This booklet is the ninth in a series of nine from the Teacher Training Institute at Hofstra University (New York) and describes the content and the approach of an institute course in which the participants use the personal computer as a personal tool within the mathematical discovery process of making conjectures, testing those conjectures, and verifying results and/or retesting. Pedagogical commentary and appropriate Pascal programs are presented for four topics, including: (1) iterated quadratic maps; (2) fractal geometry with applications; (3) conditional probability as applied to baseball league trends and results; and (4) recursion and induction in sorting routines. (JJK)