Number Theory

ISBN-13: 9781470452759

Robert Freud;Edit Gyarmati

Opis

Number Theory is a newly translated and revised edition of the most popular introductory textbook on the subject in Hungary. The book covers the usual topics of introductory number theory: divisibility, primes, Diophantine equations, arithmetic functions, and so on. It also introduces several more advanced topics including congruences of higher degree, algebraic number theory, combinatorial number theory, primality testing, and cryptography. The development is carefully laid out with ample illustrative examples and a treasure trove of beautiful and challenging problems. The exposition is both clear and precise. The book is suitable for both graduate and undergraduate courses with enough material to fill two or more semesters and could be used as a source for independent study and capstone projects. Freud and Gyarmati are well-known mathematicians and mathematical educators in Hungary, and the Hungarian version of this book is legendary there. The authors' personal pedagogical style as a facet of the rich Hungarian tradition shines clearly through. It will inspire and exhilarate readers.

Spis treści

• Introduction
• Chapter 1. Basic Notations
• Chapter 2. Congruences
• Chapter 3. Congruences of Higher Degree
• Chapter 4. Legendre and Jacobi Symbols
• Chapter 5. Prime Numbers
• Chapter 6. Arithmetic Functions
• Chapter 7. Diophantine Equations
• Chapter 8. Diophantine Approximation
• Chapter 9. Algebraic and Transcendental Numbers
• Chapter 10. Algebraic Number Fields
• Chapter 11. Ideals
• Chapter 12. Combinatorial Number Theory
• Answers and Hints
• Historical Notes
• Tables
• Index