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March 10th, 2010, 06:24 AM   #1
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does anyone know a good book in abstract algebra?

...because i wanna get good grades in this subject.
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March 10th, 2010, 10:47 PM   #2
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Re: does anyone know a good book in abstract algebra?

Dummit and Foote would be my recommendation to learn from. If you are trying to go deeper (as in, early grad level), Hungerford. If you are trying to go really deep (as in, "I want to be an algebra researcher") then Lang.
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March 11th, 2010, 03:26 AM   #3
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Re: does anyone know a good book in abstract algebra?

I've always thought that Herstein's "Abstract Algebra" was a book with a fairly low slope if this is your first algebra class. If you give a better idea about what level the class is and what preparation you have, we can offer more specific advice. cknapp's suggestions are good books too.

Have you had a proof-based course before? If so, which ones?
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March 11th, 2010, 07:15 AM   #4
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Re: does anyone know a good book in abstract algebra?

Quote:
Originally Posted by cmusick
I've always thought that Herstein's "Abstract Algebra" was a book with a fairly low slope if this is your first algebra class.
Yes. That's another good one. Would have made my list if I were thinking.
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March 18th, 2010, 12:48 PM   #5
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Re: does anyone know a good book in abstract algebra?

I first learnt from Herstein's book, and I love it. It gave me a great introduction and was much more forgiving than Lang.
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March 18th, 2010, 01:09 PM   #6
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Re: does anyone know a good book in abstract algebra?

Quote:
Originally Posted by jason.spade
It gave me a great introduction and was much more forgiving than Lang.
Lang's book is, indeed, unforgiving; certainly not a first book to learn out of.
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March 18th, 2010, 08:48 PM   #7
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Re: does anyone know a good book in abstract algebra?

[color=#008000]Contemporary Abstract Algebra by Joseph A Gallian[/color], is a terrific book for an undergraduate two semester introduction to abstract algebra. You know, Group theory 1st semester, Ring theory the next. I wish it was the book I was assigned and here's why:

It's got a good conversational feel without overwhelming you with prose. The important points do pop out, by their is an abundance of clear expository writing that really takes this book to another level of quality. Figures are used more than other books I have seen, and they're used to good effect. Clear tables, and diagrams help illuminate ideas and even suggest new ways of viewing the material. The problems are standard, but there are a lot of them, and some of them are quite interesting. It's the usual mix of computational group/ring specific questions, and more general theoretical questions.

One of my favorite parts of the book is the suggested reading, which not only contains the oft found list of the authors favorite books on a topic, it also suggests related scientific articles after each chapter,which the reader is now prepared to understand having completed the chapter. This is an invaluable tool for being introduced to finding ,reading, and responding to the scientific literature.

This is not the most efficient book, but beginners may be better off in the long run learning at a slower more thorough pace. Either way graduate books are usually to brief to be good without a teacher or even better a tutor. The book I use is [color=#BF0040]Algebra: Pure and Applied by Aigli Papantonopoulou[/color] (what a mouthful!). It's got the worst binding ever, but has many (good) exercises. This book also motivates theorems with examples, but is perhaps used to excess. On the one hand it makes sense of the theorem and they can be good to tie down abstract notions to concrete cases, but being given so many examples for free is dangerous because it might make the reader over confident in the truth of the statement before it's even proved, and its examples do not include all the interesting/useful features. The problem sets help fill in the gaps, but an overconfident reader may skip over the problems. It has figures, but they're inferior, and there is no awesome math article references.

The best option is multiple books, but if your busy schedule forces you to choose, go with the Contemporary Abstract Algebra. Send me a PM and I can help you find a cheap copy.
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March 23rd, 2010, 08:42 AM   #8
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Re: does anyone know a good book in abstract algebra?

Quote:
Originally Posted by forcesofodin
[color=#008000]Contemporary Abstract Algebra by Joseph A Gallian[/color], is a terrific book for an undergraduate two semester introduction to abstract algebra. You know, Group theory 1st semester, Ring theory the next. I wish it was the book I was assigned and here's why:
I was assigned the book, and have to disagree with the recommendation; my reasoning is:

It fails to introduce the student to the "higher level" way of looking at algebra; in particular, permutation groups and the relation between homomorphism and group action are very poorly exposited.

The ring and field theory is very elementary, and not expressed in any way that teaches the student to work with the structures-- I found myself consulting Hungerford (not an introductory text at all!) for clarification when I was learning about rings, because the theorems and structures seemed a bit magical.

The Sylow theorems are left as an appendix, and not very well introduced or motivated.

The examples and exercises don't give a strong understanding of how to work with the structures. I've found myself consistently floundering when trying to get into deeper areas, and going back to Hungerford or Herstein to relearn the material that I felt very confident with when learning from Gallian.

In short, the prose, exercises and examples make the student feel confident, but the text does not dig enough to provide a solid enough understanding for future work in algebra...
If you are feeling very lost with a more advanced book, perhaps it would be good to check out Gallian before coming back to the more advanced book, but it just doesn't provide a deep understanding of the subject.

Sorry for being contrary.
Cory
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April 3rd, 2010, 04:31 AM   #9
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Re: does anyone know a good book in abstract algebra?

You being contrary has only ever made me see another way, and I appreciate this. I must admit, I am only currently taking the undergraduate second semester algebra course at my school so I don't have the hindsight of what material was most important to have been emphasized. In fact, I really don't plan on studying more algebra for algebra's sake, and hope to acquire more only as needed for other subjects.

However the historical aspects, and the further reading sections of contemporary really do make it a worthy supplemental read. Reading math journals early on is invaluable, but it can be a daunting task without a guiding hand. It's nice to have papers references catered to your background.
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April 3rd, 2010, 02:26 PM   #10
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Re: does anyone know a good book in abstract algebra?

Quote:
Originally Posted by forcesofodin
However the historical aspects, and the further reading sections of contemporary really do make it a worthy supplemental read. Reading math journals early on is invaluable, but it can be a daunting task without a guiding hand. It's nice to have papers references catered to your background.
Certainly. There are very few books which I would actively recommend against reading. If I recommend avoiding a book, it's simply because I don't think they work as a primary text.
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