The design and implementation of a tutorial program to perform symbolic mathematics

Abstract

The purpose of this thesis is to design and implement a program that could be used for a drill in symbolic mathematics. The scope of the program with respect to the range of problems that it solves is limited to selected types from elementary algebra, trigonometry, differential calculus, and integral calculus. The program is designed, not only to give solutions (answers), but also to provide several of the intermediate steps leading to the final result. FORMAC73 and PL/1 are used to implement the program. FORMAC73 is a system and a language for manipulating mathematical expressions, symbolically. The facilities of PL/1 are available for program structure, loop control, testing, input and output operations, and manipulating the strings so as to get the intermediate steps. The program is designed to provide supplementary assistance to give students drill, practice, and review several specific topics in the stated areas. The program may also be used by instructors to check or to provide answers to particular problems, say for an examination or homework. The program does not attempt to diagnose the student‘s difficulties. The main accomplishments of this paper will be to show the potential of using FORMAC73 with the existing facilities at Virginia Commonwealth University (VCU) to develop an extensive tutorial drill; particularly in arithmetic and algebra. The paper will also show that it is possible to develop a comprehensive CAI package in symbolic mathematics by using existing symbolic mathematics systems