Students unfamiliar with the classical mathematical methods introduced in this textbook will acquire a powerful set of tools for analyzing and designing many complex information processing systems which include ANN information processing systems as an important special case. Researchers familiar with the specific areas of mathematics mentioned in this textbook will learn how their areas of expertise can be immediately applied to on-going problems in ANN system analysis and design. The book is relatively self-contained and was intentionally written for a mathematically sophisticated multidisciplinary audience consisting of advanced undergraduate students, graduate students, consultants, and researchers in the fields of cognitive science, computer science, econometrics, engineering, mathematics, mathematical biology, mathematical psychology, mathematical sociology, neural networks, and physics.