Pub. Date:
Springer New York
A Concrete Introduction to Higher Algebra / Edition 3

A Concrete Introduction to Higher Algebra / Edition 3

by Lindsay N. Childs
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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.

Product Details

ISBN-13: 9781441925619
Publisher: Springer New York
Publication date: 11/19/2010
Series: Undergraduate Texts in Mathematics , #159
Edition description: Softcover reprint of hardcover 3rd ed. 2009
Pages: 604
Sales rank: 857,251
Product dimensions: 6.10(w) x 9.20(h) x 1.30(d)

Table of Contents

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.

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