Review by Choice Review
Cameron goes somewhat against conventional wisdom by choosing rings over groups as the primary algebraic structure of study. This choice allows an introduction to the ideas of abstract algebra in a setting most students will find a bit more familiar and comfortable. After the obligatory chapter reviewing some of the basics of sets, functions, and logic, Cameron introduces the essentials of rings and fields and then the standard first topics in group theory. These first three chapters would form a reasonable core for an introductory course in abstract algebra at the undergraduate level. Subsequent chapters provide ample opportunity to delve into less traditional and/or more advanced topics. Included are chapters devoted to a rigorous treatment of vector spaces; an introduction to modules; axiomatic development of number systems; further topics in groups, rings, and fields; and a chapter on applications including an introduction to Galois theory and coding theory. This book will support a very rigorous first course in abstract algebra and contains more than enough material to fill up a two-semester course. Upper-division undergraduate and graduate students. D. S. Larson Gonzaga University
Copyright American Library Association, used with permission.
