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Advanced Modern Algebra
Joseph J. Rotman
Publisher: American Mathematical Society (2010)
Details: 1008 pages, Hardcover
Edition: 2 Series: Graduate Studies in Mathematics 114
Topics: Abstract Algebra, Algebra
This book is in the MAA's basic library list.
MAA Review[Reviewed by Fernando Q. Gouvêa, on 08/31/2010]
The new edition of Rotman's graduate algebra text comes from a different publisher at a slightly lower price. See Marion Cohen's review of the first edition, with which I concur: this is an excellent book containing much more than what is likely to be covered in a standard graduate course. It certainly fulfills the author's vision of a book that contains "many of the standard theorems and definitions that users of Algebra need to know." (The "many" in that sentence is characteristic of the author's careful writing.)
Rotman has completely rewritten the book for the new edition. Some of the changes are:
The best features of the first edition are retained, including Rotman's humane and elegant approach to mathematical exposition: things are explained in both words and symbols, there are historical (and even autobiographical) remarks, and the etymology of some unusual terms is explored. Most importantly, the author often takes the time to put on paper the kind of "here's how to think about it" advice that mathematicians often share with each other only orally.
In the introduction, Rotman says that "each generation should survey Algebra to make it serve the present time." His Advanced Modern Algebra admirably fulfills that goal.
Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College and the editor of MAA Reviews.
BLL** — The Basic Library List Committee strongly recommends this book for acquisition by undergraduate mathematics libraries.