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Math Help - Algebra textbook

  1. #1
    Forum Admin topsquark's Avatar
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    Algebra textbook

    I am taking a "strategic retreat" in my program of study. My Algebra text is actually a graduate book, and I evidently don't have enough experience with the basics to really grasp what I need to do with it.

    I have a low-level undergrad book that focusses mainly on geometric constructibility. I've learned alot from that, but the author confesses that many of the details aren't in the book. I found the going very easy with that one, but obviously the gap between it and the graduate text is rather broad.

    So I am looking for a more "fundamental" text, that would correspond maybe with advanced undergraduate level or so? My ultimate goal with this is to be able to at least understand Galois theory. I figure if I can do that I'm probably set with anything Algebraic I encounter in Quantum Field Theory.

    Thanks!

    -Dan
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    Quote Originally Posted by topsquark
    I am taking a "strategic retreat" in my program of study. My Algebra text is actually a graduate book, and I evidently don't have enough experience with the basics to really grasp what I need to do with it.

    I have a low-level undergrad book that focusses mainly on geometric constructibility. I've learned alot from that, but the author confesses that many of the details aren't in the book. I found the going very easy with that one, but obviously the gap between it and the graduate text is rather broad.

    So I am looking for a more "fundamental" text, that would correspond maybe with advanced undergraduate level or so? My ultimate goal with this is to be able to at least understand Galois theory. I figure if I can do that I'm probably set with anything Algebraic I encounter in Quantum Field Theory.

    Thanks!

    -Dan
    Funny

    What is a physicist doing in the realms of Abstract Algebra

    The book I have is by,
    John B. Fraleigh called "A First Course In Abstract Algebra".
    Great Book, well written.
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by ThePerfectHacker
    Funny

    What is a physicist doing in the realms of Abstract Algebra

    The book I have is by,
    John B. Fraleigh called "A First Course In Abstract Algebra".
    Great Book, well written.
    Thanks for the tip!

    My current goal is to learn String Field Theory, a rather abstract and certainly heavily Mathematical field of study. Most of the theoreticians doing it, whether they want to admit it or not, are essentially Mathematical Physicists.

    I had a conversation with one of my professors once when I was at Purdue studying for my PhD. (I had to leave the program uncompleted, unfortunately, due to health reasons.) He was slightly bemused that I was taking Partial Differential Equations from the Math department and he asked me why? I told him that I was interested in knowing why the techniques I had been using to solve them work, and that if I came across a type of equation I hadn't seen before I wanted to know the general theory so I would know what to do to solve it. His reply? "We'll teach you everything you need to know."

    Pffl! They don't.

    So, I'm currently out of both work and school and with a great deal of time on my hands. I've set myself the goal of trying to learn String Theory on my own, which is VERY heavily Mathematical. I know most of the Physics involved, but the Math is difficult to follow using my current knowledge base. So I decided to start learning the topology, group theory, geometry, and algebra that I will need. It's a big shopping list, but fortunately I doubt I'll have to master any of them...I suspect that a knowledge of the basics of each will probably do to get me into the subject and I can then pick up whatever else I'll need later on.

    So that's what a mere Physicist is doing mucking about in the "realms of Abstract Algebra.

    Besides, do you know how many Physics chicks are impressed by my being able to solve cubic equations by hand?

    -Dan
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    I developed an easy method of solving the depressed cubic equation maybe I will post it here some time.

    But, If you know how to simplify that "nasty" cubic, you would impress even me!
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  5. #5
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    Quote Originally Posted by ThePerfectHacker
    The book I have is by,
    John B. Fraleigh called "A First Course In Abstract Algebra".
    Great Book, well written.
    I didn't like the first two editions with their habit of referring to "the literature" for proofs of some key results. I believe the third edition is better.

    Personally I would recommend Saunders and MacLane Survey of Modern Algebra or Herstein Topics in Algebra.
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by topsquark
    Thanks for the tip!
    Besides, do you know how many Physics chicks are impressed by my being able to solve cubic equations by hand?
    Things have obviously changed from when I was an undergraduate. There
    was only the one "Physics chick" in our year.

    Though there were a significant number of "Astrophysics chicks" by the time
    I got around to studying Astro seriously.

    RonL
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  7. #7
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    Quote Originally Posted by rgep
    I didn't like the first two editions with their habit of referring to "the literature" for proofs of some key results. I believe the third edition is better.

    Personally I would recommend Saunders and MacLane Survey of Modern Algebra or Herstein Topics in Algebra.
    rgep I got the 7th edition
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  8. #8
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    Good reference textbooks

    I used the textbooks

    Quantum Field Theory for Mathematicians
    and
    First Course in Abstract Algebra with Application, 3rd Edition

    to study Quantum Theory and Algebra

    Good Luck and wish help for you.

    hehe ^_^
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  9. #9
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    Abstract Algebra by Beachy and Blair is amazing. I read it during my break.

    The book I really want to read is Field and Galois Theory by Patrick Morandi. Maybe during my summer break.
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  10. #10
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    I would consider this collection of books: Algebra
    Robert Ash usually has very clear texts.
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  11. #11
    Bar0n janvdl's Avatar
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    Quote Originally Posted by topsquark View Post
    I am taking a "strategic retreat" in my program of study...
    Quote Originally Posted by CaptainBlack View Post
    There was only the one "Physics chick" in our year.

    Though there were a significant number of "Astrophysics chicks"...
    Hehe, you guys are funny.

    I know this is off-topic but i just had to say it...
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  12. #12
    Senior Member tukeywilliams's Avatar
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    I like Artin's Algebra book. Its a classic, and well written. Hernstein's book is good too. Emil Artin's book on Galois Theory is pretty good too, but very terse and short.
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    Quote Originally Posted by tukeywilliams View Post
    Emil Artin's book on Galois Theory is pretty good too, but very terse and short.
    Maybe you know or not, but Galois theory has been revolutionized, Emil Artin's approach is the standard one taught today. So the advantage of having a book by him is that you are learning from the master himself.
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  14. #14
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by ThePerfectHacker View Post
    rgep I got the 7th edition
    haha.. i only got the sixth.. however, my professors say that almost no change at all.. is it true?
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  15. #15
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    Quote Originally Posted by kalagota View Post
    haha.. i only got the sixth.. however, my professors say that almost no change at all.. is it true?
    Yes. Now Fraliegh as an introduction text is very good. But if you want to study algebra on a more advanced level Fraleigh does a bad job near the end of the book. Especially his chapter on Galois theory. It is very poorly written, the proofs are very ugly, and worst of all the approach he uses towards Galois theory is unstandard, not the actual way it is done.
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