Topics in Algebra, 2nd Edition

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, rings etc. While it doesn't focus upon category theory and such modern topics it gives a really thorough and discursive introduction to the core topics and constantly gives direction and motivation - and excellent well integrated examples that the vast majority of modern algebra books totally lack. The discussion is conversational and gives a real sense of why methods are developed and used. And while few diagrams are used the commentary is so clear and helpful that it nonetheless brings the whole subject to life.But sad to see that scarcity value is clearly limiting access by the outlandish prices for available copies.

Herstein's Topics is the clearest, most naturally motivated exposition of abstract algebra. At any point in the text, the reader can sense the careful development of the whole. The exercises aren't a grad student's hodgepodge or filter that satisfies the publisher's urging to justify the latest edition. Dummit and Foote come across as confused and rushed in comparison. If you're absolutely new you abstract algebra, perhaps you'll feel better starting with Hungerford, then moving on to Herstein, or maybe working with them in tandem. Then cap off your journey with Van den Waerden.

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 would give this 4.5 stars, but the price and lack of availability causes me to take the floor rather than the ceiling.This is a classic that occupies the position in algebra that Baby Rudin or Apostol occupy for analysis. That is to say that this text has been used at well-regarded/selective undergraduate institutions as an introduction to algebra for students who take math seriously and already have some degree of mathematical maturity. M. Artin's text is an alternative with a much stronger geometric/linear algebraic flavor with discussion of continuous groups/symmetries, while Herstein feels more classically algebraic with more in depth coverage of fields and Galois theory and (some) aspects of finite group theory.However, I do have some qualms on the choice of topics. In keeping with a "pure" algebraic approach, group actions are *not* covered at all (not even defined). (Naturally, this also means no orbit-stabilizer theorem.). This is unfortunate, as it makes the proof of the Sylow theorems unnecessarily cumbersome, as the proof is most intuitively understood by considering group actions and orbits. Herstein actually presents three proofs of Sylow. The third one is especially involved, and while I appreciate the importance of the theorems, it seems a bit unnecessary to prove a theorem three times in an intro text.The book does not carefully make the distinction between normalizer and centralizer. The terms, as applied to subgroups, are defined in an exercise, but otherwise, N(a) is defined and used in a way where most texts would use C(a). These are, of course, the same for singleton sets {a}, but to not carefully distinguish between them will more likely than not confuse students when then subsequently need to distinguish between N(S) and C(S) for subsets S. The book follows the convention that neither rings nor integral domains need to have the identity element without mentioning that many authors do require this as part of the definitions, especially for integral domains.There's a special topics chapter, mostly on advanced ring theory, where the (little) Wedderburn theorem is proved, material probably best suited for a second semester course, but it's nice to see some 20th century mathematics appear in an intro text like this one.The exercises are indeed excellent (more than any other intro book, including Artin), and there's a lot to learn from some of the more challenging ones (much in the same way as Rudin's exercises). As a minor quibble, it's a bit too chatty for my tastes, and I prefer a leaner style without too much commentary in the text and especially not inside the proofs themselves, and Herstein does both of these things, but others find his style engaging and well-motivated.Unfortunately, the price is highway robbery, but old beaten up copies are still available if you look, and an international edition is also available.

Required Textbook, but at Amazon you get new condition at half the bookstore price, arrives on time (fast) and in great condition. Easy and quick transaction with a source you can trust. I never worry about being ready the first day of class.

Wonderful Topics in Algebra, 2nd Edition. My husband was jubilant to have this book again!

good

Excelente!