1. Limited time only! Sign up for a free 30min personal 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!

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


    User Avatar

    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


    User Avatar

  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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook