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Good Modern/Abstract Algebra book?

  1. Jul 28, 2009 #1
    The title says it all...I'm looking for a comprehensive, in depth book for an introductory/intermediate undergraduate course on Modern Algebra. I've got Fraleigh's "A First Course in Abstract Algebra" and Warner's "Modern Algebra." But Fraleigh's book is my text for this Fall's course and Warner's covers a bit too much and doesn't go as in depth on the topics I need. Also: budget is low, so the less expensive the better. Thanks.
     
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  3. Jul 28, 2009 #2

    thrill3rnit3

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    The classics are going to be more expensive, of course :tongue:

    The list goes from the most expensive to the least:

    Michael Artin's Algebra
    https://www.amazon.com/Algebra-Michael-Artin/dp/0130047635/ref=sr_1_1?ie=UTF8&qid=1248818776&sr=8-1

    Dummit and Foote's Abstract Algebra
    https://www.amazon.com/Abstract-Alg...3349/ref=sr_1_1?ie=UTF8&qid=1248818815&sr=8-1

    Serge Lang's Algebra
    https://www.amazon.com/Algebra-Serge-Lang/dp/038795385X/ref=sr_1_4?ie=UTF8&qid=1248818815&sr=8-4

    W.E. Deskins' Algebra (a Dover book)
    https://www.amazon.com/Abstract-Alg...8887/ref=sr_1_6?ie=UTF8&qid=1248818868&sr=8-6
     
    Last edited by a moderator: May 4, 2017
  4. Jul 28, 2009 #3

    xristy

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    It is worth noting that Artin is available in international edition from places like AbeBooks for much less than the US version (~ $25). I've got both and they are the same content. The quality of the international edition is perhaps a little less - thinner paper.

    Of the ones that have been cited above, Artin is I think by far the best fit for the requirements that are given. Artin has nice features such as some discussion of Riemann surfaces and Hopf fibrations and so on which connect the algebra with areas that are relevant to physics. Lang is a graduate text and I think somewhat dry. Dummit and Foote is workman-like.

    As always YMMV.
     
  5. Jul 29, 2009 #4
    Have you looked through Fraleigh? I have browsed through the older editions, and it seems the newer editions have changed quite a bit of the book. It is a very good introduction, and he included some a neat application to homology groups in the early editions. Dummit and Foote is the standard graduate text in algebra. From the Amazon reviews, it seems Artin is a non-standard unique text, which may make it a bad selection to use as a reference book while you're learning from Fraleigh. Abstract Algebra by Herstein seems to be good, never read it though. My undergraduate course used Contemporary Abstract Algebra by Gallian and was likable and easy to read.
     
  6. Jul 29, 2009 #5

    Landau

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    I second Dummit & Foote. It covers a lot of topics, and does so in a rigorous but readable fashion. Definitions, theorems and proofs are clearly indicated and seperated, as opposed to Artin.
     
  7. Jul 29, 2009 #6
    I am currently learning Abstract Algebra from Dummit and Foote. It is a great text and a must have for an algebraist.
     
  8. Jul 30, 2009 #7
    Great suggestions, thanks, all.
     
  9. Jul 30, 2009 #8

    Landau

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    You might also want to take a look at https://www.amazon.com/Algebra-Graduate-Texts-Mathematics-v/dp/0387905189, but this is a graduate book so probably too advanced for "an introductory/intermediate undergraduate course". Although some universities may use Dummit & Foote also for graduate courses, I think it is really suitable for an (2nd year) undergraduate.
     
    Last edited by a moderator: May 4, 2017
  10. Jul 30, 2009 #9
    Since they recommended Fraleigh, I think it's because the students are at that level, and Fraleigh does very well what it sets out to do: that is, provide material for a semester long course for students who are knew to proofs or not to strong with proofs, or non-mathematics students.

    Artin and Herstein, mentioned above, are very good books, but at a slightly higher level than Fraleigh, i.e. those two books will require a lot more commitment from you, but are more rewarding in return. I am not too familiar with ther books, besides Birkhoff and MacLane's Survey of Modern Algebra, which is inappropriate I think.
     
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