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, with much emphasis placed on congruence classes leading the way to finite groups and finite fields. New examples and theory are integrated 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 scattered throughout the book, with hints and answers for many of them included in an appendix.
- ISBN13 9780387989990
- Publish Date 14 January 2000 (first published 1 October 1992)
- Publish Status Active
- Publish Country US
- Imprint Springer-Verlag New York Inc.
- Edition 2nd ed. 1995. 2nd printing 2000
- Format Paperback
- Pages 522
- Language English