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Contemporary Abstract Algebra [Hardcover]

Joseph Gallian

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Book Description

July 9 2012 1133599702 978-1133599708 8
CONTEMPORARY ABSTRACT ALGEBRA, EIGHTH EDITION provides a solid introduction to the traditional topics in abstract algebra while conveying to students that it is a contemporary subject used daily by working mathematicians, computer scientists, physicists, and chemists. The text includes numerous figures, tables, photographs, charts, biographies, computer exercises, and suggested readings giving the subject a current feel which makes the content interesting and relevant for students.

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About the Author

Joseph Gallian earned his PhD from Notre Dame. In addition to receiving numerous awards for his teaching and exposition, he served, first, as the Second Vice President, and, then, as the President of the MAA. He has served on 40 national committees, chairing ten of them. He has published over 100 articles and authored six books. Numerous articles about his work have appeared in the national news outlets, including the New York Times, the Washington Post, the Boston Globe, and Newsweek, among many others.

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Amazon.com: 4.0 out of 5 stars  8 reviews
17 of 17 people found the following review helpful
5.0 out of 5 stars Best algebra book even if too expensive Sept. 22 2012
By C. Collomb - Published on Amazon.com
I have been looking for a book to review some algebra I studied over 20 years ago, and after comparing hundreds of books (yes literally!) I am glad I finally discovered this one.

Why is this book so great?

1. It covers abstract algebra from basics to Galois theory including solvability by radicals, so you should not need any other book to cover the basics before Masters level
2. The book does not assume any prerequisite and is easy to follow even if you did not touch abstract Algebra for a while
3. The book is full of examples, basic groups had like over 20 of them making sure you really get them
4. All theorems have a proof, and the proofs are well explained
5. The material is split in over 30 chapters in nearly 600 pages, making each chapter the right size to make progress and not too long to discourage others
6. Each chapter has around 50/60 exercises with the solution for half of them, making it a practical training book
7. The book size is like 3 ipads stacked together, making it practical to take anywhere at the contrary of other references like the calculus books from salas and hille

Anyways, I am a big fan of this book. The price is really crazy though, so I recommend you get a used copy of the 5th edition instead. The content is almost identical, and in absolute mathematical value identical. Nothing is missing, just some different exercises and some different examples. And for around $30 there is nothing better you can get.
14 of 15 people found the following review helpful
3.0 out of 5 stars Decent Book... but... Sept. 1 2013
By Chris A. Christopherson - Published on Amazon.com
I am a math teacher (teaching lower-level math at a university) who is reviewing abstract algebra after 20 years of not thinking much about it. I have amassed quite a number of abstract algebra books over the past few months and have been jumping around between them as I work through this stuff. I have decided to review several of them. So here's what I think of this one:

Gallian does do an admirable job of explaining concepts. There are decent examples. I think the book is a bit heavy on the applications especially near the beginning. Gallian does tend to be a bit wordy at times, but not bad. As I said, he does explain things pretty well. Based only on the actual text, I'd have given the book 4 stars.

So why only 3 stars? Because I gave the exercises only 2 stars. They very nearly enrage me. Okay, it's not so much that the exercises themselves are horrible. My gripe is that they tend to be either routine problems (that's not my gripe) or overly difficult proofs/sophisticated conceptual problems. There's not a lot in between. That's my first criticism. Next, Gallian seems to have made very little attempt to grade the problems in increasing difficulty. You look at number 3 and you're thinking about it for a week, until finally you are tired and just move on to the next section... when all along, the "meat and potatoes" problems are buried in the sorts of problems that tend to take many hours of pondering. In my opinion, that's not a good way to present the problems. Next, there needs to be MANY, many more routine, concept-building problems. The problems that are there are okay, they just need to be tripled in number with the sorts of routine concept-builders that aid in understanding and cementing definitions and methodology. Leave the abstract proofs for the end of the problem sets.

Also, and this is more of a philosophy issue, just put the damn solutions in the back of the book. It's not a secret (or at least it shouldn't be). As an instructor, I have no problem coming up with testing material on my own and I've never picked even problems from the books. In fact, I've never assigned a problem that my students haven't had the answer waiting when they need to confirm their performance. A student not knowing if he/she is doing things correctly is a sure recipe for reinforcement of bad mathematical habits when they are not doing things correctly. They need to see their faults RIGHT AWAY and clear them up. It's stupid to have a student spending weeks not knowing if he/she has the material down and going into a test that way. Immediate feedback is critical, in my opinion. And it's my opinion that all textbooks should have the solutions available. Solve and confirm. Solve and confirm. Solve and confirm. That's what builds understanding, not a mysterious cloud that a student gets lost within. Just because a math genius can rip through a problem set with no feedback, confirmation, or hint, it's no sign everyone should have to do that. Not everyone can paint a Mona Lisa and not everyone can internalize this stuff on first glance. This "mathematical maturity" argument is silliness. One does not attain "mathematical maturity" via secrecy, reinventing the wheel, or discovering all of mathematics on his/her own. And all the blood, sweat and tears spent working a problem or doing a proof is 100% in vain when the student does not know if he/she has done the thing correctly.

Anyway, getting off my soapbox, this book is decent and you could do much worse. But, at the same time, the book could be so much better with just a bit of refinement. So... not bad, but there are others I'm more fond of (which I will review).
8 of 8 people found the following review helpful
3.0 out of 5 stars Great Book, but Phenomenally Overpriced Aug. 30 2012
By Baze - Published on Amazon.com
Gallian's clear, easy-to-read text will be an excellent guide to anyone who decides to take a course in undergraduate abstract algebra. Gallian writes only the bare necessities for the student to read. Initially, this simplicity may reflect a writer who doesn't care about the student learning too much. Nothing could be further from the truth- by keeping his paragraphs, descriptions, and proofs concise, Gallian makes it easier for the student to focus on the theorems taught throughout the book. The problems that Gallian assigns as the end of each chapter begin easily, and then progress to very challenging problems. This conveniently allows the student to do extra problems depending on their comfort level with the material.

Despite that the text is very well written, and that the problem sets are quite reasonable, I might dock off two stars- because of the price. Personally, I think that it's outrageous a used copy has to sell for nearly $200. I have a copy of the 7th Ed as well, and beside the problem sets being slightly different, the material is quite similar between the 7th and 8th editions. The 8th Ed, in effect, is useless. If I were you, I'd try to save my hard-earned pennies and purchase some other edition of this book.
1 of 2 people found the following review helpful
4.0 out of 5 stars Much needed self-study guide! Nov. 13 2013
By EEngineer - Published on Amazon.com
Format:Hardcover|Verified Purchase
Very thorough introduction for those of us who need a better foundation in the basics of algebraic theory & didn't take the coursework previously.
1 of 2 people found the following review helpful
5.0 out of 5 stars Great Algebraic Reference May 27 2013
By Jennifer Long - Published on Amazon.com
Format:Hardcover|Verified Purchase
We used this book as we studied Group Theory. This book was incredibly helpful. I love all of the detailed proofs, helpful hints on problems, as well as interesting summaries of famous mathematicians related to this field. It is an accessible book, and worth the money.

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