This paper is being developed for publication. Some mistakes remain hidden until the system is used. Mathematics to the Rescue Logic, mathematics, and proofs should be a part of project documentation from the initial stages. Set Theory and Logic are important for defining the problem area. In general Formal Analysis proceeds by stating the obvious.
Simple facts determine the set of logically correct structures.
Grammar theory is useful for documenting sequential data. Sets and functions describe the structure of the problem domain and are used to document requirements and specifications. Thus maps and sets define the structure shared by the solution and the problem's environment. Design involves other mathematical methods - The calculus of relations plus an extension to the lower predicate calculus can be used for specifying designs. Statistical analysis and simulations are needed to ensure satisfactory performance as well.