Customer Reviews

Topics in Algebra

5 star:		(15)
4 star:		(5)
3 star:		(3)
2 star:		(1)
1 star:		(1)

 

 

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?

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.

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.

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.

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

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.

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. I find it to be a handy reference text now. It is not surprising that the text is still widely-used today.

Herstein uses matrices, matrix algebra, and polynomials throughout the book to provide illustrative examples for the discussions of groups, rings, modules, and fields. He is not afraid to visit other areas of mathematics ...

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.

The best introductory book I have come across. If your goal is understanding then you should definitely have this book as one of your introductory texts. Herstein's book shines in its development and extension of basic ideas. For the dedicated student or mathematically sophisticated this book can be used in lieu of an intructor led class.

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. I found it hard to follow the proofs in that book. Later I discovered Hernstein book in the library and it saved me. The proofs are very well written in Hernstein's book.