|Mark Hunacek reviews Learning Modern Algebra by Al Cuoco and Joseph J. Rotman as part of MAA Reviews.
This is an interesting, well-written book, in search of an appropriate course in which it could be used as a text.
From the title, one would think that it was intended primarily as a text for an introductory abstract algebra course, but using it that way would require a fairly radical overhaul of the traditional syllabus of such a course. This is intentional: the authors make clear in the Preface to the book that they believe that this traditional syllabus (namely number theory, followed by groups and then rings) to be not only “totally inadequate for future teachers of high school mathematics” but also “unsatisfying for other mathematics students” as well. They propose that abstract algebra should be taught in two semesters: number theory and rings in the first, groups and linear algebra in the second. Even for such a course, however, this book would likely not be appropriate for both semesters; it covers a lot of number theory and ring theory, but very little group theory and linear algebra. (More about the specific contents later.)
The primary intended audience of the book is future high school teachers. The authors take great pains to relate the material covered here to subjects that are taught in high school mathematics classes. And not just high school algebra classes: there is, for example, a fairly lengthy and quite detailed section on straightedge and compass constructions, including statements and (at least partial, and often full) proofs of many sophisticated results regarding impossible constructions.
Read the full review here.