A mathematical model for computer-aided instruction has been developed. The assumption is made that the course is divided into a hierarchy of levels of difficulty and that if a student is able to perform successfully at a given level of difficulty, he can also perform successfully at all levels of lesser difficulty. Furthermore, if a student performs successfully at one level, the probability of successful performance at the next higher level is increased. Given the initial vector of probabilities for successful performance at each level, and the expected times it takes to attempt a successful performance at each level, the model computes an instructional sequence which minimizes the expected time required for the student to complete the course by performing successfully at the highest level of difficulty. Dynamic programing is used to find this sequence. (Author)