I'm a graduate student studying at home. I find that ressources in Mathematics on the web are easier and easier to find, and I am happy for that, because I like to have different points of view about the same subject. I find that projects like StackExchange, MO and Arxiv are wonderful for every home student (and other ones too), even if the level to understand the mathematics is quite far from mine ;)

However, I would like to ask if there are some wonderful pdf specially in the domain of Algebra (group theory, rings theory, modules, commuatative algebra,...), and by that, I mean not just academic books that present the theory, but books that present theory in regard of history and present where came the definitions and theorems.

Thank you for your time :)

P.S. This post was at the origin posted at https://mathoverflow.net/questions/117645/about-studying-at-home-finding-good-pdf but was not in his place.

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    $\begingroup$ To Alan Simonin - What is your major? $\endgroup$ – Victor Dec 30 '12 at 16:24
  • $\begingroup$ What do you mean by "major" ? $\endgroup$ – Alan Simonin Dec 30 '12 at 16:30
  • $\begingroup$ I mean what subject are you major in? $\endgroup$ – Victor Dec 30 '12 at 17:25
  • $\begingroup$ My major subjects are Commutative Algebra, Advanced Probabilities, Fourier Analysis... as in French system, you choose 3 majors among 4 choices $\endgroup$ – Alan Simonin Dec 31 '12 at 7:19

Abstract Algebra: Theory and Applications looks like a nice undergraduate textbook. I have not read it, but I found some of the Sage supplements by Robert Beezer useful. (I wish I had done more computer algebra when I was learning this stuff. I think I would have learned it much faster and much deeper.)

As for graduate textbooks, I've read parts of the book by Ash, but personally it wasn't my favorite. I think the books that will form the foundation of your studies are very important and you should not only rely on freely available online books. Personally, my favorite graduate algebra textbook is Hungerford, but among my graduate student classmates, I seemed to be alone in this view. (Most of them like Dummit and Foote, which I found far too verbose.)

The importance of doing lots of problems and checking your work against correct solutions cannot be overstated. If you are studying at home, without the benefit of a professor or grader, it will be useful to have a solutions manual available for checking your work. Here are a couple of resources:

James Wilson's problems/solutions for Hungerford.

James Wilson's problems/solutions for Kleshchev's course.

I've typed up some problems/solutions and posted them here.

Finally, I highly recommend you invest in these excellent, yet inexpensive Dover books:

Problems in Group Theory by John Dixon

Basic Algebra I&II by Nathan Jacobson

  • $\begingroup$ That's a lot of great things, thank you very much ! $\endgroup$ – Alan Simonin Dec 31 '12 at 6:56

For a graduate student the book Abstract Algebra: The Basic Graduate Year by Robert B. Ash is a nice one.


You can also try A BOOK OF ABSTRACT ALGEBRA by Charles C.Pinter which is also a wonderful book on the subject.


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