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How to learn a topic?

  1. Jan 4, 2008 #1
    I've been wanting to catch back up on my physics and math. I was looking into equations on E&M, which led me to electric fields, which led me through differentiation, and on.

    I am looking up on Wikipedia what a mathematical field is. Well, it's an algebraic structure. It's also a ring. A ring has more structure than an abelian group, but less than a field. A field is not just a ring, but a commutative division ring.

    And so on. Now we have structures, fields, rings, abelian groups, and properties of commutativity to them.

    I feel I'm going in circles. I just want to know what a field is, and if it's the same as a magnetic/electric field. How can I grasp this abstract math? My brain can't seem to grasp it.

    I know a set is a group of numbers, like {1,2,3}
    I guess this could be a 1x3 matrix too, and in computers it's an array.

    How can this object called a "set" be represented as a field, structure, ring, abelian group, etc?

    Isn't a field like a 2d or 3d (or n-dimensional) surface of points?
    Last edited: Jan 4, 2008
  2. jcsd
  3. Jan 4, 2008 #2


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    You have two different definitions of field here. The algebraic structure called a field is just an abstraction of the real numbers. An electric or magnetic field is a vector field. They are complety unrelated concepts.
  4. Jan 7, 2008 #3
    Ok, then I guess my next question is, how can I learn something when one thing leads to another, on and on? I'm thinking that Wikipedia isn't a good way to learn a new subject.

    Even that link you sent says "In the rigorous mathematical treatment, (tangent) vector fields are defined on manifolds as sections of a manifold's tangent bundle. They are one kind of tensor field on the manifold."

    Now I have more terms I don't understand:
    1. rigorous mathematical treatment
    2. manifolds
    3. sections
    4. tangent bundle
    5. tensor field

    So, it really didn't help me understand, although I do understand fields to be collections of vectors. However, wikipedia seems to go on forever.

    Last edited: Jan 7, 2008
  5. Jan 7, 2008 #4


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  6. Jan 7, 2008 #5
    Thanks. I sent an application to a community college to audit a Calculus I class. I think that would be a good refresher. I also ordered an E&M textbook off Amazon. Since I have a degree in Physics (7 years old), I have covered this before.

    Anyway, when I get sufficient knowledge from the Electricity and Magnetism then I'll be at the level where I can go for my masters in Physics.

    Good advice though on getting the textbook.
    Last edited: Jan 7, 2008
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