This paper describes research towards the construction of an expert system combining the brute force power of algorithmic computation and the inductive reasoning power of a rule-based inference engine in the mathematical area of discrete structures. Little research has been conducted on extending existing expert systems' technology to computationally complex areas. This research addresses the extension of expert systems into areas such as these, where the process of inference by itself will not produce the proper results. Additionally, the research will demonstrate the benefits of combining inference engines and mathematical algorithms to attack computationally complex problems. The specific aim is to produce an expert system which embodies expert level knowledge of orthomodular lattices, graphs, structure spaces, boolean algebras, incidence relations, and projective configurations. The resulting system, implemented on a micro-computer, will provide researchers a powerful and accessible tool for exploring these discrete structures. The system's "shell" will provide a structure for developing other expert systems with similar capabilities in such related areas as coding theory, categories, monoids, automata theory, and non-standard logics.