Description
Elementary Number Theory, Gove Effinger, Gary L. Mullen
This text is intended to be used as an undergraduate introduction to the theory of numbers. The authors have been immersed in this area of mathematics for many years and hope that this text will inspire students (and instructors) to study, understand, and come to love this truly beautiful subject.
Each chapter, after an introduction, develops a new topic clearly broken out in sections which include theoretical material together with numerous examples, each worked out in considerable detail. At the end of each chapter, after a summary of the topic, there are a number of solved problems, also worked out in detail, followed by a set of supplementary problems. These latter problems give students a chance to test their own understanding of the material; solutions to some but not all of them complete the chapter.
The first eight chapters discuss some standard material in elementary number theory. The remaining chapters discuss topics which might be considered a bit more advanced. The text closes with a chapter on Open Problems in Number Theory. Students (and of course instructors) are strongly encouraged to study this chapter carefully and fully realize that not all mathematical issues and problems have been resolved! There is still much to be learned and many questions to be answered in mathematics in general and in number theory in particular.
Table of Contents
1. Divisibility in the Integers Z 2. Prime Numbers and Factorization 3. Congruences and the Sets Zn 4. Solving Congruences 5. The Theorems of Fermat and Euler 6. Applications in Modern Cryptography 7. Quadratic Residues and Quadratic Reciprocity 8. Some Fundamental Number Theory Functions 9. Diophantine Equations 10. Finite Fields 11. Some Open Problems in Number Theory A. Mathematical Induction B. Sets of Numbers Beyond the Integers
