This memo describes the step by step solution of three problems from different fields of applied mathematics. These problems are solved by typing a series of computer commands for the manipulation of symbolic mathematical expressions. These commands are best typed at the PDP-6 console, so that the Type 30 display and the wider range of keyboard symbols can be used. The syntax of commands typed at the PDP-6 will be described. These commands are translated into a string of symbols which are sent to CTSS, where they are parsed into a LISP expression, which is then evaluated. The mathematical operators which are available in the system will be described and then the step by step solution of each of the problems will be given.