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Название: Algebra: A Graduate Course (Mathematics)

Автор: Isaacs I.

Аннотация:

I love this book; its shortcomings do not even tempt me to rate it less than 5 stars. However, it is not perfect, and you should consider its shortcomings when deciding whether or not to use it for a course or add it to your collection.The book is exceptionally clear, even though it is dense. However, this book is not appropriate for a first course in abstract algebra: even if you have a strong mathematical background, it definitely requires prior experience with abstract algebra. The notation is a bit eccentric at times, but it is consistent, and once you get used to it, the book reads very easily. It is excellent for self-study.The book is organized so that advanced chapters on specific topics can be read on their own, making this book an outstanding reference, and also making it easier to design a course using this book as a text. In the occasional cases when earlier material is required, the indexing is excellent, and the definitions are clear and concise.Exercises are very illuminating, and diverse in difficulty level.At times, Isaac provides tedious (and sometimes confusing) proofs of results which are intuitively obvious and in my opinion are best left to the reader. Isaac's style of proof seems to be to include every detail, even when leaving certain details to the reader would actually make the proof easier to comprehend. This space in the book, in my opinion, should be occupied instead with concrete examples, which leads into my largest complaint:This book is almost completely devoid of concrete examples. Numerous results are proven before a single example is given, and in some cases, no examples are ever given — the reader is left to construct such examples on her own, or find them in another book. Chapters that provide more concrete examples, such as the one on permutation groups, are strictly optional and are not well-integrated into the text. Working the exercises provides some much-needed examples, but this is still a weak point of the text. This also relates to the other weak point of this text — connections to other areas of mathematics. This book is clearly written by an algebraist who sees the inherent beauty of the subject, and he does an excellent job of communicating this beauty through his writing. However, the connections to other branches of mathematics simply aren't in the book.This book is complemented by books like Lang's Algebra at a more advanced level, or Dummitt and Foote at a more elementary level. In some ways, this book is the exact opposite of Lang's: Isaacs' proofs are detailed, expanded, but tedious, and Isaacs provides few concrete examples. Lang's proofs are sparse or not present, yet Lang provides numerous examples and countless connections to other branches of mathematics.Lastly, the of this price is absolutely obscene. Although the book is excellent and certainly worth the money, the binding isn't: it completely fell apart and needed to be glued back together after only moderate use. This book held up less well than most cheap paperbacks. For $157, this lack of quality is downright criminal.