Scientific computing involves both creativity on the part of the human scientist and a great deal of mechanical drudgery that can and should he automated. In the domain of mathematical modeling, problems can be specified naturally and concisely in terms of the mathematics and physics of the application. Our goal is to minimize the time required for scientists and engineers to implement these mathematical models. Much of the necessary implementation knowledge is available in books and journal articles and can be encoded in a knowledge-based program synthesis system. SINAI'S is one such system that illustrates how to have the scientist or engineer provide the major design decisions for problem solving and have an automated assistant carry out the details of coding the algorithms into the desired target language. The basic implementation paradigm is program transformation based on objectoriented representations of the underlying mathematical and programming concepts. Mathematica is the implementation platform.