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.

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* Provides historical references noting distinguished number theory luminaries such as Euclid, de Fermat, Hilbert, Brun, and Lehmer, to name a few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

Part I The Fundamentals
Introduction: The Primes
The Fundamental Theorem of Arithmetic and Its Consequences
An Introduction to Congruences
Polynomial Congruences
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