The principal objective of the National Science Foundation Graduate Research Traineeship Program is to increase the numbers of talented U.S. undergraduates enrolling in doctoral programs in critical and emerging areas of science and engineering. Proposals were solicited from institutions whose existing facilities and staff could accommodate additional graduate students in Ph.D. programs of high quality. The program is also intended to contribute to strengthening the Nation's human resource base across all geographic sectors and among all under-represented groups. Graduate Research Traineeship awards are packages of student support. The colleges and universities that receive the awards are responsible for the selection of trainees, retention of trainees, and administration of traineeships. Rensselaer Polytechnic Institute will support Ph.D. students in applied mathematics; the program addresses the following concerns: (a) the academic need for applied mathematicians to provide academic training of students, (b) the industrial need for applied mathematicians to maintain U.S. industrial competitiveness, and (c) the need to increase the number of women and minority Ph.D. applied mathematicians. Students in the program will learn mathematical modeling, numerical computing, an outside (other than mathematical) area, as well as a substantial background in the more traditional areas of mathematics. The program includes student participation in workshops and panels on mathematical problems in industry where students can work with student-faculty teams to solve industrial problems. Current areas of departmental research include physical mathematics and modeling, nonlinear analysis, scientific computation, mathematical programming and operations research, and applied geometry.