Elements of the Theory of Numbers [Hardcover]

Thomas P. Dence (Author), Joseph B. Dence (Author)

Book Description

Publication Date: February 3, 1999 | ISBN-10: 0122091302 | ISBN-13: 978-0122091308 | Edition: 1

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.
* In-depth coverage of classical number theory
* Thorough discussion of the theory of groups and rings
* Includes application of Taylor polynomials
* Contains more advanced material than other texts
* Illustrates the results of a theorem with an example
* Excellent presentation of the standard computational exercises
* Nearly 1000 problems--many are proof-oriented, several others require the writing of computer programs to complete the computations
* Clear and well-motivated presentation
* Provides historical references noting distinguished number theory luminaries such as Euclid, de Fermat, Hilbert, Brun, and Lehmer, to name a few
* Annotated bibliographies appear at the end of all of the chapters
* Instructor's Solution Manual is free to adopters

Editorial Reviews

Review

"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

From the Back Cover

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

Product Details

• Hardcover: 517 pages
• Publisher: Academic Press; 1 edition (February 3, 1999)
• Language: English
• ISBN-10: 0122091302
• ISBN-13: 978-0122091308
• Product Dimensions: 9.4 x 6.3 x 1.2 inches
• Shipping Weight: 2 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #1,257,489 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

6 of 15 people found the following review helpful:

5.0 out of 5 stars Desparte For a Good Explanation, November 24, 1999

By 

Clare Alexander (Oxford, England) - See all my reviews

This review is from: Elements of the Theory of Numbers (Hardcover)

As a lazy undergraduate studying Number Theory, I found this book to come up with not just solutions but good ideas and easy to understand explanations. Worth buying!