A Concrete Introduction to Higher Algebra

Name: A Concrete Introduction to Higher Algebra
Author: Lindsay Childs

Specificaties

Gebonden, 604 blz. | Engels

Springer | 3e druk, 2008

ISBN13: 9780387745275

Rubricering

Hoofdrubriek : Diversen

Juridisch :

Springer 3e druk, 2008 9780387745275

Onderdeel van serie Undergraduate Texts in Mathematics

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Samenvatting

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.

Specificaties

ISBN13:9780387745275

Taal:Engels

Bindwijze:gebonden

Aantal pagina's:604

Uitgever:Springer

Druk:3

Verschijningsdatum:26-11-2008

Hoofdrubriek:Diversen

Serie:Undergraduate Texts in Mathematics

Inhoudsopgave

Numbers.- Numbers.- Induction.- Euclid's Algorithm.- Unique Factorization.- Congruence.- Congruence classes and rings.- Congruence Classes.- Rings and Fields.- Matrices and Codes.- Congruences and Groups.- Fermat's and Euler's Theorems.- Applications of Euler's Theorem.- Groups.- The Chinese Remainder Theorem.- Polynomials.- Polynomials.- Unique Factorization.- The Fundamental Theorem of Algebra.- Polynomials in ?[x].- Congruences and the Chinese Remainder Theorem.- Fast Polynomial Multiplication.- Primitive Roots.- Cyclic Groups and Cryptography.- Carmichael Numbers.- Quadratic Reciprocity.- Quadratic Applications.- Finite Fields.- Congruence Classes Modulo a Polynomial.- Homomorphisms and Finite Fields.- BCH Codes.- Factoring Polynomials.- Factoring in ?[x].- Irreducible Polynomials.