A concrete introduction to higher algebra /
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 f...
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| Format: | eBook |
| Language: | English |
| Published: |
New York :
Springer,
[1995]
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| Edition: | 2nd ed. |
| Series: | Undergraduate texts in mathematics.
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| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| 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, 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. |
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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (xv, 522 pages) : illustrations. |
| Format: | Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |
| Bibliography: | Includes bibliographical references (pages 509-512) and index. |
| ISBN: | 9781441987020 (electronic bk.) 1441987029 (electronic bk.) |