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Elements of the Theory of Numbers

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Elements of the Theory of Numbers

Thomas Dence, Joseph Dence

ISBN 0122091302
Pages 517

Elements of the Theory of Numbers teaches students how to develop, implement, and test numerical methods for standard mathematical problems. The authors have created a two-pronged pedagogical approach that integrates analysis and algebra with classical number theory. Making greater use of the language and concepts in algebra and analysis than is traditionally encountered in introductory courses, this pedagogical approach helps to instill in the minds of the students the idea of the unity of mathematics. Elements of the Theory of Numbers is a superb summary of classical material as well as allowing the reader to take a look at the exciting role of analysis and algebra in number theory.

Part I The Fundamentals Introduction: The Primes The Fundamental Theorem of Arithmetic and Its Consequences An Introduction to Congruences Polynomial Congruences Primitive Roots Residues Multiplicative Functions Part II Special Topics Representation Problems An Introduction to Number Fields Partitions Recurrence Relations Appendix I: Notation Appendix II: Mathematical Tables Appendix III: Sample Final Examinations Appendix IV: Hints and Answers to selected problems