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. I was reading the 'official' textbook for my class, Dummit&Foote, and it was a mess; I had no idea what was going on, and in particular, where all these definitions were coming from. Herstein made it 'click' into a cohesive whole. 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. The rush I get from solving a Herstein starred problem is incredible. I know that the knowledge I get from studying this book is _real_, not just memorization of certain theorems. I recommend studying out of this book in conjunction with a more standard reference type textbook. Then you get the best of both worlds.
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