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Instructive Real Analysis

  1. Sep 28, 2003 #1

    Tom Mattson

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    Has anyone ever seen this? It's an interactive online textbook in analysis in a single real variable. As an undergrad, I wussed out and took Advanced Calculus instead of Analysis, and this is a subject I've been meaning to learn. Is anyone interested in going through this?

    http://www.shu.edu/projects/reals

    It looks like it could serve as a springboard to get into more advanced books that I've found online.
     
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  3. Sep 28, 2003 #2

    Hurkyl

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    This will seem like a really silly question but...

    As long as we're sticking to real functions of a single variable (and not delving into abstract spaces and measures), what's the difference? (I'm beginning to suspect that my teacher taught us both in my advanced calc courses)
     
  4. Oct 2, 2003 #3
    i think "analysis" has to have the word "real" in front to be compared to advanced calculus.

    otherwise, things like metric spaces are included in the subject.
     
  5. Oct 2, 2003 #4

    selfAdjoint

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    To a mathematician, the word analysis by itself means functions of a complex variable. Other discplines mean other things by it. The Freudians...
     
  6. Oct 2, 2003 #5

    Hurkyl

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    I talked with a coworker, and he confirmed my suspicions; my advanced calc class did indeed delve a decent bit into real analysis, which is the source of my confusion!
     
  7. Oct 2, 2003 #6

    Nereid

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    An (almost) pure PF Mentor page!
     
  8. Oct 3, 2003 #7
    i think the term "function theory" is what is used for complex analysis.

    not all mathematicians have the same definition of "analysis."

    http://mathworld.wolfram.com/Analysis.html

     
  9. Oct 7, 2003 #8

    Tom Mattson

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    OK, sorry I took so long to get back to you. As far as I know, the thing that differentiates Advanced Calculus from Real Analysis is theorem proving. In my Adv Calc class, we covered multivariable calculus (differential and integral), vector calculus, calculus of variations, and a very little bit of PDEs. We learned nothing of spaces, measures, Lebesgue integration, etc.
     
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