Topics In Algebra

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 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 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.

This text serves as an excellent introduction to higher mathematics. This text covers more material than is covered by any undergraduate course in Algebra that I know of and Herstein presents each topic with great foresight. This text is a true classic! I am in high school and am taking courses at an university with a STRONG mathematics program. I purchased this text after noting that the class I was enrolled in was not moving at the pace I would have preffered. I flew enthusiastically through the chapters on group theory, ring theory, vector spaces, and fields. I enjoyed each chapter and at least attempted to tackle each problem. This text has given me more knowledge than any of my high school and college classes combined. Proffesionals must realize that this text is for beginners, not graduate or doctor students. Herstein's text will forever remain a classic!