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A concrete introduction to higher algebra

Author: Lindsay Childs
Publisher: New York : Springer, ©2009.
Series: Undergraduate texts in mathematics.
Edition/Format:   Print book : English : 3rd edView all editions and formats
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  Read more...
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Genre/Form: Lehrbuch
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Lindsay Childs
ISBN: 9780387745275 0387745270 9780387747255 0387747257
OCLC Number: 173498962
Description: xiv, 603 pages : illustrations ; 25 cm.
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.
Series Title: Undergraduate texts in mathematics.
Responsibility: Lindsay N. Childs.

Abstract:

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  Read more...

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From the reviews:"The user-friendly exposition is appropriate for the intended audience. Exercises often appear in the text at the point they are relevant, as well as at the end of the section or Read more...

 
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   schema:reviewBody ""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." ;
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