Elements of the Theory of Numbers


  • Thomas Dence, Ashland University, Ohio, U.S.A.
  • Joseph Dence, University of Missouri, Columbia, U.S.A.

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.
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Introductory undergraduate courses in number theory.


Book information

  • Published: January 1999
  • ISBN: 978-0-12-209130-8


"I definitely appreciate the unified approach. I think it is important that the students realize that mathematics does not consist of separate entities."
--Maureen Fenrick, Mankato State University

"The authors communicate successfully the joy they find in number theory. Students will be excited by learning from this (text)."
--Frank DeMeyer, Colorado State University
"The book's biggest advantage is its thorough integration of the relevant algebra into the development. It's about time!"
--Thomas McLaughlin, Texas Tech University

Table of Contents

Part I The FundamentalsIntroduction: The PrimesThe Fundamental Theorem of Arithmetic and Its ConsequencesAn Introduction to CongruencesPolynomial CongruencesPrimitive RootsResiduesMultiplicative Functions Part II Special TopicsRepresentation ProblemsAn Introduction to Number FieldsPartitionsRecurrence Relations Appendix I: NotationAppendix II: Mathematical TablesAppendix III: Sample Final ExaminationsAppendix IV: Hints and Answers to selected problems