This research survey at Princeton University of work on mathematical techniques as related to psychological problems concentrated on extending and increasing the precision of scientific description of human behavior. Research conducted over the past century has shown that 1) performance of individuals on a number of different kinds of tasks can be related to mental abilities of these individuals; 2) learning curves have been developed to describe the progress of an individual in his learning of several specific kinds of tasks; and 3) methods describing or measuring various types of psychological discriminations have been developed. This research tries not only to solve technical problems arising in existing theories but also to develop new theories to describe certain psychological phenomena. The major purposes are to provide more systematic and precise descriptions of such phenomena than existed previously. Included in the study are: 1) measurement and analysis of individual characteristics personality attributes; 2) analysis, of various psychological discriminations and evaluative judgments and 3) development and comparison of rational functions to describe the progress of learning and some aspects of work decrement. A review of the activities in each of these areas is presented in the text of this report.