Research relevant to problem solving and learning using trigonometric processes is described in Part I. The incorporation of learning into the process of mechanically proving trigonometric identities presents a unique and major step in the field of artificial intelligence. The processes used, and indeed some of the specific techniques and routines, are sufficiently general that they may be applied to other forms of learning. Part II is concerned with research in tree pruning as related to computer game playing. New minmax methods of pruning have been developed with particular emphasis placed upon machine learning to fix pruning parameters. With the naive scoring functions used, the machine does not play a particularly elegant game of chess, but is managing to modify its pruning behavior to improve its play. The programs are operative using the FORTRAN programming language. A sample game as played by the computer is included within this section of the report. Some results of the research dealing with the restraints the man-machine attitudes play upon human use of digital computers in problem-solving contexts are described in Part III.