Abstract Algebra [Paperback]

I. N. Herstein (Author)

Book Description

ISBN-10: 0471368792 | ISBN-13: 978-0471368793 | Publication Date: January 15, 1996 | Edition: 3

Providing a concise introduction to abstract algebra, this work unfolds some of the fundamental systems with the aim of reaching applicable, significant results.

Editorial Reviews

From the Publisher

This book offers a clear, concise, student-friendly presentation of abstract algebra, serving as either an introduction for the mathematics major or a means of exposure to many highly usable tools and techniques for the non-major's primary interest areas. It unfolds some of the fundamental algebraic systems that are both interesting and of wide use, with the goal of reaching applicable, significant results. The text provides many high quality examples and exercises, giving readers a broad overview of modern algebra that is well planned and organized. While maintaining the comprehensive, informal approach proven so successful in previous editions, the Third Edition offers new enhancements, clarifications and examples. --This text refers to the Hardcover edition.

From the Back Cover

Key Benefit: This book offers a clear, concise, reader-friendly presentation of abstract algebra, serving as either (1) an introduction for the mathematics major or (2) a means of exposure to many highly usable tools and techniques to apply in the non-major's primary interest areas. Key Topics: It unfolds some of the fundamental algebraic systems that are both interesting and of wide use, with the goal of reaching applicable, significant results. The book provides many high-quality examples and exercises, giving readers a broad overview of modern algebra that is well planned and organized. While maintaining the comprehensive, informal approach proven so successful in previous editions, this Third Edition offers new enhanc ements, clarifications and examples. --This text refers to the Hardcover edition.

Product Details

• Paperback: 272 pages
• Publisher: Wiley; 3 edition (January 15, 1996)
• Language: English
• ISBN-10: 0471368792
• ISBN-13: 978-0471368793
• Product Dimensions: 8.9 x 6 x 0.7 inches
• Shipping Weight: 14.4 ounces (View shipping rates and policies)
• Average Customer Review: 4.2 out of 5 stars  See all reviews (20 customer reviews)
• Amazon Best Sellers Rank: #236,464 in Books (See Top 100 in Books)

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43 of 45 people found the following review helpful:

5.0 out of 5 stars good book for 1st semester course, July 22, 2001

By 

R. John (austin, tx) - See all my reviews
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This review is from: Abstract Algebra (Paperback)

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 (but complete) introduction to sets, groups, symmetric groups, rings, fields and ends with some special topics (simplicity of A4, finite fields existence and uniqueness, cyclotomic polynomials, Liouville's criterion, irrationality of pi). As with most texts on the subject, there are no solutions provided.

The tone taken in the work caters to the student who has not had a course in abstract theory and proofs (ie- courses in analysis or topology ; a number theory course, in my experience, is not rigorous enough for the average student supply the necessary background).

For more difficult and robust presentations, look towards Artin's "Algebra" or Hungerford's "Algebra" (the latter being part of the Graduate Texts series).

For a more application (example-based) text (usually simpler for the less advanced student), look towards Gallian "Contemporary Abstract Algebra." This text is one of the rare occasions where the odd-numbered problems have solutions (but if that's all you're looking for, go to some of the Schaum's series). It is a bit basic (spending most of its examples on more familiar concepts), but also hits on some historical notes and examples that are good conversation pieces (something more mathematicians could use).

Also, as a sidenote, the editions have not changed the content at all. I would suggest getting an older edition...

22 of 24 people found the following review helpful:

5.0 out of 5 stars Best at what it is, September 23, 2002

By 

Cletus Bojangles "Cletus" (Atlanta, GA) - See all my reviews

This review is from: Abstract Algebra (Paperback)

(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 one is "Baby Herstein". Happily though, Baby Herstein still has content, unlike "Baby Hungerford"...

11 of 11 people found the following review helpful:

4.0 out of 5 stars Not a bad book but I am sure it could be better., February 26, 2001

By 

Khalifa Alhazaa "a_mathematician" (Doha, Qatar) - See all my reviews
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This review is from: Abstract Algebra 3e '96 (Hardcover)

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 has an optional chapter about the simplicity of the permutation group and some more results on finite abelian groups (If I am not mistaking).