Elements of the Theory of Numbers

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.

Elements of the Theory of Numbers is a comprehensive and contemporary introduction for a first course in classical number theory. The authors offer an integrated approach to the subject, making greater use than usual of the language and concepts of algebra, mathematical proof, and analysis.
The book offers a wealth of topics in two parts.
Part I consists of fundamental or core material. It includes primes, congruences, primitive roots, residues, and multiplicative functions.
Part II is a collection of more specialized topics, such as a brief look at number fields, recurrence relations, and additive number theory.
Throughout the text, the authors offer historical references and introduce topics in their historical context. Over 900 exercises are included.
"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