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Abstract Math Book?

  1. Mar 16, 2012 #1
    A good book on Abstract Algebra that covers major undergraduate and graduate topics?
    Something rigorous professional and for mathematicians.

    Not Hungerford please, or any n x $100 book.
  2. jcsd
  3. Mar 16, 2012 #2


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    What do you want to learn and how abstract would you like the book to be?

    Herstien's Topics in Algebra is a classic. You can get it used for $50.

    Sah's Book is incredibly hard - but incredibly elegant.

    But why not read a beginning book on Algebraic Geometry. You will have to learn a ton of algebra for this and a lot of abstract algebra comes form it.

    You could also get a book on Algebraic Topology and learn algebra as you need it.
  4. Mar 16, 2012 #3
    Here are the ones I know about. Ideally one should read them all. Or maybe just read Disquisitiones Arithmeticae and try to figure out how Gauss did all that at age 21.


    The classic algebra books.

    * Van der Waerden

    This was the first "modern" algebra book that presented the subject as it's taught today: set theoretical preliminaries, groups, rings, and fields. Still an excellent book.

    * Birkhoff - McLane

    A classical approach. Starts with a lot of material about concrete symmetry groups (reflections of the square, etc.) so that you really get a feel for what groups are about. Excellent book, not often mentioned these days.

    * Herstein.

    This is a desert island book. It's a real classic. It's more modern than Birkhoff-MacLane but still classical in that it doesn't talk about category theory. This is arguably THE best undergrad abstract algebra book out there.

    * Dummitt & Foote

    I'm not personally familiar with that one but it's pretty popular.

    * Hungerford. Well you didn't want to hear about that. But if you're looking at grad-level texts, it's either Hungerford or ...

    * Lang.

    Some call it comprehensive. Others call it incomprehensible. "Terse" and "austere" don't begin to describe it. As a book to learn from, personally I didn't like it. But as a reference, it's really good. There's a lot of material in there.
  5. Mar 16, 2012 #4
    Yup these are options. After searching I've come across Elements of Modern Algebra by Gilbert, still cheaper than Hungerford's. I'm not sure about Dover stuff it looks dated...
  6. Mar 16, 2012 #5
    Don't forget Artin!
  7. Mar 16, 2012 #6
    I'm now considering Dummitt & Foote based on the number of pages it has sounds comprehensive and covering a wider range of topics than others or maybe in more details...

    Though Dover still tempting but not sure about quality of content, and I mean the material there is it reliable and advanced?
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