Providing a concise introduction to abstract algebra, this work unfolds some of the fundamental systems with the aim of reaching applicable, significant results.
good book for 1st semester course
By R. John - July 22, 2001
Abstract algebra (AKA "algebraic structures", "modern algebra", or simply "algebra") can be a difficult topic depending on its presentation. The difficulty comes in the abstractness of the topic (generalizations that give us useful properties), not the complexity of the area (though, further study can provide some of this). Although the several texts I have seen are useful in their own right, I don't believe there's a better text for beginners (or, perhaps, to strengthen shady concepts for further courses) on the subject. Herstein presents concrete examples before proving abstract concepts (something students who have only had courses on the several calculus, discrete math, probability, and matrix theory will find invaluable).The text is clear and concise. The length is short without omitting any pertinent ideas (other books tend to spend a wealth of pages on anomalies -- which can be good...but then we could really make volumes on the subject). The book starts with a basic... read more
Best at what it is
By Cletus Bojangles "Cletus" - September 23, 2002
(I am writing about the 2nd edition, which I used as an undergraduate.)This book is intended for a one semester senior-level honors course at a reasonably good undergraduate institution, for which it is perfect. Students who are less interested in pure mathematics or are somewhat weaker should go to Gallian's book, which is also excellent. Students who are weaker still maybe should seek out Fraleigh.Other reviewers are correct about the group theory being the strength of this book; ring and field theory are OK but short, but remember that this book is intended for a one semester undergraduate course. (Herstein was a ring theorist. It is natural to speculate that he chose the topics he did because of the course, not because of personal interest...) The optional topics (simplicity of A_n, Liouville's Criterion, etc.) are excellent."Topics in algebra" is supposed to be a year-long version of this book. That one is sometimes called "Herstein" and this... read more
Not a bad book but I am sure it could be better.
By Khalifa Alhazaa "a_mathematician" - February 26, 2001
I want you first to know that I have only read about 3/4 of the book and I have stopped after field extentions. I am trying here to comment on the book from a relatively more advanced point of view because I have had all the subjects in depth in some other classes. I think Hersteins treatment of groups is more than excellent I would not recommend any other book for group theory at the undergraduate level. But he starts loosing this track in his treatment of rings, and I feel he starts getting faster and faster in explaing ideals and I do not think he did it very well. Field extension and Galois theory go even faster. I think you should stop reading the book after group theory and try some other book in the subject of ring theory something like Jacobson's "Basic Algebra I" for advanced students. But the book is not that bad if you can absorb things fast enough. It even has a chapter about straight edge and compass constructions which is a remarkable subject for me. It even... read more
Widely acclaimed algebra text. This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics. The book carefully ...
Concrete Abstract Algebra develops the theory of abstract algebra from numbers to Gr"obner bases, while takin in all the usual material of a traditional introductory course. In addition, there is a ...
Most abstract algebra texts begin with groups, then proceed to rings and fields. While groups are the logically simplest of the structures, the motivation for studying groups can be somewhat lost on ...