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Existing research suggests an intuitive relationship between mathematics and computer programming. These previous studies have focused primarily on the cognitive connection and have ignored the potential impact of programming on an individual's perception and application of mathematical skills. By surveying and interviewing a variety of participants, this study aims to provide a descriptive foundation for the experiential side of cognitive correlations and causalities. These phenomenological accounts, garnered from individual interviews of seven different programmers, indicate four specific areas of interest. First, learning to program provided context for many abstract concepts. Second, programming illustrated the important distinction between understanding the application of math in a specific situation and the execution of a known procedure. Third, programming habits helped participants divide complex problems into more manageable tasks. Finally, the necessity of solving a programming problem provided motivation and eliminated apprehension toward mathematics.

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This dissertation examines characteristics of a class of semi-infinite linear programming problems designated as C/C semi-infinite linear programming problems. Semi-infinite programming problems which belong to this class are problems of the form [See document] where S is a compact, convex subset of Euclidean m space and u_i : S→R, i=1,...,n are strictly concave functions while u _n+1 : S→R is convex. Certain properties of the C/C semi-infinite linear programming problems give rise to efficient solution techniques. The solution techniques are given as well as examples of their use. Of significant importance is the intimate relationship between the class of C/C semi-infinite linear programming problems and certain convex fuzzy set programming problems. The fuzzy set programming problem is defined as [See document] The convex fuzzy set programming problem is transformed to an equivalent semi-infinite linear programming problem. Characterizations of the membership functions are given which cause the equivalent semi-infinite linear programming problems to fall within the realm of C/C semi-infinite linear programming problems. Some extensions of the set inclusive programming problem are also given. / Ph. D.

Three topics are developed: interval convex programming, and program generation techniques. The interval convex programming problem is similar to the convex programming problem of the real number system except that all parameters are specified as intervals of real numbers rather than as real scalars. The interval programming solution procedure involves the solution of a series of 2n real valued convex programs where n is the dimension of the space. The solution of an interval programming problem is an interval vector which contains all possible solutions to any real valued convex program which may be realized. Attempts to improve the efficiency of the interval convex programming problem lead to the eventual development of a new solution procedure for the real valued linear programming problem, Orthogonal linear programming. This new algorithm evolved from some heuristic procedures which were initially examined in the attempt to improve solution efficiency. In the course of testing these heuristics, which were unsuccessful, procedures were developed whereby it is possible to generate discrete and continuous mathematical programs with randomly chosen parameters, but known solutions. / Ph. D.

This thesis presents the development of an interactive programming system for the IBM 7545 robot. Various methods of robot programming are discussed, and the reasons for the development of such an interactive programming system are provided. The development of this system was divided into five phases, namely, the development of the pseudo-compiler, development of the "system control" program, integration of ASSEMBLY routines, development of the "motion control" program, and the development of test programs. The approach used for each of these five stages are outlined, and a reference to the use of the system is given. A description of the development of each stage is then given, and the logic associated with all programs are described, and the purpose and operation of all subroutines are also presented. Some assumptions and limitations of the system are explained, and the operational aspects of the system are described. Additional work needed to improve this system is outlined, and the feasibility of using the concept of this system on other robot programming languages on the IBM 7545 robot are also discussed. / M.S.