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This graduate-level text teaches students how to use a small number of powerful mathematical tools for analyzing and designing a wide variety of artificial neural network (ANN) systems, including their own customized neural networks.Mathematical Methods for Neural Network Analysis and Design offers an original, broad, and integrated approach that explains each tool in a manner that is independent of specific ANN systems. Although most of the methods presented are familiar, their systematic application to neural networks is new. Included are helpful chapter summaries and detailed solutions to over 100 ANN system analysis and design problems. For convenience, many of the proofs of the key theorems have been rewritten so that the entire book uses a relatively uniform notion.This text is unique in several ways. It is organized according to categories of mathematical tools -- for investigating the behavior of an ANN system, for comparing (and improving) the efficiency of system computations, and for evaluating its computational goals -- that correspond respectively to David Marr's implementational, algorithmic, and computational levels of description. And instead of devoting separate chapters to different types of ANN systems, it analyzes the same group of ANN systems from the perspective of different mathematical methodologies.