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Is learning epsilon-delta proofs before analysis a good idea

  1. Jan 2, 2015 #1
    Hello PF people. It's my first post here, but I have been lurking around this forum for awhile now.

    I'm currently learning differential calculus using a text by Stewart and I want to attain a better comprehension of pure mathematics.

    My question is: would it be a good idea to get another text to supplement Stewart and gain a deeper understanding of how limits work using the epsilon-delta definitions at this stage of my education? or would this be a waste of time (meaning, is it better to finish integral calculus and vector calculus, then start analysis)?
  2. jcsd
  3. Jan 2, 2015 #2
    I'd say there's no harm in learning it along with your work, provided it doesn't interfere with the basics of what you're learning now. I started reading Spivak to supplement my calculus knowledge while I was in Calc II.
  4. Jan 3, 2015 #3
    Stewart isn't a terribly rigorous introduction to calculus; if you want something more mathematically pure and rigorous, Michael Spivak's ``Calculus" is a favorite in the math community for its emphasis on theory and proofs.

    Learning ##\delta - \epsilon## proofs isn't crucial to understanding limits (especially if you're just getting into calculus yourself). I would say just get comfortable with what I would call the ``foundation" of higher math. This includes:
    -Differential Calculus (derivative rules, word problems, etc.)
    -Integral Calculus (right/left sums, Riemann Integrals, FTC I and II, solids of revolution, etc.)
    -Vector Calculus (dot/cross product, equations of planes, parametrizing curves in space, curl, flux, divergence, Stokes, Green, Jacobians, etc.)
    -Diff Eq. (Laplace transforms, physics problems, etc.)
    -Linear Algebra (Vector spaces, bases, inverses, ranks, determinants, eigenvalues, eigenvectors, eigenspaces, etc.)
    -[Maybe a proofs class somewhere in here?]

    So try to bone up on the topics above (i.e., get really comfortable with it). If your aim is to pursue higher math, I wouldn't recommend skipping any steps or you might risk overwhelming yourself with too much theory without having seen many applications and how the material is related. So, there's no harm in exposing yourself to some analysis now, although it's probably more practical to wait until you have all your bases covered.
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