Object oriented design solves a fundamental programming problem arising in scientific and engineering applications of linear algebra and optimization: the separation in code of multiple levels of abstraction naturally appearing in solution algorithms for such problems. The Rice Vector Library provides C++ classes expressing core concepts (vector, function,...) of calculus in Hilbert space with minimal implementation dependence, and standardized interfaces behind which to hide application-dependent implementation details (data containers, function objects). A variety of coordinate free algorithms from linear algebra and optimization, including Krylov subspace methods and various relatives of Newton's method for nonlinear equations and constrained and unconstrained optimization, may be expressed purely in terms of this system of classes. The resulting code may be used {\em without alteration} in a wide range of control, design, and parameter esti mation applications, in serial and parallel computing environments.