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Throughout the text, the authors offer historical references and introduce topics in their historical context.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
A textbook for a one-semester course for junior or senior undergraduate mathematics majors who have completed the standard calculus sequence, but not necessarily studied algebra. Introduces the elementary material required on groups, rings, and fields. Begins with the core material, including primes, congruences, primitive roots, and multiplicative functions. Progresses to more specialized topics such as number fields, recurrence relations, and additive number theory. Includes over 900 exercises, sample examinations, and answers and hints to selected problems. Annotation c. Book News, Inc., Portland, OR (booknews.com)