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This book is wellwritten and the bibliography excellent,' declared Mathematical Reviews of John Knopfmacher's innovative study. The threepart treatment applies classical analytic number theory to a wide variety of mathematical subjects not usually treated in an arithmetical way. The first part deals with arithmetical semigroups and algebraic enumeration problems; Part Two addresses arithmetical semigroups with analytical properties of classical type; and the final part explores analytical properties of other arithmetical systems.Because of its careful treatment of fundamental concepts and theorems, this text is accessible to readers with a moderate mathematical background, i.e., three years of universitylevel mathematics. An extensive bibliography is provided, and each chapter includes a selection of references to relevant research papers or books. The book concludes with an appendix that offers several unsolved questions, with interesting proposals for further development.
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