This book is written as an introduction to higher algebra for students
with a background of a year of calculus. It has been used as a
successful undergraduate text for more than 20 years. The objective of
the book is to give students enough experience in the algebraic theory
of the integers and polynomials to appreciate the basic concepts of
abstract algebra. New sections on Luhn's formula, Cosets and equations,
and detaching coefficients are included. 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.