by Joseph B. Dence and Thomas P. Dence
List price: $143.00
Elements of the Theory of Numbers teaches students how to develop, implement, and test numerical methods for standard mathematical problems. The authors, Joseph and Thomas Dence, have developed a comprehensive, rigorous overview of number theory. This text makes greater use of the language and concepts in algebra and analysis than is traditionally encountered in introductory courses. Professors and students will welcome how the chapters are divided into two sets: Chapters 1-6 and part of Chapter 7 pertain to all readers. This set ends with a full chapter on number fields. Chapters 10-11 are considered special topics which allow flexibility for the professor.
Also, the authors have created a two-pronged pedagogical approach which integrates analysis and algebra with classical number theory. This pedagogical approach will help to instill in the minds of the students the idea of the unity of mathematics. Both professors and students will agree that Elements of the Theory of Numbers is the best summary of classical material along with a look at the exciting role of analysis and algebra in number theory.
Author Bio
Dence, Joseph B. : Ashland University
Dence, Thomas P. : Ashland University
Prologue to the Student.
Part I. The Fundamentals:
Introduction.
The Primes.
The Fundamental Theorem of Arithmetic and Its Consequences.
An Introduction to Congruencies.
Polynomial Congruencies.
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.
Name Index.
Subject Index.
Joseph B. Dence and Thomas P. Dence
ISBN13: 978-0122091308Elements of the Theory of Numbers teaches students how to develop, implement, and test numerical methods for standard mathematical problems. The authors, Joseph and Thomas Dence, have developed a comprehensive, rigorous overview of number theory. This text makes greater use of the language and concepts in algebra and analysis than is traditionally encountered in introductory courses. Professors and students will welcome how the chapters are divided into two sets: Chapters 1-6 and part of Chapter 7 pertain to all readers. This set ends with a full chapter on number fields. Chapters 10-11 are considered special topics which allow flexibility for the professor.
Also, the authors have created a two-pronged pedagogical approach which integrates analysis and algebra with classical number theory. This pedagogical approach will help to instill in the minds of the students the idea of the unity of mathematics. Both professors and students will agree that Elements of the Theory of Numbers is the best summary of classical material along with a look at the exciting role of analysis and algebra in number theory.
Author Bio
Dence, Joseph B. : Ashland University
Dence, Thomas P. : Ashland University
Table of Contents
Prologue to the Student.
Part I. The Fundamentals:
Introduction.
The Primes.
The Fundamental Theorem of Arithmetic and Its Consequences.
An Introduction to Congruencies.
Polynomial Congruencies.
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.
Name Index.
Subject Index.