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Topics in Algebra, 2nd Edition 2nd Edition

by I. N. Herstein (Author)
4.3 out of 5 stars 28 customer reviews
ISBN-13: 978-0471010906
ISBN-10: 0471010901
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Product Details

  • Paperback: 388 pages
  • Publisher: John Wiley & Sons; 2nd edition (June 20, 1975)
  • Language: English
  • ISBN-10: 0471010901
  • ISBN-13: 978-0471010906
  • Product Dimensions: 6.3 x 1 x 9.4 inches
  • Shipping Weight: 1.5 pounds (View shipping rates and policies)
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (28 customer reviews)
  • Amazon Best Sellers Rank: #82,308 in Books (See Top 100 in Books)

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Customer Reviews

Top Customer Reviews

5.0 out of 5 starsThe greatest introduction to algebra
By Chan-Ho Suh on April 4, 2000
Format: Paperback
I knew before I read Herstein that it was a very famous book known for its exposition and interesting problems. But I had no idea of the reality: it IS amazing! Herstein's approach is to just concentrate on a few basic notions and take it as far as possible before introducing new ideas. This results in very simple-seeming proofs which flow elegantly into the next theorem and proof. Incidentally, Herstein's approach is to also have a bunch of problems that are more meant to be 'tackled rather than solved.' He hopes that by trying to solve hard problems, the reader will come across ideas which are later explained in the book. At that stage, the new ideas are natural. This means these problems are very difficult, and even if you read ahead, they remain difficult. Not to say there aren't some easy ones, but I'd say somewhat less than 50% are difficult. But it's all worth it. I recommend studying out of this book in conjunction with a more standard reference type textbook. Then you get the best of both worlds.
By the way, this book contains an intro to Galois Theory! How many books intended for undergraduates have such topics and such a prestigious reputation?
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5.0 out of 5 starsClassic Text but not the Most Elementary
By James M. Cargal on July 11, 2000
Format: Paperback Verified Purchase
I wonder if all the reviews I see are of "Topics in Algebra", 2nd ed. or "Abstract Algebra", 3rd ed. The second book is a good undergraduate introduction. However, Topics could be use at the graduate level. I. N. Herstein was a great authority and his writing has unusual clarity. Topics is not only more advanced than the other but I think it is simply the better book. The first edition helped me in graduate school some thirty years ago. The treatment of group theory is particularly rich, with a thorough explication of the Sylow theorems.
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5.0 out of 5 starsA classic text for intermediate level abstract algebra
By Alexis Humphreys (alexishumphreys@att.com) on July 22, 1999
Format: Paperback
A very engaging book. The proofs are very carefully written and the flow of logic and ideas is impeccable. I once crammed before an exam and read about 120 pages in a single evening and it just "clicked", enjoying the book more and more as I read on. The definitions and proofs flow very nicely and are always at the right level of rigor. In my opinion, this is a classic of exposition in Abstract Algebra.
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4.0 out of 5 starsIf I could relearn algebra, this would be my text.
By Alex on February 4, 2011
Format: Paperback Verified Purchase
Ok, as of now, I'm not a huge fan of algebra. I feel that this is a result of using Artin's algebra text (which has a very strong flavor that you may or may not like) and the fact that algebra feels like a collection of topics as opposed to a coherent theory. However, this book makes me tolerate algebra, and I must certainly applaud it for doing so.

Herstein is one of the best mathematical writers I have read. I feel that he tops Spivak, Stillwell, and possibly even Rudin. I'd probably rank him with Axler. He writes with clarity and enthusiasm, and his obvious love for the subject is dripping off every page. Hertein is somehow able to take a very typical algebra book, and make it into something enjoyable. One important thing to note is that this book is not quite as flavored as Artin's is, and this is the result of Herstein treating conventional topics in a rather conventional way. People tend to either love or absolutely hate Artin, but no one could truly hate this book's presentation.

