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Is it even possible? Or am I just flat out wrong once again?

  1. Jan 29, 2008 #1
    Is it even possible? Or am I just flat out wrong once again!?!

    Whenever I really need to procrastinate, I turn to writing a calculus book. In this case.. For about three days I pursued the problem of whether or not you can teach topology before "rigorous Calculus".

    Is it even possible, to teach topology before rigorous Calculus (i.e. the Calculus that requires proof but is usually not yet called "Analysis")

    In the end, the following two paragraphs is pretty much the fruit of my 3 days of effort, and is probably either a) wrong, or b) written somewhere else. Writing a book is hard!


     
    Last edited: Jan 29, 2008
  2. jcsd
  3. Jan 29, 2008 #2
    i would keep reading it. i liked the axis and allies analogy.
     
  4. Jan 30, 2008 #3
    Actually with the above as a starting point, I think I see a way how to do it (present abstract topology before "rigorous Calculus") - and preferably quickly. The point is that probably it is best to just get a taste, and not go deep. Not even mention countability/uncountability, or perhaps return to that after some heaps of Calculus..

    I am wondering, is the set theory too hindering for those who haven't studied proofs before? Or can a beginner get aquainted with the notation well enough as long as there are some concrete examples?

    Anyways, here's a continuation of the train of thought...

     
    Last edited: Jan 30, 2008
  5. Jan 31, 2008 #4
    Well, anyways, it's not going to be the end of the world to finish what I started. This does at this time sort of feel like a "write your own lecture on general topology" undergraduate assignment...

    Ultimately, the punchline is --- at the time Calculus begins you assume that R is a connected space, and then prove the completeness axiom... And the advantage, whether or not it's worth it, is that somehow this can help.

     
    Last edited: Jan 31, 2008
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