A text for a one- or two-semester course at the junior or senior level for mathematics majors who have taken a course in computational linear algebra. Treatment begins with emphasis on concrete problems and progresses from number theory and polynomials through rings and fields, assuming no knowledge of proofs. Advanced chapters cover group theory, Galois theory, and unique factorization. Includes appendices on background material, chapter exercises and answers, and an introduction to the student on how to get the most from the course. Annotation c. by Book News, Inc., Portland, Or.