Abstract Algebra (Dover Books on Mathematics)

Rating:
Summary: A Readable Intro to Algebra
Review: I have worked through the first 7 of the 13 chapters with the exception of chapter 4 (a tangent on Diophantine equations.) My own personal goal was to become acquainted with group and ring theory. If you proceed past chapter 7, then you will learn about polynomial rings, quadratic domains, abstract issues in linear algebra, and other topics. From what I read, I found Deskins' book highly readable. My math background consists of three college courses that I would consider rigorous and proof-oriented. If you have less of a background then it might be more challenging; however, the book builds its concepts very methodically and logically. Rarely did it leave me scratching my head and searching through previous chapters.

Deskins includes enough exercises to get a good mental grasp of the ideas. The level of difficult ranges from the very easy, definition checking problems to the sort of challenging. I say "sort of challenging" because none of the more difficult problems seem to be quite as difficult as the most difficult problems in other books. However, I have no experience with other algebra books, so this may be a characteristic of the subject.

All in all, I highly recommend the book as a text for teaching yourself abstract algebra. It is very readable and the well-chosen exercises help you understand the material.

Rating:
Summary: A Readable Intro to Algebra
Review: I have worked through the first 7 of the 13 chapters with the exception of chapter 4 (a tangent on Diophantine equations.) My own personal goal was to become acquainted with group and ring theory. If you proceed past chapter 7, then you will learn about polynomial rings, quadratic domains, abstract issues in linear algebra, and other topics. From what I read, I found Deskins' book highly readable. My math background consists of three college courses that I would consider rigorous and proof-oriented. If you have less of a background then it might be more challenging; however, the book builds its concepts very methodically and logically. Rarely did it leave me scratching my head and searching through previous chapters.

Deskins includes enough exercises to get a good mental grasp of the ideas. The level of difficult ranges from the very easy, definition checking problems to the sort of challenging. I say "sort of challenging" because none of the more difficult problems seem to be quite as difficult as the most difficult problems in other books. However, I have no experience with other algebra books, so this may be a characteristic of the subject.

All in all, I highly recommend the book as a text for teaching yourself abstract algebra. It is very readable and the well-chosen exercises help you understand the material.

Rating:
Summary: Not perfect but still very nice
Review: I purchased this book to help me prepare for a graduate-level course as an undergrad. The book is written at a good level: not as rigorous as a typical grad textbook, but not as chatty as many modern undergrad textbooks. This allows the reader to focus on the material and have it well-explained without being distracted or treated like a junior high student. The book contains no answers for any of the exercises. If I was not using it for self-study, this wouldn't be a problem. There are a few places where he does a bit of handwaving or is a bit lazy in his definitions (see the definition of "subgroup" on p. 207 for an example), but this does not overly detract from the quality.

While it's not perfect, I'm very happy with the book for my somewhat limited purposes. I'd like to give it 3.5 stars, but I'll be generous and round to 4 since I can't.

Rating:
Summary: It's a two-sided thing.
Review: On the one hand, this book, like all Dover Mathematics books, is fairly dense, with few examples or pictures. It's a difficult read, but, again, like all Dover books, is totally comprehensive.

Now, on the other hand, this book is, hands down, the cheapest abstract algebra book you will ever find (again, this is a trait of Dover). When I bought this book on Amazon, I searched for "Abstract Algebra", and despaired when I saw prices like $80.00, $90.00, etc. To find a good textbook for under $20.00 is a godsend.

So, basically, if you're willing to put some effort into this book and plow through it (and it's no more dense, really, than most math textbooks), it's very rewarding.