THIS REPORT OF THE COMMITTEE ON THE UNDERGRADUATE PROGRAM IN MATHEMATICS (CUPM) DESCRIBES A PROPOSED FIVE-YEAR PROGRAM FOR THE UNDERGRADUATE PREPARATION OF STUDENTS IN MATHEMATICAL ENGINEERING. THE MAJOR PURPOSES OF THIS PROGRAM ARE TO PREPARE STUDENTS IN THE MATHEMATICAL SCIENCES, TO ENABLE THEM TO APPLY THIS EDUCATION TO THE COMPLICATED ENGINEERING PROBLEMS OF THE SPACE EFFORT, AND THEREBY, TO PROVIDE THE NATION WITH TECHNICAL MANPOWER HAVING A WIDE BACKGROUND IN BOTH MATHEMATICS AND ENGINEERING. INTEREST IN THIS KIND OF PROGRAM BUT WITH A DIFFERENT SPECIALIZATION ALSO HAS BEEN SHOWN BY SUCH INDUSTRIES AS ELECTRONICS AND COMMUNICATION. SINCE THE MATHEMATICAL ENGINEERING PROGRAM INVOLVES A HEAVY CONCENTRATION IN MATHEMATICS AS WELL AS INSTRUCTION IN ENGINEERING INVOLVING BOTH APPLICATION AND THEORY, THE COMMITTEE DEVELOPED THE NOTION OF A COMMON CORE OF MATERIAL IN THE BASIC PHYSICAL SCIENCES AND, MORE EXTENSIVELY, IN THE MATHEMATICAL SCIENCES. THE CORE, IN TURN, IS COMPLEMENTED BY A NUMBER OF OPTIONS, WHICH ARE MORE SPECIALIZED DEVELOPMENTS IN DEPTH AND ENSURE THAT THE STUDENT WILL BE INTRODUCED TO AT LEAST ONE BRANCH OF ENGINEERING. ORBIT MECHANICS, OPERATIONS RESEARCH, AND CONTROL THEORY ARE THREE OPTIONS WHICH ARE DESCRIBED IN DETAIL IN THIS REPORT. THIS DOCUMENT IS ALSO AVAILABLE WITHOUT CHARGE FROM CUPM CENTRAL OFFICE, P. O. BOX 1024, BERKELEY, CALIFORNIA 94701. (RP)