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I am about to take a course in undergraduate Algebra which is using Artin's Algebra. I have been studying from it and haven't really appreciated the combination of text and problems (granted, I haven't gone too deep into the text).

Now, this is the text for the class, so I would expect a nice compliment from the lecture to go along with Artin. I was thinking about getting Dummit and Foote, which seems to have high praise across the board. What are the strengths and weaknesses of Dummit and Foote, compared to Artin? Is there a better text for a class at this level?

EDIT: I really don't want a recommendation for another text, but how does Artin compare to other texts.

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marked as duplicate by Matt Samuel, Daniel W. Farlow, user122283, Empty, user149792 Sep 8 '15 at 6:07

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  • $\begingroup$ I would not recomment D&F as a companion. It is a big, structured book with dependencies and all sorts of asides, extra topics etc. It will be very easy to get lost between the stylistic differences of the two books. $\endgroup$ – guest Sep 7 '15 at 23:13
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    $\begingroup$ I'm really worried about exercises from Artin. I feel like I'm not learning what I need to by doing them. Is Dummit and Foote better for that, in you opinion? $\endgroup$ – user268311 Sep 7 '15 at 23:19
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I have and am still frequently using both books and I have to say the main thing they have going is that :

  • D&F has great exercises.
  • Artin is friendlier to the audience.

My usual advice is that one learns from Artin and then does the exercises in D&F, but overall they are both great books. From what people have said to me, D&F is better as a book to have after you already understand the content, for review it is great, but on a first pass it may not be so good. I have heard similar things in that last regard, about the textbook Rudin's principles of mathematical analysis (just for comparison if you have read it).

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  • $\begingroup$ The exercises in Artin are my main concern. Thanks for the insight! $\endgroup$ – user268311 Sep 7 '15 at 23:16
  • $\begingroup$ @BenjaminTighe Read this answer here, I agree with the comments on Artin: math.stackexchange.com/a/96526/233746 $\endgroup$ – user233746 Sep 7 '15 at 23:24
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Dummit and Foote has a more standard format, and covers a wider variety of topics, but it's extremely dry (and feels very "text-booky" to me). I didn't like it much. Take a look at Vinberg instead. Takes a very similar approach to Artin, but it's more readable in my opinion and has a more manageable number of problems (which are embedded in the section, so you're forced to solve them as you go along). I find the massive number of exercises in Artin a bit discouraging.

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  • $\begingroup$ Thank you! I'll look out for Vinberg. $\endgroup$ – user268311 Sep 7 '15 at 23:18