The working mathematician, pure or applied, uses a multitude of tools such as spectral decompositions, isomorphic representations, and functional transforms, to mention only a few. In this book we shall argue in favor of a less traditional but, we believe, highly useful tool, namely, the computer.
What we have in mind is using the computer as the mathematician's laboratory, in which he can perform experiments in order to augment his intuitive understanding of a problem, or to search for conjectures, or to produce counterexamples, or to suggest a strategy for proving a conjecture.Hence the theme of this book is experimental mathematics on the computer. It will not deal with production computing, say, the solution of a large partial differential equation, the inversion of enormous matrices, or the numerical handling of combinatorial problems. Nor will it deal with topics like proving theorems on the computer or related questions belonging to the area of artificial intelligence.