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Topics In Algebra [Paperback]

I. N. Herstein
5.0 out of 5 stars  See all reviews (1 customer review)
Price: 202.99 & FREE Delivery in the UK. Details
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Book Description

1 Jan 1975
New edition includes extensive revisions of the material on finite groups and Galois Theory. New problems added throughout.

Product details

  • Paperback: 400 pages
  • Publisher: John Wiley & Sons; 2nd Edition edition (1 Jan 1975)
  • Language: English
  • ISBN-10: 0471010901
  • ISBN-13: 978-0471010906
  • Product Dimensions: 23 x 16 x 2 cm
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Bestsellers Rank: 204,439 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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First Sentence
One of the amazing features of twentieth century mathematics has been its recognition of the power of the abstract approach. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Most Helpful Customer Reviews
3 of 4 people found the following review helpful
The book gives a clear and systematic description of the basic structures of abstract algebra. The book also includes a large number of well chosen exercises of different degree of difficulty.
In my opinion this is the best undergraduate mathematics textbook I have ever read.
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Amazon.com: 4.3 out of 5 stars  25 reviews
37 of 40 people found the following review helpful
5.0 out of 5 stars The greatest introduction to algebra 4 April 2000
By Chan-Ho Suh - Published on Amazon.com
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?
19 of 20 people found the following review helpful
5.0 out of 5 stars A classic text for intermediate level abstract algebra 22 July 1999
By Alexis Humphreys (alexishumphreys@att.com) - Published on Amazon.com
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.
20 of 22 people found the following review helpful
5.0 out of 5 stars Classic Text but not the Most Elementary 12 July 2000
By James M. Cargal - Published on Amazon.com
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.
8 of 8 people found the following review helpful
4.0 out of 5 stars If I could relearn algebra, this would be my text. 4 Feb 2011
By U of M Math Student - Published on Amazon.com
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 Elements of Algebra: Geometry, Numbers, Equations (Undergraduate Texts in Mathematics) is a good introduction to field and Galois thorey. The sheer fact that a student would need to supplement an already expensive book with others is quite annoying. Artin, on the other hand, spends a chapter on rings, and chapter on modules, a chapter of fields, and then finally a chapter on Galois thoery. The fact that Artin gives decent discussions of each of these topics has caused me to begrudgingly return to his book and start looking for buyers of this one. I feel that this is the reason that so many more classes will opt to use Artin as opposed to this book.

However, I don't think that this book is useless or will become obsolete. I feel that anyone who works through this book will easily be able to begin using a book like Lang's Algebra. So I guess the choice of whether to use this book or Artin's will come down to the professor's (or buyer's) preferences in what should be covered and where to put the emphasis.

Like I said before, I'm not a huge fan of algebra, but I did enjoy this book. So I'm guessing that if anyone who actually likes algebra picks this book up, then they would probably view this book as the greatest thing ever. One word of caution, this is a more beefed up version of his Abstract Algebra, and so only stronger undergraduates should consider using this. This book is, after all, conventionally used in honors sequences.
9 of 10 people found the following review helpful
5.0 out of 5 stars good book for an introduction to the subject 24 April 2003
By TEJUS SAWJIANI - Published on Amazon.com
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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