1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Abstract Algebra Texts

  1. Dec 2, 2005 #1

    JasonRox

    User Avatar
    Homework Helper
    Gold Member

    Does anyone know a good Abstract Algebra text?

    I currently have the text by Gallian and quite frankly I give two stars out of five.

    I'm looking for something that's more advanced, and well written.

    Any recommendations will be greatly appreciated. :biggrin:
     
  2. jcsd
  3. Dec 3, 2005 #2
    If you know linear algebra and want an advanced text, there's Herstein.

    If you want an introduction to the basics (without reliance on linear algebra), i.e. group theory, ring theory and some field theory, and without overloading yourself, then there's Fraleigh. I personally think the chapters on group theory are very well done. I haven't looked at the later parts of the book that cover rings and fields, so I can't say much about them.
     
  4. Dec 3, 2005 #3
    beginner's algebra:
    abstract algebra -- herstein
    intro to modern algebra -- gilbert/gilbert

    intermediate algebra:
    topics in algebra -- herstein

    hardcore algebra:
    noncommutative rings -- herstein
    field theory & its classical problems -- hadlock
    galois theory -- e. artin
    algebra -- grove
    algebra -- dummit/foote
     
  5. Dec 4, 2005 #4

    JasonRox

    User Avatar
    Homework Helper
    Gold Member

    Great list. :biggrin:
     
  6. Dec 5, 2005 #5

    Tom Mattson

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I will second that recommendation. We used Fraleigh in our abstract algebra class, and I enjoyed it very much.
     
  7. Dec 10, 2005 #6
    The book we used in my abstract algebra class this semester was: A first course in Abstract Algebra (2nd edition) by Joseph J Rotman. I think the general consensus in the class was that the book was bad. I felt there were too few examples and the book often discussed things that had nothing to do with the subject.
     
  8. Dec 14, 2005 #7
    you can always find some lecture notes at sites such as dmoz.org or search at sites of universities.
    at dmoz, quite frankly there are a lot of material on abstract algebra.
     
  9. Dec 22, 2005 #8

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

    my recommendations:

    I think the best beginning general abstract algebra book for linear algebra, groups, rings, fields, modules, even basic group representations: is Algebra, by Michael Artin.

    This a sophomore level book at MIT, hence a graduate book most places.

    Another classic I like is Algebra by Van der Waerden.

    Maybe the best pure linear algebra book is by Hoffman and Kunze.

    I always had trouble learning from mike's dad Emil Artin's book, Galois theory, as it is too slick for me. Herstein is also very slick, goes in one ear and out the other. I do not like it much for beginners, but the problem sets are excellent for beginners, lots of fun special problems. But for insight into a topic, Herstein is not highly recommended by professionals I know. M. Artin on the other hand is outstanding.

    At the graduate level, I like Dummit and Foote and, lets face it, it is hard to ignore Lang. But I have not taught from Dummit and Foote. Hungerford has good problems and examples, and is very systematic, but rather boring, and gives little insight into why things are true, in my opinion, but some of my best students did benefit from it in combination with other books.

    For commutative algebra I like Zariski and Samuel for a long book, and Atiyah - MacDonald for a short book.

    For homological algebra, MacLane is nice, or Northcott, or more rcently maybe Manin, if you want derived categories incuded.

    start with artin. If that is too hard, try some of the books on other people's lists.
     
  10. Dec 24, 2005 #9

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

  11. Dec 25, 2005 #10

    JasonRox

    User Avatar
    Homework Helper
    Gold Member

    That is a good book too.

    Every once in awhile I do a search, and this one seems to be one I bump into all the time.
     
  12. Dec 19, 2006 #11
    The book I found easiest to understand (while still being comprehensive) was Birkoff & Maclane's Modern Algebra
     
  13. Mar 14, 2007 #12

    radou

    User Avatar
    Homework Helper

    Just found this book on Amazon.com, seems like a good offer, anyone read it?
     
  14. Mar 14, 2007 #13

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper
    2015 Award

    Now I have taught from Dummitt and Foote, and I no longer like it.

    I recommend the books i listed above and my own web notes as better overall. Still there are some things in DF that are nice and not in my notes.


    best rec: Michael Artin, Algebra; and Van der Waerden, Modern Algebra; and Lang, Algebra.

    and Hoffman- Kunze for Linear Algebra.

    I also like my own notes but thnere is little data on them from other people.
     
