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Math Help - Field theory

  1. #1
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    Field theory

    Hi,
    I have a class that teaches how to think in mathematics i.e. read and write proofs. Right now the professor decided to deviate from the text and teach field theory which is really confusing to me since I am am Biochemistry with a math minor so I'm mostly learning applied math. I never encountered this before and its not easy to understand.

    I couldn't find any good resources to supplement the professors material. Can someone tell me some sites or books that can help?

    Thanks
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  2. #2
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    Quote Originally Posted by phillyj View Post
    Hi,
    I have a class that teaches how to think in mathematics i.e. read and write proofs. Right now the professor decided to deviate from the text and teach field theory which is really confusing to me since I am am Biochemistry with a math minor so I'm mostly learning applied math. I never encountered this before and its not easy to understand.

    I couldn't find any good resources to supplement the professors material. Can someone tell me some sites or books that can help
    In your college library there should be a number of textbooks on Abstract Algebra (it is also called Modern Algebra).
    The author Herstein is always very clear.
    Kenneth Miler has a much older text that is very easy to follow.
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  3. #3
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    I see. I wasn't checking on abstract or modern algebra. I'll give that a try. Thanks
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  4. #4
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    Ok, I checked those books but I feel they are not right for me. Let me tell you the topics, in order or appearence, that are discussed:

    [1] Properties of fields {Not very comfortable with these}

    [2] Ordered fields , includes trichotomy

    [3] Real numbers
    [a] Cuts, rational & irrational
    [b] Field operations
    [c] Order in the cuts.
    [d] Completeness

    [4] Rational numbers

    [5] Field extensions

    [6] Complex numbers
    [a] Polar representation of complex numbers {I feel hopeless looking at it}
    [b] Fundamental Theorem of Algebra

    I think we only got up to [4]. I'm going to talk to the professor and see if I can figure this out. Once again, I'm not very interested or knowledgeable about these abstract topics. Just trying to read his notes is like reading a foreign language. Although the goal of the class is just that, I still don't feel that I can grasp what he is teaching now.
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  5. #5
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    Those topics are not what one normally thinks of as Field Theory.
    As odd as this may sound, a good textbook in teacher education could help you. See if your college gives a teacher-ED course in the Real Number System. If so, look at that text book.
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  6. #6
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    Can you take a look at his document and tell me what you think? I uploaded it to google docs.
    https://docs.google.com/viewer?a=v&p...thkey=CIr_vqgH

    Thank you
    Last edited by phillyj; February 24th 2011 at 03:31 PM. Reason: forgot link
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  7. #7
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    Quote Originally Posted by phillyj View Post
    Can you take a look at his document and tell me what you think? I uploaded it to google docs.
    https://docs.google.com/viewer?a=v&p...thkey=CIr_vqgH
    It is good if you know enough set theory and logical notation to follow it.
    It depends upon you background.
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