Algebra Algebra: Lang vs Bourbaki Comparison

[SrVishi]

Hello, I have access to both Algebra (the graduate one) by Lang, and the series of Algebra Chapters 1-7 by the Bourbaki group. I am okay with Lang's style and all, and I am aware that he was in the Bourbaki group, but I was wondering what is considered the better of the two. Thanks in advance.

 

[micromass]

I was wondering what is considered the better of the two.

For what purpose? With what background knowledge?

 

[SrVishi]

I just want a complete treatment of abstract algebra, to make the transition to grad school easier as I graduate in a year (I'm becoming a senior in the fall). I had two courses in undergraduate algebra, though I have no problem with tough levels of rigor and terseness from my self study habits. I can also refer to other books like Dummit and Foote for a specific concept if I am struggling with it or need more specifics. Are there any more details you need to know? Thanks again.

 

[micromass]

Neither book is good really. Lang has very nice key insights, but much of his text is confusing and the book is riddled with errors.
As for Bourbaki... the Bourbaki style is horrible and not meant for studying. It's good as a reference though.

Try Algebra, chapter 0 from Aluffi for a very good and modern treatment of algebra.

 

[SrVishi]

Cool, I think I can also borrow Aluffi's text. Does Aluffi cover as much as Lang? Might have forgotten to specify, by I wanted a book that could (to the best of its ability) cover as much as possible.

 

[wrobel]

Lang is a good regular course for mathematitians. The book of Bourbaki is for those who are going to be a professional in algebra

Lang has very nice key insights, but much of his text is confusing and the book is riddled with errors.

examples of errors?

 

[bacte2013]

Alternatively, I also recommend "Algebra" by MacLane/Birkhoff and "Algebra" by Hungerford. Former is charming as it nicely introduce the category theory and latter is very detailed with good prose. I also think either of them will prepare you for Lang.

As a side note, I heard that Bourbaki's books in algebra have good reviews.

 

[bolbteppa]

Bourbaki's algebra is IMO the best book on the subject, even just understanding why group representation theory is at the end of the (untranslated!) chapter 8 was just so immensely illuminating and I couldn't find that answered anywhere else, but use Dummit and Foote as well and complete DF while taking in Bourbaki over time, it is a bit insane.

 

[bacte2013]

Bourbaki's algebra is IMO the best book on the subject, even just understanding why group representation theory is at the end of the (untranslated!) chapter 8 was just so immensely illuminating and I couldn't find that answered anywhere else, but use Dummit and Foote as well and complete DF while taking in Bourbaki over time, it is a bit insane.

Is English-translation version not as insightful as original? Strangely, I cannot find Chapter 8 as English-version contains Chap. 1 through 7.

 

[bolbteppa]

Is English-translation version not as insightful as original? Strangely, I cannot find Chapter 8 as English-version contains Chap. 1 through 7.

I think only chapters 1 to 7 are translated, there's a new (French) algebraic topology too. Also the manifolds book is not translated :(

 

[The Bill]

I've been using Jacobson's Basic Algebra I and II as a reference lately, and I feel I can give a tentative recommendation for it.

 

[bacte2013]

I think only chapters 1 to 7 are translated, there's a new (French) algebraic topology too. Also the manifolds book is not translated :(

I see. That is extremely unfortunate...This is one of time that I regret that learning another language, i.e. French. What are audiences for Bourbakian books? I am planning to read Algebra chapters, but I am not sure yet.

 

[Ssnow]

As said before I suggest also Paolo Aluffi "Algebra: Chapter 0"