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by Joseph B. Dence and Thomas P. Dence

Edition: 99Copyright: 1999

Publisher: Academic Press, Inc.

Published: 1999

International: No

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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.

- 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- Provides historical references noting distinguished number theory luminaries such as Euclid, de Fermat, Hilbert, Brun, and Lehmer, to name a few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

**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.

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Summary

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.

- 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

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.

Publisher Info

Publisher: Academic Press, Inc.

Published: 1999

International: No

Published: 1999

International: No

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.

- 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

**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.