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From what I understand, the book "A book of abstract algebra" by Charles C. Pinter is fairly elementary. On the other hand, the book "Algebra" by Serge Lang is very advanced. I'm assuming that just reading "A book of abstract algebra" is not enough to start Lang's book. From what I gather, the book by Dummit and Foote is somewhere in the middle - although probably closer to Lang's book. The problem is that the book by Dummit and Foote and the book by Lang overlap a lot and I can't afford both books. Now, I can maybe just read the book by Dummit and Foote, but I want to read Lang's book because it has more content and is more well known. So once I read "A book of abstract algebra" can I go immediately to Lang's book or is there some intermediate book I should read first?

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  • $\begingroup$ Use a library. ${}$ $\endgroup$
    – Shaun
    Jul 4, 2023 at 23:25

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I would strongly recommend reading the book by Dummit and Foote. It is a more elementary book than Lang's Algebra, but it is far easier to learn from. Lang's book contains a lot of material, but it is very dense, and it is better suited as a reference guide for someone that already knows the material than as an introduction for a new student.

In any case, PDFs of both books can be found online for free, if one knows where to look.

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  • $\begingroup$ 1. Is it then even worth reading the book by Charles C. Pinter? 2. Is there a different book that is similar to Dummit and Foote? I'm aware that they have free PDFs online, but I want a physical copy and Dummit&Foote is way too expensive for me. $\endgroup$
    – Hilbert
    Jul 4, 2023 at 23:16
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    $\begingroup$ If you were to only buy one book, I would personally recommend Dummit and Foote. I have also heard good things from Michael Artin's Algebra, and from what I have have skimmed on it, it seems to have a similar level of abstraction to Dummit and Foote. $\endgroup$
    – peco
    Jul 4, 2023 at 23:19
  • $\begingroup$ Alternatively, Algebra: Notes from the Underground by Aluffi is also an excellent book, released a few years ago. It is also substantially more affordable than the other two books, and personally I like its approach in teaching rings before groups. $\endgroup$
    – peco
    Jul 4, 2023 at 23:21
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    $\begingroup$ @123 since I forgot to tag $\endgroup$
    – peco
    Jul 4, 2023 at 23:30
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It is very unfortunate that you find yourself with a budget constraint for texts and notes... As @peco says, perhaps you can find these sources (and many others) on-line, "for free" (at least "free" if you don't feel compelled to print them out). (E.g., I myself do put all my course notes online...)

It is true that the later editions of S. Lang's "Algebra" attempted to be encyclopedic... and even the earlier editions were impatient-terse (as was the man himself, who I knew a bit in the late 1970's). The Dummit-Foote book is somewhat less encyclopedic, but less "impatient", so, probably more readable. :)

I do recall my first encounter with an early edition of Lang's "Algebra", about 1972, after a previous diet of antiques. :) As a proponent of (what was then the somewhat novel) "Bourbaki viewpoint", it was a revelation... and really in a very good way. :) By this year, that novelty has largely worn off, but, still, I remember my amazement at the time... :) (Especially the brief mentions of categorical ideas, homological ideas, etc.)

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