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This is the proceedings of the 1983 AMS Short Course given at Denver, Colorado. Computer communications is characterized by rapid technological advances presenting problems of a theoretical nature that are often very difficult to solve. They range from those that arise on a single chip, where communication among thousands of elements on a chip is influenced by electrical properties, to those that arise when human beings communicate with databases where the logical aspects of communications play a more important role. A variety of mathematical methods is needed to attempt to solve such problems; they vary from partial differential equations to temporal or modal logic. The article on ``Diffusion Approximation'' is probably one of the best reviews of this field. The book is unique in having contributors from a variety of different fields of computer communications. All of the articles are of high research value and are self-contained.
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