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Title A concrete introduction to higher algebra / Lindsay N. Childs.
Imprint New York ; London : Springer, ©2009.


 Internet  Electronic Book    AVAILABLE
Edition 3rd ed.
Description 1 online resource (xiv, 603 pages) : illustrations
Series Undergraduate texts in mathematics
Undergraduate texts in mathematics.
Note Previous edition: 2005.
Bibliog. Includes bibliographical references (pages 595-598) and index.
Note Available only to authorized UTEP users.
Print version record.
Subject Number theory.
Number theory -- Problems, exercises, etc.
Genre Problems and exercises.
Contents 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 -- Unique factorization -- The fundamental theorem of algebra -- Polynomials in Q[x] -- Congruences and the Chinese remainder theorem -- Fast polynomial multiplication -- Primitive roots -- Cyclic groups and crypotography -- Carmichael numbers -- Quadratic reciprocity -- Quadratic applications -- Finite fields -- Congruence classes modulo a polynomial -- Homomorphisms and finite fields -- BCH codes -- Factoring polynomials -- Factoring in Z[x] -- Irreducible polynomials.
Summary "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. A strong emphasis on congruence classes leads in a natural way to finite groups and finite fields. The new examples and theory are built in a well-motivated fashion and made relevant by many applications - to cryptography, error correction, integration, and especially to elementary and computational number theory. The later chapters include expositions of Rabin's probabilistic primality test, quadratic reciprocity, the classification of finite fields, and factoring polynomials over the integers. Over 1000 exercises, ranging from routine examples to extensions of theory, are found throughout the book; hints and answers for many of them are included in an appendix." "The new edition includes topics such as Luhn's formula, Karatsuba multiplication, quotient groups and homomorphisms, Blum-Blum-Shub pseudorandom numbers, root bounds for polynomials, Montgomery multiplication, and more."--Jacket.
Other Title Print version: Childs, Lindsay. Concrete introduction to higher algebra. 3rd ed. New York ; London : Springer, ©2009 0387745270 9780387745275