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A Concrete Introduction to Higher Algebra (Undergraduate Texts in Mathematics)

A Concrete Introduction to Higher Algebra (Undergraduate Texts in Mathematics)
Author: Lindsay N. Childs
ISBN 13: 9780387745275
ISBN 10: 387745270
Edition: 3rd
Publisher: Springer
Publication Date: 2008-11-26
Format: Hardcover
Pages: 604
List Price: $69.95

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, 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, 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.