As commented on by many reviewers, this book is especially strong in group theory. This book takes time to build up more theory than most other books, and it does so in an exciting way. However, after Herstein's discussion of groups, this book becomes quite shallow in many areas. He dedicates only one subsection to modules, and many reviewers have commented on the skimpiness of his field and Galois theory sections. This is a book that will be easily outgrown by anyone who uses it, and this is the reason I have given it four stars. I cannot really comment on what good references for undergrads would be on modules, but Stillwell's ...Read more ›
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5.0 out of 5 starsgood book for an introduction to the subject
By TEJUS SAWJIANI on April 24, 2003
Format: Paperback
I used this book as an introduction to Groups, Rings, Vector Spaces & Fields. The chapter on groups is excellent, although I found the treatment of the symmetric group a little confusing (but nothing that a quick reference to Dummit/Foote won't dispel). The chapters on Rings & Vector Spaces are very comprehensive as well. The problems range from the very simple definition manipulation kind of problems to questions that are very difficult, some of them forming tangible results by themselves (such as the one on Schur's Lemma in the Modules section).
In conclusion, this is a very good introductory textbook (even better than Artin). Read this along with Artin in order to get the geometric flavor as well. Together, the 2 books will equip a student very well to tackle lang or hungerford, and some of the beginning treatises on Commutative Algebra.
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5.0 out of 5 starsGood Introduction, useful for self study
By PST on April 23, 2004
Format: Paperback
I am an engineer by training and a sales man by profession, with a a strong liking for mathematics.
I found this book to be an very readable introduction to a subject (abstract algebra), I had never been exposed to during my engineering math - other than matirx theory, which was obviously taught extensively.
The proofs are generally easy to understand, but certainly not trivial.
A pleasure to read
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Most Recent Customer Reviews

5.0 out of 5 starsStill an absolute must to get a real sense of how - and why - algebra...

Apparently one of the wellsprings to the previous generation of algebraists, this remains the ultimate introduction to modern abstract algebra and key topics like group theory,... Read more

Published 9 months ago by Otto Scroggs
5.0 out of 5 starsFive Stars

Excelente!

Published 12 months ago by Angélica
3.0 out of 5 starsThree Stars

good

Published 20 months ago by Deif
5.0 out of 5 starsRequired Textbook

Required Textbook, but at Amazon you get new condition at half the bookstore price, arrives on time (fast) and in great condition. Read more

Published on September 6, 2011 by Ryan
3.0 out of 5 starsEasy to read, covers basic concepts

Topics is good for a first taste of Abstract Algebra. It seems very elementary to me, as I took a look at this after having gone through the book by Michael Artin. Read more

Published on October 18, 2007 by Michael C. Wilson
3.0 out of 5 starsDisadvantages, Advantages Depending on Reader's Needs

While this book may have deserved 5 stars when it first came out, as it is very well written, it has disadvantages for students today. Read more

Published on July 15, 2006 by math_grad
5.0 out of 5 starsVery nice book

This book is very nice. As an undergraduate I try to study this book to have a glimpse of abstract algebra. So far this is a pleasant experience. The proofs are clear and rigorous. Read more

Published on January 21, 2006 by Math Lover
4.0 out of 5 starsvery good but not 100% complete

I had this text for a 4th-year course in Galois theory & (somewhat) advanced group theory, like normalisers, Sylow's Theorems, conjugacy & finite abelian groups. Read more

Published on April 6, 2004
5.0 out of 5 starsClearly written proofs

I was a Computer Engineering student who wanted to learn Galois Theory. So I took a 3rd year pure math course in Abstract Algebra. The instructor used a different text book. Read more

Published on September 22, 2002 by M. Vishnu
5.0 out of 5 starsSolid introduction to abstract algebra.

I had my first exposure to abstract algebra from this book over 20 years ago. I found it to be a clearly written and well-organized text then. Read more

Published on February 27, 2002 by Allan D. Bennett

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