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Topics in Algebra, 2nd Edition 2nd Edition

27 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 (27 customer reviews)
  • Amazon Best Sellers Rank: #50,998 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

38 of 41 people found the following review helpful 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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20 of 22 people found the following review helpful 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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19 of 21 people found the following review helpful 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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8 of 8 people found the following review helpful By U of M Math Student 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
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9 of 10 people found the following review helpful 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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9 of 10 people found the following review helpful By A Customer on April 6, 2004
Format: Paperback
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. I would say that I liked the presentation and writing style in this book but I didn't think it was totally complete. There was just a section on solvability by radicals, and no other applications of Galois theory like trisecting angles, duplicating cubes, etc. Then again, it IS a topics book so it wouldn't go into something in great detail. The presentation is good, there are tons of really good problems (like baby Herstein), but the chapter on field theory is a weak point, IMO. So 4 stars, even though I hate to do it because the rest of the book is much better.
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Topics in Algebra, 2nd Edition
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