A new heuristic factorization scheme uses learning to improve the efficiency of determining the symbolic factorization of multivariable polynomials with interger coefficients and an arbitrary number of variables and terms. The factorization scheme makes extensive use of artificial intelligence techniques (e.g., model-building, learning, and…

This paper is a theoretical discussion of several functions of knowledge systems based on the idea of partial matching, that is, comparison of two or more descriptions by identification of their similarities. Several knowledge system functions are described in terms of partial or best matchings including analogical reasoning, inductive inference,…

This thesis addresses problems from two areas of theoretical computer science. The first area is that of computational learning theory, which is the study of the phenomenon of concept learning using formal mathematical models. The goal of computational learning theory is to investigate learning in a rigorous manner through the use of techniques…

A MATHEMATICAL MODEL OF ESTABLISHED AND INDUSTRIALLY VALIDATED LEARNING AND FORGETTING THEORIES IS OUTLINED, AND A COMPUTER-EXECUTED HEURISTIC ALGORITHM FOR SELECTING THE BEST SCHEDULE FOR SUBJECT PRESENTATION IS GIVEN. FUNDAMENTAL PARAMETERS OF THE MODEL INCLUDE EDUCATION POTENTIAL, TYPE OF SUBJECT MATTER, TYPE OF LEARNER, TEACHING METHODS, AND…

The cognitive method, an algorithmic method for transforming verbal word problems into equations, equation systems, inequalities, etc., is presented and discussed. The psychological and mathematical aspects of the cognitive method are also reviewed. (MP)

The problem of structuring sequences of instructional stimuli such that learning is optimized is modelled as a sequential decision problem with an imbedded mathematical model of learning providing a criterion function. Three types of optimization methods for such a representation are investigated for the specific case of paired-associate learning…