Presented are a suggested program and the course outlines for the pregraduate preparation of research mathematicians. The program set forth is designed for the first four years of a sequence of formal course study leading to the Ph.D. in a total of seven years. The proposed program of pre-graduate mathematical studies falls into two parts: Introductory Undergraduate Mathematics and Higher Undergraduate Mathematics. The former is focused on differential and integral calculus, and the latter is devoted to basic material in the fields of analysis, algebra, and geometry. The suggested program is designed with two objectives in mind: (1) the first two years must lead gradually to an appreciation of the nature and role of definitions and proofs, and an ability to employ mathematical language with precision, and (2) the last two years must be designed to merge smoothly with beginning graduate study, forming a period in which the most basic mathematical concepts, results, and methods are secured so as to provide a firm base for subsequent specialization and concentrated research. (RP)