  15. Mar 18, 2007 #14
    I will second Van Der Waerden! I have volume II and while I haven't read much of it, it's a great reference. The few proofs I've looked up are very well written and easy to follow.

    Another good book is Jacobson's Lectures in Abstract Algebra. I've only read 1 section of Volume I and but it was very readable, and the proofs were really elegant! And again, the proofs are very clear and easy to follow.

    Another good and fun to read book is Fraleigh. It's has 49 chapters so you feel like your making progress because the chapters are so small.

    Rotman's Advanced Modern Algebra is also a good book. I've read 8 sections out of this and I find it much easier to read than DF.
    I also think Rotman is a better reference than DnF, whenever I run into something I don't know, I usually have an easier time finding it in Rotman than in DnF.

    Anyways since I've only used Van Der Waerdan and Jacobson as references, my recommendation is
    Fraleigh (has less material, but easier to read)
    Rotman's Advanced Modern Algebra (has way more material, a little harder to read, but easier than DnF)

    Or maybe you should try Artin as others have suggested, I've never looked at it unfortunately.

    Hope this helps!
     
    Last edited: Mar 18, 2007
  16. Mar 19, 2007 #15

    radou

    User Avatar
    Homework Helper

    mathwonk (or anybody else), what do you make of Thomas W. Hungerford's Algebra? The reviews "sound" good, and I have found it to be in the top of the reference lists of some abstract algebra courses. The price is reasonable, too.

    Although, in the end, I believe all of these books are respectable pieces of literature, it's only about one's individual interest and will to "do the math".
     
  17. Mar 19, 2007 #16
    It is a very well organized book. When Hungerford uses a result in a proof he always points you explicitly to where the result is found. Another interesting feature is that you can skip all propositions(and there lemma's and corollaries) without any loss of continuity. The proofs are for the most part, easy to understand.

    I don't know if this is a good book to use for an introduction, it certainly is not as easy to read as other books that were mentioned in this thread like fraleigh, but then again, Hungerford, along with DnF, rotman, lang, etc are on an entirely different level because they are written for different audiences.

    Note that I've only read about half of chapter 8, hence my comments on organization; i.e., I was able to jump into it and follow along since he cites what he is using in the proofs very well.
    Hope this helps.
     
    Last edited: Mar 19, 2007
  18. Mar 19, 2007 #17
    Hi everyone,

    My class is using Hungerford's undergraduate book ("Abstract Algebra: An Introduction"), I'm personally a bit vexed with it. So far, he has given no hint as to the historical development of concepts (i.e., the motives behind them), and furthermore, his proofs, to me, fail to outline the "big picture." I often end up nodding my head through each of the individual logical steps, but fail to grasp the proof as a whole--in a intuitive sense--unless I put in considerable effort of my own. I'm asking for your suggestions of books that will remedy these two issues.

    As a note: I'm not a mathematics major. I'm looking for a better textbook because as long as I'm in this class, I might as well learn the subject properly.
     
    Last edited: Mar 19, 2007
  19. Mar 20, 2007 #18

    radou

    User Avatar
    Homework Helper

    ircdan and Knavish, thanks for the comments. There are obviously always pros and cons about specific books.

    Sounds completely familiar - but in the end (as you mentioned), it's all about one's own efforts, which present a necessary condition to "do the math".

    Anyway, I decided to order that book. :smile:
     
  20. May 8, 2007 #19

    Chris Hillman

    User Avatar
    Science Advisor

    I'd second what the others say, that Hungerford is great as a reference, not so fun as a primary text as Michael Artin. Another valuable textbook is Jacobson, Basic Algebra (two volumes, drier than Artin but not as dry as Hungerford). The classic text by Birkhoff and Mac Lane is still an excellent choice for motivation and insight, not to mention the joy of reading a book written with style.

    I'd add that one of the best short algebra textbook is Herstein, Basic Algebra. I happen to like Topics in Algebra for some things, but it seems mathwonk doesn't agree. But everyone seems to agree that Michael Artin's textbook is superb.
     
  21. May 8, 2007 #20

    radou

    User Avatar
    Homework Helper

    I started reading/solving exercises from Hungerford about 2 weeks ago, and I'm very satisfied with the book for now.

    If I keep my interest up, perhaps I'll give Artin a thought.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Abstract Algebra Texts
  1. Abstract algebra (Replies: 17)

Loading...