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.

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