Customer Reviews

Contemporary Abstract Algebra

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Abstract algebra is an inherently abstract, formal, non-intuitive subject, and while it can be made less difficult, it cannot be made easy. Gallian's book is a valiant attempt at the latter. The book shies away from precise definitions, formal proofs, and that elusive thing known as "mathematical maturity." However, abstract algebra simply cannot be satisfactorily taught without at least a minimum of these things, and is best taught in as formal of an environment as possible. As such, I cannot recommend Gallian's book to those who wish to learn abstract algebra on a late undergraduate/beginning graduate level. However, for the advanced high school student who wishes to study abstract algebra early, Gallian's book is excellent in that it does not presume that the student has had much prior exposure to advanced mathematics.

This book is totally useless. Yes, there are a lot of examples. Unfortunately, each example is "explained" in about 2 sentences, leaving the reader (me) to wonder how on earth the author jumped to these conclusions. The homework problems are only vaguely related to the book's content. Basically, each chapter goes as follows: 1. 8-10 examples that have nothing to do with homework problems. 2. Theorums that are vaguely associated with homework problems. 3. About 70 homework problems, 5 of which are solvable using the material provided in the book. The answer key to the homework problems is COMPLETELY USELESS. Just in case you missed that: the answer key to the homework problems is COMPLETELY USELESS. Get this: it actually does not contain answers most of the time. Yes, it contains answers to the simple calculation-oriented problems, but you probably didn't need the answer key to get those right, did you? How would you like to go through a complicated proof and desire to check your work, only to find that literally the only thing the answer key says for that problem is, "Look at Theorum 4.2". Seriously. This is actually what the answer key says for most problems. I'm not sure I know for sure the definition of an answer, but "Look at Theorum 4.2" is NOT an answer. All in all this book is totally useless; I want my $150 back.

This book actually develops very little math in its chapters , while throwing some very difficult problems at the reader.It is really surprising that in order to read an essential theorem like Cayley's Theorem (page 126) one is referred back to Exercise 23 , and to Exercise 9.Can't Dr Gallian have at least one self-contained Proof?? I can see that maybe he wants to make the student think , but the book has plenty of exercises for that purpose!Example 14 on page 208 is also very revealing.Here Dr Gallian talks about a very important isomorphism,but he just mentions a lot of facts without proof in the body of his proof!!!Really amazing!What can a student seeing this stuff for the first time learn from this example?? Beyond the bad presentation here are some major defects :
1.Compared to other popular Algebra textbooks used these days in the U.S , the Exercises are very difficult.I made comparisons to 3 other popular textbooks.The Exercises are harder than "A First Course In Abstract Algebra" by Fraleigh.It is harder than "Elements of Modern Algebra" by Gilbert and Gilbert , and finally it is harder than "Abstract Algebra" by Blair and Beachy.
2.It is well known to Undergraduate Educators like myself , that most students who are in undergrad math programs have no intention of going to Graduate School in Mathematics.For most of these folks it was a Shock to learn that the Undergraduate Abstract Algebra Course has a lot to do with proofs , and little with Computations.This book just adds to this Shock.It is certainly not in tune with current academic reality facing Abstract Algebra Instructors,due to the fact that it expects too much from the student.
3.In recent editions the book has become more and more applications oriented.This is completely unneccessary , and I really do not know what Dr Gallian is trying to accomplish here.
4.It seems to me that Dr Gallian has had the same approach one would have when writing a Calculus textbook: But this approach does not work in a hard subject like Abstract Algebra .This Book does not provide any insights into the actual thought processes that are required in constructing airtight Abstract Algebra Proofs. Throughout the book, one is constantly left with the question "So what are the important problems and techniques?"Dr Gallian's approach would have been perfectly OK if he was writing a Calculus book , because in Calculus just looking at a few model problems is enough to master the subject to a reasonable degree.However in higher level math courses due to the huge number of different methods and its variations , it is more important to develop insights into the subject.
This will not happen when studying this textbook.I consider this to be the BIGGEST FLAW of the book.
Conclusion: This is a very bad Abstract Algebra Book.AVOID this book if you are trying to learn something about the subject.

This was how I learned abstract algebra, this was how I started out. I also take it as only being useful for group theory. I didn't think it was bad then, it gave plenty of good motivation and nice little math bios. But now, for the most part, I relegate it to my section of "baby math" books as I do with Rudin's "Principles of Mathematical Analysis". That dreaded section of my shelf that I feel very embarrassed for reaching towards. Although, I don't mean that condescendingly for those who do read it, it is and was a great undergraduate textbook.