A Concrete Introduction to Higher Algebra - Couverture rigide

Childs, L.N.

Couverture rigide

ISBN 10 : 0387944842 ISBN 13 : 9780387944845

Editeur : Springer-Verlag New York Inc., 1995

Synopsis

This is an introduction to higher algebra for students with a background of a year of calculus. The book aims to give these students enough experience in the algebraic theory of the integers and polynomials to appreciate the basic concepts of abstract algebra. The main theoretical thread is to develop algebraic properties of the ring of integers: unique factorization into primes; congruences and congrunce classes; Fermat's theorem; the Chinese remainder theorem; and for the ring of polynomials. Concurrently with the theoretical development, the book presents a broad variety of applications, to cryptography, error-correcting codes, Latin squares, tournaments, techniques of integration and especially to elementary and computational number theory. Many of the recent advances in computational number theory are built on the mathematics which is presented in this book. Thus the book may be used as a first course in higher algebra, as originally intended, but may also serve as an introduction to modern computational number theory, or to applied algebra.

A propos du livre

Présentation de l'éditeur

This book is an informal and readable introduction to higher algebra at the post-calculus level. The concepts of ring and field are introduced through study of the familiar examples of the integers and polynomials. The new examples and theory are built in a well-motivated fashion and made relevant by many applications - to cryptography, coding, integration, history of mathematics, and especially to elementary and computational number theory. The later chapters include expositions of Rabiin's probabilistic primality test, quadratic reciprocity, and the classification of finite fields. Over 900 exercises are found throughout the book.

Détails de l'édition

• Éditeur: Springer-Verlag New York Inc.
• Date d'édition: 1995
• Langue: anglais
• ISBN 10: 0387944842
• ISBN 13: 9780387944845
• Reliure: Relié
• Numéro d'édition: 2
• Nombre de pages: 500
• Coordonnées du fabricant: non disponible
• Personne responsable: CMN Printpool Inh. Mathis Neumann; https://www.also.com/ec/cms5/en_6000/6000/index.jsp; ; Friedrich-Karl-Str. 9; Hamburg; Allemagne