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Polya Urn Models presents a complete introduction to the terminology of urns and urn models, which refer to a system of one or more containers with objects of various types. The book begins with a summary of basic issues in discrete probability that forms the foundations of probability from an urn viewpoint. With exercises, examples, and historical notes, it covers classical probability problems connected to and presented within the framework of urns, the Polya urn model, and variations in real time. The book also explores recent developments in the field as well as a broad range of applications in bioscience and computer science, in particular, data structures, algorithms, and Internet growth.