. A number of specialized missions for doctoral/postdoctoral programs are described in Chapter 5. Chapter 6 discusses a positive learning environment. Relevant professional development is described in Chapter 7.

Chapter 8 describes how faculty, departments, professional societies, and federal agencies can work together to create more successful programs.

A guide for self-evaluation by departments forms Appendix A. Appendix B includes advice to prospective doctoral students on how they can best choose a doctoral program. Appendix C is a brief discussion of master's degree programs in the mathematical sciences, a feature that may form a part of a well-rounded graduate program in the future as doctoral programs become more oriented toward wider job markets, including business and industry.